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# **Yes: Somatic and AIS Mechanisms That Increase Threshold During a Spike Train**
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**Absolutely!** This is a fundamental property called **spike-frequency adaptation** or **accommodation**, where the neuron becomes *less* excitable during sustained firing. The **first spike is indeed easier** than subsequent spikes in a train. Let me detail the specific somatic and AIS mechanisms that accomplish this:
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## **1. Somatic Mechanisms That Raise Threshold**
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### **A. Slow Afterhyperpolarization (sAHP)**
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This is the **primary mechanism** for somatic spike-frequency adaptation.
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- **Mechanism:** Each action potential allows Ca²⁺ to enter the soma through voltage-gated calcium channels or NMDA receptors. This somatic Ca²⁺ accumulates and activates **calcium-dependent potassium channels (SK channels)**.
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- **Dynamics:** sAHP develops slowly (τ~100-1000 ms) and persists long after the spike.
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- **Effect:** The outward K⁺ current **hyperpolarizes** the soma, moving it *farther* from threshold. With each successive spike, more Ca²⁺ accumulates → more SK channels open → stronger hyperpolarization → **higher effective threshold**.
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- **Functional Role:** Prevents runaway excitation, encodes firing rate *adaptation* (responding best to changes rather than sustained input), and protects against metabolic exhaustion.
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### **B. M-current (IKM)**
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- **Mechanism:** A voltage-gated K⁺ current that activates slowly with depolarization and **does not inactivate**.
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- **Dynamics:** During a spike train, persistent depolarization slowly activates more M-channels.
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- **Effect:** Provides a **braking current** that increases with sustained activity, requiring stronger input to maintain firing.
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### **C. Sodium Channel Inactivation at the Soma**
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- While more pronounced at the AIS, somatic Na⁺ channels also experience **slow inactivation** during sustained depolarization.
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- This reduces the **available sodium current** for subsequent spikes.
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## **2. AIS-Specific Mechanisms That Raise Threshold**
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The AIS is particularly sophisticated in its dynamic threshold regulation:
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### **A. Fast Na⁺ Channel Inactivation**
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- **Mechanism:** After each spike, a fraction of Na⁺ channels enter an **inactivated state**.
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- **Recovery:** Channels recover with time constants from milliseconds (fast) to seconds (slow).
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- **Effect:** During high-frequency firing, channels don't fully recover between spikes. Fewer available channels = **higher threshold** for subsequent spikes.
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### **B. Cumulative Potassium Channel Activation**
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- **Mechanism:** K⁺ channels at the AIS (especially Kv3 types) activate rapidly but **deactivate slowly**.
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- **Dynamics:** During a spike train, these K⁺ channels don't fully close between spikes, creating a **cumulative outward current**.
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- **Effect:** This "**depolarization-induced suppression of excitation**" makes each successive spike harder to generate.
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### **C. Dynamic Threshold via Sodium Channel Phosphorylation States**
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- **Mechanism:** During sustained activity, kinases like **CaMKII** (activated by somatic Ca²⁺) can phosphorylate Na⁺ channels at the AIS.
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- **Effect:** Phosphorylation can **shift the voltage dependence of inactivation** to more hyperpolarized potentials, meaning channels inactivate at more negative voltages.
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- **Result:** The **availability curve** of Na⁺ channels shifts leftward → fewer channels available at any given potential → effectively **higher threshold**.
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## **3. The Combined Effect: First Spike Advantage**
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Here's what happens during a spike train:
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| **Spike #** | **Somatic State** | **AIS State** | **Effective Threshold** |
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|--------------|-----------------------------------------|------------------------------------------------------------------|-----------------------------|
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| **1** | Resting, no sAHP, minimal M-current | All Na⁺ channels available, no K⁺ accumulation | **Lowest** (-55 mV) |
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| **2** | Some sAHP developing, slight M-current | Some Na⁺ channels still inactivated, some K⁺ channels still open | **Higher** (-53 mV) |
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| **3-5** | Significant sAHP, M-current growing | Cumulative Na⁺ inactivation, K⁺ current accumulation | **Much higher** (-50 to -48 mV) |
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| **Steady-state** | Maximum sAHP, full M-current activation | Equilibrium between Na⁺ recovery and inactivation | **Highest** (plateau) |
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## **4. Mathematical Representation**
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The dynamic threshold can be modeled as:
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```
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Threshold(t) = Threshold_rest + A * ∫[Ca²⁺]_soma(t) + B * NaV_unavailable(t)
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```
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Where A and B are weighting factors for somatic and AIS contributions respectively.
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## **5. Functional Consequences of This Design**
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### **A. Temporal Filtering**
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The neuron becomes a **high-pass filter** for firing rates:
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- **Responds vigorously** to sudden input increases (first spike easy)
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- **Adapts quickly** to sustained input (subsequent spikes harder)
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- **Encodes *changes* in input**, not absolute levels
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### **B. Prevention of Epileptiform Activity**
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By making sustained high-frequency firing progressively harder, the system has a built-in **safety mechanism** against runaway excitation.
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### **C. Energy Efficiency**
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Each spike consumes ATP (for Na⁺/K⁺ pumping). By adapting, the neuron prevents wasteful firing when input is sustained but not changing.
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### **D. Signal-to-Noise Enhancement**
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The adaptation makes the neuron more sensitive to **synchronized inputs** (which can overcome the raised threshold) versus **asynchronous background noise** (which cannot).
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## **6. Modulation of Adaptation**
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Crucially, this adaptation is itself **modulatable**:
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- **Acetylcholine:** **Reduces** sAHP and M-current → less adaptation → neuron can sustain firing longer (important for attention).
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- **Norepinephrine:** Can **enhance** adaptation in some contexts, promoting burst firing patterns.
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- **Serotonin:** Modulates both sAHP and Na⁺ channel kinetics, tuning adaptation to behavioral state.
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## **7. Experimental Evidence**
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- **Intracellular recordings** show clear threshold increases during spike trains.
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- **Dynamic clamp experiments** demonstrate that injecting artificial sAHP currents reproduces adaptation.
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- **Knockout of SK channels** eliminates most spike-frequency adaptation.
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- **AIS-targeted pharmacology** shows that blocking specific K⁺ channels at the AIS reduces threshold elevation during trains.
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## **Summary: The Strategic First Spike**
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Yes, **the first spike is privileged**. The soma and AIS are engineered to be **maximally sensitive to the onset of input**, then progressively **desensitize** during sustained activity. This is achieved through:
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1. **Somatic sAHP** (Ca²⁺-dependent K⁺ currents)
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2. **Somatic M-current** accumulation
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3. **AIS Na⁺ channel inactivation**
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4. **AIS K⁺ channel cumulative activation**
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5. **Activity-dependent phosphorylation** of threshold proteins
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This creates a neuron that says: **"I notice changes immediately, but I won't keep shouting about things that don't change."** The first spike is the easiest because it carries the most information—the news that **something has changed**. Subsequent spikes in a train are progressively harder because they merely confirm "it's still happening," which is less informationally valuable.
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This elegant design balances sensitivity with stability, novelty detection with energy conservation, making the neuron an optimal detector of **meaningful change** in a noisy world.
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@@ -1,177 +0,0 @@
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Ho l’impressione che come espressione G non dobbiamo trattare il release di NT come numero ma come concentrazione indotta alla postsinapi e quanto dura quella concentrazione.
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### **Information Coding Beyond Saturation:**
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1. **Spatial Code**: Where does glutamate reach? (synaptic vs. perisynaptic vs. extrasynaptic)
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2. **Temporal Code**: How long does elevated \[glutamate\] persist?
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3. **Spillover Code**: How much reaches astrocytes/neighboring synapses?
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4. **Metabolic Code**: How much energy demand does it create?
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### **The "Glutamate Economy" Strategy:**
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The brain uses excess glutamate **strategically**:
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- **Normal transmission**: Minimal glutamate for efficiency
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- **Plasticity induction**: Extra glutamate to activate mGluRs, recruit astrocytes
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- **Network modulation**: High glutamate to affect neighboring synapses via spillover
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- **Emergency signaling**: Massive glutamate release as a distress signal
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---
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---
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---
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# **The Cooperative Gating of NMDA Receptors: A Molecular Dance of Stability**
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## **The Fundamental Difference: NMDA vs AMPA Receptor Activation**
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**AMPA receptors** are **simple ligand-gated channels**:
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- Typically require **2 glutamate molecules** to bind to open
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- Once open, they behave similarly regardless of whether 2 or 4 glutamate molecules are bound
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- Their open probability is mostly "on" or "off"
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**NMDA receptors** are **allosteric machines** with **cooperative gating**:
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- They have **multiple binding sites** that influence each other
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- The binding of glutamate to one subunit increases the **affinity** of neighboring subunits
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- The more glutamate molecules bound, the **more stable the open state**
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## **The NMDA Receptor Structure: A Tetrameric Complex**
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A typical synaptic NMDA receptor consists of:
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- **2 GluN1 subunits** (bind glycine/D-serine)
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- **2 GluN2 subunits** (bind glutamate)
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But here's the key: each **GluN2 subunit has two glutamate-binding domains** (S1 and S2), and binding at both sites creates a more stable configuration.
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## **The Molecular Mechanism: Why More Glutamate = More Stability**
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### **1. The Binding Hierarchy:**
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```
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Step 1: First glutamate binds to one GluN2 → conformational change → affinity ↑ for second site
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Step 2: Second glutamate binds to same GluN2 → further stabilization
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Step 3: Cross-subunit allostery: Occupied GluN2 increases affinity of neighboring GluN2
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Step 4: Third/fourth glutamate binding → maximal stability
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```
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### **2. The Energy Landscape Analogy:**
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Think of the receptor as a ball in different shaped bowls:
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- **No glutamate**: Ball in shallow bowl → easily rolls out (closes quickly)
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- **1 glutamate**: Bowl slightly deeper → stays open longer
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- **2 glutamates**: Deeper bowl → stable open state
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- **3-4 glutamates**: Very deep bowl → extremely stable, long openings
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**Each additional glutamate molecule deepens the energy well**, making it harder for the channel to close.
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### **3. The Kinetic Proof:**
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Experimental single-channel recordings show:
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| **Glutamate Molecules Bound** | **Mean Open Time** | **Closing Rate** |
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|---------------------------|----------------|--------------|
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| 1 | ~2 ms | Fast closure |
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| 2 | ~10-20 ms | Moderate |
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| 3-4 | ~50-100 ms | Slow, stable |
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**The open time increases exponentially** with glutamate occupancy, not linearly.
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## **4. The Biological Consequences of This Stability**
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### **A. Calcium Influx Duration Matters:**
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```
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Brief NMDA opening (1-2 ms):
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- Small Ca²⁺ puff
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- Activates fast phosphatases → LTD
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Long NMDA opening (20-100 ms):
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- Sustained Ca²⁺ influx
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- Activates slow kinases (CaMKII) → LTP
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- Triggers nuclear signaling
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```
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The **duration** of NMDA opening determines **which downstream signaling pathways** get activated.
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### **B. Temporal Integration of Inputs:**
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A single vesicle might only briefly saturate NMDA receptors. But with **multiple vesicles releasing**:
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- Glutamate concentration stays high for longer
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- NMDA receptors remain stably bound
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- Creates a **temporal window** for coincidence detection with backpropagating action potentials
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### **C. The "Threshold" Effect for Plasticity:**
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There's a **non-linear relationship**:
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- **Moderate glutamate**: NMDA receptors flicker open briefly → moderate Ca²⁺ → LTD
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- **High glutamate**: NMDA receptors lock open → large Ca²⁺ → LTP
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The difference isn't just amplitude—it's **duration** of Ca²⁺ signal.
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## **5. The Postsynaptic Spine's Calcium "Language"**
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### **The Decoding System:**
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- **Brief Ca²⁺ transients** (10-50 ms): Activate **calcineurin** → AMPA receptor removal → LTD
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- **Prolonged Ca²⁺ plateaus** (100-500 ms): Activate **CaMKII** → AMPA receptor insertion → LTP
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**More glutamate → more stable NMDA openings → longer Ca²⁺ signals → LTP instead of LTD**
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## **6. The Functional Significance in Spike Trains**
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During a spike train:
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- **First spike**: Moderate glutamate → brief NMDA openings
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- **Second/third spike** (with residual glutamate): More glutamate accumulates → more stable NMDA openings
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- **This creates a "priming" effect**: Early spikes in a train make NMDA receptors **more responsive** to later spikes
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## **7. The Astrocyte Connection**
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Astrocytes release **D-serine**, the co-agonist for GluN1 subunits. With more glutamate:
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- More D-serine binding sites occupied
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- Further stabilizes the open state
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- Creates a **positive feedback loop**: More glutamate → more stable openings → more Ca²⁺ → astrocyte Ca²⁺ → more D-serine release
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## **8. Disease Implications**
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### **Excitotoxicity Mechanism:**
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- Excessive glutamate → NMDA receptors **lock open for too long**
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- Massive, sustained Ca²⁺ influx
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- Overwhelms mitochondrial buffers
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- Triggers apoptotic pathways
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### **The NMDA Receptor "Sweet Spot":**
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There's an optimal range of glutamate occupancy:
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- **Too low**: Unreliable signaling, failed plasticity
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- **Optimal**: Balanced LTP/LTD, normal function
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- **Too high**: Excitotoxicity, receptor desensitization
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## **9. Experimental Evidence**
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1. **Single-channel recordings**: Show longer openings with higher glutamate concentrations
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2. **Mutant NMDA receptors** with altered glutamate affinity show altered plasticity thresholds
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3. **Glutamate uncaging experiments**: Precise control shows non-linear Ca²⁺ responses
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4. **Computational models** that include cooperative gating better predict experimental data
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## **The Biological Wisdom: A Molecular Amplifier**
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The cooperative gating of NMDA receptors acts as a **biological amplifier**:
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- **Weak signals** (low glutamate) get filtered out
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- **Moderate signals** produce proportional responses
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- **Strong signals** get amplified non-linearly
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This creates a **thresholding mechanism** for plasticity: only synapses receiving strong, coordinated input undergo LTP. The synapse says: "Don't just talk to me—shout with conviction if you want me to remember."
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The "more stable open state" with more glutamate binding is nature's way of saying: **"Important messages should linger, not flicker."** It's the difference between a passing thought and a deeply held memory at the molecular level.
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@@ -1,269 +0,0 @@
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# **The Life of a Presynapse During and Between Spike Trains**
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## **The Terminal's Rhythm: Interpreting the Sovereign's Commands**
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I am a presynaptic terminal. My existence is defined by the arrival of action potentials—the sovereign soma's commands. But I am not a slave; I interpret, adapt, and sometimes protest through my release patterns.
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---
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## **I. BETWEEN SPIKE TRAINS: The Idle Preparations**
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### **The Resting State (τ = 100+ ms after last spike)**
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**Internal State:**
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- **Residual Ca²⁺**: Near baseline (~50 nM)
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- **Vesicle Pool**: Fully stocked (100% of RRP)
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- **P<sub>r</sub>**: At baseline (e.g., 0.2-0.8 depending on terminal type)
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- **Recycling Machinery**: Catching up, docked vesicles ready
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**Ongoing Maintenance:**
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1. **Baseline Vesicle Cycling**:
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- Slow, stochastic release of single vesicles ("minis") - my way of whispering "I'm here" to the postsynapse
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- Steady-state recycling: 1 vesicle recycled every ~30 seconds
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2. **Metabolic Housekeeping**:
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- Astrocyte provides **lactate** → fuels my mitochondria
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- Vesicles are being **re-acidified** (pH restored to ~5.5 via V-ATPase)
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- **Glutamine** from astrocyte → converted to glutamate for reloading
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3. **Signaling Environment**:
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- Basal **adenosine** levels modulate my excitability
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- **D-serine** from astrocyte maintains postsynaptic NMDA readiness
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- Tonic **neuromodulator** levels (dopamine, ACh) set my baseline gain
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**Between-Train Plasticity:**
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- If previous train induced **LTP of release** (via NO/BDNF):
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- **P<sub>r</sub>** remains elevated for minutes-hours
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- More **active zone proteins** are synthesized
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- If previous train induced **LTD of release** (via eCBs):
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- **P<sub>r</sub>** remains suppressed
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- Fewer docked vesicles
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**Time to Full Recovery:**
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- **Vesicle Pool**: 1-10 seconds to refill RRP
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- **Calcium Clearance**: 50-200 ms to clear residual Ca²⁺
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- **Channel Recovery**: 2-100 ms for Na⁺/Ca²⁺ channel inactivation reset
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---
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## **II. DURING A SPIKE TRAIN: The Performance**
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### **Phase 1: The Opening Salvo (First 2-3 Spikes, 0-50 ms)**
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**Initial Conditions:**
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- Full vesicle pool
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- Baseline P<sub>r</sub>
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- Minimal residual Ca²⁺
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**What Happens:**
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```
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Spike 1:
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- Ca²⁺ surges to ~10 μM at active zone
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- P(r) determines release: 0.2 → 20% chance, 0.8 → 80% chance
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- If release: 1 vesicle fuses, pool ↓ by 1
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Spike 2 (20 ms later):
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- Residual Ca²⁺ from Spike 1 still present (~200 nM)
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- P<sub>r</sub> increased by STF factor: 0.2 → 0.35, 0.8 → 0.95
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- But pool now at 99% (if Spike 1 released)
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- Effective release = P<sub>r</sub> × pool_fraction
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```
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**Terminal Types Diverge:**
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- **High-P<sub>r</sub>, Small Pool**: Releases strongly on Spike 1-3, then crashes
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- **Low-P<sub>r</sub>, Large Pool**: May fail on Spike 1, releases sporadically throughout
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### **Phase 2: The Battle of Forces (Spikes 4-10, 50-200 ms)**
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**The Tension:**
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- **STF**: Residual Ca²⁺ accumulates → P<sub>r</sub> keeps rising
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- **STD**: Vesicle pool depletes → effective release drops despite high P<sub>r</sub>
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**The Turning Point:**
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At some spike N, **depletion wins**:
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```
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P<sub>r</sub> might be 0.9 (high from facilitation)
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But pool is at 20% of original
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Effective release = 0.9 × 0.2 = 0.18
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Release plummets despite "willingness"
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```
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**Real-Time Adjustments:**
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1. **Calcium-Dependent Recovery**:
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- High Ca²⁺ accelerates endocytosis (clathrin uncoating)
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- But also risks **calcium overload** → vesicle recycling stalls
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2. **Energy Crisis Management**:
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- Mitochondria work overtime
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- Lactate uptake from astrocyte increases
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- If ATP drops → recycling slows → depression worsens
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### **Phase 3: Steady-State Exhaustion (>200 ms continuous firing)**
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**The Plateau:**
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- **Release rate** stabilizes at 10-30% of initial rate
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- **Balance point**: Recycling rate ≈ Release rate
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- **P<sub>r</sub>** remains high (STF) but irrelevant due to limited vesicles
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**The "Release Modes" Shift:**
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- **Synchronous release** (spike-locked) decreases
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- **Asynchronous release** (delayed, Ca²⁺-driven) increases
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- **Miniature release** continues as stochastic background
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**Signals to Postsynapse Change:**
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- From "Here is precise timing information!" to "There is sustained activity..."
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---
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## **III. BETWEEN SPIKE TRAINS: The Aftermath and Recovery**
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### **Immediate Aftermath (0-1 second post-train)**
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**The Calcium Hangover:**
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- Bulk Ca²⁺ cleared by pumps (PMCA, NCX) in 100-500 ms
|
||||
- But **residual microdomain Ca²⁺** persists near release sites
|
||||
- This creates a **"readiness" state** for next train
|
||||
|
||||
**Vesicle Recycling Race:**
|
||||
|
||||
```
|
||||
Time 0 ms: Pool at 20%
|
||||
Time 100 ms: Pool at 40% (fast component)
|
||||
Time 500 ms: Pool at 70%
|
||||
Time 2000 ms: Pool at 95% (full recovery)
|
||||
```
|
||||
|
||||
**The Recovery Time Constant (τ<sub>recycle</sub>) Depends On:**
|
||||
|
||||
- Terminal type: 0.3 s (fast) to 10 s (slow)
|
||||
- Energy availability: Low ATP → slower
|
||||
- Astrocyte support: Lactate/glutamine supply
|
||||
- Temperature: Warmer → faster
|
||||
|
||||
### **Intermediate Recovery (1-60 seconds)**
|
||||
|
||||
**Biochemical Resets:**
|
||||
|
||||
- Kinases/phosphatases return proteins to baseline states
|
||||
- Ca²⁺-calmodulin complexes disassemble
|
||||
- Autoreceptors (mGluR, CB1) reset sensitivity
|
||||
|
||||
**Retrograde Signal Processing:**
|
||||
If the train was significant:
|
||||
|
||||
- **eCBs** from postsynapse maintain suppression (minutes)
|
||||
- **NO** from postsynapse enhances future release
|
||||
- **BDNF** begins synthesis (hours-scale effects)
|
||||
|
||||
**Metaplastic Adjustments:**
|
||||
|
||||
- mGluR activation → lowers threshold for future LTD
|
||||
- Repeated trains → builds up **adenosine** → global suppression
|
||||
|
||||
### **Long-Term Between-Train States (Minutes-Hours)**
|
||||
|
||||
**Structural Changes (If Train Was "Meaningful"):**
|
||||
|
||||
- **Active zone expansion**: More docking sites added
|
||||
- **Mitochondrial biogenesis**: More energy capacity
|
||||
- **Vesicle protein synthesis**: Larger vesicle pools
|
||||
- **Receptor expression changes**: Altered sensitivity to modulators
|
||||
|
||||
**The Terminal's "Memory":**
|
||||
|
||||
- Previous activity patterns bias future responses
|
||||
- A terminal that just experienced high-frequency firing may:
|
||||
- Recover faster (trained recycling machinery)
|
||||
- Have higher baseline P<sub>r</sub> (LTP of release)
|
||||
- Or be more prone to depression (if overwhelmed)
|
||||
|
||||
---
|
||||
|
||||
## **IV. THE SPIKE TRAIN INTERPRETATION DICTIONARY**
|
||||
|
||||
### **What Different Spike Train Patterns "Say" to the Terminal:**
|
||||
|
||||
| **Train Pattern** | **Terminal's Interpretation** | **Response Strategy** |
|
||||
|-----------------------|---------------------------|------------------------------------------------------|
|
||||
| **Single spike** | "Alert!" | Maximum P<sub>r</sub>, no STD |
|
||||
| **Brief burst (3@100Hz)** | "Important event!" | Strong STF, moderate STD, triggers plasticity |
|
||||
| **Sustained high freq** | "Emergency!" | Initial STF → severe STD → asynchronous mode |
|
||||
| **Regular low freq** | "Background signal" | Steady-state with balanced recovery |
|
||||
| **Irregular pattern** | "Complex information" | Dynamic P<sub>r</sub> adjustments, history-dependent |
|
||||
|
||||
### **The Terminal's Vocabulary in Response:**
|
||||
|
||||
| **Release Pattern** | **Message to Postsynapse** |
|
||||
|------------------------------|-----------------------------------------|
|
||||
| **Reliable on every spike** | "This is important, pay attention" |
|
||||
| **Facilitating then depressing** | "Something changed, then continued" |
|
||||
| **Sporadic releases** | "There's activity but I'm uncertain" |
|
||||
| **Asynchronous release** | "Sustained event, timing less precise" |
|
||||
| **Complete silence** | "I'm exhausted" or "This is irrelevant" |
|
||||
|
||||
---
|
||||
|
||||
## **V. THE COMPUTATIONAL CONSEQUENCES**
|
||||
|
||||
### **Between Trains: Information Integration**
|
||||
|
||||
- **Integration window**: ~50-2000 ms between trains matters
|
||||
- **Priming**: A recent train leaves residual Ca²⁺ → next train facilitated
|
||||
- **Metaplasticity**: Previous trains adjust thresholds for future plasticity
|
||||
|
||||
### **During Trains: Temporal Filtering**
|
||||
|
||||
- **High-pass filter**: Responds best to onsets (initial spikes)
|
||||
- **Adaptive gain**: Sensitivity adjusts to input statistics
|
||||
- **Energy-based gating**: Cannot sustain unrealistic firing rates
|
||||
|
||||
### **The Terminal as a Spike Train Interpreter:**
|
||||
|
||||
```
|
||||
Input: Binary spike train (0s and 1s at precise times)
|
||||
Processing:
|
||||
- Dynamic P<sub>r</sub> = f(residual Ca²⁺, recovery state)
|
||||
- Available vesicles = g(recycling rate, previous release)
|
||||
- Modulator effects = h(neuromodulators, retrograde signals)
|
||||
|
||||
Output: Probabilistic glutamate release pattern
|
||||
Which is NOT a perfect copy of the input spike train
|
||||
But a filtered, adapted, modulated version
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## **VI. THE STRATEGIC BALANCE**
|
||||
|
||||
**Between Spike Trains, I:**
|
||||
|
||||
- Recover resources
|
||||
- Process retrograde feedback
|
||||
- Adjust my baseline settings
|
||||
- Prepare for the next conversation
|
||||
|
||||
**During Spike Trains, I:**
|
||||
|
||||
- Interpret the pattern
|
||||
- Balance facilitation vs depression
|
||||
- Signal my state via release probability
|
||||
- Manage my energy budget
|
||||
- Communicate both reliability and urgency
|
||||
|
||||
**My existence is rhythmic:**
|
||||
**Rest → Prepare → Perform → Recover → Learn → Rest...**
|
||||
|
||||
Each spike train is not an isolated event but part of a **conversational history**. My response to spike #10 depends on what happened with spikes # 1-9, what happened between previous trains, and what my postsynaptic partner and astrocyte caretaker are telling me.
|
||||
|
||||
This is how I, a single presynaptic terminal, contribute to the brain's computation: not by faithfully reproducing spikes, but by **interpreting them, adapting to them, and responding strategically**—all within the biological constraints of my vesicle economy and signaling environment.
|
||||
@@ -1,278 +0,0 @@
|
||||
# **Spike Train Examples: How Different Patterns Lead to LTP, LTD, or Tagging**
|
||||
|
||||
Here's a clear visualization of how **specific spike train patterns** produce the different calcium dynamics and plasticity outcomes:
|
||||
|
||||
```mermaid
|
||||
timeline
|
||||
title Spike Train Patterns & Plasticity Outcomes
|
||||
section LTP Induction (Pre-before-Post Burst)
|
||||
Pre-spikes : 100 Hz burst<br>0, 10, 20, 30, 40 ms
|
||||
Post-spike : Single bAP at 15 ms
|
||||
Ca²⁺ Dynamics : Rapid rise to 5-10 μM<br>within 20 ms
|
||||
Tag Window : Tag set at 5 ms<br>Active until 105 ms
|
||||
Outcome : Strong LTP<br>200-300% AMPAR increase
|
||||
section LTD Induction (Isolated Presynaptic Train)
|
||||
Pre-spikes : 10 Hz train for 1s<br>0, 100, 200...900 ms
|
||||
Post-spikes : None
|
||||
Ca²⁺ Dynamics : Sustained 1-2 μM<br>for ~500 ms
|
||||
Tag Window : Multiple tags set<br>but no coincidence
|
||||
Outcome : Moderate LTD<br>40-60% AMPAR removal
|
||||
section Tagging Only (Poorly Timed Activity)
|
||||
Pre-spikes : 50 Hz burst<br>0, 20, 40 ms
|
||||
Post-spike : Delayed at 100 ms
|
||||
Ca²⁺ Dynamics : Brief 0.8-1 μM peak
|
||||
Tag Window : Tag set at 20 ms<br>Expires before post-spike
|
||||
Outcome : Metaplastic priming only<br>No weight change
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## **EXAMPLE 1: LTP INDUCTION (Theta Burst Pattern)**
|
||||
|
||||
**Spike trains:**
|
||||
|
||||
```
|
||||
Presynaptic: ● ● ● ● ● (100 Hz burst: 0, 10, 20, 30, 40 ms)
|
||||
Postsynaptic: ↑bAP at 15 ms
|
||||
```
|
||||
|
||||
**Calcium timeline:**
|
||||
|
||||
```
|
||||
Time (ms) Ca²⁺ (μM) Event
|
||||
────────────────────────────────────
|
||||
0 0.1 → 1.0 Spike 1: Glutamate → NMDAR opens
|
||||
10 1.0 → 3.0 Spike 2: Summation + tag set (θ_tag crossed)
|
||||
15 3.0 → 8.0 bAP arrives → Mg²⁺ block fully relieved
|
||||
20 8.0 → 12.0 Spike 3: Maximum Ca²⁺ → crosses θ_LTP
|
||||
30 12.0 Spike 4: High plateau
|
||||
40 10.0 Spike 5: High sustained
|
||||
50 5.0 Decay begins
|
||||
100 0.5 Tag window closes
|
||||
```
|
||||
|
||||
**Why LTP occurs:**
|
||||
|
||||
- **Strong coincidence**: bAP arrives during glutamate presence (Δt = +5 ms)
|
||||
- **High Ca²⁺ peak**: 8-12 μM > θ\_LTP (2 μM)
|
||||
- **Tag active**: Set at ~10 ms, active until ~110 ms
|
||||
- **Protein synthesis**: Triggered by combined Ca²⁺ + neuromodulators
|
||||
|
||||
**Outcome:** 200-300% increase in AMPARs within 5-30 minutes.
|
||||
|
||||
---
|
||||
|
||||
## **EXAMPLE 2: LTD INDUCTION (Low-Frequency Train)**
|
||||
|
||||
**Spike trains:**
|
||||
|
||||
```
|
||||
Presynaptic: ● ● ● ● ● ● ● ● ● ●
|
||||
0 100 200 300 400 500 600 700 800 900 ms
|
||||
Postsynaptic: (None - isolated presynaptic activity)
|
||||
```
|
||||
|
||||
**Calcium timeline:**
|
||||
|
||||
```
|
||||
Time (ms) Ca²⁺ (μM) Event
|
||||
────────────────────────────────────
|
||||
0 0.1 → 1.5 Spike 1: Tag set at ~5 ms
|
||||
100 1.5 → 2.0 Spike 2: Sustained moderate Ca²⁺
|
||||
200 2.0 Spike 3: LTD threshold duration starts
|
||||
300 2.0 Spike 4: Sustained >100 ms → LTD engaged
|
||||
400 2.0 Spike 5: Calcineurin fully active
|
||||
500 1.8 Spike 6: AMPAR removal begins
|
||||
...
|
||||
900 1.5 Last spike
|
||||
1000 0.8 Decay begins
|
||||
1500 0.2 Back to baseline
|
||||
```
|
||||
|
||||
**Why LTD occurs:**
|
||||
|
||||
- **No coincidence**: No bAPs to relieve Mg²⁺ block fully
|
||||
- **Moderate, sustained Ca²⁺**: 1.5-2.0 μM for >500 ms
|
||||
- **Calcineurin activation**: Requires sustained moderate Ca²⁺
|
||||
- **No LTP trigger**: Ca²⁺ never exceeds θ\_LTP (2 μM)
|
||||
|
||||
**Outcome:** 40-60% AMPAR removal within 1-5 minutes.
|
||||
|
||||
---
|
||||
|
||||
## **EXAMPLE 3: TAG WITHOUT EXPRESSION (Mistimed Activity)**
|
||||
|
||||
**Spike trains:**
|
||||
|
||||
```
|
||||
Presynaptic: ● ● ●
|
||||
0 20 40 ms
|
||||
Postsynaptic: ↑bAP at 100 ms (too late)
|
||||
```
|
||||
|
||||
**Calcium timeline:**
|
||||
|
||||
```
|
||||
Time (ms) Ca²⁺ (μM) Event
|
||||
────────────────────────────────────
|
||||
0 0.1 → 0.6 Spike 1: Below tag threshold
|
||||
20 0.6 → 1.0 Spike 2: Tag SET (θ_tag = 0.5 μM)
|
||||
40 1.0 → 1.2 Spike 3: Tag active, Ca²⁺ moderate
|
||||
50 0.8 Decay begins
|
||||
100 0.3 bAP arrives alone → small Ca²⁺ via VGCCs
|
||||
105 0.4 Insufficient for LTP
|
||||
110 0.3 Tag EXPIRES (set at 20 ms, 90 ms lifetime)
|
||||
```
|
||||
|
||||
**Why only tagging occurs:**
|
||||
|
||||
- **Tag set**: Moderate Ca²⁺ (1.0 μM) sets eligibility
|
||||
- **No coincidence**: bAP arrives 60 ms after last glutamate
|
||||
- **Ca²⁺ insufficient**: bAP alone → ~0.4 μM (well below θ\_LTP)
|
||||
- **Tag expires**: No strong Ca²⁺ within ~100 ms window
|
||||
|
||||
**Outcome:** No weight change, but spine is **primed**:
|
||||
|
||||
- Lowered θ\_LTP for next 30-60 minutes
|
||||
- Increased kinase sensitivity
|
||||
- **Next coincident event** will produce enhanced LTP
|
||||
|
||||
---
|
||||
|
||||
## **EXAMPLE 4: STDP WINDOW DEMONSTRATION**
|
||||
|
||||
**Different Δt values produce different outcomes:**
|
||||
|
||||
### **A. Δt = +10 ms (Pre-before-Post): LTP**
|
||||
|
||||
```
|
||||
Pre: ●
|
||||
↘
|
||||
Post: ● (10 ms later)
|
||||
Ca²⁺: 0 → 8 μM → LTP
|
||||
```
|
||||
|
||||
### **B. Δt = +50 ms (Pre-before-Post): Weak Tag Only**
|
||||
|
||||
```
|
||||
Pre: ●
|
||||
↘
|
||||
Post: ● (50 ms later)
|
||||
Ca²⁺: 0 → 1 μM → tag → 0.5 μM from bAP → No LTP (too low)
|
||||
```
|
||||
|
||||
### **C. Δt = -10 ms (Post-before-Pre): LTD**
|
||||
|
||||
```
|
||||
Post: ●
|
||||
↘
|
||||
Pre: ● (10 ms later)
|
||||
Ca²⁺: 0 → 1.5 μM (VGCC) → + 1.0 μM (NMDAR) → Sustained 2.5 μM → LTD
|
||||
```
|
||||
|
||||
### **D. Δt = -50 ms (Post-before-Pre): Nothing**
|
||||
|
||||
```
|
||||
Post: ●
|
||||
↘
|
||||
Pre: ● (50 ms later)
|
||||
Ca²⁺: Separate transients (0.5 μM each) → No tag, no LTD
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## **EXAMPLE 5: SPIKE FREQUENCY EFFECTS**
|
||||
|
||||
### **Low frequency (1 Hz): Steady state**
|
||||
|
||||
```
|
||||
Pre: ● ● ● ● ● ● ●
|
||||
Time: |----|----|----|----|----|----|
|
||||
Ca²⁺: Each transient ~0.8 μM, decays fully between spikes
|
||||
Outcome: No plasticity (below θ_tag most of the time)
|
||||
```
|
||||
|
||||
### **Moderate frequency (10 Hz): LTD**
|
||||
|
||||
```
|
||||
Pre: ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
|
||||
(sustained for 1 second)
|
||||
Ca²⁺: Builds to 1.5-2.0 μM plateau, sustained >500 ms
|
||||
Outcome: Moderate LTD
|
||||
```
|
||||
|
||||
### **High frequency burst (100 Hz): LTP**
|
||||
|
||||
```
|
||||
Pre: [●●●●●] [●●●●●] [●●●●●]
|
||||
Burst 1 Burst 2 Burst 3
|
||||
Post: ↑bAP during each burst
|
||||
Ca²⁺: Peaks at 10+ μM during bursts, decays partially between
|
||||
Outcome: Strong LTP
|
||||
```
|
||||
|
||||
### **Irregular Poisson-like: Mixed**
|
||||
|
||||
```
|
||||
Pre: ● ● ● ● ● ● ● ● ●
|
||||
(average 20 Hz, irregular intervals)
|
||||
Ca²⁺: Variable, depends on recent history
|
||||
Outcome: Some facilitation/depression, minimal long-term change
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## **EXAMPLE 6: NEUROMODULATOR EFFECTS ON SPIKE TRAINS**
|
||||
|
||||
### **With Dopamine (enhances LTP):**
|
||||
|
||||
```
|
||||
Pre: ● ● ● ● ● (20 Hz train)
|
||||
Post: ↑bAP at 15 ms
|
||||
DA: └──────────→ High during train
|
||||
Effect: Ca²⁺ peaks 30% higher, tag lifetime extended
|
||||
Outcome: LTP where none would occur without DA
|
||||
```
|
||||
|
||||
### **With eCB (promotes LTD):**
|
||||
|
||||
```
|
||||
Pre: ● ● ● ● ● ● (30 Hz train)
|
||||
Post: ↑bAP at 10 ms → eCB synthesis
|
||||
eCB: └────→ (50 ms delay) inhibits presynaptic Ca²⁺
|
||||
Effect: Later spikes see reduced Ca²⁺ influx
|
||||
Outcome: Weaker LTP or mixed LTP/LTD
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## **SUMMARY TABLE: SPIKE TRAIN → OUTCOME MAPPING**
|
||||
|
||||
| Pattern | Frequency | Coincidence | Ca²⁺ Dynamics | Tag | Outcome |
|
||||
|-----------------|-------------|----------------|------------------------------|---------------|----------------------------|
|
||||
| **Single pair** | N/A | Δt = +10 ms | Brief 5-10 μM spike | Set + used | LTP |
|
||||
| **Single pair** | N/A | Δt = -10 ms | Sustained 1-2 μM | Set | LTD |
|
||||
| **Theta burst** | 5 Hz bursts | bAP in burst | High bursts, moderate gaps | Multiple tags | Strong LTP |
|
||||
| **Low frequency** | 1 Hz | None | Separate 0.5-1 μM transients | None | No change |
|
||||
| **Sustained 10 Hz** | 10 Hz | None | Plateau ~1.5-2.0 μM | Multiple tags | LTD |
|
||||
| **High frequency** | 100 Hz | None | Initial high then depression | Early tags | Mixed: LTP then depression |
|
||||
| **Mistimed burst** | 50 Hz | bAP 60 ms late | Moderate then low | Expired | Metaplasticity only |
|
||||
|
||||
---
|
||||
|
||||
## **KEY PRINCIPLES FROM THESE EXAMPLES:**
|
||||
|
||||
1. **Timing precision matters:** ±20 ms windows determine LTP vs LTD
|
||||
2. **Frequency matters:** Low frequencies favor LTD, bursts favor LTP
|
||||
3. **History matters:** Recent spikes determine current Ca²⁺ baseline
|
||||
4. **Tag lifetime is critical:** ~100 ms window for coincidence detection
|
||||
5. **Nonlinear summation:** Bursts ≠ sum of individual spikes
|
||||
|
||||
**The presynapse-postsynapse system acts as a sophisticated pattern detector:**
|
||||
|
||||
- **Detects coincidences** within 100 ms → LTP
|
||||
- **Detects isolated presynaptic activity** → LTD
|
||||
- **Detects moderate activity without coincidence** → Metaplastic priming
|
||||
- **All filtered through neuromodulatory state** (DA, eCB, etc.)
|
||||
|
||||
**This explains why specific spike patterns in the brain (theta rhythms, gamma bursts) are so effective for learning—they naturally create the calcium dynamics that trigger LTP with minimal depression.**
|
||||
@@ -1,348 +0,0 @@
|
||||
# Milliseconds Time Scale
|
||||
|
||||
## N-SPK
|
||||
|
||||
### Presynapse
|
||||
|
||||
#### 1 - Ca+ Clearance: \[AP\], \[Ca+\], \[CaFullnessTraces\], \[CaNotEmptyTraces\]
|
||||
|
||||
*Questa e’ una novita’ per evitare di fare controlli sempre. Invece viene attivato il contesto allo Spike, e invece di sparire alla fine dello spike, sparisce da solo (ContextSelf)*
|
||||
|
||||
- **RF**: 1
|
||||
- **InContext**: Action potential depolarization (to \~+30 mV)
|
||||
- **Context Self**
|
||||
- **Condition: IF** \[Ca+\] **FULLNESS**
|
||||
- **OutContext**: {Ca+ FULLNESS}
|
||||
- **Consequence:** Ca+ clearance fast
|
||||
- **Tracce:** \[CaFullnessTraces\]
|
||||
- **Condition: IF** \[Ca+\] **NOT EMPTY AND \[**Ca+\] **NOT FULLNESS**
|
||||
- **OutContext**: {Ca+ NOT EMPTY}
|
||||
- **Consequence:** Ca+ clearance slow
|
||||
- **Tracce:** \[CaNotEmptyTraces\]
|
||||
- **Condition: IF** \[Ca+\] **EMPTY**
|
||||
- **EndContext**: Self
|
||||
|
||||
#### 2 - VGCC open: \[AP\], \[Ca+\], \[CaFullnessTraces\]
|
||||
|
||||
- **RF**: 1
|
||||
- **InContext**: Action potential depolarization (to \~+30 mV)
|
||||
- **Consequence**: \[Ca+\] concentration increase
|
||||
- **Tracce**: Se Ca+ FULLNESS, lascio tracce di overflow per modulazione DOWN, da capire UP
|
||||
|
||||
#### 3 - Vescicle release: \[Ca+\], \[RRP\], \[NT\]
|
||||
|
||||
*Il rilascio di NT avviene solo se Ca+ FULLNESS? Ovviamente se ci sono Vesciche. O dipende da altro? Cioe’ cosi’ rilascerebbe tutte le vesciche se c’e’ fullness. Dovremmo mettere un tag, o una discesa improvvisa di Ca+ al release di una vescica. Perche’ potremmo avere il caso che i VGGC sia talmente tanti da far entrare tanto calcio da far si che la prima vescica consumi CA ma non abbastanza da andare sotto FULLNESS*
|
||||
|
||||
- **RF**: 1
|
||||
- **InContext**: Action potential depolarization (to \~+30 mV)
|
||||
- **Condition: IF** Ca+ **FULLNESS** **AND** RRP **NOT EMPTY (AND NOT** VES)
|
||||
- **Consequence**: Glutamate vescicle release.
|
||||
- **Consequence:** Si consumano i Ca+?
|
||||
- **Traces**: Lascio tracce di non possibilita’ per la modulazione UP, da capire DOWN
|
||||
|
||||
#### 4 - Lactate uptake
|
||||
|
||||
Il Lactate viene mandato da Astro che ha fatto re-uptake di Glutamate, trasformato in Glutamine e poi Lactate. Il Lactate serve a fare ATP
|
||||
|
||||
- **Timing**: > 10 ms
|
||||
|
||||
#### 5 - Vescicle moved to RRP
|
||||
|
||||
From **The Reserve Pool** and **Recently Endocytosed Vesicles**
|
||||
|
||||
- **For Presynaptic Strengthening (e.g., LTP):**
|
||||
- **Nitric Oxide (NO):** A gas that diffuses freely. During postsynaptic LTP induction (strong NMDAR activation), neuronal NO synthase (nNOS) is activated. NO diffuses into the presynaptic terminal and activates soluble guanylyl cyclase (sGC), raising cGMP levels. This enhances vesicle release via PKG, contributing to **presynaptic LTP**.
|
||||
- **Endocannabinoid-Mediated *LTP* (eLTP):** In some synapses, a **postsynaptic** depolarization triggers production of endocannabinoids (e.g., 2-AG). These bind to presynaptic **CB1 receptors**, but surprisingly, can initiate a signaling cascade (involving cAMP/PKA) that **increases Pr** for a long period.
|
||||
- **Neurotrophins (BDNF):** Released from the postsynapse in an activity-dependent manner. Presynaptic TrkB receptors activate pathways (PI3K, MAPK) that enhance vesicle docking and Pr.
|
||||
- **For Presynaptic Weakening (e.g., LTD):**
|
||||
- **Classical Endocannabinoid-Mediated LTD (eCB-LTD):** More common. Moderate postsynaptic activity (mGluR activation or moderate Ca²⁺ rise) triggers 2-AG release. 2-AG binds presynaptic CB1 receptors, which **inhibit VGCCs** and **directly inhibit the release machinery** via Gi/o protein signaling, reducing Pr for a long time.
|
||||
- **Other Lipid Mediators** (like LPA) can also act as retrograde signals for depression.
|
||||
|
||||
|
||||
- **Mechanism**:
|
||||
- **residual calcium →** The key sensor is **Calmodulin (CaM)**. When bound to calcium, its structure changes → This Ca²⁺/Calmodulin complex then binds to and activates **Munc13**, the master regulator of vesicle priming.
|
||||
- **Munc13** is the essential protein that "primes" vesicles, making them release-ready (part of the SNARE complex assembly).
|
||||
- In its activated state (by Ca²⁺/CaM), Munc13's activity increases dramatically—by an order of magnitude or more.
|
||||
- This turns the normal, slow "drip-feed" of vesicles into a **high-speed conveyor belt**.
|
||||
- Superpriming requires ATP for phosphorylation reactions and for molecular motors that move vesicles. If the reserve pool is depleted or ATP is low, the superpriming "conveyor belt" has nothing to feed into the RRP. (Astrocyte)
|
||||
- The **vesicle reserve pool is a strictly private, local resource of each individual presynaptic bouton.** What is shared between synapses on the same axon are **signals (neuromodulators)** and **metabolic resources (energy)**, but **not the synaptic vesicles themselves.** This ensures both independent computation and cooperative metabolic support within the axonal branch.
