ocrampal/organism
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Initial commit

Browse Source
This commit is contained in:
ocrampal
2026-03-07 12:26:39 +01:00
commit 8d8effaf05
13 changed files with 2583 additions and 0 deletions
Download Patch File Download Diff File Expand all files Collapse all files
neuron/appunti/behavior-PRE.md
+708
View File
@@ -0,0 +1,708 @@
# **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.