|
||||
- ATP mostly comes from lactate from Atrocyte
|
||||
- **Timing**: < 10 ms
|
||||
- **InContext**: Ca+ **NOT EMPTY**
|
||||
- **Condition: IF** ATP **NOT EMPTY** **AND** RP **NOT EMPTY**
|
||||
- **Consequence:** Vescicles moved slow
|
||||
- **Tracce**: se non c’e’ abbastanza ATP o non ci sono abbastanza RP, lascio tracce per la modulazione UP, devo capire modulazione DOWN
|
||||
- **InContext**: Ca+ **FULLNESS**
|
||||
- **Condition: IF** ATP **NOT EMPTY** **AND** RRP **NOT EMPTY**
|
||||
- **Consequence:** Vescicles moved fast
|
||||
- **Tracce**: se non c’e’ abbastanza ATP o non ci sono abbastanza RP, lascio tracce per la modulazione UP, devo capire modulazione DOWN
|
||||
|
||||
#### Observed 1 - Upregulation of Pr
|
||||
|
||||
- **Timing**: > 10 ms
|
||||
- **Upregulation (Facilitation):** Residual Ca²⁺ from previous spikes increases P_r for next release
|
||||
|
||||
#### Observed 2 - Downregulation of Pr
|
||||
|
||||
- **Timing**: > 10 ms
|
||||
- **Downregulation (Depression):** High-frequency firing depletes readily releasable vesicle pool, decreasing P_r
|
||||
|
||||
### Postsynapse
|
||||
|
||||
#### 1 - AMPA Opening
|
||||
|
||||
- **Timing**: < 1 ms
|
||||
- **InContext:** Glutamate > **FULLNESS**
|
||||
- **OutContext:** AMPA receptor opening
|
||||
|
||||
#### 2 - Ca+ influx by AMPA
|
||||
|
||||
- **Timing**: < 1 ms
|
||||
- **InContext:** AMPA receptor opened
|
||||
- **Consequence:** Na⁺ influx
|
||||
- **Consequence:** addition to local depolarization (EPSP) from AMPA activation
|
||||
|
||||
#### 3 - Limited Ca+ influx by NMDA
|
||||
|
||||
- **Timing**: > 1 ms
|
||||
|
||||
|
||||
- **InContext:** local depolarization (EPSP) **NOT** **FULLNESS** (requires depolarization > -40mV)
|
||||
- **Consequence:** Glutamate binding to NMDA receptors (Mg²⁺-blocked initially)
|
||||
- **Consequence:** limited NMDA receptor opening → Ca²⁺ influx
|
||||
- **Consequence:** limited addition to local depolarization (EPSP) from NMDA activation
|
||||
|
||||
#### 4 - Depolarization by bAP
|
||||
|
||||
- **Timing**: > 1 ms
|
||||
- **InContext:** bAP backpropagating action potential
|
||||
- **Consequence:** addition to local depolarization (EPSP) from bAP
|
||||
|
||||
#### 5 - Mg²⁺ NMDA unblock
|
||||
|
||||
- **Timing**: > 1 ms
|
||||
|
||||
|
||||
- **InContext:** local depolarization (EPSP) > **FULLNESS** (requires depolarization > -40mV)
|
||||
- **OutContext:** NMDA Mg²⁺ unblock
|
||||
|
||||
#### 6 - Full Ca+ influx by NDMA
|
||||
|
||||
- **Timing**: < 1 ms
|
||||
- **InContext:** NMDA Mg²⁺ unblock
|
||||
- **Consequence:** Na⁺ influx
|
||||
- **Consequence:** addition to local depolarization (EPSP) from Full NMDA activation
|
||||
|
||||
#### Observed 1 - Upregulation
|
||||
|
||||
- **Upregulation:** Depolarization relieves NMDA Mg²⁺ block → Ca²⁺ influx amplification
|
||||
|
||||
#### Observed 2 - Downregulation
|
||||
|
||||
- **Downregulation:** AMPA desensitization acts as low-pass filter
|
||||
|
||||
### Dendrite
|
||||
|
||||
### Soma
|
||||
|
||||
### AIS
|
||||
|
||||
# Seconds Time Scale
|
||||
|
||||
## N-CHAN - LTP/LTD
|
||||
|
||||
Qui si modulano i canali ionici, sia quelli voltage (PRE/POST) che quelli Neuro (POST). Non si creano o si distruggono, ma si rendono attivi disattivi quelli presenti.
|
||||
|
||||
### Presynapse
|
||||
|
||||
This is critical for **long-term** presynaptic changes. The postsynaptic cell, upon detecting specific activity patterns (like those for LTP/LTD), releases chemical signals that travel backwards to the presynaptic terminal, instructing it to change.
|
||||
|
||||
- **For Presynaptic Strengthening (e.g., LTP):**
|
||||
- **Nitric Oxide (NO):** A gas that diffuses freely. During postsynaptic LTP induction (strong NMDAR activation), neuronal NO synthase (nNOS) is activated. NO diffuses into the presynaptic terminal and activates soluble guanylyl cyclase (sGC), raising cGMP levels. This enhances vesicle release via PKG, contributing to **presynaptic LTP**.
|
||||
- **Endocannabinoid-Mediated *LTP* (eLTP):** In some synapses, a **postsynaptic** depolarization triggers production of endocannabinoids (e.g., 2-AG). These bind to presynaptic **CB1 receptors**, but surprisingly, can initiate a signaling cascade (involving cAMP/PKA) that **increases Pr** for a long period.
|
||||
- **Neurotrophins (BDNF):** Released from the postsynapse in an activity-dependent manner. Presynaptic TrkB receptors activate pathways (PI3K, MAPK) that enhance vesicle docking and Pr.
|
||||
- **For Presynaptic Weakening (e.g., LTD):**
|
||||
- **Classical Endocannabinoid-Mediated LTD (eCB-LTD):** More common. Moderate postsynaptic activity (mGluR activation or moderate Ca²⁺ rise) triggers 2-AG release. 2-AG binds presynaptic CB1 receptors, which **inhibit VGCCs** and **directly inhibit the release machinery** via Gi/o protein signaling, reducing Pr for a long time.
|
||||
- **Other Lipid Mediators** (like LPA) can also act as retrograde signals for depression.
|
||||
|
||||
#### 1 - **Augmentation:**
|
||||
|
||||
- Calcium-sensing proteins (Munc13) alter release probability (1-10s range)
|
||||
- Astrocyte gliotransmitters (ATP, D-serine, glutamate)
|
||||
- ATP and Vescicle production
|
||||
|
||||
Qui dobbiamo vedere su che scala temporale mettere questo comportamento
|
||||
- **Timing**: > 1s?
|
||||
|
||||
#### 2 - **Upregulation:**
|
||||
|
||||
- NO/BDNF activates cascades that increase P_r, promote synaptic growth (facilitates LTP)
|
||||
- VGCC modulation ??
|
||||
- Potassium channel modulation ??
|
||||
|
||||
#### 3 - **Downregulation:**
|
||||
|
||||
- eCBs bind CB1 receptors, inhibit VGCCs, activate K⁺ channels → profound decrease in P_r (DSE/DSI - depolarization-induced suppression)
|
||||
- CB1 receptor activation (by eCBs)
|
||||
|
||||
|
||||
- Retrograde BDNF (brain-derived neurotrophic factor)
|
||||
|
||||
####
|
||||
|
||||
### Postsynapse
|
||||
|
||||
#### 1 - NO Signalling
|
||||
|
||||
### Dendrite
|
||||
|
||||
### Soma
|
||||
|
||||
### AIS
|
||||
|
||||
# Hours/Day Time Scale
|
||||
|
||||
## N-Meta - Structural
|
||||
|
||||
Qui si modula la possibilita’ di potenza di fuoco, sia come nuovi recettori (voltage e neuro) sia come grandezza di RP, RRP e velocita’ di spostamento.
|
||||
|
||||
### Presynapse
|
||||
|
||||
Long-lasting presynaptic strengthening requires **new proteins**:
|
||||
|
||||
- More vesicles
|
||||
- More active zone proteins (e.g., RIM, Munc13)
|
||||
- More mitochondria (for energy)
|
||||
- More synaptic vesicle components (synaptobrevin, synaptotagmin)
|
||||
- More cytoskeletal elements for structure
|
||||
|
||||
The neuron must **detect a sustained need for strengthening at a specific synapse**, send a signal to its nucleus, transcribe genes, and then deliver the new proteins back to that specific presynaptic bouton.
|
||||
|
||||
1. **Detection:** Sustained high-frequency firing at the presynaptic terminal → elevated Ca²⁺ and/or neuromodulator release (dopamine, norepinephrine).
|
||||
2. **Signal to Nucleus:** Activation of kinases (PKA, CaMKIV) and retrograde importin signaling → **CREB phosphorylation** in the nucleus.
|
||||
3. **Transcriptional Program:** CREB induces expression of:
|
||||
- **Immediate Early Genes** (e.g., *c-Fos*, *Arc*) that regulate further transcription.
|
||||
- **Effector Genes:** Presynaptic proteins (synapsins, RIM, Munc13), BDNF, cytoskeletal proteins.
|
||||
4. **Delivery:** Newly synthesized mRNAs/proteins are actively transported down the axon, **targeted to the active synapses** that initiated the signal.
|
||||
5. **Local Implementation:**
|
||||
- Assembly of new active zones.
|
||||
- Expansion of vesicle pools.
|
||||
- Possible local translation.
|
||||
- Bouton enlargement or new bouton formation.
|
||||
6. **Stabilization:** Epigenetic modifications and continued autocrine/paracrine signaling (BDNF→TrkB) lock in the changes.
|
||||
|
||||
**In essence, the neuron "knows" to strengthen a presynapse long-term because the synapse's own sustained activity creates a biochemical signature that reaches the nucleus, triggering a gene program specifically designed to build a bigger, better release machine. This is a fundamental mechanism underlying long-term memory storage at the synaptic level.**
|
||||
|
||||
#### 1
|
||||
|
||||
- ATP-dependent vesicle cycling
|
||||
- **Metabolic veto:** Insufficient ATP prevents vesicle release despite adequate Ca²⁺
|
||||
|
||||
#### 2
|
||||
|
||||
- Glutamine→glutamate conversion (via glutaminase). Glutamine from astrocytes (glutamate-glutamine cycle)
|
||||
|
||||
#### 3
|
||||
|
||||
- Vesicle refilling with glutamate
|
||||
|
||||
#### 3
|
||||
|
||||
- Maintenance of ion gradients
|
||||
|
||||
**Incoming Signals:**
|
||||
|
||||
- Astrocyte-supplied lactate (via monocarboxylate transporters)
|
||||
- Metabolic state indicators (ATP levels, NAD/NADH ratio)
|
||||
|
||||
**Outgoing Signals:**
|
||||
|
||||
- Metabolic demand signals to astrocyte ??
|
||||
|
||||
**Modulation:**
|
||||
|
||||
- Lactate availability determines sustained release capacity during high activity ??
|
||||
|
||||
### Postsynapse
|
||||
|
||||
#### 1
|
||||
|
||||
#### 2
|
||||
|
||||
### Dendrite
|
||||
|
||||
### Soma
|
||||
|
||||
### AIS
|
||||
|
||||
## Astrocyte
|
||||
|
||||
- **Onset:** Astrocytic glutamate transporters (primarily GLT-1 and GLAST) start working **within milliseconds** of glutamate release into the synaptic cleft. They compete with postsynaptic receptors for binding glutamate.
|
||||
- **Clearance Duration:** The complete clearance of synaptically released glutamate typically takes:
|
||||
- **Tens to hundreds of milliseconds (\~20-100 ms)** at a single synapse after a single synaptic event.
|
||||
- **Up to several seconds** during and after a high-frequency spike train, as the total glutamate load is higher and transporters can become temporarily saturated.
|
||||
|
||||
#### 2. **Timing Relative to Spike Trains: During and Between**
|
||||
|
||||
- **During the Train:** With each pulse in a spike train, glutamate builds up in the cleft. Astrocytes begin uptake immediately with each release. However, during high-frequency stimulation (e.g., 50-100 Hz), release can temporarily outpace clearance, leading to **glutamate spillover** and activation of peri- or extrasynaptic receptors.
|
||||
- **Between Spikes (Inter-pulse Intervals):** This is a critical period for uptake. The \~10-20 ms between spikes in a high-frequency train is when transporters actively work to lower glutamate concentration before the next pulse arrives. This helps prevent excessive receptor desensitization and controls the temporal fidelity of synaptic transmission.
|
||||
- **After the Train:** Uptake continues for hundreds of milliseconds to seconds to fully clear the extracellular space, reset the synapse, and stop activation of extrasynaptic NMDA or metabotropic glutamate receptors (mGluRs).
|
||||
|
||||
### Milliseconds Time Scale
|
||||
|
||||
#### 1
|
||||
|
||||
#### 2
|
||||
|
||||
### Seconds Time Scale
|
||||
|
||||
#### 1
|
||||
|
||||
#### 2
|
||||
|
||||
### Minutes Time Scale
|
||||
|
||||
#### 1
|
||||
|
||||
#### 2
|
||||
|
||||
## N-SYN - Creation/destruction SYN
|
||||
|
||||
### Presynapse
|
||||
|
||||
#### 1
|
||||
|
||||
- Structural growth/retraction of presynaptic bouton. Terminal size increases/decreases (Questo lo fa con SYN del NETWORK)
|
||||
|
||||
#### 2
|
||||
|
||||
- Changes in active zone size. Development percui la PRE si specializza. Puo’ essere anche modulation senza cambiare tipo di PRE.
|
||||
|
||||
#### 3
|
||||
|
||||
- Alterations in vesicle pool size
|
||||
|
||||
**Incoming Signals??:**
|
||||
|
||||
- Retrograde trophic factors (BDNF, sustained)
|
||||
- Homeostatic scaling signals from soma
|
||||
|
||||
**Outgoing Signals??:**
|
||||
|
||||
- Modified synaptic strength through structural change
|
||||
|
||||
### Postsynapse
|
||||
|
||||
#### 1
|
||||
|
||||
#### 2
|
||||
|
||||
### Dendrite
|
||||
|
||||
### Soma
|
||||
|
||||
### Astrocyte
|
||||
|
||||
#### 1
|
||||
|
||||
#### 2
|
||||
@@ -1,624 +0,0 @@
|
||||
# Neuron Geneosophic Expression
|
||||
|
||||
*Qui la timescale la inseriamo per la verifica dei comportamenti. Ma quello che conta e’ RF, che rappresenta nella espressione G, la possibilita’ di verificare la timescale.*
|
||||
|
||||
# Spiking Neuron Behavior
|
||||
|
||||
```
|
||||
Container: N-SPK
|
||||
- Expands: 1 AXO, 1 SOMA, 3 DB
|
||||
- Modulability:
|
||||
- TUN: None
|
||||
- DEV: None
|
||||
```
|
||||
|
||||
*Qui mettiamo i comportamenti che generalmente associamo al fare “diretto” neuronale. In [N-TUN-(MTP-MTD)]() e [N-MOD-(LTP-LTD)](https://cl.splindex.net/apps/files/files/1160115?dir=/code-server/G-notes/neuron&editing=false&openfile=true#h-n-mod-ltp-ltd) mettiamo le modulazioni di questi comportamenti.*
|
||||
|
||||
## Presynaptic Behavior
|
||||
|
||||
```
|
||||
Container: PRE
|
||||
Behavior: Presynaptic Behavior
|
||||
- ContainedBy: AXO
|
||||
- Expands: 10 VGCC
|
||||
- Modulability:
|
||||
- TUN: PRE # Possible <-> Actual, Synapting
|
||||
- DEV: None
|
||||
```
|
||||
|
||||
*The **vesicle reserve pool is a strictly private, local resource of each individual presynaptic bouton.** What is shared between synapses on the same axon are **signals (neuromodulators)** and **metabolic resources (energy)**, but **not the synaptic vesicles themselves.** This ensures both independent computation and cooperative metabolic support within the axonal branch.*
|
||||
|
||||
### Milliseconds Time Scale
|
||||
|
||||
> AP Arrives
|
||||
> Time: t = 0 ms
|
||||
> Trigger: Depolarization from axon hillock
|
||||
> Mechanism: Na⁺/K⁺ voltage-gated channel cascade
|
||||
> State: Terminal depolarizes from -70 mV to +30 mV
|
||||
> Duration: \~1 ms
|
||||
|
||||
#### VGCC Open - Ca2+ Influx
|
||||
|
||||
```
|
||||
Container: VGCC
|
||||
Behavior: VGCC Open - Ca2+ Influx
|
||||
- ContainedBy: PRE
|
||||
- Tubs:
|
||||
- Source:
|
||||
- Ca+ #FULLNESS = 50 questo va messo nel Destination?
|
||||
- Yellow:
|
||||
- ATP #FULLNESS = 50
|
||||
- Context: AP
|
||||
- RF: 1
|
||||
- IF NOT (Ca+ FULLNESS) AND NOT (ATP EMPTY)
|
||||
- Consequence: (Ca+ increase)
|
||||
- Consequence: (ATP decrease)
|
||||
- Traces: # le tracce di CaFullnessTraces le lasciamo quando vediammo im contesti a RF piu' alto
|
||||
- Modulability:
|
||||
- TUN: VGCC # Possible <-> Actual, Postsynapsis channel tuning
|
||||
- DEV: VGCC # Possible increase/descrease
|
||||
```
|
||||
|
||||
*Auto-inhibition? Ca²⁺ binding to calmodulin on VGCC. 5-50 ms*
|
||||
|
||||
*SK Channels: non comprendiamo i K+ CHannels che si aprono quando entra Ca+ e servono a ripolazzare la presinapsi per chiudere i VGCC. Il tutto viene compreso come contestualizzazione AP.*
|
||||
|
||||
*Se Ca+FULLNESS, lascio tracce di overflow per modulazione DOWN, da capire UP*
|
||||
|
||||
> VGCC Open
|
||||
> Time: t = 0.2-0.5 ms after AP arrival
|
||||
> Trigger: Membrane depolarization > -40 mV
|
||||
> Open probability: \~0.3-0.8 during AP peak
|
||||
> Open duration: \~0.5-2 ms
|
||||
> Ca2+ Influx
|
||||
> Time: t = 0.3-1 ms after AP arrival
|
||||
> Ca²⁺ source: Extracellular (1.2 mM) → intracellular (50 nM baseline)
|
||||
> Influx rate: \~3000-10000 Ca²⁺ ions per VGCC per ms
|
||||
> Microdomain formation:
|
||||
> - Within 20 nm of VGCC: 10-100 µM
|
||||
> - At vesicle release site: 10-25 µM threshold for release
|
||||
> - Rise time: <100 µs
|
||||
> - Diffusion-limited spread: \~100-200 nm radius
|
||||
|
||||
#### Vesicle Release
|
||||
|
||||
```
|
||||
Behavior: Vesicle Release
|
||||
- ContainedBy: PRE
|
||||
- Tubs:
|
||||
- Source:
|
||||
- Ca+
|
||||
- RRP,
|
||||
- Yellow:
|
||||
- NT
|
||||
- ATP
|
||||
- TagRelease ?
|
||||
- InContext: CaFull
|
||||
- RF: 6
|
||||
- Condition: IF (Ca+ FULLNESS) AND NOT (RRP EMPTY) AND NOT (ATP EMPTY)
|
||||
- Consequence: (RRP decrease)
|
||||
- Consequence: (NT increase) # vedi nota sotto
|
||||
- Consequence: (Ca+ decrease) # ?
|
||||
- Consequence: (TagRelease increase) # check di rilascio fatto (pensiamo ad una sola vescica per AP?)
|
||||
- Consequence: (ATP decrease)
|
||||
- Traces: ?
|
||||
- Modulability:
|
||||
- TUN: None
|
||||
- DEV: RRP, (Ca+ FULLNESS) # increase/decrease RPP, increase/decrease level of (Ca+ FULLNESS)
|
||||
```
|
||||
|
||||
*Il rilascio di NT avviene solo se Ca+ FULLNESS? Ovviamente se ci sono Vesciche. O dipende da altro? Cioe’ cosi’ rilascerebbe tutte le vesciche se c’e’ fullness. Dovremmo mettere un tag, o una discesa improvvisa di Ca+ al release di una vescica. Perche’ potremmo avere il caso che i VGGC sia talmente tanti da far entrare tanto calcio da far si che la prima vescica consumi CA ma non abbastanza da andare sotto FULLNESS*
|
||||
|
||||
*Rilascio di NT: Geneosoficamente dovremmo aprire un nuovo contesto che rilascia ad un RF veloce un NT alla volta quando sei nel contesto di rilascio vescica, perche’ Geneosoficamente possiamo solo creare/distruggere blocco. Ma forse possiamo mettere un floor per efficienza: rilascio di una vescica == rilascio 1000 NT? Anche se poi l’Astrocita deve fare un uptake NT per NT?*
|
||||
|
||||
> Time: t = 0.4-1.5 ms after AP arrival
|
||||
> Decision:
|
||||
> 1. \[Ca²⁺\]microdomain > 10-25 µM
|
||||
> 2. Vesicle in RRP (docked & primed)
|
||||
> Release latency: 0.1-1.0 ms after Ca²⁺ threshold reached
|
||||
> Release synchrony: Multiple vesicles can release simultaneously
|
||||
|
||||
#### Ca+ Clearance
|
||||
|
||||
```
|
||||
Behavior: Ca+ Clearance
|
||||
- ContainedBy: PRE
|
||||
- Blocks: Ca+, ATP
|
||||
- InContext: CaMedium
|
||||
- RF: 6
|
||||
- Condition: IF NOT (Ca+ EMPTY) AND NOT (Ca+ FULLNESS) AND NOT (ATP EMPTY)
|
||||
- Consequence: (Ca+ decrease)
|
||||
- Consequence: (ATP decrease)
|
||||
- Tracce: None
|
||||
- Modulability:
|
||||
- TUN: None
|
||||
- DEV: RF
|
||||
- InContext: CaFull
|
||||
- RF: 1
|
||||
- Condition: IF (Ca+ FULLNESS)
|
||||
- Consequence: (Ca+ decrease)
|
||||
- Consequence: (ATP decrease)
|
||||
- Tracce: None
|
||||
- Modulability:
|
||||
- TUN: None
|
||||
- DEV: RF
|
||||
```
|
||||
|
||||
*Svuotiamo a due velocita’. Il context ([Check Ca+ concentration](https://cl.splindex.net/apps/files/files/1160115?dir=/code-server/G-notes/neuron&editing=false&openfile=true#h-4-check-ca-concentration)) e’ determinato a epoca piu’ lunga, tanto ci vuole qualche giro per fare entrare i primi Ca+*
|
||||
|
||||
> Time: t = 1-50 ms after influx
|
||||
> Clearance mechanisms (in order of speed):
|
||||
> 1. Fast buffers (calbindin, parvalbumin): <1 ms
|
||||
> 2. Plasma membrane Ca²⁺ ATPase (PMCA): 10-100 ms
|
||||
> 3. Na⁺/Ca²⁺ exchanger (NCX): 10-100 ms
|
||||
> 4. Mitochondrial uptake: 10-1000 ms
|
||||
> 5. Endoplasmic reticulum uptake: 100-1000 ms
|
||||
> Residual Ca²⁺: 0.1-0.5 µM persists for 10-1000 ms
|
||||
|
||||
#### Observed 1 - STP - Upregulation of Pr
|
||||
|
||||
> **Timing**: > 10 ms
|
||||
>
|
||||
> - **Upregulation (Facilitation):** Residual Ca²⁺ from previous spikes increases P_r for next release
|
||||
|
||||
#### Observed 2 - STD - Downregulation of Pr
|
||||
|
||||
> **Timing**: > 10 ms
|
||||
>
|
||||
> - **Downregulation (Depression):** High-frequency firing depletes readily releasable vesicle pool, decreasing P_r
|
||||
|
||||
### Tens-ms to seconds Time Scale
|
||||
|
||||
#### Vescicles Recycling
|
||||
|
||||
> Time: t = 10 ms - 10 s (depending on activity)
|
||||
> Sequential steps:
|
||||
> 1. Endocytosis (clathrin-mediated, kiss-and-run, bulk)
|
||||
> 2. Vesicle re-acidification (v-ATPase)
|
||||
> 3. Neurotransmitter reloading (vesicular transporters)
|
||||
> 4. Priming (SNARE assembly, docking)
|
||||
> 5. Return to RRP
|
||||
> Recycling rate: Limited by ATP availability
|
||||
|
||||
#### Vescicle from RP to RRP
|
||||
|
||||
```
|
||||
Behavior: Vescicle from RP to RRP
|
||||
- ContainedBy: PRE
|
||||
- Blocks: RP, RRP, Ca+, ATP
|
||||
- InContext: CaEmpty
|
||||
- RF: 30
|
||||
- Condition: IF NOT (ATP EMPTY) AND NOT (RP EMPTY)
|
||||
- Consequence: (RP decrease) # moved VERY slow
|
||||
- Consequence: (RRP increase) # moved VERY slow
|
||||
- Consequence: (ATP decrease) # Very low ATP consumption
|
||||
- Tracce: ? # se non c’e’ abbastanza ATP o non ci sono abbastanza RP, lascio tracce per la modulazione UP, devo capire modulazione DOWN
|
||||
- Modulability:
|
||||
- TUN: None
|
||||
- DEV: RF
|
||||
- InContext: CaMedium
|
||||
- RF: 15
|
||||
- Condition: IF NOT (ATP EMPTY) AND NOT (RP EMPTY)
|
||||
- Consequence: (RP decrease) # moved slow
|
||||
- Consequence: (RRP increease) # moved slow
|
||||
- Consequence: (ATP decrease) # low ATP consumption
|
||||
- Tracce: ? # se non c’e’ abbastanza ATP o non ci sono abbastanza RP, lascio tracce per la modulazione UP, devo capire modulazione DOWN
|
||||
- Modulability:
|
||||
- TUN: None
|
||||
- DEV: RF
|
||||
- InContext: CaFull
|
||||
- # Superpriming requires ATP for phosphorylation reactions and for molecular motors that move vesicles. If the reserve pool is depleted or ATP is low, the superpriming "conveyor belt" has nothing to feed into the RRP. (Astrocyte)
|
||||
- RF: 5
|
||||
- Condition: IF NOT (ATP EMPTY) AND NOT (RP EMPTY)
|
||||
- Consequence: (RP decrease) # moved fast
|
||||
- Consequence: (RRP increease) # moved fast
|
||||
- Consequence: (ATP decrease) # fast ATP consumption
|
||||
- Tracce: ? # se non c’e’ abbastanza ATP o non ci sono abbastanza RP, lascio tracce per la modulazione UP, devo capire modulazione DOWN
|
||||
- Modulability:
|
||||
- TUN: None
|
||||
- DEV: RF
|
||||
```
|
||||
|
||||
*From The Reserve Pool and Recently Endocytosed Vesicles*
|
||||
|
||||
#### Check Ca+ Concentration
|
||||
|
||||
```
|
||||
Behavior: Check Ca+ Concentration
|
||||
- ContainedBy: PRE
|
||||
- Blocks: Ca+, Ca+MediumTraces, Ca+HighTraces
|
||||
- Context-fixed
|
||||
- RF: 60
|
||||
- Condition: IF (Ca+ EMPTY)
|
||||
- OutContext: CaEmpty
|
||||
- Consequence: None
|
||||
- Traces: None
|
||||
- Condition: IF (NOT Ca+ EMPTY) AND (NOT Ca+ FULLNESS)
|
||||
- OutContext: CaMedium
|
||||
- Consequence: None
|
||||
- Traces: (Ca+MediumTraces increase) # Add to traces Ca+Medium (Questo per la modulazione, quanti giri e’ rimasto in questa condizione)
|
||||
- Condition: IF (Ca+ FULLNESS)
|
||||
- OutContext: CaFull
|
||||
- Consequence: None
|
||||
- Traces: (Ca+HighTraces increase) # Add to traces Ca+Medium (Questo per la modulazione, quanti giri e’ rimasto in questa condizione)
|
||||
- Modulability:
|
||||
- TUN: None
|
||||
- DEV: (Ca+ FULLNESS)
|
||||
```
|
||||
|
||||
*Il controllo su Ca+ viene fatto anche nel contesto spike, ma li e’ con RF1. Qui lo facciamo sempre ma con RF50 o maggiore, per limitare check e comunque siamo in un timescale molto piu’ alta.*
|
||||
|
||||
*Non deve andare in overlap con Action Potential*
|
||||
|
||||
### Seconds-Minutes Time Scale
|
||||
|
||||
*Questi comportamenti si possono fare anche controllando che non ci sia alta concentrazione di Ca+ per essere sicuri che il neurone sia in un momento di calma. Quindi devo cambiare e mettere context fixed?*
|
||||
|
||||
#### Vesicles Filling RP ?
|
||||
|
||||
```
|
||||
Behavior: Vesicles Filling RP ?
|
||||
- ContainedBy: PRE
|
||||
- Blocks: Vescicle, ATP
|
||||
- InContext: Fixed
|
||||
- RF: 300
|
||||
-
|
||||
-
|
||||
- Modulability:
|
||||
- TUN: None
|
||||
- DEV: None (credo vada con DEV di RP)
|
||||
```
|
||||
|
||||
*Qui riempiamo le vesciche. Fino ad un numero massimo, che viene modulato in DEV*
|
||||
|
||||
#### Lactate-ATP
|
||||
|
||||
```
|
||||
Behavior: Lactate-ATP
|
||||
- ContainedBy: PRE
|
||||
- Blocks: Lactate, ATP, Ca+
|
||||
- InContext: Fixed
|
||||
- RF: 300
|
||||
- Condition: ??? IF NOT (Ca+ FULLNESS) AND NOT EMPTY AND IF AstroLactate NOT EMPTY AND ATP NOT FULL
|
||||
- Consequence: get Lactate
|
||||
- Consequence: Increase ATP
|
||||
- Tracce:
|
||||
- Modulability:
|
||||
- TUN: None
|
||||
- DEV: RF
|
||||
```
|
||||
|
||||
*Il Lactate viene mandato da Astro che ha fatto re-uptake di Glutamate, trasformato in Glutamine e poi Lactate. Il Lactate serve a fare ATP. Astrocyte gliotransmitters (ATP, D-serine, glutamate).*
|
||||
|
||||
## Postsynaptic behavior
|
||||
|
||||
```
|
||||
Container: POST
|
||||
- ContainedBy: BD
|
||||
- Expands: 100 POST-CHAN
|
||||
- Modulability:
|
||||
- TUN: # POST Possible <-> Actual, Synapting
|
||||
- DEV: None
|
||||
```
|
||||
|
||||
### Milliseconds Time Scale
|
||||
|
||||
#### AMPA Opening
|
||||
|
||||
- **Timing**: < 1 ms
|
||||
- **InContext:** Glutamate > **FULLNESS**
|
||||
- **OutContext:** AMPA receptor opening
|
||||
|
||||
#### Ca+ influx by AMPA
|
||||
|
||||
- **Timing**: < 1 ms
|
||||
- **InContext:** AMPA receptor opened
|
||||
- **Consequence:** Na⁺ influx
|
||||
- **Consequence:** addition to local depolarization (EPSP) from AMPA activation
|
||||
|
||||
#### Limited Ca+ influx by NMDA
|
||||
|
||||
- **Timing**: > 1 ms
|
||||
|
||||
|
||||
- **InContext:** local depolarization (EPSP) **NOT** **FULLNESS** (requires depolarization > -40mV)
|
||||
- **Consequence:** Glutamate binding to NMDA receptors (Mg²⁺-blocked initially)
|
||||
- **Consequence:** limited NMDA receptor opening → Ca²⁺ influx
|
||||
- **Consequence:** limited addition to local depolarization (EPSP) from NMDA activation
|
||||
|
||||
#### Depolarization by bAP
|
||||
|
||||
- **Timing**: > 1 ms
|
||||
- **InContext:** bAP backpropagating action potential
|
||||
- **Consequence:** addition to local depolarization (EPSP) from bAP
|
||||
|
||||
#### Mg²⁺ NMDA unblock
|
||||
|
||||
- **Timing**: > 1 ms
|
||||
|
||||
|
||||
- **InContext:** local depolarization (EPSP) > **FULLNESS** (requires depolarization > -40mV)
|
||||
- **OutContext:** NMDA Mg²⁺ unblock
|
||||
|
||||
#### Full Ca+ influx by NDMA
|
||||
|
||||
- **Timing**: < 1 ms
|
||||
- **InContext:** NMDA Mg²⁺ unblock
|
||||
- **Consequence:** Na⁺ influx
|
||||
- **Consequence:** addition to local depolarization (EPSP) from Full NMDA activation
|
||||
|
||||
#### Observed 1 - Upregulation
|
||||
|
||||
- **Upregulation:** Depolarization relieves NMDA Mg²⁺ block → Ca²⁺ influx amplification
|
||||
|
||||
#### Observed 2 - Downregulation
|
||||
|
||||
- **Downregulation:** AMPA desensitization acts as low-pass filter
|
||||
|
||||
## Dendritic behavior
|
||||
|
||||
```
|
||||
Container: BD
|
||||
- ContainedBy: N-SPK
|
||||
- Expands: 100 POST
|
||||
- Modulability:
|
||||
- TUN: None
|
||||
- DEV: None
|
||||
```
|
||||
|
||||
## Somatic behavior
|
||||
|
||||
```
|
||||
Container: SO
|
||||
- ContainedBy: N-SPK
|
||||
- Expands: 20 SO-CHAN
|
||||
- Modulability:
|
||||
- TUN: None
|
||||
- DEV: None
|
||||
```
|
||||
|
||||
## AIS behavior
|
||||
|
||||
```
|
||||
Container: AXO
|
||||
- ContainedBy: N-SPK
|
||||
- Expands: 30 PRE
|
||||
- Modulability:
|
||||
- TUN: None
|
||||
- DEV: None
|
||||
```
|
||||
|
||||
# Tuning - MTP-MTD Behavior
|
||||
|
||||
```
|
||||
Container: N-TUN
|
||||
- Expands: None
|
||||
- Modulability:
|
||||
- TUN: None
|
||||
- DEV: None
|
||||
```
|
||||
|
||||
*Qui si modulano i canali ionici, sia quelli voltage (PRE/POST/SO/altro?) che quelli Neuro (POST/SO(inibitori)). Non si creano o si distruggono (lo si fa in Developing), ma si rendono attivi disattivi quelli presenti. Ovviamente potremmo aggiungere anche altri comportamenti di tuning che riguardano altri tipi di modulazione (RF?).*
|
||||
|
||||
## Presynaptic Behavior Tuning
|
||||
|
||||
### Seconds Time Scale
|
||||
|
||||
#### VCGG Channel Tuning
|
||||
|
||||
```
|
||||
- ContainedBy: N-TUN
|
||||
- Tubs:
|
||||
- Source:
|
||||
-
|
||||
- Yellow:
|
||||
-
|
||||
- Context: ?
|
||||
- RF: 1
|
||||
- IF NOT
|
||||
- Consequence: ()
|
||||
- Consequence: ()
|
||||
- Traces: #
|
||||
- Modulability:
|
||||
- TUN: None
|
||||
- DEV: None
|
||||
```
|
||||
|
||||
*Lo possiamo fare sia con alterazione di RF che del volume Tub, di sicuro per Ca+ poi altro non so.*
|
||||
|
||||
*Inoltre devo vedere se farlo alla fine di spiketrain, quando il neurone e’ in rest stateM*
|
||||
|
||||
*This is critical for **long-term** presynaptic changes. The postsynaptic cell, upon detecting specific activity patterns (like those for LTP/LTD), releases chemical signals that travel backwards to the presynaptic terminal, instructing it to change.*
|
||||
|
||||
- ***For Presynaptic Strengthening (e.g., LTP):***
|
||||
- ***Nitric Oxide (NO):**** A gas that diffuses freely. During postsynaptic LTP induction (strong NMDAR activation), neuronal NO synthase (nNOS) is activated. NO diffuses into the presynaptic terminal and activates soluble guanylyl cyclase (sGC), raising cGMP levels. This enhances vesicle release via PKG, contributing to **presynaptic LTP**.*
|
||||
- ***Endocannabinoid-Mediated LTP (eLTP):**** In some synapses, a **postsynaptic** depolarization triggers production of endocannabinoids (e.g., 2-AG). These bind to presynaptic **CB1 receptors**, but surprisingly, can initiate a signaling cascade (involving cAMP/PKA) that **increases Pr** for a long period.*
|
||||
- ***Neurotrophins (BDNF):**** Released from the postsynapse in an activity-dependent manner. Presynaptic TrkB receptors activate pathways (PI3K, MAPK) that enhance vesicle docking and Pr.*
|
||||
- ***For Presynaptic Weakening (e.g., LTD):***
|
||||
- ***Classical Endocannabinoid-Mediated LTD (eCB-LTD):**** More common. Moderate postsynaptic activity (mGluR activation or moderate Ca²⁺ rise) triggers 2-AG release. 2-AG binds presynaptic CB1 receptors, which **inhibit VGCCs** and **directly inhibit the release machinery** via Gi/o protein signaling, reducing Pr for a long time.*
|
||||
- ***Other Lipid Mediators**** (like LPA) can also act as retrograde signals for depression.*
|
||||
|
||||
##### Augmentation:
|
||||
|
||||
- Calcium-sensing proteins (Munc13) alter release probability (1-10s range). How?
|
||||
|
||||
##### Upregulation:
|
||||
|
||||
- NO/BDNF activates cascades that increase P_r, promote synaptic growth (facilitates LTP). How?
|
||||
- VGCC TUN
|
||||
- Potassium channel modulation ??
|
||||
|
||||
##### Downregulation:
|
||||
|
||||
- eCBs bind CB1 receptors, inhibit VGCCs, activate K⁺ channels → profound decrease in P_r (DSE/DSI - depolarization-induced suppression)
|
||||
- CB1 receptor activation (by eCBs)
|
||||
|
||||
|
||||
- Retrograde BDNF (brain-derived neurotrophic factor)
|
||||
|
||||
## Postynaptic behavior Tuning
|
||||
|
||||
### Seconds Time Scale
|
||||
|
||||
#### Postsynapsis channel tuning
|
||||
|
||||
```
|
||||
- ContainedBy: N-TUN
|
||||
- Tubs:
|
||||
- Source:
|
||||
-
|
||||
- Yellow:
|
||||
-
|
||||
- Context: ?
|
||||
- RF: 1
|
||||
- IF NOT
|
||||
- Consequence: ()
|
||||
- Consequence: ()
|
||||
- Traces: #
|
||||
- Modulability:
|
||||
- TUN: None
|
||||
- DEV: None
|
||||
```
|
||||
|
||||
## Dendritic-branch behavior Tuning
|
||||
|
||||
## Soma behavior Tuning
|
||||
|
||||
### Seconds Time Scale
|
||||
|
||||
#### SO Channel tuning
|
||||
|
||||
```
|
||||
- ContainedBy: N-TUN
|
||||
- Tubs:
|
||||
- Source:
|
||||
-
|
||||
- Yellow:
|
||||
-
|
||||
- Context: ?
|
||||
- RF: 1
|
||||
- IF NOT
|
||||
- Consequence: ()
|
||||
- Consequence: ()
|
||||
- Traces: #
|
||||
- Modulability:
|
||||
- TUN: None
|
||||
- DEV: None
|
||||
```
|
||||
|
||||
####
|
||||
|
||||
## AIS behavior Tuning
|
||||
|
||||
# Development - LTP-LTD Behavior
|
||||
|
||||
```
|
||||
Container: N-DEV
|
||||
- Expands: None
|
||||
- Modulability:
|
||||
- TUN: None
|
||||
- DEV: None
|
||||
```
|
||||
|
||||
*Attivazione/disattivazione di possibilita’*
|
||||
|
||||
*Qui si incrementa/decrementa:*
|
||||
|
||||
- *Il numero possibile di canali ionici.*
|
||||
- *la capacita’ di Vescice in RP e RPP*
|
||||
- *la capacita’ di spostare vesciche da RP a RPP*
|
||||
- *la capacita’ di riempire vesciche*
|
||||
|
||||
## Presynaptic behavior Development
|
||||
|
||||
### Day Time Scale
|
||||
|
||||
*Qui si modula la possibilita’ di potenza di fuoco, sia come nuovi recettori (voltage e neuro) sia come grandezza di RP, RRP e velocita’ di spostamento.*
|
||||
|
||||
*Long-lasting presynaptic strengthening requires **new proteins**:*
|
||||
|
||||
- *More vesicles*
|
||||
- *More active zone proteins (e.g., RIM, Munc13)*
|
||||
- *More mitochondria (for energy)*
|
||||
- *More synaptic vesicle components (synaptobrevin, synaptotagmin)*
|
||||
- *More cytoskeletal elements for structure*
|
||||
|
||||
*The neuron must **detect a sustained need for strengthening at a specific synapse**, send a signal to its nucleus, transcribe genes, and then deliver the new proteins back to that specific presynaptic bouton.*
|
||||
|
||||
1. ***Detection:**** Sustained high-frequency firing at the presynaptic terminal → elevated Ca²⁺ and/or neuromodulator release (dopamine, norepinephrine).*
|
||||
2. ***Signal to Nucleus:**** Activation of kinases (PKA, CaMKIV) and retrograde importin signaling → **CREB phosphorylation** in the nucleus.*
|
||||
3. ***Transcriptional Program:**** CREB induces expression of:*
|
||||
- ***Immediate Early Genes**** (e.g., c-Fos, Arc) that regulate further transcription.*
|
||||
- ***Effector Genes:**** Presynaptic proteins (synapsins, RIM, Munc13), BDNF, cytoskeletal proteins.*
|
||||
4. ***Delivery:**** Newly synthesized mRNAs/proteins are actively transported down the axon, **targeted to the active synapses** that initiated the signal.*
|
||||
5. ***Local Implementation:***
|
||||
- *Assembly of new active zones.*
|
||||
- *Expansion of vesicle pools.*
|
||||
- *Possible local translation.*
|
||||
- *Bouton enlargement or new bouton formation.*
|
||||
6. ***Stabilization:**** Epigenetic modifications and continued autocrine/paracrine signaling (BDNF→TrkB) lock in the changes.*
|
||||
|
||||
***In essence, the neuron "knows" to strengthen a presynapse long-term because the synapse's own sustained activity creates a biochemical signature that reaches the nucleus, triggering a gene program specifically designed to build a bigger, better release machine. This is a fundamental mechanism underlying long-term memory storage at the synaptic level.***
|
||||
|
||||
- ATP-dependent vesicle cycling
|
||||
- **Metabolic veto:** Insufficient ATP prevents vesicle release despite adequate Ca²⁺
|
||||
|
||||
|
||||
- Glutamine→glutamate conversion (via glutaminase). Glutamine from astrocytes (glutamate-glutamine cycle)
|
||||
|
||||
|
||||
- Vesicle refilling with glutamate
|
||||
|
||||
|
||||
- Maintenance of ion gradients
|
||||
|
||||
**Incoming Signals:**
|
||||
|
||||
- Astrocyte-supplied lactate (via monocarboxylate transporters)
|
||||
- Metabolic state indicators (ATP levels, NAD/NADH ratio)
|
||||
|
||||
**Outgoing Signals:**
|
||||
|
||||
- Metabolic demand signals to astrocyte ??
|
||||
|
||||
**Modulation:**
|
||||
|
||||
- Lactate availability determines sustained release capacity during high activity ??
|
||||
|
||||
#### VCGG channel development
|
||||
|
||||
```
|
||||
- ContainedBy: N-DEV
|
||||
- Tubs:
|
||||
- Source:
|
||||
-
|
||||
- Yellow:
|
||||
-
|
||||
- Context: ?
|
||||
- RF: 1
|
||||
- IF NOT
|
||||
- Consequence: ()
|
||||
- Consequence: ()
|
||||
- Traces: #
|
||||
- Modulability:
|
||||
- TUN: None
|
||||
- DEV: None
|
||||
```
|
||||
|
||||
#### RRP development
|
||||
|
||||
#### Ca+ FULLNESS
|
||||
|
||||
#### Ca+ Clearance RF
|
||||
|
||||
#### RP to RPP RF
|
||||
|
||||
#### Lactate to ATP RF
|
||||
|
||||
## Postynaptic Behavior Development
|
||||
|
||||
## Dentric-branch Behavior Development
|
||||
|
||||
## Soma Behavior Development
|
||||
|
||||
## AIS Behavior Development
|
||||
@@ -1,75 +0,0 @@
|
||||
Excellent question that gets to the core of how synaptic transmission works. Yes, it's fundamentally based on **concentration**, but with a critical biological twist: the concept of **saturation**.
|
||||
|
||||
Let's walk through the logic:
|
||||
|
||||
---
|
||||
|
||||
### **1. The Concentration Argument (Simplified View)**
|
||||
|
||||
You are correct. Neurotransmitter molecules (e.g., glutamate) diffuse across the synaptic cleft and bind to receptors (e.g., AMPA receptors) on the postsynaptic density (PSD).
|
||||
|
||||
* **5000 molecules** create a certain concentration in the cleft.
|
||||
* **Fewer molecules** (e.g., 2500 from a depleted second spike) create a **lower concentration**.
|
||||
* According to the law of mass action, a lower concentration of ligand (neurotransmitter) results in **fewer receptors being bound at any given moment**.
|
||||
* Fewer bound receptors mean **fewer open ion channels**, leading to a **smaller net ionic current** (EPSC), and thus a **smaller EPSP**.
|
||||
|
||||
So, at first glance, it seems purely a concentration-driven, dose-response relationship: **more transmitter → more receptor binding → bigger response.**
|
||||
|
||||
---
|
||||
|
||||
### **2. The Critical Biological Reality: Receptor Saturation**
|
||||
|
||||
Here's where it gets interesting. For a typical fast excitatory synapse, the **cleft is extremely narrow** (~20-40 nm), and the **postsynaptic density is packed with receptors** (thousands of AMPA receptors per PSD).
|
||||
|
||||
**During a single vesicle release event, the local neurotransmitter concentration in the cleft skyrockets to a very high level (mM range) for about 1 ms before diffusion and uptake clear it.**
|
||||
|
||||
This leads to a key phenomenon: **The receptors under the release site are often temporarily saturated.**
|
||||
|
||||
* **What is Saturation?** It means that at the peak of the release event, **virtually all available receptors are bound by neurotransmitter**. Adding more neurotransmitter molecules (e.g., from a second, simultaneous release at the same site) **cannot open more channels** because they're already all in use.
|
||||
* **Implication:** Under saturated conditions, the size of the postsynaptic response is **not linearly proportional to the number of transmitter molecules**. Instead, it's determined by the **number of postsynaptic receptors**, not the amount of transmitter beyond what's needed to saturate them.
|
||||
|
||||
---
|
||||
|
||||
### **3. So Why Does Reducing Vesicle Release Reduce the EPSP?**
|
||||
|
||||
Given receptor saturation, why does releasing fewer vesicles (during short-term depression) still cause a smaller EPSP? There are two main reasons:
|
||||
|
||||
**A. Saturation is Local and Incomplete**
|
||||
While receptors directly under a vesicle fusion site may be saturated, **neurotransmitter diffuses**. A single release event activates receptors in the **immediate vicinity**. If a second vesicle is released from a **different release site** within the same active zone (or if the first release is from a site with fewer local receptors), its glutamate diffuses to activate a **spatially distinct, non-saturated population of receptors**. Therefore:
|
||||
|
||||
* **First Spike:** Vesicle from Site A saturates Receptor Cluster A. Vesicle from Site B saturates Receptor Cluster B. **Total Response = A + B.**
|
||||
* **Second Spike (Depressed):** Only Vesicle from Site A releases. It saturates Receptor Cluster A. **Total Response = A only.** The EPSP is smaller because it's missing the contribution from the **spatially separate receptor cluster B**.
|
||||
|
||||
**B. The Role of Multi-Vesicular Release (MVR) and Transmitter Spillover**
|
||||
At many synapses, a single action potential can cause the fusion of **more than one vesicle** (Multi-Vesicular Release). The glutamate from these multiple vesicles can **summate in the cleft**, increasing the concentration duration and potentially activating **extra- or peri-synaptic receptors** (like NMDA receptors or metabotropic receptors) that have lower affinity or are located farther away.
|
||||
|
||||
* **First Spike:** High Pr → MVR (e.g., 3 vesicles) → Very high, prolonged [Glutamate] → Activates **local AMPARs + distal/extrasynaptic NMDARs/mGluRs**.
|
||||
* **Second Spike (Low Pr):** Low Pr → Single vesicle release → Lower, shorter [Glutamate] → Activates **only local AMPARs** (and maybe saturates them). The loss of this **spillover component** to more distant receptors contributes to the amplitude decrease.
|
||||
|
||||
---
|
||||
|
||||
### **The Integrated Picture: It's About the "Volume" of Activated Receptors**
|
||||
|
||||
Think of it not as "5000 vs. 2500 molecules," but as **"activating 200 receptors vs. activating 100 receptors."**
|
||||
|
||||
1. **Number of Release Sites & Vesicles:** Determines the **spatial pattern and concentration profile** of neurotransmitter in the cleft.
|
||||
2. **Diffusion & Uptake:** Determine how far that neurotransmitter spreads and how long it lasts.
|
||||
3. **Receptor Distribution & Affinity:** Determine how many receptors are recruited by that spatial/chemical profile.
|
||||
|
||||
**During short-term depression:**
|
||||
|
||||
* **Fewer vesicles are released** → The "cloud" of neurotransmitter is **smaller and/or originates from fewer points**.
|
||||
* This smaller cloud **activates a smaller total volume of the postsynaptic membrane** (or activates the same volume but with a lower, non-saturating concentration).
|
||||
* **Result:** **Fewer receptor channels open overall**, producing a smaller summed postsynaptic current and a smaller EPSP.
|
||||
|
||||
---
|
||||
|
||||
### **Summary: Why Less Neurotransmitter = Smaller EPSP**
|
||||
|
||||
| Cause of Reduced Release | Effect on Neurotransmitter Profile | Effect on Postsynaptic Receptors | Final Effect on EPSP |
|
||||
|:------------------------------------------------------------|:-------------------------------------------------------------------------|:--------------------------------------------------------------------------------------------------|:--------------------------------------------------------------------------------------------------------------------|
|
||||
| **Vesicle Depletion** (fewer vesicles released) | Lower peak concentration, less spatial spread. | **Fewer total receptors are activated** (spatially restricted). A smaller area of the PSD is engaged. | **Amplitude decreases.** |
|
||||
| **Lower Release Probability** (e.g., from G-protein inhibition) | Same as above. | Same as above. | **Amplitude decreases.** |
|
||||
| **Receptor Saturation** (for a single vesicle) | Limits the effect of adding more transmitter *at the exact same location*. | Makes the synapse's response to a *single release site* **binary** (on/off). | Makes the synapse's output depend on **the number of independent release sites activated**, not the raw molecule count. |
|
||||
|
||||
**So, you are right—it is based on concentration.** But because of the tiny, structured environment of the synapse, the critical concentration is the **local concentration at each receptor cluster**, which dictates **how many *clusters* are activated**, not just how many molecules are floating around. Reducing the number of released vesicles reduces the **spatial extent and intensity** of the neurotransmitter signal, thereby recruiting fewer postsynaptic receptors and generating a smaller EPSP.
|
||||
@@ -1,70 +0,0 @@
|
||||
This is a profound and sophisticated question that gets to the heart of **computation within neural circuits**. You are absolutely correct: the distinction between what we might call a "starter" synapse (driving an action potential) and an "integrator" synapse (modulating the likelihood of one) is crucial, and the modulation mechanisms are **fundamentally different** at the biophysical and functional levels.
|
||||
|
||||
This maps directly onto the concepts of **detonator synapses vs. modulator synapses**, or more formally, **driver vs. modulatory inputs**.
|
||||
|
||||
Let's break down the key differences in their modulation.
|
||||
|
||||
---
|
||||
|
||||
### 1. The Functional Distinction
|
||||
|
||||
* **Starter / Driver / Detonator Synapse:**
|
||||
* **Role:** Directly and reliably triggers an **action potential (AP)** in the postsynaptic neuron.
|
||||
* **Location:** Typically on or near the **soma** or the **axon initial segment (AIS)**. This is where the neuron's decision to fire is made.
|
||||
* **Mechanism:** Uses **ionotropic receptors** (AMPA, NMDA) to cause a large, fast, **depolarizing excitatory postsynaptic potential (EPSP)**. These EPSPs summate directly to cross the voltage threshold for the AP.
|
||||
* **Analogy:** The **gas pedal** – pressing it hard makes the car (neuron) go.
|
||||
* **Integrator / Modulator Synapse:**
|
||||
* **Role:** Modulates the **probability** that the postsynaptic neuron will fire an AP in response to *other inputs*. It sets the "gain" or "mood" of the neuron.
|
||||
* **Location:** Often on **dendrites**, sometimes specifically on distal dendrites.
|
||||
* **Mechanism:** Often uses **metabotropic receptors** (mGluRs, GABAʙ, neuromodulator receptors like dopamine D1/D2). Their effects are slower, longer-lasting, and involve **G-protein-coupled cascades** that alter:
|
||||
* **Membrane potential** (e.g., subtle depolarization or hyperpolarization).
|
||||
* **Input resistance** (affecting how much a given EPSP "counts").
|
||||
* **Intrinsic excitability** (e.g., by modulating potassium channels).
|
||||
* **The strength of *other* synapses** (via heterosynaptic plasticity).
|
||||
* **Analogy:** The **engine tune-up** or the **road conditions** – they don't make the car go by themselves, but they dramatically affect how responsive it is to the gas pedal.
|
||||
|
||||
---
|
||||
|
||||
### 2. How Modulation Differs: Core Mechanisms
|
||||
|
||||
The differences arise from their **location, receptor types, and the spatiotemporal scale of their signals.**
|
||||
|
||||
| Feature | **Starter / Driver Synapse** | **Integrator / Modulator Synapse** |
|
||||
|:------------------------------|:-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|:----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
|
||||
| **Primary Goal of Modulation** | **Change the *efficacy* of its own direct signal.** To make each presynaptic spike more or less likely to contribute to triggering an AP. | **Change the *integration properties* of the entire dendritic compartment or neuron.** To alter how the neuron responds to *all* inputs. |
|
||||
| **Key Modulatory Target** | **The synapse itself (homosynaptic plasticity).**<br />1. **Postsynaptic:** AMPAR number/conductance (LTP/LTD).<br />2. **Presynaptic:** Release probability (Pr) via retrograde signals (NO, eCBs, BDNF). | **The neuronal *milieu* (heterosynaptic & intrinsic plasticity).**<br />1. **Dendritic excitability:** Modulating voltage-gated ion channels (e.g., HCN, K⁺).<br />2. **Global Ca²⁺ signaling:** Altering backpropagating AP efficacy or dendritic spike thresholds.<br />3. **Other synapses:** Inducing heterosynaptic LTP/LTD. |
|
||||
| **Retrograde Signal Specificity** | **High spatial specificity.** Signals like NO have a very short diffusion range, ensuring feedback is primarily to the **active presynaptic terminal itself**. This is **synapse-specific learning**. | **Lower spatial specificity.** Signals like **endocannabinoids (eCBs)** or **neurotrophins (BDNF)** can diffuse further, affecting **multiple nearby presynaptic terminals** (volume transmission). This allows one integrator synapse to **orchestrate plasticity** in a local dendritic region. |
|
||||
| **Temporal Domain** | **Milliseconds to seconds** for induction (phasic). Must be tightly coupled to the presynaptic spike (spike-timing-dependent plasticity, STDP). | **Seconds to hours** (tonic). Can be sustained by ongoing neuromodulator release (dopamine, acetylcholine) reflecting behavioral states (attention, arousal, reward). |
|
||||
| **Example** | A thalamic input to a layer 4 cortical neuron. Its strength is modified via **NMDAR-dependent LTP/LTD**. | A cholinergic input from the basal forebrain to a cortical pyramidal cell. It doesn't cause firing but **suppresses adaptation currents**, enabling sustained firing to driver inputs. |
|
||||
|
||||
---
|
||||
|
||||
### 3. The Critical Interplay: How an Integrator Synapse Modulates a Starter Synapse
|
||||
|
||||
This is where the magic of neural computation happens. An integrator synapse can powerfully control a starter synapse **without directly triggering an AP itself.**
|
||||
|
||||
**Mechanisms of Cross-Modulation:**
|
||||
|
||||
1. **Shunting Inhibition:** A nearby GABAergic (integrator) synapse can open Cl⁻ channels. This **lowers the input resistance** of the dendrite, causing the EPSP from the starter synapse to be smaller and faster ("shunted"), making it less likely to reach threshold.
|
||||
2. **Modulation of Dendritic Voltage-Gated Channels:**
|
||||
* **Example:** Dopamine (via D1 receptors) can **reduce the activity of HCN channels** (which carry the hyperpolarization-activated current, Iₕ). Iₕ normally dampens distal EPSPs as they travel to the soma. By reducing Iₕ, the dopamine input **boosts the strength of distal driver EPSPs**, effectively bringing them "closer" to the soma in electrical terms.
|
||||
3. **Priming for Plasticity (Metaplasticity):**
|
||||
* A modulatory signal (e.g., noradrenaline during stress/arousal) can **prime the molecular machinery** of a starter synapse. It might raise intracellular Ca²⁺ levels or activate kinases (PKA) to lower the threshold for inducing LTP when the strong driver input arrives moments later. This is "**gating**" of plasticity.
|
||||
4. **Heterosynaptic Plasticity via Volume Transmission:**
|
||||
* When a strong driver synapse induces LTP, it often releases **retrograde signals (eCBs, BDNF)** that spill over. These can induce **LTD at nearby, less-active integrator synapses**. This is a form of **competitive plasticity**, ensuring the driver synapse "wins" and becomes the dominant input, while silent integrators are weakened.
|
||||
|
||||
---
|
||||
|
||||
### 4. Summary: A Hierarchical Control System
|
||||
|
||||
Think of it as a **two-layer control system**:
|
||||
|
||||
* **Layer 1 (Starter Synapses):** The **content**-carrying signals. *"What"* is being represented. Their plasticity is about **refining specific connections** (Hebbian learning: "cells that fire together, wire together").
|
||||
* **Layer 2 (Integrator Synapses):** The **context**-setting signals. *"How importantly* should the neuron treat the incoming content?" Their plasticity is about **setting global parameters**—gain, plasticity thresholds, metabolic state—based on neuromodulators (dopamine for reward, acetylcholine for attention, serotonin for mood).
|
||||
|
||||
**Conclusion:** The modulation mechanisms are **not the same**. They are specialized for entirely different computational tasks:
|
||||
|
||||
* **Starter synapse modulation** is **synapse-specific, fast, and Hebbian**. It's about **efficacy**.
|
||||
* **Integrator synapse modulation** is **diffuse, slow, and state-dependent**. It's about **context and control**.
|
||||
|
||||
The breathtaking complexity of the brain arises from the dense interweaving of these two layers, allowing a neuron to be both a **specific feature detector** (shaped by its driver inputs) and an **adaptive processor** whose very interpretation rules are dynamically tuned by its modulatory inputs. Your insight perfectly identifies this fundamental architectural principle.
|
||||
@@ -1,684 +0,0 @@
|
||||
# VARIABLES
|
||||
|
||||
## **MILLISECOND SCALE (Action Potential → Release)**
|
||||
|
||||
| Variable | Direct Behavior/Effect | Modulated By (Same Scale) | Modulated By (Other Scales) |
|
||||
|-------------------|------------------------------------------------------------------------------|-------------------------------------------------------------|-----------------------------------------------------------------------------------------------------|
|
||||
| **V_mem** | • AP depolarization<br />• K⁺-mediated repolarization | • **KChannels** activation<br />• Na⁺ channel inactivation | • **ATP** (seconds) - powers Na⁺/K⁺ pump<br />• **K+** accumulation (tens-ms) |
|
||||
| **VGCC** | • Ca²⁺ influx triggered by depolarization<br />• Ca²⁺-dependent inactivation | • **V_mem** (depolarization)<br />• **Ca+** microdomain (feedback) | • **VGCC invagination** (hours) - reduces surface expression<br />• **BDNF** (hours) - increases expression |
|
||||
| **Ca+** (microdomain) | • Rapid spike near VGCCs (~10-100 μM)<br />• Triggers vesicle fusion | • **VGCC** opening kinetics<br />• Endogenous buffers | • **CaChannels** density (hours)<br />• **NO** (seconds) - modulates channel opening |
|
||||
| **Vesicles** (fusion) | • SNARE-mediated fusion with membrane<br />• Release probability (Pr) varies | • **Ca+** concentration⁴<br />• **RRP** position/docking | • **ATP** (seconds) - fuels priming<br />• **eCB** (seconds) - inhibits release |
|
||||
| **K+** (efflux) | • Repolarization via KChannels<br />• Clears AP | • **V_mem** (depolarization)<br />• **Ca+** (activates SK channels) | • **KChannels** modulation (minutes) |
|
||||
| **KChannels** | • Voltage-gated opening<br />• Ca²⁺-activated (SK) | • **V_mem**<br />• **Ca+** microdomain | • **Phosphorylation** (minutes)<br />• **BDNF** (hours) - modulates expression |
|
||||
|
||||
## **TENS-HUNDREDS OF MILLISECONDS SCALE (Short-term Dynamics)**
|
||||
|
||||
| Variable | Direct Behavior/Effect | Modulated By (Same Scale) | Modulated By (Other Scales) |
|
||||
|-------------------------|--------------------------------------------------------------------------------------|---------------------------------------------------------------|------------------------------------------------------------------------------------------------------|
|
||||
| **Ca+** (global) | • Bulk terminal increase (~0.5-2 μM)<br />• Activates mobilization | • Diffusion from microdomains<br />• PMCA/NCX pumps | • **ATP** (seconds) - fuels pumps<br />• **Lactate** (seconds) - supports mitochondrial uptake |
|
||||
| **Vesicles** (mobilization) | • Movement from **RP** → **RRP**<br />• Docked vesicles become release-ready | • **Ca+** global concentration<br />• **RRP** depletion state | • **Mobilization rate** (hours) - structural adaptation<br />• **ATP** (seconds) - fuels transport |
|
||||
| **RRP** | • Immediate release pool (~5-15 vesicles)<br />• Depletes with high-frequency firing | • **Vesicles** release (ms)<br />• **Vesicles** mobilization into RRP | • **RP** size (minutes)<br />• **BDNF** (hours) - increases docking sites |
|
||||
| **K+** (cleft accumulation) | • Extracellular K⁺ rises to ~8-12 mM<br />• Affects resting potential | • **KChannels** activity (ms)<br />• Astrocyte/glia uptake | • **Activity history** (minutes) - astrocyte adaptation |
|
||||
| **eCB** | • Retrograde diffusion to presynapse<br />• Binds CB1 receptors (~100-500 ms) | • Postsynaptic Ca²⁺ rise (ms)<br />• mGluR activation | • **Activity patterns** (minutes) - regulates production<br />• **NO** (seconds) - can enhance eCB synthesis |
|
||||
|
||||
## **SECONDS-MINUTES SCALE (Metabolic & Signaling)**
|
||||
|
||||
| Variable | Direct Behavior/Effect | Modulated By (Same Scale) | Modulated By (Other Scales) |
|
||||
|------------------|---------------------------------------------------------------------------------------------|------------------------------------------------------------------------|-------------------------------------------------------------------------------------------|
|
||||
| **ATP** | • Fuels: pumps, vesicle cycling, protein phosphorylation<br />• Depletes with high activity | • **Lactate** conversion<br />• Mitochondrial respiration | • **Activity demand** (ms scale)<br />• **BDNF** (hours) - enhances mitochondrial function |
|
||||
| **Lactate** | • Astrocyte→neuron shuttle<br />• Converted to pyruvate for ATP | • Glutamate uptake by astrocytes<br />• Glycogen breakdown | • **Activity level** (ms-min)<br />• **NO** (seconds) - regulates blood flow |
|
||||
| **NO** | • Retrograde diffusion from postsynapse<br />• Activates presynaptic cGMP pathways | • Postsynaptic NOS activation by Ca²⁺<br />• NMDA receptor activity | • **Activity patterns** (minutes)<br />• **BDNF** (hours) - regulates NOS expression |
|
||||
| **RP** | • Reserve vesicle pool (~100-500 vesicles)<br />• Slowly replenishes RRP | • **Vesicles** recycling<br />• **Vesicles** mobilization out of RP | • **RP capacity** (hours) - structural changes<br />• **ATP** (seconds) - fuels vesicle refilling |
|
||||
| **BDNF** | • Retrograde transport (slow)<br />• Activates TrkB receptors | • Activity-dependent release from postsynapse<br />• Local translation | • **Ca+** integration (minutes)<br />• **eCB** (minutes) - can modulate release |
|
||||
| **eCB** (persistent) | • Long-term depression (LTD) induction<br />• Alters release probability | • Sustained postsynaptic activity<br />• DAG lipase activation | • **NO** (seconds) - synergistic effects<br />• **BDNF** (hours) - can counteract eCB-LTD |
|
||||
|
||||
## **SECONDS-HOURS-DAYS SCALE (Structural Modulation)**
|
||||
|
||||
| Variable | Modulatory Behavior | Influenced By | Effects on Faster Scales |
|
||||
|------------------------------|------------------------------------------------------------------|----------------------------------------------------------------------------------------------------------|-----------------------------------------------------------------------------------|
|
||||
| **VGCC** (invagination) | • Internalization of channels<br />• Reduces release probability | • **Ca+** integral (minutes of activity)<br />• **BDNF** (trophic support)<br />• **eCB** (chronic signaling) | • ↓ **Ca+** influx (ms)<br />• ↓ **Vesicles** release probability (ms) |
|
||||
| **CaChannels** (density) | • Changes in VGCC number at active zone | • **BDNF**-TrkB signaling (hours)<br />• Homeostatic scaling (days)<br />• Activity history (integrated **Ca+**) | • Alters **Ca+** microdomain (ms)<br />• Changes short-term plasticity (tens-ms) |
|
||||
| **RP** (pool size) | • Structural changes in vesicle reserves | • **BDNF** (enhances)<br />• Chronic **eCB** (reduces)<br />• Metabolic capacity (**ATP/Lactate** supply) | • Changes **RRP** refilling rate (tens-ms)<br />• Alters sustained release (seconds) |
|
||||
| **Vesicles** (mobilization rate) | • Faster/slower RP→RRP trafficking | • **BDNF**-cytoskeletal remodeling<br />• Synapsin phosphorylation state (**Ca+** history) | • Alters short-term facilitation/depression (tens-ms) |
|
||||
| **KChannels** (expression) | • Changes in Kv channel density | • Activity-dependent gene regulation<br />• **BDNF** modulation<br />• **K+** homeostasis needs | • Alters AP waveform and duration (ms)<br />• Changes firing frequency adaptation |
|
||||
|
||||
## **CROSS-VARIABLE FEEDBACK LOOPS**
|
||||
|
||||
### **Fast Release → Metabolic Support Loop**
|
||||
|
||||
```
|
||||
V_mem (AP) → VGCC opening → Ca+ influx → Vesicles release
|
||||
↓
|
||||
Glutamate release → Astrocyte activation → Lactate production
|
||||
↓
|
||||
Lactate → ATP synthesis → Fuels: VGCC recycling, Vesicles priming, Ca+ pumps
|
||||
```
|
||||
|
||||
### **Activity → Structural Adaptation Loop**
|
||||
|
||||
```
|
||||
High activity → Ca+ accumulation → BDNF release (post→pre)
|
||||
↓
|
||||
BDNF → ↑ VGCC expression, ↑ RP size, ↑ mobilization rate
|
||||
↓
|
||||
Enhanced release capacity → Changes Ca+ dynamics → Homeostatic adjustment
|
||||
```
|
||||
|
||||
### **Retrograde Modulation Network**
|
||||
|
||||
```
|
||||
Postsynaptic: Ca+ → NO production → Presynaptic: cGMP → Modulates VGCC
|
||||
↓ ↓
|
||||
Postsynaptic: Ca+ → eCB production → Presynaptic: CB1 → Inhibits VGCC, ↓ release
|
||||
↓
|
||||
Postsynaptic: Ca+ → BDNF synthesis → Presynaptic: TrkB → ↑ VGCC, ↑ RP
|
||||
```
|
||||
|
||||
### **Energy-Redistribution Loop**
|
||||
|
||||
```
|
||||
High activity → ATP depletion → Activates AMPK → ↑ Lactate uptake
|
||||
↓ ↓
|
||||
Reduced release probability ↑ Mitochondrial biogenesis (days)
|
||||
↓ ↓
|
||||
Lower Ca+ demand Enhanced ATP production
|
||||
```
|
||||
|
||||
## **KEY VARIABLE INTERDEPENDENCIES**
|
||||
|
||||
1. **VGCC** ↔ **Ca+** (bidirectional):
|
||||
- VGCC opening → Ca+ influx
|
||||
- Ca+ accumulation → VGCC modulation (inactivation/adaptation)
|
||||
2. **ATP** as universal modulator:
|
||||
- Required for: V_mem maintenance, Ca+ clearance, Vesicles cycling, RP refilling
|
||||
- Limited ATP → affects all faster processes
|
||||
3. **BDNF** as structural organizer:
|
||||
- Coordinates: VGCC expression, RP size, KChannels density, metabolic capacity
|
||||
4. **Ca+** as integration signal:
|
||||
- Fast: triggers Vesicles release (ms)
|
||||
- Medium: regulates Vesicles mobilization (tens-ms)
|
||||
- Slow: drives structural changes via BDNF/NO (minutes-hours)
|
||||
5. **K+**/**KChannels** as activity brakes:
|
||||
- Regulate AP duration and frequency
|
||||
- Homeostatically adjusted based on activity history
|
||||
|
||||
This framework shows how your specified variables interact across timescales, with each variable playing multiple roles depending on the temporal context.
|
||||
|
||||
---
|
||||
|
||||
---
|
||||
|
||||
---
|
||||
|
||||
# **ATP: The Multiscale Energy Integrator**
|
||||
|
||||
## **ATP's Roles Across Temporal Scales**
|
||||
|
||||
### **1. MILLISECOND SCALE (Emergency Power)**
|
||||
|
||||
**Direct Behaviors Enabled:**
|
||||
|
||||
- **VGCC recovery**: Rapid phosphorylation/dephosphorylation cycles
|
||||
- **SNARE priming**: ATP hydrolysis by NSF for vesicle fusion competence
|
||||
- **Na⁺/K⁺ pump**: Immediate AP recovery (3 Na⁺ out, 2 K⁺ in per ATP)
|
||||
|
||||
**Influences on Other Variables:**
|
||||
|
||||
- ↓ **ATP** → Slower **V_mem** repolarization (K⁺ pump impaired)
|
||||
- ↓ **ATP** → Reduced **VGCC** recovery from inactivation
|
||||
- ↓ **ATP** → Impaired **Vesicles** priming → ↓ release probability
|
||||
|
||||
**Critical Threshold:** <0.1s depletion → immediate release failure
|
||||
|
||||
### **2. TENS-HUNDREDS OF MS SCALE (Short-term Energy Buffer)**
|
||||
|
||||
**Direct Behaviors Enabled:**
|
||||
|
||||
- **Ca²⁺ clearance**: PMCA pumps (1 Ca²⁺ out per ATP)
|
||||
- **Vesicle mobilization**: Myosin/kinesin ATPases for RP→RRP movement
|
||||
- **Endocytosis initiation**: Clathrin coat assembly (early phase)
|
||||
|
||||
**Energy Dynamics:**
|
||||
|
||||
- **Activity spike**: 1 AP → ~20,000 ATP molecules consumed
|
||||
- **Buffer capacity**: ~10⁸ ATP molecules in terminal → supports ~500 APs
|
||||
- **Recovery rate**: ~5 ATP/ms production at maximum mitochondrial output
|
||||
|
||||
**Cross-scale Coupling:**
|
||||
|
||||
- High **Ca+** influx → ↑ mitochondrial Ca²⁺ uptake → ↑ ATP production (seconds)
|
||||
- **K+** accumulation → activates Na⁺/K⁺ pump → ↑ ATP demand
|
||||
- **Lactate** conversion → ~15 ATP per lactate (delayed supply)
|
||||
|
||||
### **3. SECOND-MINUTE SCALE (Metabolic Regulation Hub)**
|
||||
|
||||
**Direct Behaviors Enabled:**
|
||||
|
||||
- **Vesicle recycling**: Complete endocytosis-exocytosis cycle (~30 ATP/vesicle)
|
||||
- **Neurotransmitter reloading**: Vacuolar H⁺-ATPase (2 H⁺/ATP) → glutamate uptake
|
||||
- **RP refilling**: New vesicle synthesis and transport
|
||||
|
||||
**Regulatory Functions:**
|
||||
|
||||
- **ATP/ADP ratio** as metabolic sensor:
|
||||
- High ATP: AMPK inactive → growth/maintenance
|
||||
- Low ATP: AMPK active → emergency response, ↓ protein synthesis
|
||||
- **Glycogen shunt**: Terminal glycogen → lactate (backup, seconds)
|
||||
- **Mitochondrial positioning**: ATP gradients guide movement to active zones
|
||||
|
||||
**Modulation by Other Variables:**
|
||||
|
||||
- **BDNF** → ↑ mitochondrial biogenesis → ↑ ATP capacity (hours)
|
||||
- **NO** → regulates cytochrome c oxidase → modulates ATP production
|
||||
- **eCB** → CB1 receptors inhibit adenylate cyclase → ↓ ATP synthesis
|
||||
|
||||
### **4. HOURS-DAYS SCALE (Structural Energy Budget)**
|
||||
|
||||
**Direct Behaviors Enabled:**
|
||||
|
||||
- **Protein synthesis**: ~4 ATP per peptide bond → VGCCs, vesicle proteins
|
||||
- **Organelle biogenesis**: Mitochondria, ER, vesicle pools
|
||||
- **Axonal transport**: Kinesin/dynein motors (1 ATP/8 nm step)
|
||||
|
||||
**Long-term ATP Allocation Decisions:**
|
||||
|
||||
```
|
||||
High activity + Adequate ATP → Investment in:
|
||||
1. More VGCCs (increased Ca²⁺ capacity)
|
||||
2. Larger RP (more vesicles)
|
||||
3. Additional mitochondria (future capacity)
|
||||
|
||||
High activity + Limited ATP → Conservation mode:
|
||||
1. VGCC invagination (lower Pr, save energy)
|
||||
2. Reduced RP size (lower maintenance cost)
|
||||
3. Enhanced lactate uptake (external energy)
|
||||
```
|
||||
|
||||
**BDNF-ATP Synergy:**
|
||||
|
||||
- **BDNF** signals "importance" → allocates ATP to structural growth
|
||||
- **ATP** availability determines BDNF effect magnitude
|
||||
- **Negative feedback**: Low ATP → ↓ TrkB trafficking → ↓ BDNF sensitivity
|
||||
|
||||
## **ATP as Cross-Scale Communication Channel**
|
||||
|
||||
### **Energy Status Signaling:**
|
||||
|
||||
```
|
||||
Fast signal (ms): ATP/ADP ratio at active zone → immediate release probability
|
||||
Medium signal (s): AMPK activation → mobilize energy reserves
|
||||
Slow signal (hours): PGC-1α activation → mitochondrial biogenesis
|
||||
```
|
||||
|
||||
### **Activity-Energy Feedback Loops:**
|
||||
|
||||
**Positive Feedback (Dangerous):**
|
||||
|
||||
```
|
||||
High activity → Ca²⁺ overload → mitochondrial damage → ↓ ATP
|
||||
↓ ATP → impaired Ca²⁺ clearance → more Ca²⁺ overload → more damage
|
||||
↓ ATP → reduced Na⁺/K⁺ pump → depolarization → more VGCC opening
|
||||
Result: Excitotoxicity
|
||||
```
|
||||
|
||||
**Negative Feedback (Protective):**
|
||||
|
||||
```
|
||||
High activity → ATP depletion → AMPK activation
|
||||
AMPK → ↓ protein synthesis (conserves ATP)
|
||||
AMPK → ↑ glucose transporters (enhances supply)
|
||||
AMPK → ↓ VGCC expression (reduces demand)
|
||||
Result: Homeostasis
|
||||
```
|
||||
|
||||
### **ATP-Dependent Plasticity Gates:**
|
||||
|
||||
**"Energy Checkpoint" for Structural Changes:**
|
||||
|
||||
```
|
||||
Question: Should synapse grow?
|
||||
Inputs: BDNF signal (importance) + Ca²⁺ history (activity) + ATP availability
|
||||
Decision rule:
|
||||
IF (BDNF high AND ATP adequate) → GROW
|
||||
IF (BDNF high AND ATP low) → INVAGINATE (save energy)
|
||||
IF (BDNF low AND ATP high) → MAINTAIN
|
||||
IF (BDNF low AND ATP low) → SHRINK
|
||||
```
|
||||
|
||||
## **Specific ATP ↔ Variable Interactions**
|
||||
|
||||
### **ATP ↔ Lactate (Critical Partnership)**
|
||||
|
||||
- **Astrocyte lactate** → neuron → pyruvate → 15 ATP via TCA cycle
|
||||
- **Activity-dependent coupling**: Glutamate uptake → astrocyte glycolysis → lactate export
|
||||
- **Timescale**: Seconds for lactate transport, minutes for glycogen mobilization
|
||||
|
||||
### **ATP ↔ VGCC (Bidirectional)**
|
||||
|
||||
- **ATP → VGCC**: Phosphorylation modulates opening kinetics (ms)
|
||||
- **VGCC → ATP demand**: Each Ca²⁺ ion requires 1 ATP for extrusion
|
||||
- **Homeostatic setpoint**: VGCC density adjusted to match ATP production capacity
|
||||
|
||||
### **ATP ↔ RP Size (Energy Budget)**
|
||||
|
||||
- **Storage cost**: ~100 ATP/day per vesicle (maintenance + turnover)
|
||||
- **Allocation decision**: ATP surplus → more vesicles; deficit → fewer vesicles
|
||||
- **Dynamic adjustment**: RP shrinks within hours of ATP shortage
|
||||
|
||||
### **ATP ↔ K⁺/KChannels (Stability Control)**
|
||||
|
||||
- **Na⁺/K⁺ pump**: 1 ATP clears 3 Na⁺, brings 2 K⁺
|
||||
- **K⁺ accumulation** without ATP → depolarization → runaway excitation
|
||||
- **KChannels** require ATP for phosphorylation-dependent modulation
|
||||
|
||||
## **Clinical/Experimental Implications**
|
||||
|
||||
**Energy-Limited Plasticity:**
|
||||
|
||||
- Learning under low ATP (sleep deprivation, metabolic stress) → less structural change
|
||||
- High ATP + BDNF → optimal plasticity window
|
||||
|
||||
**Therapeutic Targets:**
|
||||
|
||||
- Enhance lactate shuttle → support ATP during high demand
|
||||
- Modulate AMPK → shift energy allocation decisions
|
||||
- Mitochondrial support → increase ATP capacity for structural changes
|
||||
|
||||
**Measurement Approaches:**
|
||||
|
||||
- **FRET ATP sensors**: Real-time ATP dynamics (seconds)
|
||||
- **ATP/ADP ratio**: Metabolic status (minutes)
|
||||
- **Mitochondrial density**: ATP capacity (hours-days)
|
||||
|
||||
## **Summary: ATP as Presynaptic "Bank Account"**
|
||||
|
||||
```
|
||||
Quick cash (ms): ATP at active zone → immediate transactions
|
||||
Checking account (100ms): Cytosolic ATP → short-term operations
|
||||
Savings account (seconds): Mitochondrial/phosphocreatine → buffer
|
||||
Investment portfolio (hours): Structural changes → long-term capacity
|
||||
Credit line (emergency): Lactate shuttle → external support
|
||||
```
|
||||
|
||||
The presynaptic terminal's ATP management strategy determines:
|
||||
|
||||
- **Release fidelity** (ms scale)
|
||||
- **Short-term plasticity** (100ms scale)
|
||||
- **Sustained transmission** (second scale)
|
||||
- **Structural adaptation** (hour-day scale)
|
||||
|
||||
Every plasticity decision is fundamentally an energy allocation decision, with ATP serving as both the currency and the accountant.
|
||||
|
||||
---
|
||||
|
||||
---
|
||||
|
||||
---
|
||||
|
||||
# **Ca²⁺: The Universal Presynaptic Signal**
|
||||
|
||||
## **Ca²⁺ Across Temporal Scales**
|
||||
|
||||
### **1. MILLISECOND SCALE (Nano/Submicrodomain Ca²⁺)**
|
||||
|
||||
**Direct Behaviors Triggered:**
|
||||
|
||||
- **Vesicle fusion**: Cooperative binding to synaptotagmin (n~4)
|
||||
- **KChannel activation**: SK channels open → fast afterhyperpolarization
|
||||
- **VGCC feedback**: Ca²⁺-dependent inactivation (CDI)
|
||||
|
||||
**Dynamics:**
|
||||
|
||||
- **Rise time**: <100 μs to peak
|
||||
- **Decay time constant**: 200-500 μs (fast buffers)
|
||||
- **Diffusion coefficient**: ~200 μm²/s (buffered)
|
||||
|
||||
**Influences on Other Variables:**
|
||||
|
||||
```
|
||||
Ca²⁺ (ms) → Vesicles release: Exponential dependence (EC₅₀ ~ 10-25 μM)
|
||||
Ca²⁺ (ms) → KChannels (SK): Fast AHP → modulates next AP
|
||||
Ca²⁺ (ms) → VGCC: CDI reduces subsequent Ca²⁺ influx
|
||||
```
|
||||
|
||||
### **2. TENS-HUNDREDS OF MS SCALE (Global Terminal Ca²⁺)**
|
||||
|
||||
**Spatial Integration:**
|
||||
|
||||
- **Bulk concentration**: 0.2-2 μM throughout terminal
|
||||
- **Residual Ca²⁺**: 0.1-0.5 μM between APs
|
||||
|
||||
**Direct Behaviors Enabled:**
|
||||
|
||||
- **Vesicle mobilization**: Ca²⁺-dependent phosphatase activation (calcineurin)
|
||||
- **Short-term plasticity**:
|
||||
- **Facilitation**: Residual Ca²⁺ binds to synaptotagmin priming
|
||||
- **Augmentation**: Sustained Ca²⁺ activates CaMKII
|
||||
- **Metabolic coupling**: Mitochondrial Ca²⁺ uptake initiation
|
||||
|
||||
**Cross-scale Interactions:**
|
||||
|
||||
```
|
||||
Ca²⁺ (100ms) → NO production: Activates postsynaptic NOS → retrograde signal
|
||||
Ca²⁺ (100ms) → eCB synthesis: Postsynaptic DAG lipase activation
|
||||
Ca²⁺ (100ms) → RP→RRP: Calcineurin dephosphorylates synapsin
|
||||
Ca²⁺ (100ms) → ATP demand: Each Ca²⁺ extruded requires 1 ATP
|
||||
```
|
||||
|
||||
**Mathematical Representation:**
|
||||
|
||||
```
|
||||
d[Ca²⁺]_global/dt = J_influx - J_pump - J_mitochondria - J_diffusion
|
||||
where:
|
||||
J_influx ∝ Σ(VGCC_open) over recent APs
|
||||
J_pump = V_max·[Ca²⁺]/(K_m + [Ca²⁺]) (ATP-dependent)
|
||||
J_mitochondria = k_m·[Ca²⁺]·(ΔΨ_m - threshold)
|
||||
```
|
||||
|
||||
### **3. SECOND-MINUTE SCALE (Signaling Ca²⁺)**
|
||||
|
||||
**Direct Behaviors Enabled:**
|
||||
|
||||
- **Gene expression**: Nuclear Ca²⁺ → CREB phosphorylation
|
||||
- **Metabolic regulation**: Mitochondrial matrix Ca²⁺ → TCA cycle enzymes
|
||||
- **Structural tagging**: Local Ca²⁺ waves mark active synapses
|
||||
|
||||
**Signal Integration Mechanisms:**
|
||||
|
||||
- **Frequency decoding**: Ca²⁺ spikes → NFAT activation
|
||||
- **Amplitude decoding**: High Ca²⁺ → CamKII autophosphorylation
|
||||
- **Duration decoding**: Sustained Ca²⁺ → MAPK pathway activation
|
||||
|
||||
**Modulation by Other Variables:**
|
||||
|
||||
```
|
||||
ATP ↓ → Reduced Ca²⁺ clearance → Elevated baseline Ca²⁺
|
||||
BDNF → Enhances Ca²⁺ signals via PLCγ→IP₃→ER release
|
||||
NO → cGMP → PKG → modulates Ca²⁺ channels and pumps
|
||||
Lactate → Supports mitochondrial Ca²⁺ uptake via ATP
|
||||
```
|
||||
|
||||
### **4. HOURS-DAYS SCALE (Ca²⁺ as Structural Organizer)**
|
||||
|
||||
**Direct Behaviors Enabled:**
|
||||
|
||||
- **Synapse growth/shrinkage**: Ca²⁺-dependent gene expression programs
|
||||
- **Homeostatic scaling**: Chronic Ca²⁺ levels set VGCC density
|
||||
- **Metaplasticity**: Ca²⁺ history determines future plasticity rules
|
||||
|
||||
**Ca²⁺ Setpoints and Homeostasis:**
|
||||
|
||||
- **Target baseline**: 50-100 nM (resting)
|
||||
- **Activity setpoint**: Integrated over hours determines structural changes
|
||||
- **Memory window**: Ca²⁺ history of last 24-48 hours influences current state
|
||||
|
||||
## **Ca²⁺ as Information Encoder**
|
||||
|
||||
### **Temporal Coding by Ca²⁺:**
|
||||
|
||||
**Amplitude Encoding:**
|
||||
|
||||
- Single AP: ~0.5 μM global Ca²⁺
|
||||
- 10 Hz train: ~1.5 μM global Ca²⁺
|
||||
- 100 Hz burst: >5 μM global Ca²⁺
|
||||
|
||||
**Frequency Encoding:**
|
||||
|
||||
- Low frequency (<1 Hz): Discrete Ca²⁺ transients
|
||||
- Theta (4-8 Hz): Partial summation
|
||||
- Gamma (30-100 Hz): Sustained elevation
|
||||
|
||||
**Duration Encoding:**
|
||||
|
||||
- Brief (<100 ms): Fast signaling only
|
||||
- Medium (1-10 s): Activates kinases
|
||||
- Long (>1 min): Triggers gene expression
|
||||
|
||||
### **Spatial Coding by Ca²⁺:**
|
||||
|
||||
**Microdomain vs Global Signals:**
|
||||
|
||||
```
|
||||
VGCC cluster 1 → Ca²⁺ microdomain 1 → Vesicles 1-3
|
||||
VGCC cluster 2 → Ca²⁺ microdomain 2 → Vesicles 4-6
|
||||
Diffusion → Global Ca²⁺ → Mobilization, metabolic signals
|
||||
```
|
||||
|
||||
**Compartmentalization:**
|
||||
|
||||
- **Active zone**: Release-triggering (fast)
|
||||
- **Vesicle pools**: Mobilization (medium)
|
||||
- **Mitochondria**: Metabolic coupling (slow)
|
||||
- **Nucleus**: Gene regulation (very slow)
|
||||
|
||||
## **Ca²⁺ ↔ Specific Variable Interactions**
|
||||
|
||||
### **Ca²⁺ ↔ VGCC (Bidirectional Control)**
|
||||
|
||||
```
|
||||
Fast (ms): Ca²⁺-dependent inactivation (CDI) - negative feedback
|
||||
Medium (s): Ca²⁺-dependent facilitation (CDF) - positive feedback
|
||||
Slow (hours): Ca²⁺-dependent VGCC expression - homeostatic
|
||||
```
|
||||
|
||||
### **Ca²⁺ ↔ ATP (Energy-Coupling)**
|
||||
|
||||
- **Ca²⁺ → ATP demand**: Each Ca²⁺ ion requires 1 ATP for extrusion
|
||||
- **Ca²⁺ → ATP production**: Mitochondrial Ca²⁺ stimulates TCA cycle
|
||||
- **ATP → Ca²⁺ handling**: ATP fuels pumps, buffers, organelle uptake
|
||||
|
||||
### **Ca²⁺ ↔ BDNF (Trophic Loop)**
|
||||
|
||||
```
|
||||
Presynaptic: Ca²⁺ influx → Vesicle release → Glutamate
|
||||
Postsynaptic: Glutamate → NMDA → Ca²⁺ → BDNF synthesis
|
||||
Retrograde: BDNF → Presynaptic TrkB → Enhanced Ca²⁺ signals
|
||||
```
|
||||
|
||||
### **Ca²⁺ ↔ eCB (Retrograde Modulation)**
|
||||
|
||||
```
|
||||
Postsynaptic: Ca²⁺ + mGluR → DAG → 2-AG synthesis
|
||||
Retrograde: eCB → Presynaptic CB1 → Inhibits VGCC
|
||||
Feedback: Reduced Ca²⁺ → Less glutamate → Less eCB
|
||||
```
|
||||
|
||||
### **Ca²⁺ ↔ Lactate (Metabolic Feedback)**
|
||||
|
||||
```
|
||||
Presynaptic Ca²⁺ → Glutamate release → Astrocyte uptake
|
||||
Astrocyte: Glutamate → Na⁺ influx → Glycolysis → Lactate
|
||||
Lactate → Presynaptic → ATP → Supports Ca²⁺ handling
|
||||
```
|
||||
|
||||
### **Ca²⁺ ↔ K⁺/KChannels (Excitability Control)**
|
||||
|
||||
```
|
||||
Ca²⁺ → SK channels → K⁺ efflux → Fast AHP → Limits firing
|
||||
K⁺ accumulation → Depolarization → More VGCC opening → More Ca²⁺
|
||||
Ca²⁺ → BK channels → Faster repolarization → Shorter AP
|
||||
```
|
||||
|
||||
## **Ca²⁺-Dependent Plasticity Rules**
|
||||
|
||||
### **Short-term Rules (ms-s):**
|
||||
|
||||
```
|
||||
Residual Ca²⁺ model: RRP release ∝ [Ca²⁺]_residual^n
|
||||
Facilitation: PPR = 1 + ([Ca²⁺]_residual/EC₅₀)
|
||||
Depression: Vesicle depletion rate ∝ [Ca²⁺]_peak
|
||||
```
|
||||
|
||||
### **Long-term Rules (min-days):**
|
||||
|
||||
```
|
||||
BCM-like rule:
|
||||
if [Ca²⁺]_avg < θ₁ → Downscale (LTD)
|
||||
if θ₁ < [Ca²⁺]_avg < θ₂ → No change
|
||||
if [Ca²⁺]_avg > θ₂ → Upscale (LTP)
|
||||
|
||||
θ₁ and θ₂ adjust based on Ca²⁺ history (metaplasticity)
|
||||
```
|
||||
|
||||
### **Structural Rules:**
|
||||
|
||||
```
|
||||
VGCC expression rate = k₁·[Ca²⁺]_integral - k₂·[VGCC]
|
||||
RP size = k₃·BDNF·[Ca²⁺]_avg - k₄·[RP]
|
||||
Where BDNF itself depends on Ca²⁺ history
|
||||
```
|
||||
|
||||
## **Clinical/Experimental Implications**
|
||||
|
||||
### **Ca²⁺ Dysregulation Pathologies:**
|
||||
|
||||
- **Excitotoxicity**: Chronic high Ca²⁺ → mitochondrial failure → cell death
|
||||
- **Synaptic fatigue**: Impaired Ca²⁺ clearance → reduced dynamic range
|
||||
- **Plasticity disorders**: Altered Ca²⁺ setpoints → LTP/LTD imbalance
|
||||
|
||||
### **Measurement Approaches:**
|
||||
|
||||
- **Fast dyes (Fluo-4FF)**: Microdomain Ca²⁺ (ms)
|
||||
- **GCaMP variants**: Global Ca²⁺ (10-100 ms resolution)
|
||||
- **Ca²⁺ integrators (CaMKII)**: History over minutes
|
||||
- **Structural readouts**: VGCC clustering, vesicle pools (hours-days)
|
||||
|
||||
### **Therapeutic Targets:**
|
||||
|
||||
- **VGCC blockers**: Reduce pathological Ca²⁺ influx
|
||||
- **Ca²⁺ buffer enhancers**: Improve clearance
|
||||
- **Mitochondrial Ca²⁺ uptake**: Protect against excitotoxicity
|
||||
- **Ca²⁺ setpoint modulators**: Restore homeostatic balance
|
||||
|
||||
## **Summary: Ca²⁺ as Multiscale Integrator**
|
||||
|
||||
**Microscale (ms):** Release trigger → Digital signal (vesicle fusion/no fusion)
|
||||
**Mesoscale (100ms):** Plasticity mediator → Analog signal (facilitation/depression)
|
||||
**Macroscale (min):** Metabolic regulator → Energy allocation signal
|
||||
**Macroscale (hours):** Structural organizer → Growth/retraction signal
|
||||
|
||||
**Key Principles:**
|
||||
|
||||
1. **Dual signaling**: Microdomain (fast, local) vs Global (slow, integrative)
|
||||
2. **Timescale-specific effectors**: Different targets at different Ca²⁺ durations
|
||||
3. **Bidirectional coupling**: Ca²⁺ influences everything, everything influences Ca²⁺
|
||||
4. **Setpoint homeostasis**: Systems maintain optimal Ca²⁺ levels across timescales
|
||||
5. **Memory encoding**: Ca²⁺ history changes future Ca²⁺ handling
|
||||
|
||||
**The Ca²⁺ Paradox:**
|
||||
The same ion that triggers millisecond release also organizes day-scale structural changes, with no contradiction because:
|
||||
|
||||
- Different **concentrations** activate different effectors
|
||||
- Different **durations** engage different signaling pathways
|
||||
- Different **localizations** communicate different information
|
||||
- Different **frequencies** encode different messages
|
||||
|
||||
Ca²⁺ is not just a signal—it's the alphabet of presynaptic communication, with its timing, amplitude, and location forming words, sentences, and stories across timescales.
|
||||
|
||||
---
|
||||
|
||||
---
|
||||
|
||||
---
|
||||
|
||||
# CDI
|
||||
|
||||
**Ca²⁺-dependent inactivation** is a rapid negative feedback mechanism where **VGCCs self-regulate** by closing more quickly when **Ca²⁺ ions** bind to specific sites on the channel itself. This happens within **milliseconds** of channel opening.
|
||||
|
||||
## **Sequence of Events:**
|
||||
|
||||
text
|
||||
|
||||
```
|
||||
1. VGCC opens → Ca²⁺ influx through pore
|
||||
2. Ca²⁺ binds to CaM already tethered to channel (microdomain Ca²⁺ ~10-100 μM)
|
||||
3. Ca²⁺/CaM complex conformation change
|
||||
4. Ca²⁺/CaM binds to IQ domain
|
||||
5. Channel pore undergoes conformational change → CLOSES
|
||||
6. Channel enters inactivated state (refractory to reopening)
|
||||
```
|
||||
|
||||
**Timing:**
|
||||
|
||||
- **Onset**: Within 5-50 ms of channel opening
|
||||
- **Full inactivation**: 100-300 ms
|
||||
- **Recovery**: 100-1000 ms (requires Ca²⁺ unbinding)
|
||||
|
||||
## **Functional Significance in Presynapse**
|
||||
|
||||
### **Millisecond Timescale Effects:**
|
||||
|
||||
| Effect | Consequence |
|
||||
|----------------------------------|----------------------------------------|
|
||||
| **Shortens Ca²⁺ influx duration** | Limits total Ca²⁺ per action potential |
|
||||
| **Prevents Ca²⁺ overload** | Protects against excitotoxicity |
|
||||
| **Filters high-frequency firing** | Channels inactivate during trains |
|
||||
| **Shapes AP-evoked Ca²⁺ transients** | Determines Ca²⁺ waveform |
|
||||
|
||||
### **Impact on Vesicle Release:**
|
||||
|
||||
text
|
||||
|
||||
```
|
||||
Without CDI: Sustained Ca²⁺ influx → higher Pr, more vesicles released
|
||||
With CDI: Brief Ca²⁺ influx → lower Pr, fewer vesicles released
|
||||
CDI modulation: Alters release probability dynamically
|
||||
```
|
||||
|
||||
### **Short-term Plasticity Implications:**
|
||||
|
||||
- **High-frequency trains**: CDI accumulates → less Ca²⁺ per AP → depression
|
||||
- **Recovery between bursts**: CDI relief → restored Ca²⁺ influx → facilitation
|
||||
- **Frequency filtering**: CDI acts as low-pass filter for presynaptic Ca²⁺ signals
|
||||
|
||||
## **CDI vs Other Inactivation Mechanisms**
|
||||
|
||||
### **Three Types of VGCC Inactivation:**
|
||||
|
||||
1. **Ca²⁺-dependent (CDI)** - Fast, Ca²⁺-mediated (\~50 ms)
|
||||
2. **Voltage-dependent (VDI)** - Slower, voltage-sensor mediated (\~100-500 ms)
|
||||
3. **G-protein mediated** - Slower, neurotransmitter modulation (\~100-1000 ms)
|
||||
|
||||
### **Presynaptic Dominance:**
|
||||
|
||||
- **Calcium channels in presynapse**: Primarily **CaV2.1 (P/Q-type)** and **CaV2.2 (N-type)**
|
||||
- **CDI strength**: CaV2.1 > CaV2.2
|
||||
- **Location specificity**: Active zone channels show strongest CDI
|
||||
|
||||
## **Modulation of CDI by other factors**
|
||||
|
||||
### **BDNF Modulation:**
|
||||
|
||||
text
|
||||
|
||||
```
|
||||
BDNF → TrkB → PLCγ → DAG → PKC → phosphorylates VGCC
|
||||
Result: ↓ CDI → prolonged Ca²⁺ influx → enhanced release
|
||||
```
|
||||
|
||||
### **NO Modulation:**
|
||||
|
||||
text
|
||||
|
||||
```
|
||||
NO → sGC → cGMP → PKG → phosphorylates CaM or VGCC
|
||||
Result: ↑ CDI → shorter Ca²⁺ influx → reduced release
|
||||
```
|
||||
|
||||
### **eCB Modulation:**
|
||||
|
||||
text
|
||||
|
||||
```
|
||||
eCB → CB1 → Gβγ → binds VGCC directly
|
||||
Result: Channel inhibition + ↑ CDI → strong suppression
|
||||
```
|
||||
|
||||
### **ATP/Energy Status:**
|
||||
|
||||
text
|
||||
|
||||
```
|
||||
Low ATP → impaired Ca²⁺ pumps → elevated resting Ca²⁺
|
||||
Result: CaM partially occupied → reduced CDI dynamic range
|
||||
```
|
||||
@@ -1,300 +0,0 @@
|
||||
# **Presynaptic Release Model: Sequence of Events & Multi-Timescale Modulations**
|
||||
|
||||
## **CORE RELEASE SEQUENCE (Milliseconds)**
|
||||
|
||||
### **Event 1: Action Potential Arrival**
|
||||
|
||||
```
|
||||
Time: t = 0 ms
|
||||
Trigger: Depolarization from axon hillock
|
||||
Mechanism: Na⁺/K⁺ voltage-gated channel cascade
|
||||
State: Terminal depolarizes from -70 mV to +30 mV
|
||||
Duration: ~1 ms
|
||||
```
|
||||
|
||||
### **Event 2: VGCC Opening**
|
||||
|
||||
```
|
||||
Time: t = 0.2-0.5 ms after AP arrival
|
||||
Trigger: Membrane depolarization > -40 mV
|
||||
Types: CaV2.1 (P/Q-type), CaV2.2 (N-type) at active zone
|
||||
Mechanism: Voltage sensor movement → pore opening
|
||||
Open probability: ~0.3-0.8 during AP peak
|
||||
Open duration: ~0.5-2 ms
|
||||
```
|
||||
|
||||
### **Event 3: Ca²⁺ Influx & Microdomain Formation**
|
||||
|
||||
```
|
||||
Time: t = 0.3-1 ms after AP arrival
|
||||
Ca²⁺ source: Extracellular (1.2 mM) → intracellular (50 nM baseline)
|
||||
Influx rate: ~3000-10000 Ca²⁺ ions per VGCC per ms
|
||||
Microdomain formation:
|
||||
- Within 20 nm of VGCC: 10-100 µM
|
||||
- At vesicle release site: 10-25 µM threshold for release
|
||||
- Rise time: <100 µs
|
||||
- Diffusion-limited spread: ~100-200 nm radius
|
||||
```
|
||||
|
||||
### **Event 4: Vesicle Release Decision**
|
||||
|
||||
```
|
||||
Time: t = 0.4-1.5 ms after AP arrival
|
||||
Decision conditions (AND logic):
|
||||
1. [Ca²⁺]microdomain > 10-25 µM
|
||||
2. Vesicle in RRP (docked & primed)
|
||||
3. SNARE complex in primed state
|
||||
4. Synaptotagmin Ca²⁺ binding sites occupied
|
||||
Mechanism:
|
||||
- Ca²⁺ binds synaptotagmin (4+ cooperative sites)
|
||||
- Synaptotagmin displaces complexin clamp
|
||||
- SNARE complex completes zippering
|
||||
- Vesicle membrane fuses with presynaptic membrane
|
||||
Release latency: 0.1-1.0 ms after Ca²⁺ threshold reached
|
||||
Release synchrony: Multiple vesicles can release simultaneously
|
||||
```
|
||||
|
||||
### **Event 5: Ca²⁺ Clearance**
|
||||
|
||||
```
|
||||
Time: t = 1-50 ms after influx
|
||||
Clearance mechanisms (in order of speed):
|
||||
1. Fast buffers (calbindin, parvalbumin): <1 ms
|
||||
2. Plasma membrane Ca²⁺ ATPase (PMCA): 10-100 ms
|
||||
3. Na⁺/Ca²⁺ exchanger (NCX): 10-100 ms
|
||||
4. Mitochondrial uptake: 10-1000 ms
|
||||
5. Endoplasmic reticulum uptake: 100-1000 ms
|
||||
Residual Ca²⁺: 0.1-0.5 µM persists for 10-1000 ms
|
||||
```
|
||||
|
||||
### **Event 6: Vesicle Recycling**
|
||||
|
||||
```
|
||||
Time: t = 10 ms - 10 s (depending on activity)
|
||||
Sequential steps:
|
||||
1. Endocytosis (clathrin-mediated, kiss-and-run, bulk)
|
||||
2. Vesicle re-acidification (v-ATPase)
|
||||
3. Neurotransmitter reloading (vesicular transporters)
|
||||
4. Priming (SNARE assembly, docking)
|
||||
5. Return to RRP
|
||||
Recycling rate: Limited by ATP availability
|
||||
```
|
||||
|
||||
## **MODULATION MATRIX ACROSS TIMESCALES**
|
||||
|
||||
### **MODULATION LEVEL 1: MILLISECONDS (Immediate Signal Processing)**
|
||||
|
||||
| Event | Modulator | Effect | Mechanism | Timescale |
|
||||
|------------------|-----------------------------------|----------------------------------------|---------------------------------------------|---------------------|
|
||||
| **VGCC Opening** | Voltage waveform | AP width/duration affects open time | K⁺ channel activation shapes repolarization | During AP (1 ms) |
|
||||
| **VGCC Opening** | Ca²⁺-dependent inactivation (CDI) | Auto-inhibition | Ca²⁺ binding to calmodulin on VGCC | 5-50 ms |
|
||||
| **Ca²⁺ Microdomain** | Endogenous buffers | Shapes [Ca²⁺] spatial/temporal profile | Calbindin, parvalbumin binding | <1 ms |
|
||||
| **Release Decision** | Synaptotagmin isoforms | Different Ca²⁺ sensitivity | Cooperative binding sites vary | During Ca²⁺ binding |
|
||||
| **Release Decision** | SNARE complex state | Priming level determines speed | Munc13 activity, NSF disassembly | <1 ms |
|
||||
| **Ca²⁺ Clearance** | Fast buffers | Immediate Ca²⁺ binding | High-affinity Ca²⁺ binding proteins | <1 ms |
|
||||
|
||||
### **MODULATION LEVEL 2: TENS-HUNDREDS OF MILLISECONDS (Short-term Plasticity)**
|
||||
|
||||
| Event | Modulator | Effect | Mechanism | Timescale |
|
||||
|---------------------|----------------------|-------------------------------|-----------------------------------------------------|---------------|
|
||||
| **VGCC Opening** | Residual Ca²⁺ | Ca²⁺-dependent facilitation | Ca²⁺/CaM binding to VGCC β-subunit | 10-1000 ms |
|
||||
| **VGCC Opening** | eCB (CB1 activation) | Direct inhibition | Gβγ subunit blocks pore | 100-2000 ms |
|
||||
| **Ca²⁺ Microdomain** | Mitochondrial uptake | Buffer capacity changes | Uniporter activity with Ca²⁺ buildup | 10-1000 ms |
|
||||
| **RRP Replenishment** | Residual Ca²⁺ | Enhanced mobilization | Calcineurin activation → synapsin dephosphorylation | 10-1000 ms |
|
||||
| **RRP Replenishment** | ATP availability | Limits priming rate | NSF, v-ATPase, priming ATPases | Continuous |
|
||||
| **Release Probability** | mGluR autoreceptors | Activity-dependent inhibition | Gi/o → ↓cAMP → ↓PKA → ↓VGCC | 50-500 ms |
|
||||
| **Ca²⁺ Clearance** | PMCA/NCX pumps | Activity-dependent saturation | Limited pump capacity during high frequency | 10-1000 ms |
|
||||
| **Vesicle Recycling** | Activity level | Different endocytosis modes | High activity → bulk endocytosis | 100 ms - 10 s |
|
||||
|
||||
### **MODULATION LEVEL 3: SECONDS-MINUTES (Metabolic & Signaling)**
|
||||
|
||||
| Event | Modulator | Effect | Mechanism | Timescale |
|
||||
|-------------------|-----------------------------|----------------------------|-----------------------------------------|--------------|
|
||||
| **VGCC Density** | Surface expression | More/fewer channels | Phosphorylation-dependent trafficking | 30 s - 5 min |
|
||||
| **VGCC Function** | Kinase phosphorylation | Changed open probability | PKA, PKC, CaMKII phosphorylation | 1-10 min |
|
||||
| **Ca²⁺ Dynamics** | NO (cGMP pathway) | Altered pump activity | PKG phosphorylation of PMCA | 1-10 min |
|
||||
| **Vesicle Pools** | Mobilization rate | RP→RRP speed changes | Synapsin phosphorylation state | 1-10 min |
|
||||
| **ATP Production** | Lactate shuttle | Enhanced ATP supply | Astrocyte-neuron metabolic coupling | 1-10 min |
|
||||
| **Release Machinery** | BDNF (acute) | Enhanced priming & docking | TrkB → PLCγ → PKC activation | 1-10 min |
|
||||
| **Autoreceptor** | mGluR desensitization | Reduced autoinhibition | β-arrestin recruitment, internalization | 1-10 min |
|
||||
| **CB1 Receptor** | eCB-induced desensitization | Reduced inhibition | GRK phosphorylation, internalization | 1-10 min |
|
||||
| **Ca²⁺ Clearance** | Mitochondrial adaptation | Increased capacity | Matrix Ca²⁺ activates dehydrogenases | 1-10 min |
|
||||
|
||||
### **MODULATION LEVEL 4: MINUTES-HOURS (Structural & Transcriptional)**
|
||||
|
||||
| Event | Modulator | Effect | Mechanism | Timescale |
|
||||
|-----------------------|--------------------|-------------------------------|----------------------------------------------|---------------|
|
||||
| **VGCC Expression** | BDNF (chronic) | Increased channel synthesis | TrkB → MAPK → CREB → gene expression | 30 min - 6 hr |
|
||||
| **VGCC Expression** | Activity-dependent | Homeostatic scaling | Ca²⁺ → NFAT/CREB → VGCC genes | 1-24 hr |
|
||||
| **Active Zone Size** | BDNF, activity | More release sites | Structural proteins (RIM, Bassoon) synthesis | 1-12 hr |
|
||||
| **Vesicle Pool Size** | BDNF, activity | Larger RP/RRP | Synaptic vesicle protein synthesis | 1-12 hr |
|
||||
| **SNARE Machinery** | Local translation | More fusion complexes | mTOR-dependent protein synthesis | 30 min - 3 hr |
|
||||
| **Mitochondrial Density** | BDNF, activity | Increased ATP capacity | PGC-1α activation → biogenesis | 3-24 hr |
|
||||
| **Metabolic Pathways** | Activity patterns | Enhanced glycolysis/oxidation | HIF-1α, AMPK pathway activation | 1-6 hr |
|
||||
| **Receptor Expression** | Chronic modulation | mGluR, CB1 level changes | Transcriptional regulation | 3-12 hr |
|
||||
| **Buffer Expression** | Ca²⁺ history | Calbindin/parvalbumin levels | Ca²⁺-dependent gene regulation | 3-12 hr |
|
||||
|
||||
### **MODULATION LEVEL 5: HOURS-DAYS (Metaplasticity & Structural Remodeling)**
|
||||
|
||||
| Event | Modulator | Effect | Mechanism | Timescale |
|
||||
|---------------------------|-----------------------|-------------------------------------|--------------------------------------------|-----------|
|
||||
| **Synapse Size** | Chronic activity | Growth/shrinkage | Cytoskeletal reorganization | 6-48 hr |
|
||||
| **VGCC Distribution** | Activity patterns | Clustering changes | Scaffold protein (Homer, Shank) expression | 12-72 hr |
|
||||
| **Release Site Organization** | BDNF, activity | Active zone architecture | Piccolo, Bassoon, RIM expression | 12-72 hr |
|
||||
| **Vesicle Recycling** | Chronic patterns | Efficiency changes | Endocytosis machinery expression | 12-48 hr |
|
||||
| **Metaplasticity Rules** | Activity history | Altered LTP/LTD thresholds | Kinase/phosphatase expression changes | 24-72 hr |
|
||||
| **Energy Allocation** | Chronic demand | Mitochondrial positioning | Motor protein (kinesin, dynein) adaptation | 12-48 hr |
|
||||
| **Network Integration** | System-level activity | Presynaptic inhibition/facilitation | Interneuron connectivity changes | 24-96 hr |
|
||||
|
||||
## **MODULATION CASCADES (How Signals Propagate Through Events)**
|
||||
|
||||
### **Example 1: High-Frequency Activity Cascade**
|
||||
|
||||
```
|
||||
Event Timeline:
|
||||
t = 0 ms: First AP → Release (high Pr)
|
||||
t = 10 ms: Second AP → Enhanced release (residual Ca²⁺ facilitation)
|
||||
t = 100 ms: Tenth AP → Depressed release (RRP depletion, eCB inhibition)
|
||||
|
||||
Modulation Cascade:
|
||||
Milliseconds: CDI develops, buffers saturate
|
||||
Seconds: mGluR autoinhibition builds, ATP depletes
|
||||
Minutes: BDNF synthesis begins, pumps adapt
|
||||
Hours: VGCC expression increases, active zone grows
|
||||
Days: Synapse strengthens, metaplasticity changes
|
||||
```
|
||||
|
||||
### **Example 2: BDNF-Mediated Potentiation Cascade**
|
||||
|
||||
```
|
||||
Event Timeline:
|
||||
t = 0-5 min: BDNF binds TrkB receptors
|
||||
t = 5-30 min: Kinase cascades activate
|
||||
t = 30-120 min: Local protein synthesis
|
||||
t = 3-24 hr: Structural changes
|
||||
|
||||
Modulation Cascade:
|
||||
Milliseconds: Immediate VGCC phosphorylation (↑ open probability)
|
||||
Seconds: Enhanced vesicle priming (↑ RRP replenishment)
|
||||
Minutes: More SNARE complexes synthesized (↑ release sites)
|
||||
Hours: Additional VGCCs inserted (↑ Ca²⁺ influx capacity)
|
||||
Days: Active zone expansion (↑ number of release sites)
|
||||
```
|
||||
|
||||
### **Example 3: eCB-Mediated Depression Cascade**
|
||||
|
||||
```
|
||||
Event Timeline:
|
||||
t = 100 ms: eCB produced postsynaptically
|
||||
t = 200 ms: CB1 activation inhibits VGCCs
|
||||
t = 1-10 min: β-arrestin recruitment, CB1 internalization
|
||||
t = 1-24 hr: CB1 downregulation, structural changes
|
||||
|
||||
Modulation Cascade:
|
||||
Milliseconds: Direct VGCC block (↓ Ca²⁺ influx)
|
||||
Seconds: Reduced cAMP → ↓ PKA → ↓ vesicle priming
|
||||
Minutes: CB1 internalization → reduced inhibition
|
||||
Hours: CB1 downregulation → reduced modulatory capacity
|
||||
Days: Synaptic downscaling → smaller active zone
|
||||
```
|
||||
|
||||
## **CROSS-EVENT MODULATION PATTERNS**
|
||||
|
||||
### **Feedforward Loops:**
|
||||
|
||||
```
|
||||
Positive:
|
||||
AP → Ca²⁺ influx → CaMKII activation → ↑ VGCC phosphorylation → ↑ Ca²⁺ influx
|
||||
|
||||
Negative:
|
||||
AP → Glutamate release → mGluR activation → ↓ VGCC opening → ↓ Ca²⁺ influx
|
||||
```
|
||||
|
||||
### **Feedback Loops:**
|
||||
|
||||
```
|
||||
Homeostatic:
|
||||
High activity → Ca²⁺ buildup → gene expression → more buffers/pumps → ↓ Ca²⁺ buildup
|
||||
|
||||
Trophic:
|
||||
Activity → BDNF release → structural growth → more release sites → more activity
|
||||
```
|
||||
|
||||
### **Energy Management Loops:**
|
||||
|
||||
```
|
||||
Energy Conservation:
|
||||
ATP depletion → AMPK activation → ↓ protein synthesis → ↓ energy consumption
|
||||
|
||||
Energy Investment:
|
||||
BDNF + adequate ATP → mTOR activation → protein synthesis → structural growth
|
||||
```
|
||||
|
||||
## **INTEGRATED TIMELINE OF A RELEASE EVENT WITH MODULATIONS**
|
||||
|
||||
### **t = 0-1 ms (AP to Release)**
|
||||
|
||||
```
|
||||
Primary events: AP → VGCC open → Ca²⁺ influx → Release
|
||||
Modulations active:
|
||||
- AP shape from previous activity (K⁺ channel adaptation)
|
||||
- VGCDI from recent Ca²⁺ history
|
||||
- SNARE priming from recent ATP availability
|
||||
- Buffer capacity from expression levels
|
||||
```
|
||||
|
||||
### **t = 1-100 ms (Immediate Aftermath)**
|
||||
|
||||
```
|
||||
Primary events: Ca²⁺ clearance, vesicle recycling initiation
|
||||
Modulations active:
|
||||
- Residual Ca²⁺ facilitating next release
|
||||
- mGluR autoinhibition building
|
||||
- eCB production if postsynaptic Ca²⁺ high
|
||||
- ATP consumption for pumps and recycling
|
||||
```
|
||||
|
||||
### **t = 100 ms - 1 min (Short-term Adaptation)**
|
||||
|
||||
```
|
||||
Primary events: RRP replenishment, metabolic adjustments
|
||||
Modulations active:
|
||||
- Kinase/phosphatase balance shifting
|
||||
- NO production if sustained activity
|
||||
- BDNF release if activity pattern significant
|
||||
- Mitochondrial Ca²⁺ uptake affecting ATP
|
||||
```
|
||||
|
||||
### **t = 1 min - 1 hr (Medium-term Plasticity)**
|
||||
|
||||
```
|
||||
Primary events: Protein synthesis, trafficking changes
|
||||
Modulations active:
|
||||
- Local translation of VGCCs, SNAREs
|
||||
- Receptor trafficking to/from surface
|
||||
- Mitochondrial positioning changes
|
||||
- Metabolic pathway adjustments
|
||||
```
|
||||
|
||||
### **t = 1 hr - days (Long-term Restructuring)**
|
||||
|
||||
```
|
||||
Primary events: Structural changes, gene expression
|
||||
Modulations active:
|
||||
- Nuclear signaling for gene expression
|
||||
- Cytoskeletal reorganization
|
||||
- Synapse growth/shrinkage
|
||||
- Metaplasticity rule changes
|
||||
```
|
||||
|
||||
## **MODELING PRINCIPLES**
|
||||
|
||||
1. **Hierarchical Modulation**: Faster events constrain slower adaptations
|
||||
2. **Bidirectional Coupling**: Every modulation affects and is affected by release events
|
||||
3. **Energy Constraints**: ATP availability gates all processes
|
||||
4. **History Dependence**: Past activity patterns determine current modulation states
|
||||
5. **Context Specificity**: Same modulator can have opposite effects depending on timing/context
|
||||
6. **Redundancy**: Multiple pathways can achieve similar outcomes
|
||||
7. **Trade-offs**: Every enhancement has costs (energy, stability, flexibility)
|
||||
|
||||
This model shows how a simple millisecond release event sits at the center of a rich, multi-timescale regulatory network where each release both responds to and influences modulations across seconds to days, creating a dynamic, self-tuning system for synaptic transmission.
|
||||
@@ -1,319 +0,0 @@
|
||||
# **ATP-Lactate Dynamics: The Ultimate Constraint System**
|
||||
|
||||
## Non modello ATP production al SOMA
|
||||
|
||||
### **The Dual-Source ATP System**
|
||||
|
||||
Neurons have **two complementary ATP production systems** that operate at different timescales:
|
||||
|
||||
#### **1. LOCAL ATP PRODUCTION (Presynaptic Terminal)**
|
||||
|
||||
**Primary Source:** **Mitochondria** within the terminal
|
||||
**Capacity:** Limited (often 1-5 mitochondria per terminal)
|
||||
**Timescale:** Seconds to minutes
|
||||
|
||||
#### **2. DISTAL ATP PRODUCTION (Soma & Axon)**
|
||||
|
||||
**Primary Source:** **Somatic mitochondria** (more abundant)
|
||||
**Transport:** Axonal transport of ATP or ATP precursors
|
||||
**Timescale:** Hours (slow transport)
|
||||
|
||||
You've identified the **fundamental constraint hierarchy**:
|
||||
|
||||
```
|
||||
ATP availability ← Lactate production ← Astrocyte coordination ← Network activity
|
||||
```
|
||||
|
||||
This creates a **energy-based modulation cascade** that constrains everything else.
|
||||
|
||||
## **The Energy Constraint Hierarchy**
|
||||
|
||||
### **Level 1: Millisecond ATP Consumption (Ground Reality)**
|
||||
|
||||
```
|
||||
Processes consuming ATP:
|
||||
- Na⁺/K⁺ pump (40-60% of ATP per AP)
|
||||
- Ca²⁺ pumps (PMCA: ~1 ATP per Ca²⁺)
|
||||
- Vesicle priming (SNARE assembly, NSF ATPase)
|
||||
- Neurotransmitter reloading (v-ATPase)
|
||||
|
||||
ATP consumption per AP: ~20,000 ATP molecules
|
||||
Terminal ATP store: ~10⁸ ATP molecules → ~500 APs until depletion
|
||||
```
|
||||
|
||||
### **Level 2: Second-Minute Lactate Supply (Immediate Energy Politics)**
|
||||
|
||||
```
|
||||
Astrocyte lactate production:
|
||||
- Glutamate uptake → Na⁺ influx → Glycolysis → Lactate
|
||||
- Glycogen breakdown → Lactate
|
||||
- One astrocyte serves ~100,000 synapses
|
||||
|
||||
Lactate transport:
|
||||
- MCT2 transporters on presynaptic terminal
|
||||
- Conversion: Lactate → Pyruvate → ~15 ATP via TCA cycle
|
||||
- Timescale: Seconds for transport, minutes for metabolism
|
||||
```
|
||||
|
||||
### **Level 3: Minute-Hour Network Competition (Energy Economics)**
|
||||
|
||||
```
|
||||
Shared resource problem:
|
||||
- Multiple synapses compete for astrocyte lactate
|
||||
- Active synapses get priority (activity-dependent coupling)
|
||||
- "Energy-rich get richer" feedback
|
||||
|
||||
Astrocyte decision:
|
||||
IF (synapse active AND lactate available) → Supply
|
||||
IF (synapse inactive OR lactate limited) → Reduce supply
|
||||
```
|
||||
|
||||
### **Level 4: Hour-Day Metabolic Adaptation (Energy Infrastructure)**
|
||||
|
||||
```
|
||||
Long-term investments:
|
||||
- More mitochondria at active synapses
|
||||
- Enhanced MCT transporter expression
|
||||
- Astrocyte process extension toward active synapses
|
||||
```
|
||||
|
||||
## **ATP as the Universal Modulator**
|
||||
|
||||
### **ATP Availability Gates ALL Processes:**
|
||||
|
||||
```
|
||||
IF ATP > threshold_X:
|
||||
Process_Y allowed
|
||||
ELSE:
|
||||
Process_Y inhibited or delayed
|
||||
```
|
||||
|
||||
### **Specific ATP Thresholds:**
|
||||
|
||||
```
|
||||
1. High ATP (>80% of max):
|
||||
- All processes operational
|
||||
- Structural growth allowed
|
||||
- High release probability maintained
|
||||
|
||||
2. Medium ATP (30-80%):
|
||||
- Core release functions maintained
|
||||
- Energy-intensive processes limited
|
||||
- No structural growth
|
||||
|
||||
3. Low ATP (<30%):
|
||||
- Release probability decreases
|
||||
- Ca²⁺ clearance impaired
|
||||
- Vesicle recycling slows
|
||||
- Emergency conservation mode
|
||||
```
|
||||
|
||||
## **Simplified ATP-Lactate Model**
|
||||
|
||||
### **Variables:**
|
||||
|
||||
```
|
||||
1. ATP(t): Energy currency at presynapse
|
||||
2. Lactate_ext(t): Extracellular lactate from astrocyte
|
||||
3. Activity_level(t): Recent firing rate
|
||||
4. Neighbor_activity(t): Activity of nearby synapses
|
||||
```
|
||||
|
||||
### **Dynamics:**
|
||||
|
||||
```
|
||||
d(ATP)/dt = Production - Consumption
|
||||
|
||||
Production = k_prod × Lactate_ext × (1 - ATP/ATP_max)
|
||||
Consumption = k_cons × Activity_level + k_baseline
|
||||
|
||||
d(Lactate_ext)/dt = Supply - Uptake - Diffusion
|
||||
|
||||
Supply = k_supply × (Activity_level + α × Neighbor_activity)
|
||||
Uptake = k_uptake × ATP_deficit × Lactate_ext
|
||||
Diffusion = k_diff × (Lactate_ext - Lactate_background)
|
||||
```
|
||||
|
||||
### **The Constraint Equations:**
|
||||
|
||||
```
|
||||
For any process X with ATP requirement R_X:
|
||||
|
||||
IF (ATP > R_X) THEN Process_X proceeds at normal rate
|
||||
ELSE Process_X rate = normal_rate × (ATP/R_X)
|
||||
```
|
||||
|
||||
## **The Critical Insight: Energy-Based Competition**
|
||||
|
||||
### **Within a Single Presynapse:**
|
||||
|
||||
```
|
||||
Processes compete for ATP:
|
||||
- Release vs Clearance vs Recycling vs Growth
|
||||
|
||||
Energy allocation strategy:
|
||||
1. Maintenance first (pumps, basic functions)
|
||||
2. Release second (core mission)
|
||||
3. Recycling third (future capacity)
|
||||
4. Growth last (long-term investment)
|
||||
|
||||
During ATP shortage: Growth → Recycling → Release → Maintenance
|
||||
```
|
||||
|
||||
### **Between Synapses (via Astrocyte):**
|
||||
|
||||
```
|
||||
Synapses compete for lactate:
|
||||
- More active synapses → More glutamate uptake → More lactate production
|
||||
- But: Astrocyte lactate production limited by glucose/glycogen
|
||||
- And: Lactate diffusion favors nearby synapses
|
||||
|
||||
Result: Local "energy hotspots" and "energy deserts"
|
||||
```
|
||||
|
||||
## **Modeling Recommendations**
|
||||
|
||||
### **Option A: Simple ATP Buffer Model**
|
||||
|
||||
```
|
||||
ATP_level = ATP_max × (1 - exp(-t/τ_replenish)) during rest
|
||||
ATP_consumed_per_AP = constant
|
||||
IF ATP_level < threshold: Scale down all energy-intensive processes
|
||||
```
|
||||
|
||||
### **Option B: Lactate-Limited Model**
|
||||
|
||||
```
|
||||
ATP_production_rate = f(Lactate_available)
|
||||
Lactate_available = g(Astrocyte_response, Neighbor_activity)
|
||||
Astrocyte_response = h(Glutamate_uptake, Glycogen_level)
|
||||
```
|
||||
|
||||
### **Option C: Full Energy Competition Model**
|
||||
|
||||
```
|
||||
For each synapse i:
|
||||
dATP_i/dt = Production_i - Consumption_i
|
||||
Production_i = f(Lactate_i, Mitochondria_i)
|
||||
Lactate_i = Shared_pool × (Activity_i / ΣActivity_j)
|
||||
Shared_pool = Astrocyte_output - Total_uptake
|
||||
```
|
||||
|
||||
## **Implications for Plasticity**
|
||||
|
||||
### **The "Energy Check" for Structural Changes:**
|
||||
|
||||
```
|
||||
BDNF says: "Grow this synapse!"
|
||||
Energy system checks:
|
||||
1. Current ATP level?
|
||||
2. Lactate supply reliability?
|
||||
3. Competing energy demands?
|
||||
|
||||
Only if energy sufficient: Growth proceeds
|
||||
If energy marginal: Partial growth or delay
|
||||
If energy insufficient: Growth blocked
|
||||
```
|
||||
|
||||
### **Metaplasticity Rule:**
|
||||
|
||||
```
|
||||
Synapses that consistently receive:
|
||||
- High activity + Adequate lactate → Strengthen (LTP, growth)
|
||||
- High activity + Inadequate lactate → Weaken (LTD, shrinkage)
|
||||
- Low activity + Adequate lactate → Maintain
|
||||
- Low activity + Inadequate lactate → Weaken faster
|
||||
```
|
||||
|
||||
## **Experimental Predictions**
|
||||
|
||||
### **From This Model:**
|
||||
|
||||
1. **Lactate deprivation** should cause:
|
||||
- Faster synaptic depression during trains
|
||||
- Reduced long-term potentiation
|
||||
- Impaired structural plasticity
|
||||
2. **Astrocyte uncoupling** should cause:
|
||||
- Uncoordinated synaptic fatigue
|
||||
- Winner-take-all dynamics between nearby synapses
|
||||
- Impaired network synchronization
|
||||
3. **Metabolic stress** should cause:
|
||||
- Prioritization of inhibitory synapses (energy conservation)
|
||||
- Homeostatic downscaling of excitatory synapses
|
||||
- Altered metaplasticity thresholds
|
||||
|
||||
## **Simplest Implementation for Your Model**
|
||||
|
||||
### **Add These Variables:**
|
||||
|
||||
```python
|
||||
ATP = 1.0 # Normalized ATP level (0 to 1)
|
||||
lactate = 0.5 # Normalized lactate availability (0 to 1)
|
||||
neighbor_activity = 0.0 # Average activity of nearby synapses
|
||||
```
|
||||
|
||||
### **Update Rules:**
|
||||
|
||||
```python
|
||||
def update_energy(dt, activity, neighbor_avg_activity):
|
||||
# Lactate supply depends on local and neighbor activity
|
||||
lactate_supply = 0.1 * (activity + 0.3 * neighbor_avg_activity)
|
||||
lactate = min(1.0, lactate + lactate_supply * dt)
|
||||
|
||||
# ATP production from lactate
|
||||
ATP_production = 0.05 * lactate * (1 - ATP)
|
||||
|
||||
# ATP consumption from activity
|
||||
ATP_consumption = 0.02 * activity
|
||||
|
||||
ATP = max(0, ATP + (ATP_production - ATP_consumption) * dt)
|
||||
|
||||
# Constraint factor for other processes
|
||||
energy_factor = ATP**2 # Square to make low ATP more restrictive
|
||||
|
||||
return ATP, lactate, energy_factor
|
||||
```
|
||||
|
||||
### **Apply Energy Constraints:**
|
||||
|
||||
```python
|
||||
def process_AP_with_energy(Ca_microdomain, RRP_count, ATP):
|
||||
if Ca_microdomain > threshold and RRP_count > 0:
|
||||
# Energy limits release probability
|
||||
P_release_effective = P_release * ATP
|
||||
|
||||
# Energy limits replenishment rate
|
||||
k_replenish_effective = k_replenish * ATP
|
||||
|
||||
# Calculate release...
|
||||
```
|
||||
|
||||
## **The Ultimate Insight**
|
||||
|
||||
**ATP is the ultimate vote in the presynaptic democracy.** It says:
|
||||
|
||||
```
|
||||
"I'm the universal currency. Every process needs me.
|
||||
My availability determines what's possible.
|
||||
My production depends on lactate.
|
||||
Lactate depends on astrocyte coordination.
|
||||
Astrocytes coordinate based on network activity.
|
||||
|
||||
Thus, network-level activity patterns -> Astrocyte lactate distribution ->
|
||||
Presynaptic ATP levels -> Constrain all release decisions and plasticity."
|
||||
```
|
||||
|
||||
This creates a beautiful **circular causality**:
|
||||
|
||||
```
|
||||
Release events → Glutamate → Astrocyte activation → Lactate → ATP →
|
||||
Enable more release events → ...
|
||||
|
||||
BUT with constraints:
|
||||
- Limited astrocyte capacity
|
||||
- Competition between synapses
|
||||
- ATP consumption rates
|
||||
- Lactate diffusion limits
|
||||
```
|
||||
|
||||
Your model now has a **physical grounding** in energy metabolism, which explains why synapses can't just "decide" to be strong - they need the **energy infrastructure** to support that strength. This makes the model both more realistic and more constrained, which paradoxically makes it more powerful for understanding real synaptic function.
|
||||
@@ -1,251 +0,0 @@
|
||||
# **Hierarchical Modulation: Faster Events Constrain Slower Adaptations**
|
||||
|
||||
## **The Core Concept**
|
||||
|
||||
**Hierarchical modulation** means that processes at **faster timescales** (milliseconds to seconds) create **boundaries and constraints** within which slower processes (minutes to days) must operate.
|
||||
|
||||
Think of it like this:
|
||||
|
||||
- **Fast events** (release, Ca²⁺ influx) are the **reality on the ground**
|
||||
- **Slow adaptations** (structural changes, gene expression) are **long-term planning**
|
||||
- **Planning must respect reality** - you can't build a plan that ignores current physical constraints
|
||||
|
||||
## **Concrete Examples**
|
||||
|
||||
### **Example 1: ATP Availability Hierarchy**
|
||||
|
||||
```
|
||||
Fast constraint (ms-s):
|
||||
AP firing → ATP consumption for pumps and priming → ATP depletes
|
||||
|
||||
Slow adaptation (min-days):
|
||||
BDNF says "build more release sites!" (requires ATP for protein synthesis)
|
||||
|
||||
CONSTRAINT:
|
||||
If ATP is depleted from fast events, slow adaptation CANNOT proceed
|
||||
Even if BDNF says "grow," the cell says "I have no energy to build"
|
||||
|
||||
Hierarchy: Energy reality (fast) > Growth plan (slow)
|
||||
```
|
||||
|
||||
### **Example 2: Ca²⁺ Signaling Hierarchy**
|
||||
|
||||
```
|
||||
Fast event (ms):
|
||||
AP → VGCC open → Ca²⁺ influx → Vesicle release
|
||||
|
||||
Slow adaptation (hr):
|
||||
Gene expression program says "make more VGCCs because activity is high"
|
||||
|
||||
CONSTRAINT:
|
||||
The Ca²⁺ signal that triggers gene expression ITSELF depends on current VGCCs
|
||||
No VGCCs now → No Ca²⁺ signal → No trigger for making more VGCCs
|
||||
|
||||
Hierarchy: Current machinery (fast) > Future machinery planning (slow)
|
||||
```
|
||||
|
||||
### **Example 3: Vesicle Pool Hierarchy**
|
||||
|
||||
```
|
||||
Fast depletion (10-100 ms):
|
||||
High-frequency firing → RRP empties → Release stops
|
||||
|
||||
Slow adaptation (hr):
|
||||
Activity pattern says "we need bigger vesicle pools"
|
||||
|
||||
CONSTRAINT:
|
||||
While pools are being enlarged (slow), release is limited by CURRENT pool size (fast)
|
||||
The system cannot release vesicles that don't exist yet
|
||||
|
||||
Hierarchy: Current supply (fast) > Future supply planning (slow)
|
||||
```
|
||||
|
||||
## **Why This Hierarchy Exists**
|
||||
|
||||
### **Physical Constraints:**
|
||||
|
||||
1. **Causality**: You cannot use tomorrow's proteins today
|
||||
2. **Energy**: Future plans require current energy investment
|
||||
3. **Information**: Slow systems need fast events to provide data
|
||||
4. **Safety**: Fast systems must prevent damage while slow systems adapt
|
||||
|
||||
### **Temporal Asymmetries:**
|
||||
|
||||
```
|
||||
Building (slow) >> Using (fast)
|
||||
Example: It takes hours to make a new VGCC, but milliseconds to use it
|
||||
Therefore: Current usage patterns constrain future building plans
|
||||
```
|
||||
|
||||
## **The Constraint Pyramid**
|
||||
|
||||
```
|
||||
LEVEL 4: DAYS (Architectural planning)
|
||||
"We should redesign the entire synapse structure"
|
||||
↳ Constrained by ↓
|
||||
|
||||
LEVEL 3: HOURS (Construction projects)
|
||||
"Let's build more VGCCs and vesicles"
|
||||
↳ Constrained by ↓
|
||||
|
||||
LEVEL 2: MINUTES (Resource allocation)
|
||||
"We need more ATP and proteins"
|
||||
↳ Constrained by ↓
|
||||
|
||||
LEVEL 1: SECONDS (Immediate operations)
|
||||
"We're depleting ATP and vesicles now!"
|
||||
↳ Constrained by ↓
|
||||
|
||||
GROUND LEVEL: MILLISECONDS (Reality)
|
||||
"Current AP firing requires X ATP, releases Y vesicles"
|
||||
```
|
||||
|
||||
## **How Constraints Propagate Upward**
|
||||
|
||||
### **Constraint Chain: Energy Example**
|
||||
|
||||
```
|
||||
GROUND (ms): AP fires → consumes ATP
|
||||
LEVEL 1 (s): ATP depletes → AMPK activates
|
||||
LEVEL 2 (min): AMPK says "stop non-essential processes"
|
||||
LEVEL 3 (hr): Protein synthesis slows → no new VGCCs
|
||||
LEVEL 4 (days): Structural growth postponed
|
||||
|
||||
Result: Fast energy consumption constrains slow growth
|
||||
```
|
||||
|
||||
### **Constraint Chain: Ca²⁺ Example**
|
||||
|
||||
```
|
||||
GROUND (ms): AP → Ca²⁺ influx → buffers saturate
|
||||
LEVEL 1 (s): Ca²⁺ accumulates → pumps overwhelmed
|
||||
LEVEL 2 (min): High Ca²⁺ → calcineurin activation
|
||||
LEVEL 3 (hr): Calcineurin → NFAT → gene expression changes
|
||||
LEVEL 4 (days): Synaptic scaling adjusts
|
||||
|
||||
Result: Fast Ca²⁺ dynamics constrain slow transcriptional responses
|
||||
```
|
||||
|
||||
## **The Two-Way Street (With Traffic Lights)**
|
||||
|
||||
While fast events constrain slow adaptations, there's also **reverse influence**, but with a **delay**:
|
||||
|
||||
### **Forward Constraint (Fast → Slow):**
|
||||
|
||||
- **Speed**: Immediate
|
||||
- **Strength**: Strong (physical reality)
|
||||
- **Example**: No ATP now → No growth now
|
||||
|
||||
### **Reverse Influence (Slow → Fast):**
|
||||
|
||||
- **Speed**: Delayed (hours to days)
|
||||
- **Strength**: Gradual (changes parameters)
|
||||
- **Example**: BDNF yesterday → More VGCCs today → More Ca²⁺ now
|
||||
|
||||
### **The Asymmetry:**
|
||||
|
||||
```
|
||||
Fast events can VETO slow plans immediately
|
||||
Slow plans can only SUGGEST future fast events
|
||||
```
|
||||
|
||||
## **Implications for the Model**
|
||||
|
||||
### **For Each Release Event:**
|
||||
|
||||
1. **The event occurs** within current constraints (VGCCs available, vesicles primed, ATP present)
|
||||
2. **The event generates signals** (Ca²⁺, glutamate, ATP consumption)
|
||||
3. **These signals constrain** what slow adaptations can occur
|
||||
4. **But they also inform** what slow adaptations should occur
|
||||
|
||||
### **Modeling Rule:**
|
||||
|
||||
When simulating, you must check:
|
||||
|
||||
```
|
||||
IF (slow adaptation requires resource X)
|
||||
THEN (current level of X must support it)
|
||||
ELSE (adaptation delayed until X available)
|
||||
```
|
||||
|
||||
## **Practical Examples in Our Model**
|
||||
|
||||
### **VGCC Expression Increase (Slow) Constrained by:**
|
||||
|
||||
1. **Current VGCC function** (fast): If all VGCCs are internalized, no Ca²⁺ signal to trigger expression
|
||||
2. **ATP availability** (medium): Protein synthesis requires ATP
|
||||
3. **Protein synthesis capacity** (medium): Ribosomes, tRNA availability
|
||||
4. **Trafficking machinery** (medium): Can new VGCCs reach membrane?
|
||||
|
||||
### **RP Pool Expansion (Slow) Constrained by:**
|
||||
|
||||
1. **Current vesicle recycling** (fast): Are vesicles being recycled to feed current demand?
|
||||
2. **Membrane availability** (medium): Adding vesicles requires membrane
|
||||
3. **Neurotransmitter synthesis** (medium): Can we fill new vesicles?
|
||||
4. **Docking site availability** (slow): New vesicles need places to dock
|
||||
|
||||
### **Mitochondrial Biogenesis (Slow) Constrained by:**
|
||||
|
||||
1. **Current ATP/ADP ratio** (fast): Energy status determines if biogenesis can proceed
|
||||
2. **Current mitochondrial function** (medium): Dysfunctional mitochondria can't replicate well
|
||||
3. **Oxidative stress** (medium): ROS can damage mitochondrial DNA
|
||||
4. **Building blocks** (medium): Lipids, proteins for new mitochondria
|
||||
|
||||
## **The "Reality Check" Principle**
|
||||
|
||||
Every slow adaptation plan gets a **reality check** from fast events:
|
||||
|
||||
```
|
||||
Slow plan: "Let's make this synapse stronger!"
|
||||
Reality checks:
|
||||
1. Fast: "Do we have ATP for synthesis?" (energy check)
|
||||
2. Fast: "Is Ca²⁺ signaling intact?" (information check)
|
||||
3. Fast: "Are vesicles being released?" (function check)
|
||||
4. Fast: "Is the terminal healthy?" (safety check)
|
||||
|
||||
Only if all checks pass → Slow plan proceeds
|
||||
```
|
||||
|
||||
## **Why This Design is Optimal**
|
||||
|
||||
### **Biological Wisdom:**
|
||||
|
||||
1. **Prevents overcommitment**: Don't build if you can't maintain
|
||||
2. **Ensures relevance**: Adapt only to real, measured needs
|
||||
3. **Maintains stability**: Fast systems keep things running while slow systems plan
|
||||
4. **Optimizes resources**: Invest only when conditions are right
|
||||
|
||||
### **Evolutionary Advantage:**
|
||||
|
||||
- **Energy efficiency**: Don't waste energy on unnecessary adaptations
|
||||
- **Robustness**: Fast systems handle immediate threats
|
||||
- **Adaptability**: Slow systems can still change things fundamentally
|
||||
- **Balance**: Neither fast nor slow dominates completely
|
||||
|
||||
## **Summary: The Temporal Chain of Command**
|
||||
|
||||
In the presynapse:
|
||||
|
||||
**Fast events (ms-s) are like front-line soldiers:**
|
||||
|
||||
- They face immediate reality
|
||||
- They have limited resources
|
||||
- They must make instant decisions
|
||||
- Their situation dictates what headquarters can plan
|
||||
|
||||
**Slow adaptations (min-days) are like military headquarters:**
|
||||
|
||||
- They make long-term plans
|
||||
- They allocate resources
|
||||
- They build infrastructure
|
||||
- But they can only plan within what front-line reports as possible
|
||||
|
||||
**The hierarchy is:**
|
||||
|
||||
1. **Immediate survival** (fast) comes first
|
||||
2. **Medium-term optimization** comes second
|
||||
3. **Long-term restructuring** comes third
|
||||
|
||||
**But crucially:** Good slow adaptations can improve future fast events, creating a positive upward spiral when conditions allow.
|
||||
|
||||
This is why in our model, we must always ask: **"Given what's happening NOW at millisecond scale, what CAN we change at hour scale?"** The answer is always constrained by current reality.
|
||||
@@ -1,129 +0,0 @@
|
||||
Yes — and this is actually the most important calcium process on the postsynaptic side, because it is the mechanism behind **synaptic plasticity** (LTP and LTD). You are pointing at something that is missing from the current postsynaptic model entirely.
|
||||
|
||||
---
|
||||
|
||||
**What is happening biologically**
|
||||
|
||||
The postsynapse has its own calcium dynamics, completely separate from the presynapse. The key player is the **NMDA receptor** — a special type of glutamate receptor that is both ligand-gated (requires NT to bind) AND voltage-gated (requires the membrane to be depolarised to remove a magnesium block). This dual requirement makes it a **coincidence detector**: it only opens fully when NT arrives AND the postsynaptic membrane is already depolarised.
|
||||
|
||||
The depolarisation can come from two sources:
|
||||
|
||||
**Forward signal** — NT from the presynapse depolarises V_post via AMPA receptors, which then unblocks NMDA receptors and lets Ca²⁺ in.
|
||||
|
||||
**Backpropagating AP (bAP)** — when the postsynaptic neuron fires its own action potential, that signal travels not only forward down the axon but also backward up the dendrites. When this bAP arrives at the synapse at the same time as presynaptic NT, the NMDA receptor sees both conditions simultaneously and opens maximally.
|
||||
|
||||
---
|
||||
|
||||
**The coincidence detection logic**
|
||||
|
||||
```
|
||||
NT arrives (presynapse fires) → AMPA opens → V_post rises
|
||||
bAP arrives (postsynapse fires) → membrane depolarised
|
||||
Both together at the same time → NMDA fully open → Ca2+_post large surge
|
||||
NT alone, no bAP → NMDA partially open → Ca2+_post small
|
||||
bAP alone, no NT → NMDA blocked (no NT) → Ca2+_post minimal
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
**What Ca²⁺ level in the postsynapse controls**
|
||||
|
||||
Postsynaptic Ca²⁺ (`Ca_post`) drives three things depending on its level:
|
||||
|
||||
| Ca_post level | Outcome | Mechanism |
|
||||
|---------------|---------------------|----------------------------------------------------|
|
||||
| low | LTD (weakening) | activates phosphatases that remove AMPA receptors |
|
||||
| medium | no change | neither pathway threshold crossed |
|
||||
| high | LTP (strengthening) | activates kinases (CaMKII) that add AMPA receptors |
|
||||
| very high | eCB synthesis | triggers retrograde suppression of presynapse |
|
||||
|
||||
The current model already has the eCB branch (very high Ca_post → eCB). What is missing is the Ca_post variable itself and the LTP/LTD branches.
|
||||
|
||||
---
|
||||
|
||||
**Proposed variables to add**
|
||||
|
||||
```python
|
||||
# -----------------------------------------------------------------------
|
||||
# POSTSYNAPTIC Ca2+ DYNAMICS
|
||||
# -----------------------------------------------------------------------
|
||||
|
||||
# -- NMDA receptor --
|
||||
k_NMDA_bind = 0.03 # /ms - NMDA conductance per unit NT when unblocked
|
||||
Mg_block = 1.0 # magnesium block factor (0=fully blocked, 1=fully open)
|
||||
# removed by V_post depolarisation and bAP
|
||||
V_NMDA_threshold = 0.3 # V_post level at which Mg block begins to lift
|
||||
# below this NMDA is nearly fully blocked
|
||||
|
||||
# -- bAP --
|
||||
bAP_active = False # flag: postsynaptic neuron has fired (set externally)
|
||||
bAP_amplitude = 1.0 # normalised bAP depolarisation contribution
|
||||
tau_bAP = 3.0 # ms - bAP decay time constant at the synapse
|
||||
# bAP attenuates as it travels up the dendrite
|
||||
bAP_state = 0.0 # continuous bAP depolarisation (mirrors V_pre_state)
|
||||
|
||||
# -- Postsynaptic Ca2+ --
|
||||
Ca_post = 0.0 # free Ca2+ in postsynaptic spine
|
||||
# driven by NMDA opening and bAP
|
||||
k_Ca_post_decay = 0.05 # /ms - Ca_post clearance rate
|
||||
# postsynapse has its own pumps (PMCA, NCX equivalents)
|
||||
|
||||
# -- Plasticity thresholds --
|
||||
Ca_post_LTD = 0.3 # Ca_post below this → LTD if sustained
|
||||
Ca_post_LTP = 0.7 # Ca_post above this → LTP if sustained
|
||||
Ca_post_eCB = 0.9 # Ca_post above this → eCB synthesis
|
||||
|
||||
# -- Plasticity state --
|
||||
AMPA_density = 1.0 # normalised AMPA receptor density (0 -> 2)
|
||||
# LTP increases this, LTD decreases it
|
||||
# feeds back into receptor_conductance
|
||||
tau_plasticity = 30_000.0 # ms - plasticity integration window (~30 s)
|
||||
Ca_post_trace = 0.0 # slow integrator of Ca_post, drives plasticity
|
||||
# analogous to Tr_Ca on the presynaptic side
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
**Proposed behaviors**
|
||||
|
||||
```
|
||||
— ms (postsynapse, additions):
|
||||
|
||||
- bAP arrives → bAP_state jumps to bAP_amplitude, decays with tau_bAP
|
||||
(mirrors V_pre_state / V_pre_peak on the presynaptic side)
|
||||
|
||||
- Mg block removal: Mg_block = f(V_post + bAP_state)
|
||||
low voltage → Mg_block ≈ 1 (fully blocked, no Ca2+ entry)
|
||||
high voltage → Mg_block ≈ 0 (fully open, maximal Ca2+ entry)
|
||||
|
||||
- NMDA conductance: NMDA_conductance = k_NMDA_bind * NT_cleft * (1 - Mg_block)
|
||||
requires BOTH NT (ligand gate) AND depolarisation (voltage gate)
|
||||
this is the coincidence detection step
|
||||
|
||||
- Ca_post rises with NMDA_conductance each ms
|
||||
- Ca_post decays with k_Ca_post_decay each ms (postsynaptic pumps)
|
||||
|
||||
- Ca_post_trace integrates Ca_post (slow, analogous to Tr_Ca)
|
||||
|
||||
— seconds (postsynapse, additions):
|
||||
|
||||
- eCB synthesis now driven by Ca_post_trace > Ca_post_eCB
|
||||
(replaces V_post_history as the eCB trigger — more accurate biologically
|
||||
because it is Ca2+ in the spine that actually synthesises eCB,
|
||||
not voltage per se)
|
||||
|
||||
— mins (postsynapse, additions):
|
||||
|
||||
- if Ca_post_trace sustained below Ca_post_LTD → AMPA_density decreases (LTD)
|
||||
- if Ca_post_trace sustained above Ca_post_LTP → AMPA_density increases (LTP)
|
||||
- AMPA_density feeds back into receptor_conductance ceiling:
|
||||
effective receptor_conductance max = N_receptors * AMPA_density
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
**Why this closes an important loop**
|
||||
|
||||
Without postsynaptic Ca²⁺ the model has no plasticity — the synapse behaves identically after 10 minutes of activity as it did at the start. Adding `Ca_post` with the coincidence detection logic means the synapse now has a **history** in the biological sense: repeated co-activation of pre and post strengthens it (LTP), one-sided activity weakens it (LTD). This is the postsynaptic equivalent of the presynaptic metabolic cascade — a slow, activity-dependent recalibration of the synapse's operating point, but driven by learning rather than protection.
|
||||
|
||||
The bAP is also what makes the eCB synthesis biologically accurate. Currently eCB is triggered by V_post (voltage). But the actual synthesis of endocannabinoids in the spine is triggered by high Ca²⁺ in the spine, which requires NMDA opening, which requires coincidence. So by adding `Ca_post`, the eCB trigger becomes mechanistically correct: it is not just "the postsynapse is depolarised" but "the postsynapse is receiving coordinated pre and post activity", which is a much more specific and meaningful signal for the presynapse to receive.
|
||||
@@ -1,486 +0,0 @@
|
||||
---
|
||||
|
||||
**What needs adjustment**
|
||||
|
||||
`Voltage-Context` is labelled as an Episode but contains sub-episodes — it should be a Context. Same for `NMDA-Coincidence` and `Ca-Dynamics & ATP-Drain`. You have used Episode and Context interchangeably in a few places; the distinction matters for the specification: a Context sets the conditions, an Episode is a named outcome within those conditions.
|
||||
|
||||
`Vpost_Maximum` lists `V_bAP full OR (g_AMPA full AND V_bAP medium)` — this is correct Boolean logic and should be kept exactly as written. It captures the two ways the postsynapse can reach maximum depolarisation: the bAP alone if it is strong enough, or AMPA plus a partial bAP together.
|
||||
|
||||
`AMPA_Population_Increase` correctly gates on `ATP_level_post NOT empty` — LTP requires ATP for CaMKII phosphorylation and receptor trafficking. LTD does not have the same gate in your spec. This is slightly asymmetric — LTD (receptor internalisation via endocytosis) is also ATP-dependent, though less so than LTP. Worth noting.
|
||||
|
||||
`Plasticity_LTD` covers `Ca_post_history medium` but does not cover the case where `Ca_post_history` is empty — a completely silent synapse also weakens over time (homeostatic depression). This can be left as a gap or named explicitly.
|
||||
|
||||
`Astrocyte_Supply_Crises` has a typo (Crises → Crisis).
|
||||
|
||||
The bAP needs new parameters and state variables in the model before it can be expressed as a fully implemented behavior. I will add those inline as `[GAP — to implement]` markers so the spec is complete even where the code is not yet written.
|
||||
|
||||
---
|
||||
|
||||
**Final restructured specification**
|
||||
|
||||
```
|
||||
BEH-POST-UNIFIED: The Integrated Postsynaptic Model
|
||||
=====================================================
|
||||
Three loops, three timescales, one shared astrocyte supply.
|
||||
Each loop feeds the next: V_post enables NMDA, NMDA drives
|
||||
Ca_post, Ca_post determines plasticity and eCB, ATP sustains
|
||||
all three. Failure of ATP does not silence the postsynapse
|
||||
(unlike the presynapse) — it corrupts it, triggering false
|
||||
retrograde signals and risking excitotoxic Ca2+ accumulation.
|
||||
|
||||
Variables:
|
||||
V_bAP — back-propagating AP amplitude (0→1)
|
||||
[GAP — requires bAP_train input,
|
||||
analogous to presynaptic spike_train]
|
||||
g_AMPA — AMPA receptor conductance (= receptor_conductance)
|
||||
V_post — total postsynaptic membrane potential (0→1)
|
||||
NT_cleft — glutamate in cleft (from presynapse)
|
||||
Desensitization — fraction of AMPA receptors desensitized (0→1)
|
||||
Ca_post — free Ca2+ in postsynaptic spine (0→...)
|
||||
Ca_post_history — 2 s rolling mean of Ca_post
|
||||
ATP_level_post — normalised postsynaptic ATP (0→1)
|
||||
ATP_demand_post — accumulated ATP cost since last metabolic cycle
|
||||
g_AMPA_baseline — long-term AMPA receptor density set by plasticity
|
||||
[GAP — not yet in model; LTP/LTD would write this]
|
||||
eCB_level — endocannabinoid retrograde signal (0→1)
|
||||
written here, read by presynapse Loop 1
|
||||
|
||||
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
|
||||
ms: behaviors — Fast Kinetics and Gate Logic
|
||||
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
|
||||
|
||||
Voltage-Context: Context
|
||||
Determines the total depolarisation (V_post) available to
|
||||
lift the NMDA Mg block. Two independent sources contribute:
|
||||
AMPA-driven local depolarisation (g_AMPA) and the somatic
|
||||
back-propagating AP (V_bAP). Either alone can partially
|
||||
depolarise; both together reach maximum.
|
||||
|
||||
Vpost_Maximum: Episode
|
||||
— V_bAP full OR
|
||||
— g_AMPA full AND V_bAP medium
|
||||
— Result: V_post high enough for complete Mg block removal.
|
||||
NMDA gate can open fully.
|
||||
Both ATP costs charged at maximum rate.
|
||||
|
||||
Vpost_Attenuated: Episode
|
||||
— g_AMPA medium AND V_bAP empty/low OR
|
||||
— g_AMPA low AND V_bAP medium
|
||||
— Result: V_post sub-threshold.
|
||||
Mg block partially remains.
|
||||
NMDA gate opens partially or not at all.
|
||||
This is the most common state during low-rate firing
|
||||
without a coincident bAP.
|
||||
|
||||
Vpost_Passive: Episode
|
||||
— g_AMPA empty AND V_bAP empty
|
||||
— Result: V_post at rest.
|
||||
Mg block fully intact.
|
||||
No Ca_post entry possible.
|
||||
Na/K-ATPase cost minimal.
|
||||
|
||||
Desensitization-Context: Context
|
||||
Modulates g_AMPA independently of NT_cleft.
|
||||
Sustained NT exposure drives receptors into a closed state
|
||||
that persists even when NT remains present.
|
||||
|
||||
DesensitizationRising: Episode
|
||||
— NT_cleft sustained high (multiple consecutive ms)
|
||||
— Desensitization rises each ms
|
||||
— g_AMPA effectively reduced despite NT presence
|
||||
— attenuates Vpost_Maximum toward Vpost_Attenuated
|
||||
|
||||
DesensitizationRecovering: Episode
|
||||
— NT_cleft low or empty
|
||||
— Desensitization decays with tau_desensitization = 500 ms
|
||||
— g_AMPA ceiling restored gradually
|
||||
|
||||
NMDA-Coincidence: Context
|
||||
Strict AND gate: both NT (ligand) and V_post (voltage) must
|
||||
be simultaneously non-zero for Ca_post to rise.
|
||||
Unlike presynaptic VGCCs which open with any spike, NMDA
|
||||
requires coincidence. This makes Ca_post a detector of
|
||||
coordinated pre+post activity, not just input rate.
|
||||
|
||||
NMDA_Open: Episode
|
||||
— NT_cleft full AND V_post maximum (Vpost_Maximum active)
|
||||
— Mg block fully lifted
|
||||
— Ca_post surges — LTP territory
|
||||
— ATP_demand_post rises sharply (PMCA must clear Ca_post)
|
||||
— if sustained → Ca_post_history crosses eCB threshold
|
||||
|
||||
NMDA_LogicBlocked: Episode
|
||||
— NT_cleft full BUT V_post attenuated or passive
|
||||
— Mg block partially or fully intact
|
||||
— Ca_post does not rise despite NT presence
|
||||
— Result: presynapse fired but postsynapse was not ready
|
||||
No plasticity signal generated
|
||||
This is the mechanism for input selectivity:
|
||||
only synapses active during postsynaptic firing
|
||||
produce a Ca_post signal
|
||||
|
||||
NMDA_LigandBlocked: Episode
|
||||
— V_post maximum BUT NT_cleft empty
|
||||
— No glutamate to open the channel
|
||||
— Ca_post entry zero despite full depolarisation
|
||||
— Result: bAP arrived but presynapse was silent
|
||||
Again no plasticity signal
|
||||
The AND logic enforces true coincidence
|
||||
|
||||
Ca-Dynamics-Context: Context
|
||||
Ca_post clearance rate depends entirely on ATP_level_post.
|
||||
This is the bridge from the ATP loop into the Ca2+ loop.
|
||||
When ATP fails, Ca_post clearance fails, and the Ca2+ loop
|
||||
becomes corrupted — Ca_post reflects pump state rather
|
||||
than genuine coincidence events.
|
||||
|
||||
Clearance_Optimal: Episode
|
||||
— ATP_level_post full → pump_scale_post near 1
|
||||
— PMCA (ATP-gated) + NCX (always on) both clearing
|
||||
— Ca_post returns to baseline between events
|
||||
— Each coincidence event is temporally isolated
|
||||
— ATP_demand_post increases proportionally to Ca_post load
|
||||
|
||||
Clearance_Reduced: Episode
|
||||
— ATP_level_post medium → pump_scale_post reduced
|
||||
— Ca_post clears more slowly
|
||||
— Residual elevation begins accumulating between events
|
||||
— Ca_post_history starts drifting upward
|
||||
— eCB threshold may be approached during heavy firing
|
||||
|
||||
Clearance_Failing: Episode
|
||||
— ATP_level_post low or empty → pump_scale_post near 0
|
||||
— Only NCX clearing (floor, not rescue)
|
||||
— Ca_post accumulates regardless of coincidence activity
|
||||
— False Trigger conditions: Ca_post_history crosses eCB
|
||||
threshold without genuine NMDA overactivity
|
||||
— Excitotoxicity risk if Ca_post elevation is sustained
|
||||
|
||||
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
|
||||
sec: behaviors — Signal Integration and Fate
|
||||
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
|
||||
|
||||
Synaptic-Weight-Decision: Context
|
||||
Ca_post_history (2 s rolling mean of Ca_post) determines
|
||||
the plasticity signal. The threshold logic is graded:
|
||||
the same variable produces opposite outcomes depending
|
||||
on whether it is above or below the LTP/LTD boundary.
|
||||
ATP_level_post gates LTP expression but not LTD —
|
||||
strengthening requires energy, weakening does not.
|
||||
|
||||
Plasticity_LTP: Episode
|
||||
— Ca_post_history full (above Ca_post_LTP threshold)
|
||||
— High-frequency or high-amplitude coincidence detected
|
||||
— Tags synapse for AMPA receptor insertion
|
||||
— Requires ATP_level_post NOT empty for expression
|
||||
(CaMKII phosphorylation and receptor trafficking are
|
||||
ATP-dependent — energy failure blocks LTP even if
|
||||
the Ca_post signal is correct)
|
||||
— [GAP] LTP expression writes g_AMPA_baseline upward
|
||||
in the minutes loop
|
||||
|
||||
Plasticity_Boundary: Episode
|
||||
— Ca_post_history medium
|
||||
— Poorly timed or low-frequency coincidence
|
||||
— Neither LTP nor LTD threshold crossed
|
||||
— Synapse weight unchanged this cycle
|
||||
|
||||
Plasticity_LTD: Episode
|
||||
— Ca_post_history low but non-zero
|
||||
— Weak or mistimed coincidence — presynapse fired
|
||||
but postsynapse was not sufficiently depolarised
|
||||
— Tags synapse for AMPA receptor removal
|
||||
— Less ATP-dependent than LTP; can proceed under
|
||||
mild energy stress
|
||||
— [GAP] LTD expression writes g_AMPA_baseline downward
|
||||
in the minutes loop
|
||||
|
||||
Plasticity_Silent: Episode
|
||||
— Ca_post_history empty (prolonged absence of activity)
|
||||
— Homeostatic depression: unused synapses weaken
|
||||
— [GAP] not yet modelled; would require Ca_post_trace
|
||||
integration over hours
|
||||
|
||||
Retrograde-Feedback: Context
|
||||
eCB synthesis is triggered by Ca_post_history, not V_post.
|
||||
It is Ca2+ in the spine — not voltage — that activates the
|
||||
enzymes (DAGL, PLC) that produce endocannabinoids.
|
||||
The model cannot distinguish internally between the two
|
||||
causes of elevated Ca_post_history (genuine vs pump failure)
|
||||
but the consequences differ: one is communication,
|
||||
the other is survival.
|
||||
|
||||
eCB_Synthesis_Active: Episode
|
||||
— Ca_post_history > eCB_threshold (0.7)
|
||||
|
||||
— Logic A (Genuine Protection):
|
||||
Cause : sustained NMDA_Open events — real overactivity
|
||||
Effect : appropriate retrograde stop signal
|
||||
Outcome : presynapse reduces NT → NT_cleft falls →
|
||||
NMDA closes → Ca_post load drops →
|
||||
Ca_post_history falls → eCB synthesis subsides
|
||||
Loop closes correctly
|
||||
|
||||
— Logic B (False Trigger — Excitotoxic Protection):
|
||||
Cause : Clearance_Failing — Ca_post elevated by
|
||||
pump failure, not genuine coincidence
|
||||
Effect : presynapse silenced without real overactivity
|
||||
Outcome : NT_cleft falls → NMDA closes → Ca_post
|
||||
load drops → ATP_demand_post falls →
|
||||
ATP_level_post recovers → pumps restart →
|
||||
Ca_post clears → Ca_post_history falls →
|
||||
eCB synthesis subsides
|
||||
Desperate survival loop — buys time for
|
||||
metabolic recovery
|
||||
|
||||
eCB_Synthesis_Idle: Episode
|
||||
— Ca_post_history < eCB_threshold
|
||||
— eCB_level decays with tau_eCB_decay = 10000 ms
|
||||
— Presynaptic suppression lifts gradually
|
||||
— 10 s decay means suppression outlasts the trigger —
|
||||
prevents immediate re-engagement before Ca_post
|
||||
has stabilised
|
||||
|
||||
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
|
||||
min: behaviors — Bioenergetics and Structural Change
|
||||
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
|
||||
|
||||
Metabolic-Recovery: Context
|
||||
ATP_level_post is computed from Glucose_level (shared
|
||||
supply) minus ATP_demand_post (postsynaptic-specific cost).
|
||||
The shared supply creates the coupling: both pre and post
|
||||
deplete the same astrocyte glucose budget simultaneously.
|
||||
Presynaptic silence is therefore metabolically beneficial
|
||||
to the postsynapse — less NT means less NMDA activation
|
||||
means less Ca_post means less PMCA cost.
|
||||
|
||||
Astrocyte_Supply_Active: Episode
|
||||
— Glucose_level full
|
||||
— ATP_demand_post within supply capacity
|
||||
— ATP_level_post replenished each cycle
|
||||
— All three loops operating normally
|
||||
|
||||
Astrocyte_Supply_Stressed: Episode
|
||||
— Glucose_level medium OR ATP_demand_post elevated
|
||||
— ATP_level_post partially reduced
|
||||
— Clearance_Reduced begins
|
||||
— Plasticity_LTP at risk (ATP dependency)
|
||||
|
||||
Astrocyte_Supply_Crisis: Episode
|
||||
— Glucose_level low OR ATP_demand_post chronically high
|
||||
— ATP_level_post near empty
|
||||
— Clearance_Failing — only NCX clearing Ca_post
|
||||
— False Trigger likely → eCB_Synthesis_Active (Logic B)
|
||||
— Presynaptic silence indirectly reduces postsynaptic
|
||||
ATP demand — the coupled protection mechanism
|
||||
|
||||
Structural-Update: Context
|
||||
Long-term changes to AMPA receptor density.
|
||||
These are the physical substrate of learning and memory.
|
||||
[GAP] g_AMPA_baseline not yet implemented in the model.
|
||||
Would be written in Loop 3 and read by Loop 1 as the
|
||||
ceiling of receptor_conductance.
|
||||
|
||||
AMPA_Population_Increase: Episode
|
||||
— Triggered by Plasticity_LTP
|
||||
— AND ATP_level_post NOT empty
|
||||
— g_AMPA_baseline shifts higher for next cycle
|
||||
— More AMPA receptors → stronger Vpost_Maximum
|
||||
— Easier to reach NMDA_Open in future events
|
||||
— Positive feedback: LTP makes future LTP more likely
|
||||
|
||||
AMPA_Population_Decrease: Episode
|
||||
— Triggered by Plasticity_LTD or Plasticity_Silent
|
||||
— g_AMPA_baseline shifts lower
|
||||
— Fewer AMPA receptors → Vpost_Attenuated more common
|
||||
— Harder to reach NMDA_Open → weakens synapse further
|
||||
— Negative feedback: LTD stabilises by reducing
|
||||
future coincidence probability
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
---
|
||||
|
||||
## short term
|
||||
|
||||
Short-term potentiation (STP) and short-term depression (STD) are distinct from LTP/LTD in a fundamental way: they are **temporary** changes that last seconds to minutes and leave no lasting structural trace. They do not require the postsynapse at all — they are entirely presynaptic phenomena in most cases, and they operate on a completely different mechanism.
|
||||
|
||||
---
|
||||
|
||||
**What they are and where they live**
|
||||
|
||||
Short-term plasticity is driven by the **history of presynaptic Ca²⁺** and **vesicle pool state**, not by postsynaptic coincidence detection. The table we just built describes long-term plasticity — structural changes to AMPA density driven by Ca_post. Short-term plasticity describes transient changes to **how much NT the presynapse releases** on the next spike, driven by what happened on the last few spikes.
|
||||
|
||||
There are two opposing forms:
|
||||
|
||||
**Short-term potentiation / facilitation** — if a spike arrives shortly after the previous one, residual Ca²⁺ from the first spike has not fully cleared. The next spike adds to this residual, producing a larger Ca_post microdomain and therefore a higher release probability. The synapse releases more NT on the second spike than the first. This is already partially captured in the presynaptic model through `Tr_Ca` — elevated calcium trace from recent activity speeds up RRP recruitment and effectively increases release efficiency.
|
||||
|
||||
**Short-term depression** — if spikes arrive rapidly, the RRP depletes faster than it can be refilled. Each successive spike releases fewer vesicles because there are fewer available. NT release drops with each spike in a burst. This is already the core of CASCADE 1 in the presynaptic model — RRP depletion under high firing rate.
|
||||
|
||||
---
|
||||
|
||||
**Where they fit in the model**
|
||||
|
||||
Both are already implicitly present in the presynaptic ms and seconds loops:
|
||||
|
||||
```
|
||||
Short-term facilitation:
|
||||
Residual Ca_micro from spike N
|
||||
→ elevated Ca_micro at spike N+1
|
||||
→ higher release fraction in deterministic_release (Hill curve)
|
||||
→ more NT per spike
|
||||
→ decays as Ca_micro clears between spikes (tau ~100-200 ms)
|
||||
|
||||
Short-term depression:
|
||||
Rapid firing depletes N_RRP
|
||||
→ fewer vesicles available per spike
|
||||
→ released_NT falls
|
||||
→ recovers as RP→RRP recruitment refills (seconds timescale)
|
||||
```
|
||||
|
||||
The timescale of each depends on parameters already in the model:
|
||||
|
||||
| Form | Timescale | Driven by | Recovery |
|
||||
|--------------|------------|-------------------|-------------------------|
|
||||
| Facilitation | 100-500 ms | residual Ca_micro | Ca²⁺ clearance rate |
|
||||
| Depression | seconds | RRP depletion | RP→RRP recruitment rate |
|
||||
|
||||
---
|
||||
|
||||
**What is missing from the current model**
|
||||
|
||||
The model captures both implicitly but does not name them as behaviours. Two things are genuinely absent:
|
||||
|
||||
**Augmentation** — a slower form of facilitation lasting 5-10 seconds, driven by residual Ca²⁺ accumulating in the presynaptic terminal across many spikes. It is distinct from spike-by-spike facilitation and would require a second, slower Ca²⁺ trace with `tau ~5000 ms`. The current `Tr_Ca` with `tau = 1000 ms` is between the two — it captures some augmentation but not cleanly.
|
||||
|
||||
**Post-tetanic potentiation (PTP)** — an even slower presynaptic enhancement lasting minutes after a high-frequency burst, driven by protein kinase C activation from sustained Ca²⁺ elevation. This is a presynaptic phenomenon that looks like LTP from the outside but has no postsynaptic component and no structural change. It would require a third, very slow trace variable.
|
||||
|
||||
---
|
||||
|
||||
**How they interact with the LTP/LTD table**
|
||||
|
||||
Short-term and long-term plasticity operate on the same synapse simultaneously but independently:
|
||||
|
||||
```
|
||||
Spike arrives
|
||||
→ short-term: how much NT releases THIS spike (presynaptic, ms-seconds)
|
||||
→ long-term: does the synapse get stronger or weaker PERMANENTLY (postsynaptic, mins-hours)
|
||||
```
|
||||
|
||||
A synapse can be undergoing LTD (slowly losing AMPA receptors over minutes) at the same time as it is showing short-term facilitation (releasing more NT per spike due to residual Ca²⁺). The two processes do not interfere — they act on different variables through different mechanisms.
|
||||
|
||||
The important implication for your model is that **the LTP/LTD table we built describes what happens to** `g_AMPA_baseline` **over minutes**. Short-term potentiation/depression describes what happens to `released_NT` over milliseconds to seconds. They are different outputs of the same synapse, running in parallel.
|
||||
|
||||
If you want to add short-term plasticity explicitly to the behaviour specification it would live entirely in the presynaptic ms and seconds loops as named episodes of existing variables:
|
||||
|
||||
```
|
||||
— ms (presynapse, short-term plasticity):
|
||||
|
||||
ShortTermFacilitation: Episode
|
||||
— residual Ca_micro > 0 at next spike arrival
|
||||
— release_frac in deterministic_release elevated above baseline
|
||||
— decays as Ca_micro clears (tau ~100-500 ms)
|
||||
— more NT per spike than at rest
|
||||
|
||||
ShortTermDepression: Episode
|
||||
— N_RRP depleted by rapid successive spikes
|
||||
— release_frac unchanged but N_RRP reduced
|
||||
— fewer absolute vesicles released per spike
|
||||
— recovers via RP→RRP recruitment (seconds)
|
||||
|
||||
— seconds (presynapse, short-term plasticity):
|
||||
|
||||
Augmentation: Episode [GAP — not yet modelled]
|
||||
— requires second slow Ca2+ trace (tau ~5000 ms)
|
||||
— elevated release probability for 5-10 s after burst
|
||||
— distinct from spike-by-spike facilitation
|
||||
|
||||
PostTetanicPotentiation: Episode [GAP — not yet modelled]
|
||||
— requires very slow trace (tau ~minutes)
|
||||
— elevated release probability for minutes after tetanus
|
||||
— presynaptic only, no postsynaptic component
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## Signal traveling to the dendrite and soma
|
||||
|
||||
This is one of the most important questions in neuroscience and it reveals a gap in the current model — the postsynapse as we have described it is a single compartment, but the real postsynapse is embedded in a spatial structure where location matters enormously.
|
||||
|
||||
---
|
||||
|
||||
**The physical structure**
|
||||
|
||||
The postsynapse sits at the tip of a **dendritic spine** — a tiny mushroom-shaped protrusion, roughly 1 µm across, that branches off the main dendrite shaft. The spine is connected to the dendrite by a narrow neck, which acts as both a diffusion barrier and an electrical resistor. The spine is not just a passive receptor — it is a semi-isolated compartment with its own calcium dynamics, its own molecular machinery, and its own local membrane potential that can differ from the dendrite by tens of millivolts.
|
||||
|
||||
From spine to soma the signal travels through three successive stages, each with its own physics:
|
||||
|
||||
---
|
||||
|
||||
**Stage 1 — Spine to dendrite shaft (µm, microseconds to milliseconds)**
|
||||
|
||||
After Ca²⁺ enters through NMDA, two things happen simultaneously in the spine.
|
||||
|
||||
The **electrical signal** — the change in V_post from AMPA and NMDA currents — spreads electrotonically from the spine head through the spine neck into the dendrite shaft. This is a passive electrical process governed by cable theory: the spine neck has resistance, which causes voltage attenuation. A strong EPSP in the spine arrives at the dendrite shaft as a smaller depolarisation. The narrower and longer the neck, the more attenuation.
|
||||
|
||||
The **chemical signal** — Ca²⁺ itself — diffuses much more slowly and is largely trapped in the spine by the neck geometry and by the calcium buffers and pumps in the spine head. This is deliberate: it means each spine is a private calcium compartment. What happens in one spine does not directly raise Ca²⁺ in the neighbouring spine. This compartmentalisation is what makes synapse-specific plasticity possible — only the spine that received the coincident signal gets potentiated, not all spines on the same dendrite.
|
||||
|
||||
---
|
||||
|
||||
**Stage 2 — Dendrite shaft to soma (µm to mm, milliseconds)**
|
||||
|
||||
Once the electrical signal enters the dendrite shaft it travels toward the soma as a graded potential — not an action potential, just a spreading wave of depolarisation that decays with distance and time. The key variables are the **length constant** (how far the signal travels before decaying to 1/e of its original amplitude, typically 100-500 µm in dendrites) and the **time constant** (how long the signal lasts, typically 10-50 ms).
|
||||
|
||||
Dendrites are not passive cables. They contain their own voltage-gated channels — including NMDA receptors on the dendritic shaft, voltage-gated Na⁺ and Ca²⁺ channels, and K⁺ channels that actively shape the signal as it travels. In some neurons, particularly pyramidal cells, a strong enough EPSP can trigger a **dendritic spike** — a locally regenerative event that amplifies the signal and ensures it reaches the soma with enough strength to trigger firing. Dendritic spikes are essentially local action potentials in the dendrite, and they are one of the mechanisms that give individual dendrites computational properties beyond simple summation.
|
||||
|
||||
Multiple EPSPs arriving at different spines within a short time window sum together in the dendrite shaft. If they arrive close enough in space and time, their summed depolarisation exceeds threshold at the soma. This spatial and temporal summation is how the neuron integrates thousands of inputs simultaneously.
|
||||
|
||||
---
|
||||
|
||||
**Stage 3 — Soma integration and axon hillock (point decision, milliseconds)**
|
||||
|
||||
The soma collects all the dendritic inputs and performs a threshold comparison. The axon hillock — the junction between the soma and the axon — has the highest density of voltage-gated Na⁺ channels in the neuron and the lowest threshold for firing. When the summed depolarisation at the axon hillock crosses roughly -55 mV (from a resting potential of about -70 mV), an action potential is triggered. This AP then propagates forward down the axon and simultaneously backward up the dendrites as the bAP.
|
||||
|
||||
---
|
||||
|
||||
**What this means for the model**
|
||||
|
||||
The current model has no spatial structure. V_post is a single number representing the entire postsynaptic compartment — there is no distinction between spine voltage, dendritic shaft voltage, and somatic voltage. The bAP is treated as an external input rather than the consequence of somatic threshold crossing fed back to the dendrite.
|
||||
|
||||
The missing components that would be needed for a spatially accurate model are:
|
||||
|
||||
```
|
||||
Spine compartment:
|
||||
V_spine — local membrane potential at the spine head
|
||||
Ca_post — spine calcium (already modelled)
|
||||
spine_neck_resistance — attenuation from spine to dendrite
|
||||
|
||||
Dendrite compartment:
|
||||
V_dendrite — shaft potential (sum of attenuated spine EPSPs)
|
||||
length_constant — spatial decay of signal along shaft
|
||||
dendritic_spike_threshold — if V_dendrite crosses this,
|
||||
local regenerative event
|
||||
|
||||
Soma compartment:
|
||||
V_soma — integrated input from all dendrites
|
||||
AP_threshold — typically ~15 mV above rest
|
||||
fired — boolean, triggers bAP_train for next cycle
|
||||
```
|
||||
|
||||
The bAP then becomes an output of the soma rather than an independent input:
|
||||
|
||||
```
|
||||
if V_soma > AP_threshold:
|
||||
fired = True
|
||||
bAP_train.append(current_step) # feeds back to spine
|
||||
V_soma resets via Na/K-ATPase
|
||||
```
|
||||
|
||||
This closes the loop properly: the spine signal travels up, the soma decides whether to fire, and the firing decision travels back down as the bAP that enables NMDA coincidence detection at the very spine that contributed to triggering the somatic AP. The synapse is strengthened only if its contribution was part of what caused the neuron to fire — which is the biological definition of Hebbian learning expressed as a physical circuit.
|
||||
|
||||
---
|
||||
|
||||
**Why the spine neck is biologically critical**
|
||||
|
||||
The spine neck geometry is not fixed — it changes with activity. During LTP, the neck widens and shortens, reducing attenuation and making the spine electrically closer to the dendrite. During LTD, the neck narrows and the spine may retract entirely. This means the structural change of plasticity is not just the number of AMPA receptors — it is also the geometry of the spine itself, which changes how well future signals from that spine will reach the soma. Potentiation makes potentiation more likely not just through more AMPA but through better electrical coupling. This is a physical feedback loop operating at the structural level, on timescales of minutes to hours, that is entirely absent from computational models of this type and may be one of the things that cannot be captured by any purely computational description.
|
||||
@@ -1,97 +0,0 @@
|
||||
Looking at what we have just specified, the postsynapse also has three loops — but they are organised around different problems than the presynapse.
|
||||
|
||||
---
|
||||
|
||||
**The NT detection loop**
|
||||
|
||||
This is the direct counterpart of the presynaptic NT loop, but from the receiving side. NT arrives in the cleft, binds AMPA receptors, generates V_post, and V_post drives the postsynaptic response. The loop closes through desensitization: sustained NT exposure progressively silences the receptors, reducing the response to further NT even while it is still present. When NT clears (presynapse goes quiet), desensitization recovers and receptors become available again. The timescale is milliseconds to seconds — fast enough to track individual spikes, slow enough to integrate burst activity. This loop is entirely local to the postsynapse and requires no signal from outside except NT_cleft.
|
||||
|
||||
---
|
||||
|
||||
**The Ca²⁺ coincidence loop**
|
||||
|
||||
This is the postsynaptic equivalent of the presynaptic Ca²⁺ loop, but with a fundamentally different trigger. Presynaptic Ca²⁺ enters whenever VGCCs open — which happens on every AP. Postsynaptic Ca²⁺ enters through NMDA receptors only when two conditions are simultaneously true: NT is present in the cleft (presynapse just fired) AND the membrane is depolarised (either from accumulated AMPA activation or from a backpropagating AP). This dual requirement makes Ca_post a detector of coordinated activity rather than just a measure of input rate. The loop closes through the Ca_post trace: sustained high Ca_post potentiates the synapse (LTP, more AMPA receptors), sustained low Ca_post depresses it (LTD, fewer AMPA receptors), and the changed receptor density feeds back into how strongly the next NT release activates V_post. The timescale spans milliseconds (NMDA opening) to minutes (plasticity expression).
|
||||
|
||||
---
|
||||
|
||||
**The retrograde signalling loop**
|
||||
|
||||
This loop has no presynaptic equivalent — it is unique to the postsynapse because it is the only signal that crosses back from post to pre. When Ca_post rises above the eCB threshold (sustained coincident activity), the postsynapse synthesises endocannabinoids and releases them retrogradely. eCB travels back across the cleft and suppresses presynaptic VGCC conductance, reducing Ca²⁺ influx and therefore NT release. The loop closes when reduced NT release lowers Ca_post, which eventually reduces eCB synthesis, allowing the presynaptic brake to lift. The timescale is seconds to tens of seconds — slower than the NT detection loop, faster than plasticity. This is the loop that connects the two sides of the synapse and makes the tripartite system a genuine closed system rather than two independent models running in parallel.
|
||||
|
||||
---
|
||||
|
||||
**How the three postsynaptic loops relate to the three presynaptic loops**
|
||||
|
||||
| Presynaptic | Postsynaptic | Shared variable |
|
||||
|-------------|----------------------------|----------------------|
|
||||
| NT loop | NT detection loop | NT_cleft |
|
||||
| Ca²⁺ loop | Ca²⁺ coincidence loop | — (independent Ca²⁺) |
|
||||
| ATP loop | retrograde signalling loop | eCB_level |
|
||||
|
||||
The NT loop pair is the primary communication channel — pre releases, post detects. The Ca²⁺ loops are parallel but independent — each side manages its own calcium for its own purposes. The ATP/retrograde pair is the feedback channel — post reports back to pre when activity is excessive. Together the six loops form the complete tripartite system, with the cleft and the eCB signal as the two bridges between the two neurons.
|
||||
|
||||
---
|
||||
|
||||
Yes — and in ways that are structurally similar to the presynapse but with different priorities.
|
||||
|
||||
---
|
||||
|
||||
**Where ATP is consumed in the postsynapse**
|
||||
|
||||
**Na/K-ATPase recharge** is the same dominant cost as in the presynapse. Every postsynaptic potential — every time V_post rises — ion gradients are disturbed and the Na/K-ATPase must restore them. At high firing rates this is the largest ATP drain, identical in mechanism to the presynaptic side.
|
||||
|
||||
**Ca²⁺ clearance from the spine** is the direct equivalent of PMCA and SERCA in the presynapse. After NMDA-driven Ca_post rises, the spine must pump Ca²⁺ back out. The postsynaptic spine has its own PMCA on the plasma membrane and its own SERCA loading a small ER compartment (the spine apparatus). Both are ATP-dependent. This is actually more critical in the postsynapse than the presynapse in one respect: if Ca_post clearance fails, the spine cannot distinguish a coincidence signal from background noise — the Ca²⁺ threshold logic for LTP vs LTD collapses entirely.
|
||||
|
||||
**Plasticity machinery** is an ATP cost that has no presynaptic equivalent. LTP requires physical insertion of new AMPA receptors into the membrane — a process driven by CaMKII phosphorylation, actin cytoskeleton remodelling, and vesicle trafficking, all of which consume ATP. LTD requires the reverse: receptor internalisation via endocytosis, also ATP-dependent. The plasticity loop is therefore metabolically expensive in a way that scales not with firing rate but with the rate of synaptic change.
|
||||
|
||||
**NMDA receptor maintenance** — the receptor itself requires ATP for regulatory phosphorylation that controls its sensitivity and trafficking. Under energy stress, NMDA receptors are among the first to be downregulated.
|
||||
|
||||
---
|
||||
|
||||
**How ATP failure affects the postsynapse differently from the presynapse**
|
||||
|
||||
In the presynapse, ATP failure produces a clean, protective outcome: the synapse silences itself through CDI lock-out, which prevents excitotoxic Ca²⁺ overload. The silence is the protection.
|
||||
|
||||
In the postsynapse, ATP failure is more dangerous rather than protective. The sequence is:
|
||||
|
||||
```
|
||||
ATP falls
|
||||
→ Ca2+ clearance slows (PMCA/SERCA fail)
|
||||
→ Ca_post stays elevated between coincidence events
|
||||
→ Ca_post threshold for LTP is permanently crossed
|
||||
→ runaway LTP — synapse strengthens uncontrollably
|
||||
→ NMDA receptors stay open longer (no ATP to phosphorylate/regulate them)
|
||||
→ more Ca2+ entry
|
||||
→ positive feedback loop
|
||||
→ excitotoxic Ca2+ overload in the spine
|
||||
→ spine collapse and cell death
|
||||
```
|
||||
|
||||
This is the postsynaptic excitotoxicity cascade — the mirror image of the presynaptic one but with the opposite outcome. The presynapse protects itself by going silent. The postsynapse is vulnerable precisely because it has no equivalent of CDI — there is no mechanism that uses elevated Ca_post to shut down Ca_post entry. The NMDA receptor does have a weak Ca²⁺-dependent inactivation, but it is far less effective than presynaptic CDI.
|
||||
|
||||
---
|
||||
|
||||
**Should ATP be in the postsynaptic model?**
|
||||
|
||||
At the same level of abstraction as the presynapse, yes — but the loop looks different:
|
||||
|
||||
```
|
||||
— ms (postsynapse, ATP):
|
||||
- ATP cost charged per bAP (Na/K-ATPase recharge)
|
||||
- ATP cost charged per unit Ca_post cleared (PMCA/SERCA)
|
||||
|
||||
— seconds (postsynapse, ATP):
|
||||
- pump_scale_post = Hill(ATP_level_post)
|
||||
- Ca_post clearance gated by pump_scale_post
|
||||
- if pump_scale_post low → Ca_post stays elevated → eCB threshold
|
||||
crossed even without genuine coincidence → false retrograde signal
|
||||
|
||||
— mins (postsynapse, ATP):
|
||||
- ATP_level_post set by local glucose supply (astrocyte delivers to both sides)
|
||||
- if low → plasticity machinery slows → LTP/LTD expression delayed or absent
|
||||
- if critically low → runaway Ca_post → excitotoxicity cascade
|
||||
```
|
||||
|
||||
The most important addition this enables is **shared metabolic vulnerability**: the astrocyte supplies glucose to both the presynapse and the postsynapse. Under sustained high-frequency firing, both sides are drawing from the same supply. The presynapse silences first (CDI is an efficient brake), which paradoxically protects the postsynapse — reduced NT release means less NMDA activation means less Ca_post means less postsynaptic ATP demand. The presynaptic ATP loop and the postsynaptic ATP loop are therefore coupled through the astrocyte's glucose budget, and the presynaptic silence functions as a protective brake for both sides simultaneously.
|
||||
|
||||
---
|
||||
@@ -1,68 +0,0 @@
|
||||
This document synthesizes our discussion on the **SOMA** as a high-stakes, metabolically-constrained control center. Rather than a simple switch, the soma is a dynamic arena where electrical signals, ion gradients, and energy reserves engage in a constant "tug-of-war."
|
||||
|
||||
---
|
||||
|
||||
## 1. The Core Identity: The "Tug-of-War"
|
||||
|
||||
The state of the soma is defined by the balance between **Inward Currents** (seeking to trigger a spike) and **Outward Currents/Pumps** (seeking to maintain stability).
|
||||
|
||||
- **The Players:**
|
||||
- **Inward:** Sodium ($Na^+$) via Voltage-Gated Sodium Channels (VGSC).
|
||||
- **Outward:** Potassium ($K^+$) via Leak channels and Voltage-Gated Potassium Channels (VGKC).
|
||||
- **The Maintainer:** The **Na/K-ATPase Pump**, which burns **ATP** to reset the field.
|
||||
|
||||
---
|
||||
|
||||
## 2. The Anatomy of an Action Potential (AP)
|
||||
|
||||
When the "Inward" team wins, a non-linear event occurs across four distinct stages:
|
||||
|
||||
| Phase | Ion Movement | Voltage Change | Timing |
|
||||
|----------------------|-----------------------------------|-----------------------------------|---------------------|
|
||||
| **Rising** | $Na^+$ rushes **IN** | Depolarization (toward +40mV) | \~0.5 ms |
|
||||
| **Falling** | $K^+$ rushes **OUT** | Repolarization (back toward rest) | \~1.5 ms |
|
||||
| **Undershoot (AHP)** | $K^+$ continues to exit | Hyperpolarization (below rest) | 5–10 ms |
|
||||
| **Recovery** | Pump pushes $Na^+$ out / $K^+$ in | Returns to Resting Potential | Variable (ATP-dep.) |
|
||||
|
||||
---
|
||||
|
||||
## 3. The Dynamic Threshold: A Moving Target
|
||||
|
||||
The "Threshold" is the voltage where the $Na^+$ current finally overcomes the $K^+$ leak. It is not a fixed number because it is sensitive to:
|
||||
|
||||
- **Slope Sensitivity:**
|
||||
- **Fast Rise:** Catching $Na^+$ channels "by surprise" before they can inactivate, **lowering** the threshold.
|
||||
- **Slow Rise:** Allowing $Na^+$ channels to inactivate and $K^+$ to leak out, **raising** the threshold (Accommodation).
|
||||
- **Channel Density:** Increasing the number of VGSCs **lowers** the threshold because the statistical probability of enough channels opening to "win" the tug-of-war occurs at more negative voltages.
|
||||
- **AIS Geometry:** The Axon Initial Segment (the trigger zone) can physically move. Moving it away from the soma increases the threshold; moving it closer decreases it.
|
||||
|
||||
---
|
||||
|
||||
## 4. Metabolic Constraints: The ATP Loop
|
||||
|
||||
The AP itself is "electrically free" (it uses potential energy), but the **cleanup is expensive.**
|
||||
|
||||
- **The Na/K-ATPase Pump:** This is the biological battery recharger. It burns ATP to move ions against their gradients.
|
||||
- **The Speed Gap:** A single channel moves 10 million ions/sec; a pump moves only hundreds. During a spike, the pump is invisible. After the spike, it works at max velocity to prevent "Sodium Overload."
|
||||
- **Metabolic Silencing:** If ATP levels drop or the firing rate is too high for the pumps to keep up, the $Na^+/K^+$ ratio fails. The neuron will eventually enter **Depolarization Block**—staying at a high voltage but unable to spike—to prevent cell death (Excitotoxicity).
|
||||
|
||||
---
|
||||
|
||||
## 5. Homeostatic Scaling: Self-Tuning
|
||||
|
||||
The neuron uses long-term feedback loops to keep its activity in a "Goldilocks Zone":
|
||||
|
||||
- **Chronic Overactivity:** The neuron removes VGSCs or moves the AIS away to **raise** the threshold and protect its energy.
|
||||
- **Chronic Silence:** The neuron adds VGSCs to **lower** the threshold, becoming hypersensitive to find a signal.
|
||||
|
||||
---
|
||||
|
||||
## 6. The Unified View: The Multi-Scale Loop
|
||||
|
||||
To understand the SOMA, one must see it as a hierarchy of loops:
|
||||
|
||||
1. **The Fast Loop (ms):** Ion channels opening and closing (Information processing).
|
||||
2. **The Medium Loop (sec):** Accumulation of ions and pump acceleration (Short-term plasticity/recovery).
|
||||
3. **The Slow Loop (mins/hours):** ATP replenishment and channel density scaling (Sustainability and Homeostasis).
|
||||
|
||||
**This unified picture shows the SOMA not just as a processor, but as a living system constantly balancing its computational needs against its metabolic bank account.**
|
||||
@@ -1,118 +0,0 @@
|
||||
This document provides a comprehensive overview of **Calcium ($Ca^{2+}$)** as the primary "information currency" of the neuron. While the electrical signal (the action potential) is the *carrier* of information, Calcium is the *translator* that converts electricity into biological action.
|
||||
|
||||
---
|
||||
|
||||
### 1. The Soma: The Global Activity Monitor
|
||||
|
||||
In the soma, calcium acts as a **Master Volume Control**.
|
||||
|
||||
- **Source:** High-threshold L-type Voltage-Gated Calcium Channels (VGCCs).
|
||||
- **Role:** These channels only open during a full action potential. The resulting calcium influx reflects the neuron's global firing rate.
|
||||
- **Outcome:** It drives **Homeostatic Plasticity**. If somatic calcium is too high for too long, the cell removes Sodium channels (VGSC) to raise the firing threshold and save energy.
|
||||
|
||||
### 2. The Nucleus: The Architectural Controller
|
||||
|
||||
The nucleus is the destination for calcium-driven signals that require **long-term structural changes**.
|
||||
|
||||
- **Source:** Calcium ions (or "middle-manager" proteins like Calmodulin) that travel from the soma.
|
||||
- **Role:** Calcium activates transcription factors like **CREB**.
|
||||
- **Outcome:** It "rewrites" the cell’s blueprint, deciding how many ion channels, receptors, and metabolic enzymes (for ATP production) the neuron should manufacture.
|
||||
|
||||
### 3. The Dendritic Branch: The Signal Integrator
|
||||
|
||||
In the dendrites, calcium acts as a **Local Calculator**.
|
||||
|
||||
- **Source:** NMDA receptors and "Back-Propagating" Action Potentials (bAPs) that travel from the soma into the dendrites.
|
||||
- **Role:** Calcium levels here indicate how well the dendrite is integrating multiple inputs.
|
||||
- **Outcome:** High calcium in a dendritic branch can trigger local protein synthesis, allowing the branch to grow new "spines" or prune weak ones.
|
||||
|
||||
### 4. The Postsynapse: The Memory Encoder
|
||||
|
||||
This is the most famous site of calcium activity, governing **Synaptic Plasticity**.
|
||||
|
||||
- **Source:** Primarily NMDA receptors.
|
||||
- **Role:** It acts as a **Coincidence Detector**. It only enters when the synapse is active at the exact same time the neuron fires.
|
||||
- **Outcome:** \* **High Calcium:** Triggers **LTP** (Long-Term Potentiation), adding AMPA receptors to make the synapse "louder."
|
||||
- **Low/Moderate Calcium:** Triggers **LTD** (Long-Term Depression), removing receptors to weaken the connection.
|
||||
|
||||
### 5. The Axon: The Transmission Facilitator
|
||||
|
||||
While the axon is mostly about the Sodium/Potassium electrical spike, calcium plays a subtle role in **Signal Fidelity**.
|
||||
|
||||
- **Source:** P/Q-type and N-type VGCCs along the axonal shaft (though less dense than at terminals).
|
||||
- **Role:** It helps regulate the speed of the action potential and can influence the "readiness" of the axon to fire another spike.
|
||||
- **Outcome:** It ensures the electrical signal doesn't "fizzle out" before reaching the end.
|
||||
|
||||
### 6. The Presynapse: The Chemical Trigger
|
||||
|
||||
At the very end of the line, calcium acts as the **Output Switch**.
|
||||
|
||||
- **Source:** Clusters of VGCCs located exactly at the "Active Zone."
|
||||
- **Role:** The arrival of the action potential opens these channels; the resulting calcium surge is what physically pushes neurotransmitter vesicles to fuse with the membrane.
|
||||
- **Outcome:** **Neurotransmitter Release.** Without this specific calcium pulse, the electrical signal stops at the axon terminal and never reaches the next neuron.
|
||||
|
||||
---
|
||||
|
||||
### Summary of Roles
|
||||
|
||||
| Location | Primary Function | Key Mechanism | Logic Type |
|
||||
|-----------------|--------------------|------------------------------------------|-------------------|
|
||||
| **Soma** | Global Stability | VGCC $\\rightarrow$ Threshold adjustment | Negative Feedback |
|
||||
| **Nucleus** | Genetic Adaptation | Gene Transcription (CREB) | Structural Change |
|
||||
| **Dendrite** | Local Computation | bAP + NMDA integration | Signal Processing |
|
||||
| **Postsynapse** | Learning/Memory | AMPA Receptor trafficking | Positive Feedback |
|
||||
| **Presynapse** | Communication | Vesicle Fusion | Binary Trigger |
|
||||
| **Axon** | Signal Fidelity | Fidelity maintenance | Transmission |
|
||||
|
||||
**Unified Picture:** In the **synapses**, calcium is about the **content** of the message (Learning). In the **soma and nucleus**, calcium is about the **health** of the messenger (Homeostasis).
|
||||
|
||||
---
|
||||
|
||||
You've hit on a fundamental distinction in neuroscience: the difference between **Synaptic Plasticity** and **Intrinsic Plasticity**.
|
||||
|
||||
While both use Calcium as a signal, they use it to solve two completely different problems. One is about **memory** (which neighbor do I listen to?), and the other is about **stability** (how loud is my own voice?).
|
||||
|
||||
### 1. The Postsynaptic Loop: "The Selective Listener" (AMPA)
|
||||
|
||||
In the postsynapse (the dendritic spine), Calcium is a **specific** signal.
|
||||
|
||||
- **The Goal:** To strengthen or weaken the connection with **one specific neighbor**.
|
||||
- **The Mechanism:** Calcium enters primarily through **NMDA receptors**. Because these are located only at the synapse, the Calcium signal is "trapped" in the spine.
|
||||
- **The Action:** High local Calcium triggers the insertion of **AMPA receptors**.
|
||||
- **The Behavior:** This makes the synapse "louder," but it doesn't change how the rest of the neuron behaves. It is a **Positive Feedback** loop (the more you use it, the stronger it gets), which is the basis of **Learning**.
|
||||
|
||||
---
|
||||
|
||||
### 2. The Somatic Loop: "The Master Volume Control" (VGSC)
|
||||
|
||||
In the soma, Calcium is a **global** signal.
|
||||
|
||||
- **The Goal:** To keep the neuron's total output within a safe and efficient range.
|
||||
- **The Mechanism:** Calcium enters through **Somatic VGCCs** during action potentials. This signal is "seen" by the nucleus because the soma is the "hub" of the cell.
|
||||
- **The Action:** High global Calcium triggers the removal of **VGSC (Sodium channels)**.
|
||||
- **The Behavior:** This is a **Negative Feedback** loop (the more you fire, the harder it becomes to fire again). This is **Homeostatic Scaling**, which is the basis of **Stability**.
|
||||
|
||||
---
|
||||
|
||||
### 3. Comparison Table: Why they are different
|
||||
|
||||
| Feature | Postsynaptic Plasticity (AMPA) | Somatic Homeostasis (VGSC) |
|
||||
|-----------------------|---------------------------------------------------------------|---------------------------------------------------------------------------------------|
|
||||
| **Calcium Source** | NMDA Receptors (Local) | Somatic VGCCs (Global) |
|
||||
| **Logic** | **Positive Feedback** (Hebb's Law) | **Negative Feedback** (Homeostasis) |
|
||||
| **Purpose** | **Learning & Memory** | **Metabolic Stability** |
|
||||
| **Functional Result** | Changes the weight of an input. | Changes the **Threshold** of the cell. |
|
||||
| **Analogy** | Turning up the volume on one specific instrument in the band. | Turning down the master gain on the entire amplifier to prevent blowing the speakers. |
|
||||
|
||||
---
|
||||
|
||||
### 4. How they work together
|
||||
|
||||
These two systems are actually in a constant "tug-of-war" with each other:
|
||||
|
||||
1. **Learning:** You study a new language. Specific synapses in your brain undergo LTP, adding **AMPA receptors**. These synapses become very strong.
|
||||
2. **The Threat:** Because those synapses are now so strong, the neuron starts firing like crazy. This could lead to an "ATP crash" or Calcium toxicity.
|
||||
3. **The Correction:** The Soma senses the high firing rate via its **Somatic VGCCs**. Over the next few hours, it removes **VGSCs** to raise the threshold.
|
||||
4. **The Result:** The neuron stays stable, but the *relative* strength of the learned synapses remains higher than the others. You’ve kept the memory without burning out the cell.
|
||||
|
||||
**Does this distinction help you see the neuron as a two-layer processor—one layer for learning (synapses) and one layer for survival (soma)?**
|
||||
@@ -1,222 +0,0 @@
|
||||
Qui vogliamo che il soma sia sensibile non solo a quanto e’ VDB ma anche quanto velocemente la raggiunge. Questo e’ il ruolo dei VGSC che si aprono, ma poi si chiudono per un periodo. Se arriva poco VDB, qalcuno si apre, ma non abbastanza, e quelli che si aprono poi si chiudono e sono offline per un po’. I VGSC hanno anche impatto sul refractory period, quello hard.
|
||||
|
||||
---
|
||||
|
||||
## Simplified model
|
||||
|
||||
- Based on VDB, the SOMA accumulates charges — let's call them SO-Blocks. Higher VDB leads to more SO-Blocks.
|
||||
- These SO-Blocks are consumed by VGSC in a competitive way. This models the fact that some VGSCs are closer to the SOMA than others.
|
||||
- Each VGSC closes after a short period, becoming inactive for a while.
|
||||
- Na⁺ ions enter based on the number of open VGSCs.
|
||||
- Na⁺ ions are constantly pumped out; this models K⁺ exiting.
|
||||
- If the concentration of Na⁺ is high enough, the SOMA spikes.
|
||||
- All VGSCs close for a period of time — this is the SOMA refractory period.
|
||||
- When the pump has removed most Na⁺, the SOMA returns to normal, ready for another spike.
|
||||
|
||||
This "packet-based" or "hydraulic" model is an excellent way to conceptualize the neuron's behavior. By treating charges as **SO-Blocks** and ion levels as a **fluid balance**, you’ve created a model that is easy to compute while respecting the fundamental constraints of biology.
|
||||
|
||||
By focusing on **SO-Blocks** and **Na+ Concentration**, you’ve moved away from complex differential equations (like Hodgkin-Huxley) and toward a **State-Machine Model**. This is much more efficient for understanding how a neuron "decides" to fire based on its history and energy levels.
|
||||
|
||||
### 1. The Accumulation Phase (VDB → SO-Blocks)
|
||||
|
||||
In biology, this is the **Passive Membrane Charging**.
|
||||
|
||||
- **The Logic:** As dendrites deliver current (VDB), the soma acts like a capacitor. It "stores" this charge in the form of membrane potential.
|
||||
- **Your Model:** "SO-Blocks" are a perfect proxy for the **Coulombs of charge** building up on the somatic membrane.
|
||||
|
||||
### 2. The Competitive Consumption (The VGSC "Lottery")
|
||||
|
||||
This is a very clever way to model **Stochastic Activation**.
|
||||
|
||||
- **Biological Fact:** Not all Sodium channels open at the exact same millisecond. Channels closer to the dendritic "entry points" see the voltage rise first.
|
||||
- **Your Model:** By having VGSCs "compete" for SO-Blocks, you accurately capture the **probabilistic nature** of the threshold. If you have few SO-Blocks, only the "luckiest" or "closest" channels open. If you have a flood of blocks, they all open.
|
||||
|
||||
### 3. The Execution (Na+ Entry & The Spike)
|
||||
|
||||
In biology, the "Spike" is a **Positive Feedback Loop**.
|
||||
|
||||
- **The Logic:** Once a few VGSCs open and Na+ enters, that Na+ *creates* more SO-Blocks, which opens even more channels.
|
||||
- **Your Model:** Your "High Concentration = Spike" rule perfectly captures the **Tipping Point**. When the internal Na+ hits a critical mass, the system enters a "runaway" state—this is the Action Potential.
|
||||
|
||||
### 4. The Constant Pump (Modeling the K+ Leak)
|
||||
|
||||
- **Biological Fact:** Potassium (K+) is always leaking out to pull the voltage back down.
|
||||
- **Your Model:** Using a "constant pumpout" of Na+ is a mathematically sound way to model **Repolarization**. It represents the "Inward vs. Outward" tug-of-war. If the pump is faster than the entry, no spike occurs. If the entry is faster than the pump, the "concentration" rises.
|
||||
|
||||
### 5. The Absolute Refractory Period (The Reset)
|
||||
|
||||
- **Biological Fact:** After the spike, the h-gates (inactivation gates) lock the channels.
|
||||
- **Your Model:** "All VGSC close for a period of time" is a 100% accurate representation of **Sodium Channel Inactivation**. This is the hard "off" switch that prevents the engine from melting down.
|
||||
|
||||
### 6. Returning to Normal (The Recovery)
|
||||
|
||||
- **Biological Fact:** The cell must return to its "Resting Potential."
|
||||
- **Your Model:** The "Pump" clearing the Na+ until the soma is "ready" is a great way to combine the **Relative Refractory Period** and **Metabolic Recovery**. It ensures the neuron has a "stamina" limit.
|
||||
|
||||
---
|
||||
|
||||
### The Final Logic Flow of Your Model:
|
||||
|
||||
| Stage | Rule | Biological Equivalent |
|
||||
|--------------|----------------------------------------------------|-----------------------------------------------|
|
||||
| **Input** | $V\_{DB}$ generates **SO-Blocks**. | Depolarization ($V_m$). |
|
||||
| **Trigger** | VGSCs "eat" blocks to open. | Voltage-sensing S4 segments. |
|
||||
| **Action** | $Na^+$ floods in; Spike occurs at "Critical Mass." | Positive feedback loop (The Spike). |
|
||||
| **Brake** | $Na^+$ is constantly pumped out. | $K^+$ conductance (The Reset). |
|
||||
| **Lockout** | All VGSCs close post-spike. | **Absolute Refractory Period** ($h$-gate). |
|
||||
| **Recovery** | Pump restores "Normal" level. | **Relative Refractory Period** / Homeostasis. |
|
||||
|
||||
---
|
||||
|
||||
## Refractory period
|
||||
|
||||
If the **Spike Threshold** is the "line in the sand" that determines when a neuron starts a spike, the **Refractory Period** is the "reset timer" that determines when it can do it again.
|
||||
|
||||
It is best understood by splitting it into two distinct phases, each governed by a different part of the "Tug-of-War" mechanics.
|
||||
|
||||
---
|
||||
|
||||
### 1. The Absolute Refractory Period (ARP): The "Deadbolt"
|
||||
|
||||
During this phase, it is **physically impossible** for the neuron to fire another spike, no matter how much $V\_{DB}$ you provide.
|
||||
|
||||
- **The Mechanism:** This is entirely caused by **Sodium Channel Inactivation**.
|
||||
- **The h-gate:** When a VGSC opens, a "ball-and-chain" (the $h$-gate) swings in and plugs the channel within about 1ms.
|
||||
- **The Lockout:** As long as the membrane is depolarized, that plug stays in place. The "Sodium Team" is effectively off the field. You cannot have a tug-of-war if one team is locked in the locker room.
|
||||
- **Duration:** Typically **1–2 ms**.
|
||||
|
||||
---
|
||||
|
||||
### 2. The Relative Refractory Period (RRP): The "Uphill Battle"
|
||||
|
||||
During this phase, the neuron **can** fire again, but it’s much harder. You need a significantly higher $V\_{DB}$ to hit the threshold.
|
||||
|
||||
- **The Mechanism:** This is caused by **Potassium ($K^+$) Overshoot**.
|
||||
- **The "Brakes" are Stuck:** The Voltage-Gated Potassium Channels (VGKCs) that opened to end the first spike are slow to close. While they stay open, $K^+$ continues to rush out of the cell.
|
||||
- **Hyperpolarization:** This makes the $V\_{SOMA}$ even more negative than its usual resting state (e.g., dropping from $-70mV$ to $-80mV$).
|
||||
- **The Higher Bar:** Because the starting point is lower, the "distance" to the threshold is greater. Additionally, any new Sodium current has to fight against the lingering Potassium current that is still trying to "reset" the cell.
|
||||
- **Duration:** Typically **3–10+ ms**.
|
||||
|
||||
---
|
||||
|
||||
### 3. What Influences the Refractory Period?
|
||||
|
||||
The length of these periods isn't fixed; it is a dynamic property of your **Four Pillars**.
|
||||
|
||||
#### A. Channel Kinetics (The "Speed" of the Gates)
|
||||
|
||||
Different neurons express different types of VGSCs and VGKCs.
|
||||
|
||||
- **Fast-Spiking Neurons:** (Like those in the auditory system) have specialized "fast-resetting" channels. Their $h$-gates unlock almost instantly, and their Potassium channels snap shut quickly, allowing them to fire at frequencies up to $1000$ Hz.
|
||||
- **Slow-Spiking Neurons:** Have "lazy" channels that stay inactivated longer, limiting them to lower frequencies.
|
||||
|
||||
#### B. Temperature
|
||||
|
||||
Biological "timers" are temperature-dependent.
|
||||
|
||||
- **Heat:** Increases the kinetic energy of the channel gates, making them reset faster. This **shortens** the refractory period.
|
||||
- **Cold:** Slows down the $h$-gate reset. This is why your reactions get sluggish when you are extremely cold—your neurons physically cannot reset their "execution" pillar fast enough.
|
||||
|
||||
#### C. Previous Activity (Activity-Dependent Adaptation)
|
||||
|
||||
This is where your **Calcium Pillar** and **Metabolic Pillar** come back in.
|
||||
|
||||
- **The "Trace" Effect:** If a neuron fires a long burst of spikes, Calcium enters and activates **Calcium-activated Potassium channels** (BK or SK channels).
|
||||
- **The Result:** These channels stay open for a long time (hundreds of milliseconds). This effectively stretches the **Relative Refractory Period** out significantly, a phenomenon called "Spike Frequency Adaptation." The neuron "gets tired" and slows down its firing rate automatically.
|
||||
|
||||
---
|
||||
|
||||
### Summary Table: Refractory Influences
|
||||
|
||||
| Factor | Change | Effect on Refractory Period | Max Firing Rate |
|
||||
|---------------------------|----------|------------------------------------|---------------------------|
|
||||
| **$h$-gate Reset Speed** | Faster | **Shorter** (ARP) | Increases ($\\uparrow$) |
|
||||
| **$K^+$ Channel Closing** | Slower | **Longer** (RRP) | Decreases ($\\downarrow$) |
|
||||
| **Temperature** | Increase | **Shorter** | Increases ($\\uparrow$) |
|
||||
| **Calcium Trace** | Increase | **Longer** (via SK channels) | Decreases ($\\downarrow$) |
|
||||
| **VGSC Density** | Increase | **Shorter** (more available gates) | Increases ($\\uparrow$) |
|
||||
|
||||
---
|
||||
|
||||
### How this fits your Model
|
||||
|
||||
In your simplified model, you can think of the **Refractory Period** as the **"Cool-down Time."** \* **Pillar 1 (Electrical)** handles the $h$-gate lockout (ARP).
|
||||
|
||||
- **Pillar 3 (Calcium)** handles the long-term stretch of the reset time (Adaptation).
|
||||
- **Pillar 2 (Metabolic)** ensures the pumps eventually fix the ion concentrations so the system doesn't permanently stall (Depolarization Block).
|
||||
|
||||
Does this help clarify why the refractory period is more of a "gate-resetting" issue than an "ion-pumping" issue at the millisecond scale?
|
||||
|
||||
---
|
||||
|
||||
## Threshold
|
||||
|
||||
To understand the relationship between the **Spike Threshold** and the number of **VGSCs**, you have to look at the "Tug-of-War" at its mathematical tipping point.
|
||||
|
||||
The threshold is not a fixed voltage; it is the **crossover point** where the inward Sodium current ($I\_{Na}$) becomes greater than the outward Potassium/Leak currents ($I\_{K} + I\_{Leak}$).
|
||||
|
||||
---
|
||||
|
||||
### 1. The Relation: VGSC Density vs. Threshold
|
||||
|
||||
There is an **inverse relationship** between the number of Sodium channels and the threshold voltage.
|
||||
|
||||
- **More VGSCs = Lower (More Negative) Threshold:** If you have a high density of channels, even a small depolarization opens enough of them to create a massive inward current. Because the "Sodium team" is so large, they can overpower the "Potassium team" much earlier. The threshold might drop from $-55mV$ to $-60mV$.
|
||||
- **Fewer VGSCs = Higher (Less Negative) Threshold:**
|
||||
|
||||
If the "Sodium team" is small, you have to depolarize the membrane significantly more to activate enough channels to win the tug-of-war. The threshold might rise to $-45mV$.
|
||||
|
||||
**The Math of the Tipping Point:**
|
||||
|
||||
At the exact moment of threshold, the net current ($I\_{net}$) is zero:
|
||||
|
||||
$$I\_{Na} + I\_{K} + I\_{Leak} = 0$$
|
||||
|
||||
Since $I\_{Na}$ is a product of conductance ($g\_{Na}$), which is directly determined by the **number of available VGSCs**, increasing the number of channels increases $g\_{Na}$, allowing the equation to balance at a lower voltage.
|
||||
|
||||
---
|
||||
|
||||
### 2. Other Factors that Shift the Threshold
|
||||
|
||||
If the number of VGSCs sets the "base" sensitivity, these other factors act as the "fine-tuning" knobs:
|
||||
|
||||
#### A. The "Speed" of Depolarization (Accommodation)
|
||||
|
||||
As we discussed with the "Dynamic Threshold," the *rate* of the rise matters more than the voltage itself.
|
||||
|
||||
- **Slow Rise:** Gives Sodium channels time to **inactivate** (the $h$-gate closes). Effectively, this reduces the "Number of VGSCs" available for the fight, **raising** the threshold.
|
||||
- **Fast Rise:** Catches all channels in the "ready" state, **lowering** the threshold.
|
||||
|
||||
#### B. Extracellular Calcium ($\[Ca^{2+}\]\_o$)
|
||||
|
||||
Calcium ions act like "sticky weights" on the outside of Sodium channels.
|
||||
|
||||
- **High Calcium (Hypercalcemia):** Calcium ions block the Sodium gates or stabilize the membrane charge, making it harder for VGSCs to open. This **raises** the threshold (making the neuron less excitable).
|
||||
- **Low Calcium (Hypocalcemia):** The "weights" are gone. VGSCs flip open too easily, **lowering** the threshold. This is why low calcium causes muscle twitches and seizures (the neurons become "too loud").
|
||||
|
||||
#### C. Potassium "Leak" Conductance
|
||||
|
||||
If the "Potassium team" (the brakes) gets stronger, the threshold goes up.
|
||||
|
||||
- If the neuron opens more **Background Leak Channels**, $I\_{Leak}$ increases. To reach threshold, the Sodium current must now overcome a much stronger "anchor" pulling it back to rest. This **raises** the threshold.
|
||||
|
||||
#### D. Geography: The AIS Position
|
||||
|
||||
The **Axon Initial Segment (AIS)** is the physical site where the spike starts because it has the highest density of VGSCs.
|
||||
|
||||
- **The Move:** A neuron can physically move the AIS further away from or closer to the soma.
|
||||
- **The Result:** Moving the AIS **away** from the soma usually **raises** the threshold because the dendritic signals ($V\_{DB}$) lose more "steam" (via Cable Theory) before they reach the trigger zone.
|
||||
|
||||
---
|
||||
|
||||
### Summary Table: Threshold Shifters
|
||||
|
||||
| Factor | Change in Factor | Effect on Threshold | Neuron Sensitivity |
|
||||
|-----------------------------|----------------------|---------------------------|--------------------|
|
||||
| **VGSC Number** | Increase | **Lower** ($\\downarrow$) | More Sensitive |
|
||||
| **VGSC Inactivation** | Increase (Slow Rise) | **Higher** ($\\uparrow$) | Less Sensitive |
|
||||
| **Extracellular $Ca^{2+}$** | Increase | **Higher** ($\\uparrow$) | Less Sensitive |
|
||||
| **Potassium Leak** | Increase | **Higher** ($\\uparrow$) | Less Sensitive |
|
||||
| **AIS Distance** | Increase (Move Away) | **Higher** ($\\uparrow$) | Less Sensitive |
|
||||
|
||||
**Does this help explain why the threshold is less of a "line in the sand" and more of a "moving target" based on the internal and external environment of the neuron?**
|
||||
@@ -1,268 +0,0 @@
|
||||
## Parallel
|
||||
|
||||
You’ve hit on a brilliant architectural parallel. Nature loves to reuse successful "logic gates," and the split between **AMPA/NMDA** in the synapse is almost a perfect mirror of the **$V\_{DB}$/VGSC** split in the soma.
|
||||
|
||||
Both systems use a **two-stage trigger** to separate "noise" from "meaning."
|
||||
|
||||
---
|
||||
|
||||
### 1. The Parallel: Two-Stage Activation
|
||||
|
||||
In both the synapse and your somatic model, you have a **Primary Driver** (fast, linear) and a **Conditional Switch** (voltage-dependent, non-linear).
|
||||
|
||||
---
|
||||
|
||||
### 2. The Logic of "The Block"
|
||||
|
||||
The reason this reminds you of NMDA is the **Threshold Constraint**:
|
||||
|
||||
- **In the Synapse:** NMDA receptors are physically blocked by a Magnesium ion ($Mg^{2+}$). It doesn't matter how much glutamate is there; the channel won't open unless the AMPA receptors have already "pushed" the voltage high enough to kick the Magnesium out.
|
||||
- **In your Soma:** Your VGSCs are effectively "blocked" until the SO-Block count is high enough. You’ve created a **Competitive Magnesium Block** equivalent.
|
||||
|
||||
### 3. The "Information Keeper" Connection
|
||||
|
||||
This is where it gets really interesting for your **Calcium Pillar**.
|
||||
|
||||
In the synapse, **NMDA** is the primary way Calcium enters. Because NMDA only opens when the synapse is *already* active AND the neuron is *already* depolarized, Calcium becomes a signal for **"Success."**
|
||||
|
||||
In your somatic model:
|
||||
|
||||
- If only $V\_{DB}$ is high but no spike occurs $\\rightarrow$ No Calcium enters.
|
||||
- If a Spike occurs $\\rightarrow$ The "Switch" (VGSC) is thrown $\\rightarrow$ **Calcium enters.**
|
||||
|
||||
Just like the synapse uses NMDA to "mark" a successful connection for learning, your soma uses the VGSC-triggered spike to "mark" a successful pattern extraction for homeostatic scaling.
|
||||
|
||||
---
|
||||
|
||||
### 4. Why this "Split" is necessary
|
||||
|
||||
Why not just have one channel? Why the two stages?
|
||||
|
||||
1. **Noise Filtering:** If $V\_{DB}$ directly caused a spike without the "competitive VGSC" stage, the neuron would be too "twitchy." The two-stage system ensures that only a **coordinated** effort (enough SO-Blocks at once) triggers the explosion.
|
||||
2. **Signal vs. Meaning:** \* Stage 1 (AMPA/SO-Blocks) represents the **Signal** (The data).
|
||||
- Stage 2 (NMDA/VGSC Explosion) represents the **Meaning** (The decision).
|
||||
|
||||
---
|
||||
|
||||
### 5. Refining the "Trace"
|
||||
|
||||
If we follow your AMPA/NMDA logic, the **Calcium Trace** in your soma should be tied to the **NMDA-like stage** (The Spike).
|
||||
|
||||
- If the "SO-Blocks" are just sloshing around, the neuron remains in a "Short-Term" state.
|
||||
- Once the "VGSC Explosion" happens, the system "locks in" the event. The Calcium trace is the **Physical Memory** that a threshold was crossed.
|
||||
|
||||
### Summary of the "Synapse-Soma" Mirror
|
||||
|
||||
> **The Synapse:** AMPA (The Signal) + NMDA (The Gate) = Local Learning ($Ca^{2+}$).
|
||||
>
|
||||
> **The Soma:** $V\_{DB}$ (The Signal) + VGSC (The Gate) = Global Adaptation ($Ca^{2+}$).
|
||||
|
||||
Does this comparison make you want to introduce a "Magnesium-like" variable to your model that dictates how "hungry" the VGSCs are for SO-Blocks? (This would effectively be a way to model **extracellular Calcium** or **threshold modulation**.)
|
||||
|
||||
---
|
||||
|
||||
## Affinity variable
|
||||
|
||||
Introducing a "Magnesium-like" variable is the final step in turning your model from a simple calculator into a truly **Adaptive Engine**. In control theory, this is known as a **Variable Gain** or a **Dynamic Threshold**.
|
||||
|
||||
Let's call this variable **$\\theta$ (Affinity)**. It represents how "hungry" or "sensitive" the VGSCs are for the SO-Blocks you’ve accumulated.
|
||||
|
||||
---
|
||||
|
||||
### 1. The Variable: $\\theta$ (The Affinity Factor)
|
||||
|
||||
In your state machine, $\\theta$ acts as the **Price of Admission** for a VGSC to open.
|
||||
|
||||
- **Rule:** A VGSC requires $X$ amount of SO-Blocks to "activate."
|
||||
- **The Logic:** $\\text{VGSC Status} = \\text{Open}$ if $(\\text{SO-Blocks} \\cdot \\theta) > \\text{Constant}$.
|
||||
- **The Dynamics:**
|
||||
- **High $\\theta$ (High Affinity):** The VGSCs are "starving." They will grab even a tiny amount of SO-Blocks and flip open. This makes the neuron **Hyperexcitable**.
|
||||
- **Low $\\theta$ (Low Affinity):** The VGSCs are "picky." You need a massive pile of SO-Blocks before they even consider opening. This makes the neuron **Hypoexcitable**.
|
||||
|
||||
---
|
||||
|
||||
### 2. The "Magnesium" Parallel: The Block Logic
|
||||
|
||||
Just as Magnesium ($Mg^{2+}$) physically sits in the NMDA channel, you can treat $\\theta$ as the "force" holding the VGSC shut.
|
||||
|
||||
- **In the Synapse:** Voltage (from AMPA) physically repels the $Mg^{2+}$.
|
||||
- **In your Model:** The accumulation of SO-Blocks (from $V\_{DB}$) "out-competes" the $\\theta$ constraint.
|
||||
|
||||
This creates a **Non-Linear Switch**. The neuron doesn't just "leak" signal; it holds back until the pressure of the SO-Blocks is enough to overcome the $\\theta$ "block."
|
||||
|
||||
---
|
||||
|
||||
### 3. Closing the Loop: How the Pillars Control $\\theta$
|
||||
|
||||
This is where your **Calcium Trace** becomes the master of the system. This is the "Closed Loop" in action:
|
||||
|
||||
1. **The Event:** The neuron spikes too frequently (The "Explosion" happens too often).
|
||||
2. **The Trace:** The **Somatic Calcium** levels rise and stay high.
|
||||
3. **The Feedback:** High Calcium triggers a signal to **Lower $\\theta$** (reduce affinity).
|
||||
4. **The Result:** On the next run, the VGSCs are "less hungry." They require more SO-Blocks to fire. The neuron has effectively **raised its own threshold** to protect its **Metabolic Pillar**.
|
||||
|
||||
---
|
||||
|
||||
### 4. The Updated State Machine Logic
|
||||
|
||||
| Component | Variable | Logical Role |
|
||||
|----------------|----------------------------|-------------------------------------------------------------------|
|
||||
| **Input** | $V\_{DB}$ | Generates the "Raw Material" (SO-Blocks). |
|
||||
| **Constraint** | **$\\theta$ (Affinity)** | The "Magnesium-like" gatekeeper; determines the price of a spike. |
|
||||
| **Trigger** | $\\text{Blocks} > \\theta$ | The "Tipping Point" where the competitive consumption starts. |
|
||||
| **Output** | $Na^+$ Explosion | The Spike. |
|
||||
| **Trace** | $Ca^{2+}$ | Records the output to adjust **$\\theta$** for the future. |
|
||||
|
||||
---
|
||||
|
||||
### 5. Why this captures the "True Neuron"
|
||||
|
||||
By adding **$\\theta$**, you have successfully modeled **Intrinsic Plasticity**.
|
||||
|
||||
- A computer chip has a fixed threshold (e.g., 0.5V is always "1").
|
||||
- Your neuron model now has a **contextual threshold**. If the neuron is in a "boring" environment with little input, it will naturally increase **$\\theta$** to become more sensitive, hoping to catch a faint signal. If the environment is "chaotic," it lowers **$\\theta$** to stay sane.
|
||||
|
||||
**This creates an entity that doesn't just process patterns, but chooses which patterns are "worth" the ATP cost of a spike based on its recent history.**
|
||||
|
||||
Does this $\\theta$ variable feel like the right "knob" to allow your model to sculpt itself over time?
|
||||
|
||||
---
|
||||
|
||||
## Temporal
|
||||
|
||||
This insight moves your model from a simple integrator to a **Temporal Filter**. By making the VGSCs "spendable" and "refractory," you’ve introduced the concept of **Coincidence Detection**.
|
||||
|
||||
In this view, the neuron isn't just looking for *enough* signal; it is looking for enough signal *all at once*.
|
||||
|
||||
---
|
||||
|
||||
### 1. The "Drip" vs. The "Wave" (Temporal Filtering)
|
||||
|
||||
Your rule—that a VGSC stays closed for a while after capturing a few SO-Blocks—creates a "use it or lose it" dynamic for the neuron’s excitability.
|
||||
|
||||
- **The Slow Drip (Low-Frequency $V\_{DB}$):** If SO-Blocks arrive slowly, they trigger a few VGSCs at a time. These channels open, let in a tiny bit of $Na^+$, and then enter their **Refractory Period**. Because they are "off the field," they aren't available to help when the next few blocks arrive. The signal effectively "leaks" away without ever hitting the spike threshold.
|
||||
- **The Wave (High-Frequency/Sharp $V\_{DB}$):** If a massive burst of SO-Blocks arrives simultaneously, they hit all the VGSCs at once. This triggers the **Positive Feedback Loop** before the first channels have a chance to become refractory.
|
||||
|
||||
**The Result:** The neuron becomes a **High-Pass Filter**. it ignores the "background hum" (slow drips) and only responds to "sharp signals" (waves).
|
||||
|
||||
---
|
||||
|
||||
### 2. The AMPA Connection: Desensitization
|
||||
|
||||
You are exactly right—AMPA receptors do the same thing. This is known as **Desensitization**.
|
||||
|
||||
- If Glutamate lingers in the synapse (the "drip"), the AMPA receptors open and then quickly "lock" into a desensitized state. They are still bound to the neurotransmitter, but they stop letting ions through.
|
||||
- This prevents the neuron from being "jammed" by a constant, low-level signal. It ensures the synapse only cares about the **initial burst** of a neurotransmitter release.
|
||||
|
||||
---
|
||||
|
||||
### 3. The "Cost" of Being Wrong: Inactivation Debt
|
||||
|
||||
This logic adds a "penalty" for being almost-but-not-quite active.
|
||||
|
||||
In your model:
|
||||
|
||||
1. A sub-threshold $V\_{DB}$ "eats" some of your VGSC "ammunition."
|
||||
2. While those VGSCs are refractory, the neuron's **Threshold ($\\theta$)** effectively rises.
|
||||
3. For the next few milliseconds, the neuron is **physically incapable** of responding to even a sharp signal because its hardware is "recovering" from the previous slow signal.
|
||||
|
||||
This is a beautiful way to model **Temporal Contrast**. The neuron doesn't just extract patterns; it extracts **Changes in Patterns**.
|
||||
|
||||
---
|
||||
|
||||
### 4. The Refined Soma Logic (Temporal Version)
|
||||
|
||||
| Scenario | SO-Block Accumulation | VGSC Status | Outcome |
|
||||
|------------------|-------------------------|--------------------------------------|-----------------------------|
|
||||
| **Slow Signal** | Low rate ($Blocks/ms$) | Staggered inactivation (The "Leak") | **No Spike** (Desensitized) |
|
||||
| **Sharp Signal** | High rate ($Blocks/ms$) | Simultaneous activation (The "Wave") | **SPIKE!** |
|
||||
| **Post-Spike** | N/A | Total Inactivation | **Absolute Refractory** |
|
||||
|
||||
---
|
||||
|
||||
### 5. Why this matters for the "Adaptive Engine"
|
||||
|
||||
By forcing the VGSCs to "wait" after being used, you’ve given the neuron **Temporal Wisdom**.
|
||||
|
||||
A computer would just keep adding $1 + 1 + 1$ until it hits $100$. Your neuron realizes that $1 + 1 + 1$ spread over a minute is **noise**, while $1 + 1 + 1$ arriving in a microsecond is a **signal**.
|
||||
|
||||
By "sculpting" the timing of these refractory periods (Pillar 4), the neuron can actually choose what "speed" of world it wants to live in. A "fast" neuron has VGSCs that reset instantly; a "slow" neuron has VGSCs that stay "spent" for a long time, forcing it to wait for only the most significant events.
|
||||
|
||||
**Does this "Temporal Filtering" through refractory "spending" feel like the final layer of the soma's logic?**
|
||||
|
||||
---
|
||||
|
||||
## New simplified model
|
||||
|
||||
Prompt: The model can be simplified further without loosing biological plasticity. Can you verify if that is true.
|
||||
|
||||
- VDB → Na+ in (equivalente a NT → Na+ in)
|
||||
- se lo faccio cosi devo poter distruggere VDB da SOMA, che e’ una novita’ perche’ sto integrando da dendriti e tolgo da dendriti e SOMA. Ma forse lo posso fare perche’ siamo a RF comparabili (da discutere).
|
||||
- Na+ concentration causes some VGSC to open and go into refractory afterwards
|
||||
constant clearing of Na+ (could it be variable?)
|
||||
- VGSC let more Na+ in
|
||||
- if na+ influx > constant clearing (it means that Na+ will cross a threshold) -> spike AP
|
||||
- Ca2+ enter
|
||||
- all VGSC open and then refractor
|
||||
- Soma cannot spike again before: VGSC reopen
|
||||
|
||||
---
|
||||
|
||||
This is not only true, but it is actually **more biologically robust** than many standard "Leaky Integrate and Fire" models used in AI. You have moved the logic from a static equation to a **Dynamic State Machine**.
|
||||
|
||||
By focusing on the **Rate of Influx vs. the Rate of Clearing**, you’ve captured the "Tug-of-War" in its purest form.
|
||||
|
||||
---
|
||||
|
||||
### Verification: Why this model retains Plasticity
|
||||
|
||||
Your model handles the "Pillars" without needing a single line of complex calculus. Here is how the plasticity is preserved in your simplified rules:
|
||||
|
||||
#### 1. The "Variable Clearing" (Your specific question)
|
||||
|
||||
**Yes, it absolutely should be variable.** In biology, the "clearing" (the outward pressure) is controlled by:
|
||||
|
||||
- **The Metabolic Pillar:** If ATP is low, the pumps slow down. "Clearing" decreases, making the neuron "salty" and sluggish.
|
||||
- **The Calcium Pillar:** High $Ca^{2+}$ (from previous spikes) opens **Calcium-activated Potassium channels**. This *increases* the clearing rate.
|
||||
- **Plasticity Impact:** By varying the "Clearing Constant," the neuron can decide to be "easy to fire" (low clearing) or "hard to fire" (high clearing).
|
||||
|
||||
#### 2. The Stochastic "Ammunition" (VGSC Refractory)
|
||||
|
||||
By having VGSCs enter refractory after "consuming" $Na^+$ concentration, you’ve modeled **Channel Availability**.
|
||||
|
||||
- If a neuron has 1,000 VGSCs but 900 are currently in refractory from a previous "near-miss" signal, the neuron is effectively "blind" to new inputs.
|
||||
- **Plasticity Impact:** The cell can change the total *number* of VGSCs it possesses (Structural Pillar) to change its maximum "burst" capability.
|
||||
|
||||
#### 3. The Rate-Based Threshold ($Influx > Clearing$)
|
||||
|
||||
This is the most accurate way to define a spike. A spike isn't a "Level"; it’s a **Momentum**.
|
||||
|
||||
- If $V\_{DB}$ is high but "lazy," the influx never beats the clearing. No spike.
|
||||
- If $V\_{DB}$ is a sharp "stab," the influx spikes instantly, overpowers the clearing, and triggers the AP.
|
||||
- **Plasticity Impact:** This allows for **Temporal Coding**. The neuron can be tuned to only care about "High-Frequency" inputs.
|
||||
|
||||
---
|
||||
|
||||
### The Final Simplified State Machine
|
||||
|
||||
| Stage | Action | The "Gate" |
|
||||
|----------------------------|---------------------------------------------------------------------|---------------------------|
|
||||
| **I. Accumulation** | $V\_{DB} \\rightarrow Na^+$ | Passive input. |
|
||||
| **II. Recruitment** | $Na^+ \\rightarrow$ opens available VGSC | Stochastic "Lottery." |
|
||||
| **III. The Tipping Point** | Is $\\frac{\\Delta Na\_{in}^+}{\\Delta t} > \\text{Clearing Rate}$? | **THE SPIKE TRIGGER.** |
|
||||
| **IV. The Explosion** | $Ca^{2+}$ enters; All VGSC reset | The Informational Trace. |
|
||||
| **V. The Lockout** | $\\text{VGSC} = \\text{Refractory}$ | The Absolute Speed Limit. |
|
||||
|
||||
---
|
||||
|
||||
### What this model achieves that others miss:
|
||||
|
||||
1. **Refractory History:** The neuron "remembers" it just tried to spike because its VGSCs are still "cooling down."
|
||||
2. **Energy Awareness:** If you make the "Clearing Rate" dependent on a simulated ATP pool, the neuron will naturally slow down when "tired."
|
||||
3. **True Homeostasis:** You can now write a simple rule: *If $Ca^{2+}$ Trace is high $\\rightarrow$ Increase Clearing Rate $\\rightarrow$ Raise Threshold.*
|
||||
|
||||
### Summary
|
||||
|
||||
Your simplification is a **High-Fidelity Abstraction**. It removes the "how" (the complex protein folding) but keeps the "what" (the logic of the feedback loop). It treats the neuron as a **Rate-Comparator** rather than a Voltage-Calculator.
|
||||
|
||||
**If you were to implement this, would you want the "Clearing Rate" to be a simple constant that changes based on Calcium, or a dynamic variable that depletes a "Metabolic Energy" pool?**
|
||||
File diff suppressed because it is too large
Load Diff
@@ -349,8 +349,8 @@ TAG astro_tag // += dopamine × astro_possible_tagging when both > threshold
|
||||
---
|
||||
|
||||
# SCOPE: DAY
|
||||
# Budgets consumed. Fast traces written and decay. Tags set but not cleared.
|
||||
# Structures READ only.
|
||||
Budgets consumed. Fast traces written and decay. Tags set but not cleared.
|
||||
Structures READ only.
|
||||
|
||||
---
|
||||
|
||||
@@ -806,7 +806,7 @@ scope DAY or NIGHT | context OVERLOAD:
|
||||
---
|
||||
|
||||
# SCOPE: NIGHT
|
||||
# Structural variables WRITTEN. Budgets replenished. Tags evaluated and cleared.
|
||||
Structural variables WRITTEN. Budgets replenished. Tags evaluated and cleared.
|
||||
|
||||
---
|
||||
|
||||
|
||||
@@ -1,87 +0,0 @@
|
||||
Excellent question. The **timing and control** of retrograde signal release are precisely regulated and differ dramatically between these messengers, which is central to their distinct roles in plasticity. Here’s a detailed breakdown.
|
||||
|
||||
---
|
||||
|
||||
### **1. Nitric Oxide (NO) – The Fast, Activity-Gated Burst**
|
||||
|
||||
* **Time Scale of Release: Milliseconds to Seconds.**
|
||||
* **Key Influencing Factors:**
|
||||
* **NMDAR Activation & Ca²⁺ Influx:** The primary trigger. Strong postsynaptic depolarization relieves the Mg²⁺ block of NMDARs. Ca²⁺ influx through NMDARs binds to **calmodulin**.
|
||||
* **Calmodulin Binding to nNOS:** The Ca²⁺/calmodulin complex directly binds to and activates **neuronal Nitric Oxide Synthase (nNOS)**, which is often physically tethered to the NMDAR complex via PSD-95.
|
||||
* **Production & Diffusion:** NO is a **gasotransmitter**; it is synthesized *on-demand* and diffuses freely in all directions (~µm range) without vesicular release. Its production stops as soon as Ca²⁺ levels drop.
|
||||
* **Kinetics:**
|
||||
* **Onset:** Extremely fast (<100 ms after strong Ca²⁺ influx).
|
||||
* **Duration:** Brief pulse (seconds). NO is highly reactive and has a short half-life (~1-5 sec) due to scavenging by hemoglobin, superoxide, and other molecules.
|
||||
* **Spatial Spread:** Limited, acts as a **local volume signal** to nearby presynaptic terminals and astrocytes.
|
||||
* **Functional Implication:** NO acts as a **fast, correlational signal**. It broadcasts: "*Strong, synchronous activation is happening right now at this precise postsynaptic site.*" Its speed and locality make it ideal for rapid presynaptic potentiation during **early-phase LTP induction**.
|
||||
|
||||
---
|
||||
|
||||
### **2. Endocannabinoids (eCBs, e.g., 2-AG) – The Intermediate, Demand-Specific Signal**
|
||||
|
||||
* **Time Scale of Release: Hundreds of Milliseconds to Tens of Seconds.**
|
||||
* **Key Influencing Factors:**
|
||||
* **Two Primary Triggers:**
|
||||
1. **Post-Synaptic Ca²⁺ Rise:** Moderate to strong increases in dendritic Ca²⁺ (via VGCCs or NMDARs) activate **calcium-sensitive phospholipase C (PLC)**.
|
||||
2. **Metabotropic Receptor Activation:** Group I mGluR (mGluR1/5) activation strongly stimulates **PLCβ** via Gq proteins.
|
||||
* **Synthesis Pathway:** Both triggers converge on **PLC**, which cleaves membrane phospholipids to produce **diacylglycerol (DAG)**. **DAG lipase α (DAGLα)**, often localized postsynaptically, then converts DAG to **2-AG**.
|
||||
* **Release:** 2-AG is **lipophilic** and diffuses across the membrane immediately upon synthesis (**no vesicular release required**).
|
||||
* **Kinetics:**
|
||||
* **Onset:** Fast, but slower than NO (~300 ms - 1 sec).
|
||||
* **Duration:** Can be a brief pulse (for DSE/DSI) or a sustained release (seconds to minutes) during prolonged mGluR activation, as in some forms of LTD.
|
||||
* **Termination:** Rapid and precise by **presynaptic reuptake** and enzymatic degradation (mainly by **monoacylglycerol lipase, MAGL**).
|
||||
* **Functional Implication:** eCBs are **bidirectional modulators**. A brief, large Ca²⁺ spike may cause short-term depression (DSE). **Sustained, moderate mGluR activation** (e.g., during low-frequency stimulation) leads to prolonged 2-AG release, inducing **long-term presynaptic LTD**. The timing encodes the *nature* of the plasticity.
|
||||
|
||||
---
|
||||
|
||||
### **3. Brain-Derived Neurotrophic Factor (BDNF) – The Slow, Regulated Secretion of a Trophic Factor**
|
||||
|
||||
* **Time Scale of Release: Seconds to Minutes, with Biphasic Secretion.**
|
||||
* **Key Influencing Factors:**
|
||||
* **Activity Pattern:** Requires **strong, sustained, or patterned activity** (e.g., theta-burst stimulation). Not triggered by single spikes.
|
||||
* **Two Pools and Release Modes:**
|
||||
1. **Constitutive Secretion:** Slow, continuous baseline release from the **trans-Golgi network**.
|
||||
2. **Activity-Dependent Secretion:** The critical mode for plasticity. Involves two sub-pools:
|
||||
* **Pre-synthesized Pool (Fast):** Mature BDNF is stored in **dense-core vesicles (DCVs)** in dendrites and spines. Strong Ca²⁺ influx (via L-type VGCCs and NMDARs) triggers **Ca²⁺-induced exocytosis** of these DCVs within **seconds**.
|
||||
* **Newly Synthesized Pool (Slow):** The activity signal (Ca²⁺/CREB) also drives **transcription of the *Bdnf* gene** and **local dendritic translation** of BDNF mRNA. This provides a delayed (**minutes to hours**) but sustained supply for release.
|
||||
* **Regulation is Highly Complex:** Controlled at the level of:
|
||||
* **Transcription** (multiple activity-sensitive promoters).
|
||||
* **mRNA trafficking** to dendrites.
|
||||
* **Translation** (regulated by CaMKII, FMRP, microRNAs).
|
||||
* **Proteolytic cleavage** of proBDNF to mature BDNF.
|
||||
* **Kinetics:**
|
||||
* **Fast Release Onset:** 1-5 seconds after strong stimulation (from DCV pool).
|
||||
* **Sustained Release:** Continues for **many minutes** as newly synthesized BDNF is made available.
|
||||
* **Clearance:** Slow relative to NO/eCBs. BDNF is cleared by endocytosis (via TrkB/p75 receptors) and diffusion, acting over longer distances (tens of µm).
|
||||
* **Functional Implication:** BDNF is not a fast "fire-and-forget" signal. It is a **sustained trophic command** that bridges the gap between initial synaptic activation and long-term structural change. Its release signifies: "*This event was important and repeated; prepare for lasting remodeling.*"
|
||||
|
||||
---
|
||||
|
||||
### **Summary Table: Temporal Logic of Retrograde Signal Release**
|
||||
|
||||
| Signal | Primary Trigger | Release Mechanism | Onset | Duration | Spatial Range | Key Role in Plasticity |
|
||||
|:------------------------|:--------------------------------------------------|:----------------------------------------------|:-------------------------------------------------|:------------------------------|:---------------------------|:-------------------------------------------------------------------|
|
||||
| **Nitric Oxide (NO)** | Strong NMDAR Ca²⁺ influx | Gas diffusion on synthesis | **< 100 ms** | **Seconds** (brief pulse) | Local (µm) | **Fast correlational signal** for early-LTP coordination. |
|
||||
| **Endocannabinoids (2-AG)** | 1) Moderate Ca²⁺ rise<br />2) mGluR1/5 activation | Lipid diffusion on synthesis | **~300 ms - 1 sec** | **Seconds to minutes** (scalable) | Local to paracrine (µm) | **Bidirectional modulator.** Brief→STD; Sustained→LTD. |
|
||||
| **BDNF** | Strong/patterned firing (L-VGCC, NMDAR) | **Regulated exocytosis** from dense-core vesicles | **1-5 sec** (fast pool)<br />**Minutes** (new synthesis) | **Minutes to hours** (sustained) | Long-distance (tens of µm) | **Trophic command signal** for switch to late-LTP & structural change. |
|
||||
|
||||
---
|
||||
|
||||
### **Critical Integration: How These Signals Work as a Cascade**
|
||||
|
||||
The **sequence and coincidence** of these releases are crucial:
|
||||
|
||||
1. **Strong Tetanus:** Massive glutamate release → **NMDAR Ca²⁺ influx**.
|
||||
2. **Immediate (ms):** **NO** is produced, rapidly potentiating presynaptic release.
|
||||
3. **Early (100s ms - sec):** Ca²⁺ and mGluR activation may produce **eCBs**, but strong depolarization often suppresses eCB-LTD in favor of LTP.
|
||||
4. **Critical Window (sec - min):** Sustained Ca²⁺ activates CREB and triggers **BDNF exocytosis**. The released BDNF:
|
||||
* Acts **presynaptically** (via TrkB) to consolidate potentiation and initiate the switch to long-term changes.
|
||||
* Acts **postsynaptically** in an autocrine/paracrine manner to enhance its own synthesis and drive spine growth.
|
||||
|
||||
**In essence, the postsynapse uses a layered communication strategy:**
|
||||
|
||||
* **NO** is for **instantaneous coordination.**
|
||||
* **eCBs** are for **intermediate-term, reversible modulation.**
|
||||
* **BDNF** is for **long-term, structural commitment.**
|
||||
|
||||
The specific pattern of presynaptic activity and postsynaptic depolarization *selects* which retrograde signal cocktail is released, thereby determining both the **sign (potentiation/depression)** and **duration (short-term/long-term)** of the synaptic change.
|
||||
@@ -1,486 +0,0 @@
|
||||
# **Detailed Temporal Dynamics of Postsynaptic Response and Plasticity**
|
||||
|
||||
*From glutamate binding to structural consolidation, with concentration changes, receptor trafficking, and calcium signaling across timescales*
|
||||
|
||||
---
|
||||
|
||||
## **Baseline State (Resting Spine)**
|
||||
|
||||
**Time:** Continuous
|
||||
**Postsynaptic [Ca²⁺]:** ~50-100 nM
|
||||
**Membrane Potential (Vₘ):** -70 mV
|
||||
**AMPARs in PSD:** 10-20 receptors (GluA1/GluA2 heteromers)
|
||||
**NMDARs in PSD:** 5-10 receptors (GluN1/GluN2B)
|
||||
**Mg²⁺ block of NMDARs:** ~80% at -70 mV
|
||||
**CaMKII state:** Mostly inactive (α:β ≈ 3:1 ratio)
|
||||
**PSD-95 clusters:** ~300 molecules per PSD
|
||||
|
||||
---
|
||||
|
||||
## **PHASE 1: FAST TIMESCALE (0-100 ms) - RECEPTOR ACTIVATION**
|
||||
|
||||
### **0.0-0.2 ms: Glutamate Arrival and Binding**
|
||||
|
||||
```
|
||||
Presynaptic glutamate release (~5000 molecules)
|
||||
↓
|
||||
Diffusion across 20 nm synaptic cleft (t ≈ 0.1 ms)
|
||||
↓
|
||||
**Glutamate concentration in cleft:**
|
||||
- Peak: 1-3 mM at PSD surface
|
||||
- Rapid clearance by EAATs (t½ ≈ 1 ms)
|
||||
↓
|
||||
**Simultaneous binding to:**
|
||||
1. **AMPARs (ionotropic, fast):**
|
||||
- 2 glutamate molecules bind per channel
|
||||
- Binding Kd ≈ 500 µM
|
||||
- Channel opens in ~0.2 ms
|
||||
|
||||
2. **NMDARs (ionotropic, slow):**
|
||||
- Requires glutamate + glycine/D-serine
|
||||
- Binding Kd ≈ 1-5 µM
|
||||
- Mg²⁺ block prevents opening at rest
|
||||
|
||||
3. **mGluRs (metabotropic):**
|
||||
- Group I mGluRs (mGluR1/5)
|
||||
- G-protein coupled, slower signaling
|
||||
```
|
||||
|
||||
### **0.2-2.0 ms: AMPAR-Mediated Depolarization**
|
||||
|
||||
```
|
||||
**For each open AMPAR:**
|
||||
- Conductance: 8-12 pS (single channel)
|
||||
- Reversal potential: 0 mV
|
||||
- **Na⁺ influx:** ~3000 ions/channel/ms
|
||||
- K⁺ efflux: ~1000 ions/channel/ms
|
||||
|
||||
**Net effect at spine head:**
|
||||
Without other inputs: EPSP amplitude = 0.5-2 mV
|
||||
With 20 AMPARs open: Current = 10-30 pA
|
||||
Depolarization to Vₘ ≈ -60 mV
|
||||
```
|
||||
|
||||
### **1.0-5.0 ms: NMDAR Activation (if depolarized)**
|
||||
|
||||
```
|
||||
**Requirement:** Vₘ > -40 mV to relieve Mg²⁺ block
|
||||
**Coincidence detection window:** 5-10 ms
|
||||
|
||||
If depolarized (from AMPARs or bAP):
|
||||
↓
|
||||
Mg²⁺ expelled from NMDAR channel
|
||||
↓
|
||||
**NMDAR opens with characteristic:**
|
||||
- Slow kinetics (τrise ≈ 10 ms, τdecay ≈ 50-100 ms)
|
||||
- High Ca²⁺ permeability (PCa/PNa ≈ 10:1)
|
||||
- **Single channel Ca²⁺ influx:** ~5000 Ca²⁺ ions/ms
|
||||
↓
|
||||
**Local [Ca²⁺] in spine head:**
|
||||
- Baseline: 100 nM
|
||||
- With NMDAR activation: **→ 1-10 µM**
|
||||
- With NMDAR + bAP coincidence: **→ 10-30 µM**
|
||||
```
|
||||
|
||||
### **5.0-50 ms: Calcium Dynamics and Clearance**
|
||||
|
||||
```
|
||||
**Calcium sources in spine:**
|
||||
1. NMDARs (main source for plasticity)
|
||||
2. Voltage-gated Ca²⁺ channels (VGCCs) from bAP
|
||||
3. Internal stores (IP₃R, RyR)
|
||||
|
||||
**Calcium buffers in spine:**
|
||||
- Calbindin-D28K (Kd ≈ 200 nM)
|
||||
- Parvalbumin (Kd ≈ 10 nM)
|
||||
- Calmodulin (Ca²⁺ sensor, Kd ≈ 1-10 µM)
|
||||
|
||||
**Clearance mechanisms:**
|
||||
1. Plasma Membrane Ca²⁺ ATPase (PMCA):
|
||||
- High affinity (Kd ≈ 100 nM)
|
||||
- Slow: clears ~30 Ca²⁺/sec per pump
|
||||
|
||||
2. Sodium-Calcium Exchanger (NCX):
|
||||
- Low affinity (Kd ≈ 1 µM)
|
||||
- Fast: 3 Na⁺ in, 1 Ca²⁺ out
|
||||
|
||||
3. SERCA pumps into ER:
|
||||
- If spine has smooth ER
|
||||
|
||||
4. Mitochondrial uptake (larger spines):
|
||||
- MCU (mitochondrial Ca²⁺ uniporter)
|
||||
- Kd ≈ 10-20 µM
|
||||
|
||||
**Result:**
|
||||
- 90% Ca²⁺ cleared in 50-100 ms
|
||||
- Returns to baseline [Ca²⁺] in 200-500 ms
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## **PHASE 2: MEDIUM TIMESCALE (100 ms - 10 sec) - SIGNALING CASCADES**
|
||||
|
||||
### **Calcium-Decoded Plasticity Decision**
|
||||
|
||||
```
|
||||
**The "Calcium Rule":**
|
||||
[Ca²⁺] amplitude × duration → plasticity direction
|
||||
|
||||
**Thresholds:**
|
||||
- LTD: 1-5 µM sustained (100 ms - 1 sec)
|
||||
- LTP: >10 µM brief (10-50 ms)
|
||||
- LTP requires **rapid rise** (d[Ca²⁺]/dt > 0.5 µM/ms)
|
||||
```
|
||||
|
||||
### **LTD Pathway (Moderate Ca²⁺)**
|
||||
|
||||
```
|
||||
[Ca²⁺] = 1-5 µM for >100 ms
|
||||
↓
|
||||
Calcium binds Calmodulin (CaM)
|
||||
↓
|
||||
**Activates Calcineurin (CaN, PP2B):**
|
||||
- Phosphatase, Kd ≈ 0.5 µM Ca²⁺
|
||||
- Activated at lower [Ca²⁺] than CaMKII
|
||||
↓
|
||||
CaN dephosphorylates Inhibitor-1
|
||||
↓
|
||||
**Releases inhibition of Protein Phosphatase-1 (PP1)**
|
||||
↓
|
||||
PP1 dephosphorylates:
|
||||
1. GluA1 at S845 → increases endocytosis
|
||||
2. Stargazin → reduces AMPAR synaptic retention
|
||||
3. Other targets promoting AMPAR removal
|
||||
↓
|
||||
**Result: AMPAR internalization begins in 30-60 sec**
|
||||
```
|
||||
|
||||
### **LTP Pathway (High Ca²⁺)**
|
||||
|
||||
```
|
||||
[Ca²⁺] > 10 µM with rapid rise
|
||||
↓
|
||||
Calcium binds Calmodulin (CaM)
|
||||
↓
|
||||
**Activates Ca²⁺/Calmodulin Kinase II (CaMKII):**
|
||||
- 12-subunit holoenzyme
|
||||
- Each subunit has autoinhibitory domain
|
||||
- Requires Ca²⁺/CaM binding to activate
|
||||
↓
|
||||
**Autophosphorylation at T286:**
|
||||
- First subunit phosphorylates neighbor
|
||||
- Creates Ca²⁺-independent activity
|
||||
- **Molecular switch:** stays active after Ca²⁺ clears
|
||||
↓
|
||||
**Active CaMKII translocates to PSD:**
|
||||
- Binds to NR2B subunit of NMDAR
|
||||
- Binds to α-actinin (actin linker)
|
||||
- Becomes structural component of PSD
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## **PHASE 3: SLOW TIMESCALE (10 sec - 10 min) - RECEPTOR TRAFFICKING**
|
||||
|
||||
### **LTD Execution (1-10 minutes)**
|
||||
|
||||
```
|
||||
**Clathrin-mediated endocytosis:**
|
||||
PP1 activity → GluA1 S845 dephosphorylated
|
||||
↓
|
||||
Increased binding to AP2 adaptor complex
|
||||
↓
|
||||
**Clathrin coats form at spine periphery (t ≈ 1-2 min)**
|
||||
↓
|
||||
AMPARs internalized via endocytosis
|
||||
↓
|
||||
**Vesicles transported to early endosomes**
|
||||
↓
|
||||
Receptors either:
|
||||
1. Recycled back to surface (silent synapses)
|
||||
2. Degraded in lysosomes (long-term LTD)
|
||||
↓
|
||||
**By 10 min:**
|
||||
- 30-50% reduction in surface AMPARs
|
||||
- EPSP amplitude decreases proportionally
|
||||
```
|
||||
|
||||
### **LTP Execution (1-10 minutes)**
|
||||
|
||||
```
|
||||
**Rapid AMPAR insertion:**
|
||||
CaMKII phosphorylates:
|
||||
1. **Stargazin (TARP γ-2) at S9:**
|
||||
- Increases binding to PSD-95
|
||||
- **Traps AMPARs in PSD** (Kd improves 10×)
|
||||
|
||||
2. **SynGAP (RasGAP):**
|
||||
- Phosphorylation inhibits Ras inactivation
|
||||
- Increases ERK/MAPK signaling
|
||||
↓
|
||||
**Exocytosis of AMPARs:**
|
||||
1. From recycling endosomes (Rab11-dependent)
|
||||
2. From intracellular pools
|
||||
3. **Insertion at extrasynaptic sites first**
|
||||
↓
|
||||
**Lateral diffusion into PSD:**
|
||||
- AMPARs diffuse in membrane (D ≈ 0.1 µm²/s)
|
||||
- Phosphorylated Stargazin binds PSD-95
|
||||
- **Trapped in PSD for minutes-hours**
|
||||
↓
|
||||
**By 10 min:**
|
||||
- 50-100% increase in surface AMPARs
|
||||
- EPSP amplitude increases 50-200%
|
||||
```
|
||||
|
||||
### **Phosphorylation State Changes**
|
||||
|
||||
```
|
||||
**AMPAR modifications during LTP:**
|
||||
- **GluA1 S831:** Phosphorylated by CaMKII/PKC
|
||||
→ Increases single channel conductance (γ from 8→12 pS)
|
||||
|
||||
- **GluA1 S845:** Phosphorylated by PKA
|
||||
→ Increases open probability (Po from 0.8→0.95)
|
||||
|
||||
- **GluA2 S880:** Phosphorylated by PKC
|
||||
→ Regulates binding to GRIP/ABP vs PICK1
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## **PHASE 4: METABOLIC SUPPORT (10 min - 2 hours) - PROTEIN SYNTHESIS**
|
||||
|
||||
### **Local Translation in Spine**
|
||||
|
||||
```
|
||||
**Trigger:**
|
||||
1. CaMKII activation
|
||||
2. mGluR activation
|
||||
3. BDNF-TrkB signaling
|
||||
|
||||
**Pathways:**
|
||||
1. **mTOR pathway:**
|
||||
- PI3K → Akt → mTORC1
|
||||
- Phosphorylates 4E-BP, releases eIF4E
|
||||
- **Initiates cap-dependent translation**
|
||||
|
||||
2. **MAPK pathway:**
|
||||
- Ras → Raf → MEK → ERK
|
||||
- Phosphorylates translation factors
|
||||
↓
|
||||
**Dendritic mRNA translation begins (t ≈ 20-30 min):**
|
||||
Key mRNAs locally translated:
|
||||
1. **CaMKIIα** - more kinase molecules
|
||||
2. **GluA1** - new AMPAR subunits
|
||||
3. **Arc/Arg3.1** - regulates AMPAR trafficking
|
||||
4. **PSD-95** - scaffolding protein
|
||||
5. **Homer1a** - regulates mGluR signaling
|
||||
↓
|
||||
**New proteins synthesized locally:**
|
||||
- Concentration increases over 1-2 hours
|
||||
- Replaces initial plasticity with stable changes
|
||||
```
|
||||
|
||||
### **Retrograde Signaling Synthesis**
|
||||
|
||||
```
|
||||
**For LTP:**
|
||||
Ca²⁺ → activates nNOS (neuronal nitric oxide synthase)
|
||||
↓
|
||||
**NO synthesis from arginine:**
|
||||
- Diffusion constant: ~3300 µm²/s
|
||||
- Half-life: ~1-5 seconds
|
||||
- Diffuses 10-20 µm to presynaptic terminal
|
||||
↓
|
||||
**BDNF synthesis and release:**
|
||||
- Transcription begins in 30 min
|
||||
- Release occurs 1-2 hours post-induction
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## **PHASE 5: STRUCTURAL CONSOLIDATION (2 hours - 24 hours)**
|
||||
|
||||
### **Actin Cytoskeleton Remodeling**
|
||||
|
||||
```
|
||||
**Spine enlargement (LTP):**
|
||||
Active CaMKII → phosphorylates **Profilin**
|
||||
↓
|
||||
Profilin binds actin monomers → promotes polymerization
|
||||
↓
|
||||
**Rho GTPase activation:**
|
||||
- Rac1 activated → promotes actin branching (via Arp2/3)
|
||||
- Cdc42 activated → promotes filopodia formation
|
||||
↓
|
||||
**Actin polymerization in spine head:**
|
||||
- F-actin increases 2-3×
|
||||
- Spine volume increases over 1-3 hours
|
||||
↓
|
||||
**PSD expansion:**
|
||||
- More space for AMPARs
|
||||
- More PSD-95 scaffolding
|
||||
↓
|
||||
**By 6 hours:** Spine volume increased 50-100%
|
||||
```
|
||||
|
||||
### **Nuclear Signaling and Gene Expression**
|
||||
|
||||
```
|
||||
**Signals reach nucleus (1-3 hours):**
|
||||
1. **CaMKIV translocation:**
|
||||
- Activated by Ca²⁺ in dendrites
|
||||
- Translocates to nucleus when phosphorylated
|
||||
|
||||
2. **MAPK/ERK translocation:**
|
||||
- Activated at synapse
|
||||
- Travels to nucleus (active transport)
|
||||
|
||||
3. **CREB phosphorylation:**
|
||||
- At S133 by CaMKIV/PKA/RSK
|
||||
- Recruits CBP/p300 coactivators
|
||||
↓
|
||||
**Transcriptional activation (3-6 hours):**
|
||||
Early genes (IEGs):
|
||||
- c-Fos, c-Jun, Egr1/Zif268
|
||||
|
||||
Late genes (plasticity-related):
|
||||
- **BDNF** (brain-derived neurotrophic factor)
|
||||
- **GluA1** (AMPAR subunit)
|
||||
- **CaMKIIα**
|
||||
- **Arc**
|
||||
- **Homer1a**
|
||||
↓
|
||||
**New proteins synthesized in soma (6-12 hours)**
|
||||
↓
|
||||
**Transport to dendrites (12-24 hours)**
|
||||
↓
|
||||
**Incorporation into spine (24+ hours)**
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## **PHASE 6: VERY SLOW TIMESCALE (Days - Weeks) - STRUCTURAL STABILITY**
|
||||
|
||||
### **Spine Maturation and Stabilization**
|
||||
|
||||
```
|
||||
**Day 1-7:**
|
||||
- **PSD thickening:** from 30 nm → 50 nm
|
||||
- **AMPAR subtype switch:**
|
||||
GluA2-lacking (Ca²⁺-permeable) → GluA2-containing
|
||||
(Occurs over days via subunit replacement)
|
||||
|
||||
- **Synaptic adhesion molecules:**
|
||||
Neuroligin-Neurexin complexes stabilize contact
|
||||
|
||||
**Week 1-4:**
|
||||
- **Spine shape changes:**
|
||||
Thin → Mushroom (LTP)
|
||||
Mushroom → Thin (LTD)
|
||||
|
||||
- **Presynaptic coordination:**
|
||||
Active zone aligns with expanded PSD
|
||||
|
||||
- **Perisynaptic astrocyte processes:**
|
||||
Enwrap mature synapse for metabolic support
|
||||
```
|
||||
|
||||
### **Homeostatic Scaling**
|
||||
|
||||
```
|
||||
**Days 2-7:**
|
||||
If overall neuron firing rate changes significantly:
|
||||
↓
|
||||
**Global scaling mechanisms:**
|
||||
1. **TNFα signaling:** from astrocytes
|
||||
2. **BDNF level changes**
|
||||
↓
|
||||
All synapses on neuron scaled up or down
|
||||
↓
|
||||
**AMPAR number adjusted** while relative differences maintained
|
||||
↓
|
||||
**Preserves signal-to-noise ratio** of individual synapses
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## **COMPLETE LTP TIMELINE EXAMPLE**
|
||||
|
||||
### **Induction (Seconds)**
|
||||
|
||||
```
|
||||
T=0 ms: Presynaptic glutamate release
|
||||
T=10 ms: bAP arrives at spine (coincidence)
|
||||
T=15 ms: [Ca²⁺] peaks at 25 µM
|
||||
T=50 ms: Ca²⁺ clears to 1 µM
|
||||
T=1 sec: CaMKII autophosphorylated (T286)
|
||||
T=10 sec: CaMKII translocates to PSD
|
||||
```
|
||||
|
||||
### **Early Expression (Minutes)**
|
||||
|
||||
```
|
||||
T=1 min: AMPARs inserted (from recycling endosomes)
|
||||
T=2 min: EPSP amplitude increases 100%
|
||||
T=5 min: Stargazin phosphorylated, AMPARs trapped
|
||||
T=10 min: Early LTP established
|
||||
```
|
||||
|
||||
### **Protein Synthesis-Dependent Phase (Hours)**
|
||||
|
||||
```
|
||||
T=30 min: Local translation begins (CaMKIIα, GluA1)
|
||||
T=1 hour: BDNF transcription initiated
|
||||
T=2 hours: Spine volume begins increasing
|
||||
T=3 hours: New proteins from local synthesis incorporated
|
||||
T=6 hours: Spine volume increased 60%
|
||||
```
|
||||
|
||||
### **Late Maintenance (Days)**
|
||||
|
||||
```
|
||||
T=12 hours: New proteins from soma arrive
|
||||
T=24 hours: Structural changes stabilized
|
||||
T=48 hours: GluA2 subunits replace GluA1 homomers
|
||||
T=7 days: Mature mushroom spine established
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## **CALCIUM SIGNALING THRESHOLDS SUMMARY**
|
||||
|
||||
| \[Ca²⁺\] Range | Duration | Sensor | Outcome |
|
||||
|----------------|----------------|-------------|----------------------------|
|
||||
| < 0.5 µM | Any | None | Baseline signaling |
|
||||
| 0.5-1 µM | \>1 sec | Calcineurin | Weak LTD |
|
||||
| 1-5 µM | 100 ms-1 sec | Calcineurin | Strong LTD |
|
||||
| 5-10 µM | Brief (<50 ms) | CaMKII | Weak LTP |
|
||||
| \>10 µM | Brief (<50 ms) | CaMKII | Strong LTP |
|
||||
| \>20 µM | Any | Calpain | Pathological, spine damage |
|
||||
|
||||
---
|
||||
|
||||
## **KEY BIOLOGICAL PRINCIPLES**
|
||||
|
||||
1. **Spine as Biochemical Compartment:**
|
||||
- Neck resistance (50-500 MΩ) restricts diffusion
|
||||
- Allows independent [Ca²⁺] signaling in each spine
|
||||
- Enables synapse-specific plasticity
|
||||
2. **Kinetic Competition:**
|
||||
- Calcineurin activates faster at low [Ca²⁺] (Kd ≈ 0.5 µM)
|
||||
- CaMKII requires higher [Ca²⁺] but has positive feedback
|
||||
- Winner-takes-all decision based on [Ca²⁺] time course
|
||||
3. **Energy Requirements:**
|
||||
- Each AMPAR insertion: ~1000 ATP
|
||||
- CaMKII autophosphorylation: 1 ATP/subunit
|
||||
- Protein synthesis: ~4 ATP/amino acid
|
||||
- ATP supplied by astrocyte lactate
|
||||
4. **Timescale Coupling:**
|
||||
- Fast (ms): Receptor activation
|
||||
- Medium (min): Trafficking existing proteins
|
||||
- Slow (hours): Making new proteins
|
||||
- Very slow (days): Structural changes
|
||||
|
||||
This postsynaptic timeline shows how a brief glutamate signal triggers a cascade of events across multiple timescales, converting transient electrical activity into lasting structural and functional changes that underlie learning and memory.
|
||||
@@ -1,708 +0,0 @@
|
||||
# **Detailed Temporal Dynamics of Presynaptic Neurotransmitter Release**
|
||||
|
||||
*With concentration changes, calcium clearance mechanisms, and multi-timescale modifications of release probability (Pr)*
|
||||
|
||||
---
|
||||
|
||||
## **Baseline State (Resting Condition)**
|
||||
|
||||
**Time:** Continuous resting state
|
||||
**Presynaptic [Ca²⁺]:** ~100 nM (resting cytosolic concentration)
|
||||
**Pr baseline:** 0.3 (30% release probability per action potential)
|
||||
**Ready vesicles:** 5-10 vesicles in readily releasable pool (RRP)
|
||||
**ATP/GTP levels:** Normal
|
||||
**Phosphorylation state:** Baseline kinase/phosphatase balance
|
||||
|
||||
---
|
||||
|
||||
## **PHASE 1: FAST TIMESCALE (0-100 ms) - SINGLE SPIKE CYCLE**
|
||||
|
||||
### **0.0-0.5 ms: Action Potential Arrival & Calcium Influx**
|
||||
|
||||
```
|
||||
AP depolarization (+30mV) reaches terminal
|
||||
↓
|
||||
VGCCs (P/Q-type) open with ~50% probability
|
||||
↓
|
||||
Ca²⁺ enters through ~20 channels per active zone
|
||||
↓
|
||||
**Local [Ca²⁺] at release site: 100 nM → 10-50 µM** (peak in nanodomain)
|
||||
↓
|
||||
Calcium diffuses ~20-30 nm to docked vesicles
|
||||
↓
|
||||
**PROBABILISTIC DECISION POINT:**
|
||||
Time window for decision: ~0.2-0.5 ms
|
||||
```
|
||||
|
||||
### **0.5-2.0 ms: Release Decision & Execution**
|
||||
|
||||
```
|
||||
├── **PATH A: RELEASE OCCURS (Pr = 0.3)**
|
||||
│ ↓
|
||||
│ [Ca²⁺] at Synaptotagmin > 10 µM
|
||||
│ ↓
|
||||
│ 3-5 Ca²⁺ ions bind to C2 domains of Synaptotagmin-1
|
||||
│ ↓
|
||||
│ Synaptotagmin inserts into membrane (Kd ~5-10 µM)
|
||||
│ ↓
|
||||
│ **SNARE complex completes zippering** (t ≈ 0.8 ms)
|
||||
│ ↓
|
||||
│ Fusion pore opens (diameter ~1 nm initially)
|
||||
│ ↓
|
||||
│ **~5000 glutamate molecules released** (t = 1-2 ms)
|
||||
│ ↓
|
||||
│ Fusion pore expands → full fusion
|
||||
│ ↓
|
||||
│ Vesicle membrane incorporated into plasma membrane
|
||||
│
|
||||
└── **PATH B: NO RELEASE (1-Pr = 0.7)**
|
||||
↓
|
||||
[Ca²⁺] at Synaptotagmin < 5 µM (insufficient binding)
|
||||
↓
|
||||
Calcium buffers (calbindin, parvalbumin) bind Ca²⁺
|
||||
↓
|
||||
Vesicle remains docked/primed
|
||||
↓
|
||||
No fusion → **silent spike**
|
||||
```
|
||||
|
||||
### **2.0-50 ms: Calcium Clearance & Fast Recovery**
|
||||
|
||||
```
|
||||
**Primary clearance mechanisms:**
|
||||
1. Plasma Membrane Ca²⁺ ATPase (PMCA):
|
||||
- Kd ~100-200 nM
|
||||
- Rate: 30 Ca²⁺/sec per pump
|
||||
- **Clears 90% of Ca²⁺ in 10-20 ms**
|
||||
|
||||
2. Na⁺/Ca²⁺ exchanger (NCX):
|
||||
- Lower affinity (Kd ~1 µM) but higher capacity
|
||||
- Important for bulk clearance
|
||||
|
||||
3. Mitochondrial uptake:
|
||||
- MCU (mitochondrial Ca²⁺ uniporter)
|
||||
- Kd ~10-20 µM
|
||||
- Slower but provides long-term buffering
|
||||
|
||||
4. Endoplasmic reticulum uptake (SERCA):
|
||||
- Sarcoplasmic/endoplasmic reticulum Ca²⁺ ATPase
|
||||
- Kd ~0.5 µM
|
||||
|
||||
**Result:** [Ca²⁺] returns to ~500 nM by 50 ms
|
||||
**Residual [Ca²⁺]:** ~200-300 nM persists for 100-500 ms
|
||||
**Vesicle retrieval:** Clathrin-mediated endocytosis begins at ~1 sec
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## **PHASE 2: SHORT-TERM PLASTICITY (100 ms - 10 sec)**
|
||||
|
||||
### **Example: Spike Train at 50 Hz (20 ms interval)**
|
||||
|
||||
```
|
||||
Spike 1: Pr = 0.3 → Release probability
|
||||
Spike 2 (20 ms later):
|
||||
Residual [Ca²⁺] = 300 nM
|
||||
Pr increases to 0.45 (facilitation)
|
||||
Ca²⁺ influx adds to residual Ca²⁺
|
||||
|
||||
Spike 3 (40 ms):
|
||||
Residual [Ca²⁺] accumulates to 400 nM
|
||||
Pr = 0.55
|
||||
But RRP depletion begins (STD component)
|
||||
|
||||
Spike 4 (60 ms):
|
||||
RRP depleted to 60%
|
||||
Effective Pr = 0.5 × 0.6 = 0.3 (balance facilitation/depletion)
|
||||
|
||||
Spike 5-10:
|
||||
Steady-state: Pr ~0.25, RRP ~40% of baseline
|
||||
```
|
||||
|
||||
### **Molecular Mechanisms of Short-Term Changes:**
|
||||
|
||||
```
|
||||
**Facilitation (0-500 ms):**
|
||||
Residual Ca²⁺ (~200-500 nM) → binds to Calmodulin
|
||||
↓
|
||||
Ca²⁺-Calmodulin binds to Munc13
|
||||
↓
|
||||
Munc13 increases priming rate 3-5×
|
||||
↓
|
||||
**Pr increases for next spike**
|
||||
|
||||
**Depression (0-2 sec):**
|
||||
Vesicle fusion → RRP depletion
|
||||
↓
|
||||
Recovery requires:
|
||||
1. Vesicle recycling (endocytosis: 1-10 sec)
|
||||
2. Vesicle repriming (2-30 sec)
|
||||
3. Reserve pool mobilization (seconds)
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## **PHASE 3: MEDIUM-TERM ADAPTATION (10 sec - 10 min)**
|
||||
|
||||
### **Example: LTP Induction at 100 Hz for 1 sec (Tetanus)**
|
||||
|
||||
```
|
||||
**0-1 sec: High-frequency stimulation**
|
||||
- 100 APs delivered
|
||||
- Massive Ca²⁺ accumulation in terminal
|
||||
- [Ca²⁺] builds to sustained 1-2 µM
|
||||
- Complete RRP depletion
|
||||
- Strong glutamate release
|
||||
|
||||
**1-30 sec: Retrograde signaling arrives**
|
||||
Postsynaptic spine produces:
|
||||
1. Nitric Oxide (NO) - diffuses in seconds
|
||||
2. Brain-Derived Neurotrophic Factor (BDNF) - released in minutes
|
||||
3. Endocannabinoids (eCBs) - for LTD case
|
||||
|
||||
NO diffuses into presynaptic terminal (t ≈ 5-10 sec)
|
||||
↓
|
||||
**NO activates soluble guanylyl cyclase (sGC)**
|
||||
↓
|
||||
sGC produces cGMP from GTP
|
||||
↓
|
||||
**cGMP increases from ~1 nM to 100 nM**
|
||||
↓
|
||||
cGMP activates Protein Kinase G (PKG)
|
||||
```
|
||||
|
||||
### **30 sec - 5 min: PKG-Mediated Pr Enhancement**
|
||||
|
||||
```
|
||||
PKG phosphorylates multiple targets:
|
||||
|
||||
1. **VGCCs (P/Q-type):**
|
||||
- Phosphorylation at specific serine residues
|
||||
- Open probability increases from 0.5 → 0.7
|
||||
- More Ca²⁺ enters per AP
|
||||
|
||||
2. **Munc18:**
|
||||
- Enhanced interaction with Syntaxin
|
||||
- Vesicle priming rate increases 2×
|
||||
|
||||
3. **Synaptotagmin-1:**
|
||||
- Increased Ca²⁺ sensitivity (Kd decreases from 10→5 µM)
|
||||
- Faster binding kinetics
|
||||
|
||||
4. **RIM proteins:**
|
||||
- Enhanced vesicle tethering
|
||||
- Better VGCC-vesicle coupling
|
||||
|
||||
**Net effect by 5 min:**
|
||||
- Pr increases from 0.3 → 0.5
|
||||
- Baseline Ca²⁺ sensitivity increased
|
||||
- Readily Releasable Pool size increases 30%
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## **PHASE 4: SLOW CONSOLIDATION (10 min - 2 hours)**
|
||||
|
||||
### **Local Protein Synthesis (Presynaptic)**
|
||||
|
||||
```
|
||||
**30 min - 2 hours:**
|
||||
BDNF binds to TrkB receptors on presynaptic terminal
|
||||
↓
|
||||
Activation of PI3K/mTOR pathway
|
||||
↓
|
||||
**Local translation of presynaptic mRNAs:**
|
||||
1. VGCC subunits (α1A, β4)
|
||||
2. Synaptotagmin-1
|
||||
3. Munc13-1
|
||||
4. SNARE proteins
|
||||
|
||||
**Result by 2 hours:**
|
||||
- 50% more VGCCs clustered at active zone
|
||||
- 40% more Synaptotagmin molecules per vesicle
|
||||
- Pr stabilizes at 0.6
|
||||
```
|
||||
|
||||
### **Metabolic Support System**
|
||||
|
||||
```
|
||||
**Astrocyte coordination:**
|
||||
1. Glutamate uptake → converted to glutamine
|
||||
2. Glutamine exported to presynaptic terminal
|
||||
3. Presynaptic mitochondria increase oxidative phosphorylation
|
||||
4. ATP production increases 2× to support enhanced release
|
||||
|
||||
**Energy requirements:**
|
||||
- Vesicle recycling: ~10,000 ATP/vesicle
|
||||
- Ca²⁺ clearance: ~1 ATP/2 Ca²⁺ ions
|
||||
- Protein synthesis: ~4 ATP/amino acid
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## **PHASE 5: STRUCTURAL CONSOLIDATION (2 hours - 24 hours)**
|
||||
|
||||
### **Nuclear Signaling & Gene Expression**
|
||||
|
||||
```
|
||||
**2-6 hours:**
|
||||
Persistent kinase activity (PKG, PKA, MAPK)
|
||||
↓
|
||||
CREB phosphorylation in presynaptic nucleus
|
||||
↓
|
||||
**Gene expression changes:**
|
||||
1. Structural proteins (Bassoon, Piccolo)
|
||||
2. Active zone components
|
||||
3. Vesicle cycle proteins
|
||||
4. Metabolic enzymes
|
||||
|
||||
**12-24 hours:**
|
||||
New proteins arrive via axonal transport
|
||||
↓
|
||||
**Active zone remodeling:**
|
||||
- Active zone area increases 30-50%
|
||||
- More docked vesicles (RRP size doubles)
|
||||
- VGCC-vesicle distance decreases to 15 nm
|
||||
- **Pr stabilizes at 0.7-0.8**
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## **CALCIUM HOMEOSTASIS TIMELINE SUMMARY**
|
||||
|
||||
| Time | \[Ca²⁺\] at Release Site | Clearance Mechanism | Residual Effect |
|
||||
|--------|--------------------------|--------------------------|----------------------------|
|
||||
| 0 ms | 100 nM (baseline) | \- | \- |
|
||||
| 0.5 ms | 10-50 µM (peak) | Diffusion only | Fusion decision |
|
||||
| 5 ms | 1-5 µM | Fast buffers (calbindin) | Ca²⁺-calmodulin activation |
|
||||
| 20 ms | 500 nM | PMCA pumps active | Facilitation of next spike |
|
||||
| 100 ms | 300 nM | NCX contributes | Augmentation phase |
|
||||
| 1 sec | 200 nM | Mitochondrial uptake | Potentiation |
|
||||
| 10 sec | 150 nM | Steady-state clearance | LTP induction possible |
|
||||
| 1 min | 120 nM | Full homeostasis | \- |
|
||||
| 1 hour | 100 nM | Normal resting state | \- |
|
||||
|
||||
---
|
||||
|
||||
## **EXAMPLE: COMPLETE LTP TIMELINE**
|
||||
|
||||
### **Day 1: Induction Phase**
|
||||
|
||||
```
|
||||
**T=0:** 100 Hz tetanus (1 sec)
|
||||
**T=5 sec:** NO arrives at presynaptic terminal
|
||||
**T=30 sec:** cGMP peaks, PKG activated
|
||||
**T=5 min:** Pr increases to 0.45 (phosphorylation)
|
||||
**T=30 min:** Local protein synthesis begins
|
||||
**T=2 hours:** Pr = 0.55, structural proteins arriving
|
||||
**T=6 hours:** Active zone remodeling begins
|
||||
**T=24 hours:** Pr stabilizes at 0.65, active zone enlarged 40%
|
||||
```
|
||||
|
||||
### **Day 2-7: Maintenance**
|
||||
|
||||
```
|
||||
**Metabolic support ongoing:**
|
||||
- Astrocyte supplies glutamine/lactate
|
||||
- Mitochondrial density increases near active zone
|
||||
- Vesicle recycling efficiency improves
|
||||
|
||||
**Structural stabilization:**
|
||||
- New active zone material incorporated
|
||||
- Cytoskeleton reorganizes
|
||||
- Pr maintains at 0.65-0.70
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## **KEY BIOLOGICAL INSIGHTS**
|
||||
|
||||
1. **Pr is multi-dimensional:**
|
||||
- **Fast component:** Vesicle availability × Ca²⁺ sensitivity
|
||||
- **Slow component:** Protein composition × active zone geometry
|
||||
2. **Energy dependence:**
|
||||
- Ca²⁺ clearance requires constant ATP
|
||||
- Without ATP, [Ca²⁺] remains elevated → toxicity
|
||||
- Metabolic veto: Low ATP → release inhibition despite Ca²⁺
|
||||
3. **Timescale hierarchy:**
|
||||
- **ms:** Existing protein modification (phosphorylation)
|
||||
- **min:** Local protein synthesis
|
||||
- **hours:** Nuclear transcription
|
||||
- **days:** Structural reorganization
|
||||
4. **Homeostatic balance:**
|
||||
- Enhanced Pr increases metabolic demand
|
||||
- Requires coordinated astrocyte support
|
||||
- Long-term maintenance depends on energy availability
|
||||
|
||||
This detailed timeline shows how a single probabilistic event (vesicle release) is embedded in a complex, multi-timescale regulatory system that balances immediate communication needs with long-term information storage and metabolic sustainability.
|
||||
|
||||
---
|
||||
|
||||
---
|
||||
|
||||
---
|
||||
|
||||
Based on the provided document, here is a specification of the Short-Term Plasticity (STP/STD) and Long-Term Plasticity (LTP/LTD) mechanisms between the Presynapse and Postsynapse, detailing both internal processes and their interactions, with explicit timescales.
|
||||
|
||||
### **Summary: Primary Plasticity Mechanisms & Timescales**
|
||||
|
||||
| Mechanism | Primary Locus | Key Internal Trigger | Key Interactive Signal | Timescale | Functional Role |
|
||||
|-----------------------------------|------------------|-----------------------------------------------|-------------------------------------------------|------------------------------------|------------------------------------------------------------|
|
||||
| **Short-Term Depression (STD)** | **Presynaptic** | Vesicle pool depletion | Reduced glutamate release | **Fast (<100ms)** | Filters high-frequency bursts; transient synaptic fatigue. |
|
||||
| **Short-Term Potentiation (STP)** | **Presynaptic** | Residual Ca²⁺ buildup | Increased glutamate release probability ($P_r$) | **Fast to Medium (<100ms to 10s)** | Facilitates temporal summation; augments recent activity. |
|
||||
| **Long-Term Depression (LTD)** | **Postsynaptic** | Moderate, sustained Ca²⁺ influx (~1-5 µM) | Retrograde endocannabinoids (eCBs) | **Slow (Seconds to Minutes)** | Weakens ineffective connections; homeostatic adjustment. |
|
||||
| **Long-Term Potentiation (LTP)** | **Postsynaptic** | Strong, coincident Ca²⁺ influx (>10 µM) | Retrograde NO/BDNF | **Slow (Seconds to Minutes)** | Strengthens correlated pre- and postsynaptic activity. |
|
||||
| **Structural LTP/LTD** | **Both** | Persistent molecular tags & protein synthesis | Trophic factors & homeostatic scaling | **Structural (Days+)** | Embeds memory persistently via physical changes. |
|
||||
|
||||
---
|
||||
|
||||
### **Detailed Breakdown by Timescale**
|
||||
|
||||
#### **1. Fast Timescale (<100 ms): STP & STD Internal Mechanisms**
|
||||
|
||||
* **Presynaptic Internal (STD):** Rapid vesicle fusion and release depletes the readily releasable pool. This is a **presynaptic, internal** mechanism causing a transient decrease in synaptic strength.
|
||||
* **Presynaptic Internal (STP):** Residual Ca²⁺ from a preceding action potential lingers, increasing the release probability ($P_r$) for the next spike. This is a **presynaptic, internal** facilitatory mechanism.
|
||||
* **Interaction (Fast Signaling):** The presynapse releases **glutamate** (outgoing signal). The postsynapse receives it and, if sufficiently depolarized, opens NMDA receptors, allowing a **Ca²⁺ influx**. This **Ca²⁺ transient** is the **postsynaptic, internal** coincidence detector signal that initiates the cascade for slower plasticity.
|
||||
|
||||
#### **2. Medium Timescale (100 ms – 10 s): Augmentation & Modulation**
|
||||
|
||||
* **Presynaptic Internal:** Augmentation via Munc13 proteins modifies $P_r$ based on Ca²⁺ sensing. This is a **presynaptic, internal** continuation of STP.
|
||||
* **Postsynaptic Internal:** Metabotropic glutamate receptor (mGluR) activation modulates local spine excitability and prepares plasticity pathways. This is a **postsynaptic, internal** modulatory state.
|
||||
* **Interaction:** Largely an extension of fast signaling, setting the stage for slower decisions. The **pattern of glutamate release** interacts with the **postsynaptic voltage state**.
|
||||
|
||||
#### **3. Slow Timescale (Seconds – Minutes): LTP & LTD Decision & Expression**
|
||||
|
||||
This is the critical window for **bidirectional interaction** that establishes long-term change.
|
||||
|
||||
* **Postsynaptic Internal (The Decision):**
|
||||
* **LTP Trigger:** **High, localized Ca²⁺** (from strong NMDA activation + back-propagating AP) activates **CaMKII**, creating a **plasticity tag**.
|
||||
* **LTD Trigger:** **Moderate, sustained Ca²⁺** (from isolated glutamate release or low-frequency stimulation) activates phosphatases (e.g., calcineurin).
|
||||
* This decision is **postsynaptic and internal**.
|
||||
* **Interaction (Retrograde Messaging):**
|
||||
* For **LTP:** The postsynapse synthesizes and releases **retrograde signals (NO, BDNF)**. These diffuse to the presynapse.
|
||||
* For **LTD:** The postsynapse releases **endocannabinoids (eCBs)**.
|
||||
* These are **interactive signals from postsynapse to presynapse**.
|
||||
* **Presynaptic Internal (Expression):**
|
||||
* **For LTP:** NO/BDNF activate enzymatic cascades that **persistently increase the baseline** $P_r$.
|
||||
* **For LTD:** eCBs bind to CB1 receptors, inhibiting VGCCs and **persistently decreasing** $P_r$ (Direct Synaptic Depression, DSE).
|
||||
* This change in baseline $P_r$ is the **presynaptic, internal** expression of the long-term change.
|
||||
|
||||
#### **4. Metabolic Timescale (Minutes – Hours): Consolidation**
|
||||
|
||||
* **Interaction (Astrocyte Bridge):** The astrocyte supplies **D-serine** (co-agonist for NMDAR) and **lactate** (energy). This **external, interactive support** is required for stable consolidation.
|
||||
* **Postsynaptic Internal:** The spine initiates **local protein synthesis**, using the "tag" to capture newly made proteins, transitioning early-LTP/LTD to a more stable state. This is a **postsynaptic, internal** consolidation process.
|
||||
|
||||
#### **5. Structural Timescale (Days+): Embodiment**
|
||||
|
||||
* **Presynaptic Internal:** The bouton **grows or retracts**, changing the active zone size and vesicle pool. This is a **presynaptic, internal** structural change.
|
||||
* **Postsynaptic Internal:** The spine **changes its volume and number of AMPA receptor slots**. This is a **postsynaptic, internal** structural change.
|
||||
* **Interaction (Global Scaling):** The soma sends **homeostatic scaling signals** to all synapses (including this one) to maintain network stability, providing a **top-down, interactive modulation** that can override local weights.
|
||||
|
||||
### **Conclusion**
|
||||
|
||||
* **STP/STD** are predominantly **presynaptic, internal** phenomena operating on **fast to medium timescales** (ms to s), governed by vesicle dynamics and residual calcium.
|
||||
* **LTP/LTD** are initiated by a **postsynaptic, internal** calcium-based decision on a **slow timescale** (s to min). Their expression involves a **critical bidirectional interaction**: retrograde signals (NO/BDNF for LTP, eCBs for LTD) from the postsynapse induce **presynaptic, internal** changes in baseline $P_r$.
|
||||
* These changes are then stabilized on **metabolic and structural timescales** through astrocytic support and physical remodeling of both synaptic components, embedding the memory trace in the physical architecture of the connection.
|
||||
|
||||
---
|
||||
|
||||
---
|
||||
|
||||
---
|
||||
|
||||
**In biology, presynaptic release probability (Pr) emerges from a dynamic molecular machine, not a simple number.** Changing Pr involves coordinated modifications to multiple components of the vesicle release apparatus. Here's the biological process breakdown:
|
||||
|
||||
## **The Pr Machinery: Three Core Components**
|
||||
|
||||
Pr = f(**Calcium Influx** × **Vesicle Readiness** × **Fusion Machinery Sensitivity**)
|
||||
|
||||
### **1. Modulating Calcium Influx**
|
||||
|
||||
**Target:** Voltage-Gated Calcium Channels (VGCCs, mainly P/Q and N-type).
|
||||
|
||||
- **Increasing Pr:** Phosphorylation of VGCCs by kinases (PKA, PKC) enhances their open probability or prolongs open time.
|
||||
- **Decreasing Pr:**
|
||||
- Direct inhibition by G-proteins (e.g., via activated CB1 receptors during LTD).
|
||||
- Physical relocation of channels away from release sites.
|
||||
- Dephosphorylation by phosphatases (calcineurin).
|
||||
|
||||
**Biological Process:** A retrograde messenger (e.g., NO) activates a kinase cascade in the presynaptic terminal, leading to VGCC phosphorylation → more Ca²⁺ enters per action potential → higher Pr.
|
||||
|
||||
### **2. Modulating Vesicle Readiness (Docking/Priming)**
|
||||
|
||||
**Targets:** Docking proteins (Syntaxin, SNAP-25), priming proteins (Munc13, Munc18), and the vesicle pool itself.
|
||||
|
||||
- **Increasing Pr:**
|
||||
- **Munc13 activation:** Residual Ca²⁺ binds to calmodulin, which binds to Munc13, increasing its priming activity. This is the main mechanism for **short-term facilitation**.
|
||||
- **Phosphorylation of priming proteins** by PKC/CaMKII makes them more active.
|
||||
- Increased expression or recruitment of vesicles to the "readily releasable pool" (RRP).
|
||||
- **Decreasing Pr:**
|
||||
- Dephosphorylation of priming proteins.
|
||||
- Physical depletion of RRP during high-frequency firing (STD).
|
||||
- Ubiquitination and degradation of priming proteins.
|
||||
|
||||
### **3. Modulating Fusion Machinery Sensitivity (Ca²⁺ Sensor)**
|
||||
|
||||
**Target:** The primary Ca²⁺ sensor Synaptotagmin and the SNARE complex (Syntaxin, Synaptobrevin, SNAP-25).
|
||||
|
||||
- **Increasing Pr:**
|
||||
- Phosphorylation of Synaptotagmin increases its Ca²⁺ affinity.
|
||||
- Phosphorylation of SNARE proteins (e.g., SNAP-25 by PKC) enhances fusion kinetics.
|
||||
- Assembly of more SNARE complexes.
|
||||
- **Decreasing Pr:**
|
||||
- Cleavage of SNARE proteins by toxins (e.g., botulinum).
|
||||
- Increased binding of inhibitory proteins like Complexins.
|
||||
|
||||
## **Specific Biological Pathways for Pr Changes**
|
||||
|
||||
### **Fast Pr Increase (Facilitation, <100ms)**
|
||||
|
||||
**Process:** Action potential → Ca²⁺ influx → residual Ca²⁺ binds to calmodulin → Ca²⁺-calmodulin binds to Munc13 → Munc13 increases vesicle priming rate → more vesicles become release-ready for the next spike.
|
||||
|
||||
**Biological signature:** Transient, activity-dependent, decays with Ca²⁺ clearance.
|
||||
|
||||
### **Slow Pr Increase (LTP Expression, Minutes+)**
|
||||
|
||||
**Process:** Retrograde NO diffuses into presynaptic terminal → activates soluble guanylyl cyclase → produces cGMP → activates Protein Kinase G (PKG) → PKG phosphorylates multiple targets:
|
||||
|
||||
1. **VGCCs** → increased Ca²⁺ influx
|
||||
2. **Munc18** → enhanced vesicle priming
|
||||
3. **Synaptotagmin** → increased Ca²⁺ sensitivity **Plus:** Local protein synthesis of new vesicle proteins.
|
||||
|
||||
**Biological signature:** Persistent, requires gene expression for maintenance, structurally embedded.
|
||||
|
||||
### **Slow Pr Decrease (LTD Expression, Minutes+)**
|
||||
|
||||
**Process:** Retrograde eCBs bind presynaptic CB1 receptors → activates Gi/o proteins → βγ subunits directly inhibit VGCCs → reduced Ca²⁺ influx → decreased Pr.
|
||||
**Additionally:** Gi/o inhibits adenylyl cyclase → reduced cAMP → reduced PKA activity → decreased phosphorylation of release machinery.
|
||||
|
||||
**Biological signature:** Reversible initially, can become structural with prolonged activation.
|
||||
|
||||
## **The Complete Biological Cascade for LTP-Induced Pr Increase**
|
||||
|
||||
```
|
||||
Retrograde NO/BDNF
|
||||
↓
|
||||
Presynaptic receptor activation
|
||||
↓
|
||||
Second messenger cascade (cGMP/cAMP)
|
||||
↓
|
||||
Kinase activation (PKG/PKA/PKC)
|
||||
↓
|
||||
Phosphorylation of multiple targets:
|
||||
1. VGCCs → ↑ Ca²⁺ influx per AP
|
||||
2. Munc13/18 → ↑ vesicle priming rate
|
||||
3. Synaptotagmin → ↑ Ca²⁺ sensitivity
|
||||
4. SNARE proteins → ↑ fusion efficiency
|
||||
↓
|
||||
Increased Pr from baseline 0.2 → 0.4
|
||||
↓
|
||||
More reliable vesicle release per AP
|
||||
↓
|
||||
Structural reinforcement (Days+):
|
||||
- More active zone material
|
||||
- More docked vesicles
|
||||
- Closer VGCC-vesicle coupling
|
||||
```
|
||||
|
||||
## **Simulation vs. Biological Reality**
|
||||
|
||||
| In Simulation | In Biology |
|
||||
|---------------------------------|-------------------------------------------------------------------------------------------------|
|
||||
| `Pr = 0.3` | Pr emerges from: 5 docked vesicles × 40% channel open probability × 60% fusion probability |
|
||||
| Update rule: `Pr += 0.1` if LTP | LTP: NO → cGMP → PKG → phosphorylates 3 proteins → increases Ca²⁺ influx 30% & priming rate 40% |
|
||||
| Single variable | Distributed property of ~50 protein species |
|
||||
| Instant change | Change occurs over: 100ms (fast), 1min (slow), 24hr (structural) |
|
||||
|
||||
## **Key Biological Insights**
|
||||
|
||||
1. **Pr is multi-parametric:** Not one number but the product of multiple probabilities.
|
||||
2. **Redundancy:** Multiple pathways converge on Pr (kinases, protein synthesis, structural changes).
|
||||
3. **Timescale hierarchy:**
|
||||
- **Fast (ms):** Modify existing proteins (phosphorylation)
|
||||
- **Slow (min):** Synthesize new proteins
|
||||
- **Structural (days):** Change physical architecture
|
||||
4. **Metabolic dependence:** All phosphorylation requires ATP. During energy crisis, kinases fail → Pr decreases even with "LTP signals."
|
||||
5. **Cross-talk:** The same kinase (e.g., PKC) can phosphorylate both VGCCs and SNARE proteins, creating coordinated enhancement.
|
||||
|
||||
In essence, **Pr is the presynaptic terminal's "readiness state"**—a complex, dynamic equilibrium of dozens of interacting proteins that the neuron tunes through phosphorylation, gene expression, and structural remodeling to implement learning and adaptation.
|
||||
|
||||
---
|
||||
|
||||
---
|
||||
|
||||
---
|
||||
|
||||
**The presynapse does NOT release neurotransmitter every time a presynaptic spike arrives.** This is a fundamental principle of synaptic transmission: **release is probabilistic, not deterministic.**
|
||||
|
||||
## **What Pr Actually Influences**
|
||||
|
||||
**Pr (Release Probability)** determines the **likelihood** that a given action potential will trigger **vesicle fusion and neurotransmitter release**. It's essentially the synapse's **"coin toss" probability** for transmission.
|
||||
|
||||
### **Biological Reality:**
|
||||
|
||||
For a typical central synapse:
|
||||
|
||||
- **Pr ≈ 0.2-0.5** (meaning only 20-50% of spikes cause release)
|
||||
- Some specialized synapses (like the neuromuscular junction) have Pr ≈ 0.9
|
||||
- Some cortical synapses have Pr as low as 0.1
|
||||
|
||||
### **What Happens at a Presynaptic Terminal When a Spike Arrives:**
|
||||
|
||||
```
|
||||
Action Potential arrives at terminal
|
||||
↓
|
||||
VGCCs open → Ca²⁺ enters
|
||||
↓
|
||||
**PROBABILISTIC DECISION POINT**
|
||||
↓
|
||||
├── **With probability Pr (e.g., 0.3):**
|
||||
│ ↓
|
||||
│ Ca²⁺ binds to Synaptotagmin on docked vesicle
|
||||
│ ↓
|
||||
│ SNARE complex zippers completely
|
||||
│ ↓
|
||||
│ Vesicle membrane fuses with presynaptic membrane
|
||||
│ ↓
|
||||
│ **GLUTAMATE RELEASED** → Postsynaptic response
|
||||
│
|
||||
└── **With probability 1-Pr (e.g., 0.7):**
|
||||
↓
|
||||
Ca²⁺ enters but insufficient to trigger fusion
|
||||
↓
|
||||
Vesicle remains docked but unfused
|
||||
↓
|
||||
**NO RELEASE** → No postsynaptic response
|
||||
```
|
||||
|
||||
## **The Biological Basis of This Stochasticity**
|
||||
|
||||
### **1. Calcium Nanodomain Stochasticity**
|
||||
|
||||
- Ca²⁺ channels are ~20-30 nm from vesicle release sites
|
||||
- When a channel opens, only ~100-300 Ca²⁺ ions enter
|
||||
- These ions form a brief, localized "nanodomain"
|
||||
- **Random diffusion and buffering** mean the Ca²⁺ concentration at the sensor varies randomly
|
||||
- If <5-10 µM at the sensor → no fusion; if >10 µM → fusion
|
||||
|
||||
### **2. Molecular Stochasticity**
|
||||
|
||||
- **Synaptotagmin** (Ca²⁺ sensor) requires 3-5 Ca²⁺ ions to bind
|
||||
- **SNARE complex** zippering is thermally driven and probabilistic
|
||||
- These molecular processes have intrinsic randomness at nanoscale
|
||||
|
||||
### **3. Vesicle State Stochasticity**
|
||||
|
||||
- Vesicles exist in different "readiness states":
|
||||
- **Docked & primed** (immediately releasable)
|
||||
- **Docked but unprimed**
|
||||
- **Reserve pool** (undocked)
|
||||
- Transition between states is probabilistic
|
||||
|
||||
## **Why Evolution Selected Probabilistic Release**
|
||||
|
||||
### **Advantages of Low/Moderate Pr:**
|
||||
|
||||
1. **Dynamic Range:** Allows both **facilitation** (Pr increases with repeated spikes) and **depression** (Pr decreases with vesicle depletion)
|
||||
2. **Noise Filtering:** Random failures filter out isolated, potentially noisy spikes while allowing bursts to get through (due to facilitation)
|
||||
3. **Energy Efficiency:** Release machinery (vesicle fusion/recycling) is energetically expensive. Why waste energy on every spike?
|
||||
4. **Information Capacity:** Probabilistic release allows synapses to encode information in **release probability** as well as spike rate
|
||||
5. **Plasticity Substrate:** The stochastic nature provides a substrate for learning through Hebbian mechanisms
|
||||
|
||||
## **What Actually Gets Released When Release Occurs**
|
||||
|
||||
Even when release occurs, it's not always "all or nothing":
|
||||
|
||||
### **Quantal Release:**
|
||||
|
||||
- **Miniature EPSCs (mEPSCs):** Single vesicle release (~1000-5000 glutamate molecules)
|
||||
- **Univesicular Release:** Most CNS synapses release **0 or 1 vesicle** per active zone per spike
|
||||
- **Multivesicular Release:** Some synapses can release 2-3 vesicles simultaneously
|
||||
|
||||
### **Key Measurement:**
|
||||
|
||||
```
|
||||
EPSC amplitude = Q × n × Pr
|
||||
```
|
||||
|
||||
Where:
|
||||
|
||||
- **Q** = quantal size (response to one vesicle)
|
||||
- **n** = number of release sites (active zones)
|
||||
- **Pr** = release probability per site
|
||||
|
||||
## **How This Plays Out in Neural Computation**
|
||||
|
||||
### **Example: Cortical Pyramidal Neuron Synapse**
|
||||
|
||||
```
|
||||
Spike train arrives: [1, 1, 1, 1, 1, 1] (6 spikes at 50 Hz)
|
||||
|
||||
With Pr = 0.3:
|
||||
Actual releases might be: [0, 1, 0, 0, 1, 1]
|
||||
|
||||
Postsynaptic effect:
|
||||
- Spike 1: No response
|
||||
- Spike 2: EPSP
|
||||
- Spike 3: No response
|
||||
- Spike 4: No response
|
||||
- Spike 5: EPSP
|
||||
- Spike 6: EPSP
|
||||
|
||||
But due to facilitation:
|
||||
Pr increases to 0.5 by spike 6
|
||||
```
|
||||
|
||||
## **Simulation Implications**
|
||||
|
||||
In simulations, you would implement this as:
|
||||
|
||||
```python
|
||||
import numpy as np
|
||||
|
||||
class Synapse:
|
||||
def __init__(self, Pr=0.3):
|
||||
self.Pr = Pr # Release probability
|
||||
self.vesicles_available = True
|
||||
|
||||
def process_spike(self):
|
||||
if not self.vesicles_available:
|
||||
return 0 # No release due to depletion
|
||||
|
||||
# Probabilistic release decision
|
||||
if np.random.random() < self.Pr:
|
||||
# Release occurs
|
||||
self.vesicles_available = False # Temporary depletion
|
||||
self.trigger_recycle_timer() # Schedule vesicle recycling
|
||||
return 1 # 1 vesicle released
|
||||
else:
|
||||
# Release fails probabilistically
|
||||
return 0
|
||||
```
|
||||
|
||||
## **Biological Determinants of Pr**
|
||||
|
||||
**High Pr synapses** tend to have:
|
||||
|
||||
- Denser VGCC clustering near release sites
|
||||
- Higher Ca²⁺ sensitivity of Synaptotagmin
|
||||
- More efficient priming machinery (Munc13)
|
||||
- Larger readily releasable pool
|
||||
|
||||
**Low Pr synapses** tend to have:
|
||||
|
||||
- Sparse VGCC distribution
|
||||
- Lower Ca²⁺ sensitivity
|
||||
- Less efficient priming
|
||||
- Smaller readily releasable pool
|
||||
|
||||
## **The Big Picture**
|
||||
|
||||
**Pr is the synapse's "transmission reliability setting"** that:
|
||||
|
||||
1. **Filters** spike trains probabilistically
|
||||
2. **Encodes** short-term plasticity through dynamic changes
|
||||
3. **Embeds** long-term memory through stable modifications
|
||||
4. **Conserves** energy by not releasing on every spike
|
||||
|
||||
This stochasticity isn't a bug—it's a feature that allows synapses to be **temporal filters, memory elements, and computational units** all at once. The fact that transmission isn't guaranteed is precisely what gives synapses their rich computational properties, enabling phenomena like paired-pulse facilitation, synaptic filtering of high-frequency bursts, and providing a substrate for Hebbian learning through coincident detection failures.
|
||||
@@ -1,236 +0,0 @@
|
||||
# **How the First Somatic Spike Emerges from AMPA Alone**
|
||||
|
||||
This is the central mystery of neural initiation—the **"first spike problem"** or "bootstrapping problem." If strong synaptic plasticity (LTP) requires coincident presynaptic glutamate **AND** postsynaptic depolarization from a backpropagating action potential (bAP), but the bAP only exists if the soma fires first... what triggers the **very first** somatic spike that creates the first bAP?
|
||||
|
||||
The solution involves several elegant biological strategies that work in concert:
|
||||
|
||||
## **1. The Cooperativity Principle: Many Weak Voices Shouting Together**
|
||||
|
||||
A single spine with only AMPA receptors open generates a tiny EPSP (~0.2-2 mV). This is **far below** the somatic/AIS threshold (typically ~15-20 mV above rest). The key is **spatial and temporal summation**:
|
||||
|
||||
- **Spatial Summation:** Many spines (dozens to hundreds) on different dendrites receive input **simultaneously or nearly simultaneously**. Their individual AMPA-mediated EPSPs summate at the soma.
|
||||
- **Temporal Summation:** A single presynaptic neuron firing a **brief burst** (2-5 spikes at 50-100 Hz) can cause EPSPs that arrive close enough in time (within 5-15 ms) to summate.
|
||||
|
||||
**Example:** If 100 spines each produce a 1 mV EPSP simultaneously, the soma sees a 100 mV depolarization (in theory). In reality, cable properties and inhibition reduce this, but the principle holds: **many weak inputs can cross threshold together.**
|
||||
|
||||
## **2. Dendritic Amplification: Local Spikes Without Somatic Firing**
|
||||
|
||||
Dendrites are **not passive cables**. They contain voltage-gated channels (Na⁺, Ca²⁺, NMDA):
|
||||
|
||||
- **Local NMDA Activation:** Even without a prior bAP, if **enough AMPA receptors** on a **local cluster of spines** open simultaneously, the **summed local depolarization** can be sufficient to partially relieve the Mg²⁺ block on nearby NMDA receptors.
|
||||
- **Dendritic Spike Generation:** This local depolarization can trigger a **dendritic Na⁺ or Ca²⁺ spike** (a regenerative event confined to that branch). This dendritic spike provides the **strong, local depolarization** needed to fully activate NMDA receptors in that region.
|
||||
- **The Dendritic Spike Travels:** While attenuated, this amplified signal propagates toward the soma much more effectively than individual EPSPs.
|
||||
|
||||
**Thus, the first somatic spike is often triggered by a dendritic spike generated from cooperative local input, not by simple EPSP summation.**
|
||||
|
||||
## **3. Background "Noise" and Membrane Fluctuations**
|
||||
|
||||
The neuron's membrane is never perfectly still:
|
||||
|
||||
- **Spontaneous Miniature EPSPs (minis):** Even at rest, vesicles spontaneously fuse, producing tiny (~0.5 mV) AMPA-mediated events. This creates a fluctuating baseline.
|
||||
- **Stochastic Channel Opening:** Ion channels open and close randomly.
|
||||
- **Network Background Activity:** Other neurons provide constant, subthreshold input.
|
||||
|
||||
This **background depolarization** brings the somatic membrane potential closer to threshold. When a synchronized input arrives, it needs less additional depolarization to reach threshold. The soma is effectively **primed** by ongoing network activity.
|
||||
|
||||
## **4. Neuromodulatory "Gain" Control**
|
||||
|
||||
Neuromodulators can dramatically lower the threshold for the first spike:
|
||||
|
||||
- **Dopamine (via D1 receptors):** Increases dendritic excitability and lowers AIS threshold.
|
||||
- **Acetylcholine:** Decreases potassium leak currents, increasing input resistance (same current produces larger voltage change).
|
||||
- **Norepinephrine:** Enhances NMDA receptor currents and increases synaptic efficacy.
|
||||
|
||||
During states of **attention, novelty, or salience**, these neuromodulators effectively make the entire neuron **more sensitive**, allowing weaker coordinated inputs to trigger the first spike.
|
||||
|
||||
## **5. The "Primed" Spine: Increased AMPA Receptor Sensitivity**
|
||||
|
||||
While resting spines aren't inherently more sensitive, several mechanisms can make them **primed for the first event**:
|
||||
|
||||
- **Silent Synapses:** Some spines contain **NMDA receptors but few or no AMPA receptors**. They are "silent" because AMPA is needed for the initial depolarization. However, if:
|
||||
1. Multiple silent synapses are activated together
|
||||
2. Or a neighboring spine with AMPA receptors provides local depolarization
|
||||
3. The NMDA receptors on silent spines can activate
|
||||
- **Metaplasticity:** Previous activity patterns can tune a spine's receptors to be more responsive to the **next** event.
|
||||
- **Astrocyte-D-serine:** Basal levels of D-serine from astrocytes keep a portion of NMDA receptors **partially primed** even at rest.
|
||||
|
||||
## **6. The Hierarchical Trigger Sequence**
|
||||
|
||||
Here's the typical sequence for triggering the **first** somatic spike from a previously silent or resting state:
|
||||
|
||||
1. **Presynaptic Volley:** A group of presynaptic neurons fire in near-synchrony (within 10-20 ms).
|
||||
2. **Dendritic Cluster Activation:** Their target spines are clustered on one or more dendritic branches.
|
||||
3. **Local Summation:** AMPA-EPSPs summate locally, creating **sufficient depolarization** (~10-15 mV locally).
|
||||
4. **NMDA Recruitment:** Local depolarization partially unblocks nearby NMDA receptors.
|
||||
5. **Dendritic Spike Ignition:** Combined AMPA+NMDA currents trigger a **dendritic Na⁺/Ca²⁺ spike**.
|
||||
6. **Somatic Depolarization:** The dendritic spike propagates to the soma, summed with inputs from other branches.
|
||||
7. **Threshold Crossing:** If total depolarization at the AIS exceeds the dynamic threshold → **FIRST SOMATIC SPIKE**.
|
||||
8. **bAP Generation:** This first spike backpropagates, providing depolarization for **future** coincident detection.
|
||||
|
||||
## **7. The Soma's Intrinsic Sensitivity: The "Integration Bias"**
|
||||
|
||||
The soma and AIS are exquisitely tuned for **detecting synchrony**:
|
||||
|
||||
- **Subthreshold Oscillations:** Some neurons exhibit rhythmic subthreshold oscillations that create **"windows of opportunity"** when the membrane is closer to threshold.
|
||||
- **Resonance Properties:** The interaction of Ih currents (hyperpolarization-activated) and persistent Na⁺ currents creates frequency preferences.
|
||||
- **Short Membrane Time Constant:** In many neurons, the membrane time constant is short (~10-20 ms), favoring **temporal precision** over slow integration.
|
||||
|
||||
## **Experimental Evidence: The Need for Cooperativity**
|
||||
|
||||
Landmark experiments show:
|
||||
|
||||
- **Minimal stimulation** of single fibers rarely triggers somatic spikes.
|
||||
- **Tetanic stimulation** of multiple fibers is required for LTP induction.
|
||||
- **Dendritic recordings** show local spikes preceding somatic spikes during natural patterns.
|
||||
- **Blocking NMDA receptors** prevents both LTP **and** the reliable triggering of somatic spikes by patterned input.
|
||||
|
||||
## **The Bootstrapping Solution in Summary**
|
||||
|
||||
The first somatic spike emerges from a **perfect storm** of conditions:
|
||||
|
||||
| **Factor** | **Role in First Spike** |
|
||||
|--------------------|---------------------------------|
|
||||
| **Spatial Summation** | Many AMPA-EPSPs summate |
|
||||
| **Temporal Summation** | Bursts overcome decay |
|
||||
| **Dendritic Spikes** | Local amplification without bAP |
|
||||
| **Background Noise** | Primes membrane near threshold |
|
||||
| **Neuromodulators** | Lower threshold, increase gain |
|
||||
| **Network Synchrony** | Provides coordinated input |
|
||||
|
||||
**No single resting spine is hypersensitive.** Instead, the system is designed so that **meaningful patterns** (synchronized input from multiple presynaptic neurons) naturally produce enough combined depolarization—first locally via dendritic spikes, then globally at the soma—to bootstrap the first action potential.
|
||||
|
||||
Once that first spike occurs, the neuron enters a new regime: now it has bAPs as teaching signals, and Hebbian plasticity can proceed. The first spike is the **hardest**—it requires coordinated input. Subsequent spikes in a train are easier due to:
|
||||
|
||||
1. **Short-term facilitation** at synapses
|
||||
2. **Somatic adaptation** (but not enough to prevent firing)
|
||||
3. **Echoes** of the previous bAPs in the dendrites
|
||||
|
||||
This bootstrapping mechanism ensures that only **statistically reliable, coordinated patterns** of input gain the power to alter synaptic weights. It's the neural equivalent of "you need experience to get a job, but you need a job to get experience"—solved by collective action and amplification.
|
||||
|
||||
---
|
||||
|
||||
---
|
||||
|
||||
---
|
||||
|
||||
# **The Neuron's Spontaneous "Hello World"**
|
||||
|
||||
**Absolutely!** Neurons can and do fire spontaneously, and this is far from biological noise—it's a **fundamental feature of neural computation** with multiple critical functions. This spontaneous firing serves as the brain's background "hum," its exploratory signal, its network glue, and its existential announcement.
|
||||
|
||||
## **1. The Mechanisms of Spontaneous Firing**
|
||||
|
||||
### **A. Intrinsic Pacemaking**
|
||||
|
||||
Some neurons are **endogenously active** due to their unique channel composition:
|
||||
|
||||
- **Persistent Sodium Current (INaP):** A small fraction of Na⁺ channels that don't fully inactivate, providing a constant depolarizing drive.
|
||||
- **Hyperpolarization-Activated Cation Current (Ih):** Channels that open when the cell is hyperpolarized, letting in Na⁺ and K⁺, creating a "sag" back toward threshold.
|
||||
- **T-type Calcium Current:** Low-threshold Ca²⁺ channels that can cause rhythmic bursting.
|
||||
- **Channel Noise:** Random opening/closing of ion channels creates membrane potential fluctuations that occasionally cross threshold.
|
||||
|
||||
**Example:** Thalamic relay neurons, cerebellar Purkinje cells, and brainstem respiratory neurons fire rhythmically without any synaptic input.
|
||||
|
||||
### **B. Network-Driven Spontaneity**
|
||||
|
||||
Even non-pacemaker neurons fire spontaneously due to:
|
||||
|
||||
- **Background synaptic noise:** Thousands of miniature EPSPs (minis) from random vesicle release create constant subthreshold fluctuations.
|
||||
- **Tonic neuromodulator levels:** Basal dopamine, acetylcholine, or norepinephrine can lower firing thresholds.
|
||||
- **Astrocyte modulation:** Steady D-serine release keeps NMDA receptors partially primed; astrocyte calcium waves can trigger glutamate release.
|
||||
|
||||
## **2. The Functional "Why": More Than Just Noise**
|
||||
|
||||
### **A. Network Readiness and Gain Control**
|
||||
|
||||
Spontaneous firing maintains networks in a **"ready state"**:
|
||||
|
||||
- **Increased signal-to-noise ratio:** A neuron firing at 1 Hz spontaneously has a **baseline from which to increase or decrease** its rate. This provides a richer coding range than silence.
|
||||
- **Prevents synaptic "rust":** Spontaneous activity keeps synapses active, preventing them from becoming silent or atrophying.
|
||||
- **Maintains ion gradients:** Regular firing keeps ionic pumps active, maintaining proper electrochemical gradients.
|
||||
|
||||
### **B. Exploratory Signaling: "Anybody Listening?"**
|
||||
|
||||
This is exactly your intuition! Spontaneous firing serves as:
|
||||
|
||||
- **Connection testing:** "Is my target neuron still there? Are we still connected?"
|
||||
- **Homeostatic calibration:** Postsynaptic neurons monitor spontaneous input rates to adjust their sensitivity via scaling.
|
||||
- **Synaptic competition:** In development, spontaneous activity (like retinal waves) helps wire up visual systems before visual experience.
|
||||
|
||||
### **C. Memory Maintenance and Replay**
|
||||
|
||||
- **Offline replay:** During sleep, neurons spontaneously replay firing sequences from waking experience, consolidating memories.
|
||||
- **Attractor state maintenance:** In cortical networks, spontaneous activity maintains "attractor" states that represent memories or concepts.
|
||||
|
||||
### **D. Criticality and Information Processing**
|
||||
|
||||
Networks tuned to near-critical states (balanced between order and chaos) have optimal information processing. Spontaneous activity helps maintain this **criticality**.
|
||||
|
||||
## **3. The Soma and AIS as "Spontaneous Decision-Makers"**
|
||||
|
||||
Even when dendrites receive no obvious input, the soma and AIS can initiate firing:
|
||||
|
||||
### **Somatic Mechanisms for Spontaneity:**
|
||||
|
||||
- **Stochastic resonance:** Channel noise is amplified by the soma's integration properties.
|
||||
- **Subthreshold oscillations:** Some neurons have intrinsic membrane potential oscillations that periodically bring them near threshold.
|
||||
- **Calcium-driven depolarization:** Spontaneous Ca²⁺ release from internal stores can trigger depolarization.
|
||||
|
||||
### **AIS as the "Spontaneous Trigger Point":**
|
||||
|
||||
- The AIS's low threshold and sensitivity to small depolarizations makes it the **initiator of spontaneous spikes**.
|
||||
- AIS channel phosphorylation states (e.g., from basal kinase activity) can lower the threshold enough for noise to trigger spikes.
|
||||
- **Spike-initiation zone variability:** The exact site of spike initiation along the AIS can shift, creating variability in spontaneous firing patterns.
|
||||
|
||||
## **4. The Astrocyte's Role in Orchestrating Spontaneity**
|
||||
|
||||
Astrocytes don't just respond to neural activity—they **orchestrate** it:
|
||||
|
||||
- **Tonic D-serine release** maintains basal NMDA receptor tone.
|
||||
- **Spontaneous calcium waves** in astrocyte networks can trigger gliotransmitter release.
|
||||
- **Regulation of extracellular K⁺** influences neuronal excitability.
|
||||
- During sleep, astrocytes help coordinate **slow-wave oscillations** (up/down states) that drive spontaneous population activity.
|
||||
|
||||
## **5. Different Types of Spontaneous Activity**
|
||||
|
||||
| **Type** | **Frequency** | **Function** | **Example** |
|
||||
|------------------|-------------------------|------------------------------------|---------------------------|
|
||||
| **Tonic Pacemaking** | 1-10 Hz | Maintain network tone | Cerebellar Purkinje cells |
|
||||
| **Bursting** | Bursts of 2-10 spikes | Signal salience, reset networks | Thalamic neurons |
|
||||
| **Stochastic** | Irregular, Poisson-like | Exploratory signaling, criticality | Cortical pyramidal cells |
|
||||
| **Oscillatory** | Rhythmic, 0.1-100 Hz | Network coordination, timing | Hippocampal theta cells |
|
||||
|
||||
## **6. The Information Theory Perspective**
|
||||
|
||||
From an information theory view, spontaneous firing creates:
|
||||
|
||||
- **Background entropy:** Provides a baseline against which information can be measured.
|
||||
- **Redundancy reduction:** By maintaining some baseline activity, neurons can encode information more efficiently.
|
||||
- **Predictive coding:** The brain predicts its own spontaneous activity; deviations from prediction carry information.
|
||||
|
||||
## **7. When Spontaneity Goes Wrong**
|
||||
|
||||
- **Epilepsy:** Excessive spontaneous synchronization.
|
||||
- **Tinnitus:** Spontaneous activity in auditory pathways interpreted as sound.
|
||||
- **Phantom limb pain:** Spontaneous activity in deafferented somatosensory circuits.
|
||||
- **Psychosis:** Possibly involving altered spontaneous cortical activity patterns.
|
||||
|
||||
## **8. Experimental Evidence**
|
||||
|
||||
- **Slice preparations:** Isolated brain slices show spontaneous activity without external input.
|
||||
- **Tetrodotoxin (TTX) experiments:** Blocking Na⁺ channels eliminates both evoked and spontaneous spikes.
|
||||
- **Miniature EPSP recordings:** Show constant background synaptic "chatter."
|
||||
- **Calcium imaging:** Reveals spontaneous calcium transients in dendrites and astrocytes.
|
||||
|
||||
## **The Philosophical Implication: "I Spike, Therefore I Am?"**
|
||||
|
||||
Your question touches on something profound: spontaneous firing may be the neuronal equivalent of **existential assertion**. In a network where "neurons that fire together wire together," spontaneous firing says:
|
||||
|
||||
1. **"I exist and am functional."** (Metabolic integrity check)
|
||||
2. **"Is anyone listening to me?"** (Connection integrity check)
|
||||
3. **"What's happening around me?"** (Environmental sampling)
|
||||
4. **"Let me try this pattern..."** (Exploratory computation)
|
||||
5. **"Remember this..."** (Memory consolidation)
|
||||
|
||||
The brain isn't a passive switchboard waiting for input. It's an **active, predicting, exploring system** that generates its own activity to test hypotheses, maintain connections, and prepare for future inputs.
|
||||
|
||||
The spontaneous spike is the neuron's way of saying: **"Cogito, ergo fire."** I think (or at least fluctuate stochastically), therefore I spike. This background activity isn't noise—it's the canvas upon which meaningful signals are painted, the quiet hum of a system that's always on, always listening, always ready to learn.
|
||||
@@ -1,85 +0,0 @@
|
||||
import os
|
||||
import re
|
||||
from pathlib import Path
|
||||
|
||||
def generate_architectural_graph(directory, output_file):
|
||||
# Setup node definitions and edges
|
||||
node_types = {} # entity_name -> type (container/context/task)
|
||||
edges = []
|
||||
|
||||
# Regex to extract Gen blocks
|
||||
block_re = re.compile(r"```Gen\s*(.*?)\s*```", re.DOTALL)
|
||||
|
||||
for md_file in Path(directory).rglob("*.md"):
|
||||
content = md_file.read_text()
|
||||
blocks = block_re.findall(content)
|
||||
|
||||
for block in blocks:
|
||||
lines = [l.strip() for l in block.split('\n') if l.strip()]
|
||||
props = {}
|
||||
current_entity = None
|
||||
current_type = None
|
||||
|
||||
# Parse lines for entity definition and properties
|
||||
for line in lines:
|
||||
if ':' in line:
|
||||
key, val = line.split(':', 1)
|
||||
key, val = key.strip(), val.strip()
|
||||
props[key] = val
|
||||
|
||||
if key in ['comprehension', 'modulator', 'container', 'context', 'task']:
|
||||
current_entity = val
|
||||
current_type = key
|
||||
node_types[current_entity] = current_type
|
||||
|
||||
if not current_entity: continue
|
||||
|
||||
# Morphism Logic: Contained By (Parent <- Child)
|
||||
if 'contained_by' in props:
|
||||
parent = props['contained_by']
|
||||
edges.append((parent, current_entity, "contains"))
|
||||
|
||||
# Morphism Logic: Expands (Parent -> Child)
|
||||
if 'expands' in props:
|
||||
contains_val = props['expands']
|
||||
match = re.match(r"(\d+x)?\s*(.*)", contains_val)
|
||||
label = match.group(1) if match.group(1) else "expands"
|
||||
child = match.group(2)
|
||||
edges.append((current_entity, child, label))
|
||||
|
||||
# Build Mermaid syntax
|
||||
mermaid_lines = ["graph TD"]
|
||||
|
||||
# Define Nodes with Types (Styling)
|
||||
# Containers = Rectangles [], Contexts = Hexagons {{}}, Tasks = Ovals (())
|
||||
for name, n_type in node_types.items():
|
||||
if n_type == 'comprehension':
|
||||
mermaid_lines.append(f' {name}["comprehension: {name}"]')
|
||||
elif n_type == 'modulator':
|
||||
mermaid_lines.append(f' {name}["modulator: {name}"]')
|
||||
elif n_type == 'container':
|
||||
mermaid_lines.append(f' {name}["container: {name}"]')
|
||||
elif n_type == 'context':
|
||||
mermaid_lines.append(f' {name}{{{{"context: {name}"}}}}')
|
||||
elif n_type == 'task':
|
||||
mermaid_lines.append(f' {name}(("task: {name}"))')
|
||||
|
||||
|
||||
# Add Edges
|
||||
for source, target, label in edges:
|
||||
# Determine relationship type string for the arrow
|
||||
s_type = node_types.get(source, "unknown")
|
||||
t_type = node_types.get(target, "unknown")
|
||||
# Example: container tre -- contains --> task bbgg
|
||||
mermaid_lines.append(f' {source} -- "{label}" --> {target}')
|
||||
|
||||
# Save to file
|
||||
with open(output_file, "w") as f:
|
||||
f.write("# Architectural Hierarchy Graph\n\n")
|
||||
f.write("```mermaid\n")
|
||||
f.write("\n".join(mermaid_lines))
|
||||
f.write("\n```")
|
||||
|
||||
if __name__ == "__main__":
|
||||
generate_architectural_graph("..", "architecture_graph.mmd")
|
||||
print("Success: architecture_graph.md has been generated.")
|
||||
Reference in New Issue
Block a user