From 59bd854a1ce7a12d37b88e5af4364e2813b1e6f9 Mon Sep 17 00:00:00 2001 From: ocrampal Date: Thu, 9 Apr 2026 15:05:10 +0200 Subject: [PATCH] vari commenti --- neuron/BEH-SOMA.md | 43 ++-- .../2026-04-09-threshold-refractory-period.md | 222 ++++++++++++++++++ 2 files changed, 241 insertions(+), 24 deletions(-) diff --git a/neuron/BEH-SOMA.md b/neuron/BEH-SOMA.md index 9a68e70..626a5ef 100644 --- a/neuron/BEH-SOMA.md +++ b/neuron/BEH-SOMA.md @@ -10,11 +10,18 @@ Qui comprendiamo: The soma is the cell body of the neuron — a roughly spherical structure, typically 10 to 30 micrometres across, that sits at the convergence point of all dendritic branches and at the origin of the axon. It is the decision-making centre of the neuron: its job is to continuously monitor the summed electrical input arriving from the dendrites and decide, moment by moment, whether that input is strong enough to warrant sending a signal forward. That decision takes the form of an action potential — a brief, explosive electrical event that propagates down the axon to the next neuron in the circuit and simultaneously backward up the dendrites as the bAP that enables postsynaptic plasticity. -The soma receives V_dend — the summed dendritic potential — as a continuous input. This potential reflects the aggregate activity of every active spine on every dendritic branch, weighted by the electrical properties of each branch. The soma integrates this input across time through its own membrane capacitance: it accumulates charge when depolarising currents arrive and loses charge continuously through passive membrane leak. The result is a somatic membrane potential, V_soma, that rises when dendritic input is strong and sustained, and falls when input weakens or stops. V_soma is not a simple sum of inputs — it is a leaky integrator, always decaying toward rest, always requiring ongoing input to stay elevated. +The soma receives VDB — the summed dendritic potential — as a continuous input. This potential reflects the aggregate activity of every active spine on every dendritic branch, weighted by the electrical properties of each branch. The soma integrates this input across time through its own membrane capacitance: it accumulates charge when depolarising currents arrive and loses charge continuously through passive membrane leak. The result is a somatic membrane potential, VSOMA, that rises when dendritic input is strong and sustained, and falls when input weakens or stops. VSOMA is not a simple sum of inputs — it is a leaky integrator, always decaying toward rest, always requiring ongoing input to stay elevated. -The critical site of decision is not the soma body itself but the axon hillock — the narrow region where the soma tapers into the beginning of the axon. The axon hillock has the lowest threshold for firing of any part of the neuron, because it has the highest density of voltage-gated sodium channels. These channels are sensitive to voltage: when V_soma at the hillock crosses the firing threshold — typically about 15 millivolts above the resting membrane potential — they open explosively, allowing a massive inward rush of sodium that drives V_soma rapidly to its peak. This is the action potential. It is an all-or-nothing event: once the threshold is crossed, the AP fires to its full amplitude regardless of how far above threshold the triggering input was. The size of the AP does not encode the strength of the input — only whether it was strong enough to cross the threshold at all. +While Na+ enter K+ exit. In order to spike, the flux of Na+ entering must be grater than K+ exiting. Timing andquantity is also important. -Immediately after firing, the soma enters a refractory period. The same sodium channels that opened to produce the AP become inactivated — they cannot reopen until the membrane has repolarised past its resting level, which requires the delayed activation of potassium channels that pull V_soma below rest into a brief hyperpolarisation. During this absolute refractory period, no input, however strong, can trigger another AP. During the subsequent relative refractory period, firing is possible but requires a stronger-than-normal input because the membrane is recovering. This refractory mechanism sets the maximum firing rate of the neuron and ensures that APs are discrete, separated events rather than a continuous depolarisation. +The critical site of decision is not the soma body itself but the axon hillock — the narrow region where the soma tapers into the beginning of the axon. The axon hillock has the lowest threshold for firing of any part of the neuron, because it has the highest density of voltage-gated sodium channels (VGSC). These channels are sensitive to voltage: when VSOMA at the hillock crosses the firing threshold — typically about 15 millivolts above the resting membrane potential — they open explosively, allowing a massive inward rush of sodium (Na+) that drives VSOMA rapidly to its peak. This is the action potential. It is an all-or-nothing event: once the threshold is crossed, the AP fires to its full amplitude regardless of how far above threshold the triggering input was. The size of the AP does not encode the strength of the input — only whether it was strong enough to cross the threshold at all. + +Immediately after firing, the soma enters a refractory period. The same sodium channels that opened to produce the AP become inactivated — they cannot reopen until the membrane has repolarised past its resting level, which requires the delayed activation of potassium channels that pull VSOMA below rest into a brief hyperpolarisation. During this absolute refractory period, no input, however strong, can trigger another AP. During the subsequent relative refractory period, firing is possible but requires a stronger-than-normal input because the membrane is recovering. This refractory mechanism sets the maximum firing rate of the neuron and ensures that APs are discrete, separated events rather than a continuous depolarisation. + +The reason the pump isn't the "timer" for the refractory period is scale. +A single action potential only changes the internal sodium concentration by a fraction of 1% (approx. 0.0001 mM). +The neuron does not need to "pump out" that sodium to fire again. It has enough "buffer" to fire hundreds or even thousands of times before the internal sodium concentration becomes a problem. +Peer Correction: If the neuron had to wait for the pump to reset the concentration before every spike, our brains would run at about 1 Hz (1 spike per second) instead of 100–500 Hz. The pump is the "slow recharger," not the "instant reset." The metabolic cost of all this activity falls heavily on the soma. Every action potential disturbs the sodium and potassium gradients across the entire soma membrane — sodium rushes in during the rising phase, potassium rushes out during repolarisation. The Na/K-ATPase pump must then restore these gradients by actively moving three sodium ions out for every two potassium ions in, at the cost of one ATP molecule per pump cycle. At high firing rates this cost is substantial — a neuron firing at 100 Hz consumes ATP at a rate that would exhaust its local reserves in seconds without continuous resupply. The astrocyte network surrounding the soma provides this supply through glucose delivery and lactate shuttling, making the soma's ability to sustain firing directly dependent on the metabolic health of its supporting glial environment. @@ -32,35 +39,23 @@ The soma is therefore not a simple threshold device. It is a dynamic integrator In this model we decide to simplify: -- We do not model the axon hillock as a separate compartment — threshold crossing is computed directly from V_soma +- We do not model the axon hillock as a separate compartment — threshold crossing is computed directly from VSOMA - We do not model neuromodulatory inputs — threshold and gain are fixed parameters -- We do not model subthreshold oscillations — V_soma is a simple leaky integrator +- We do not model subthreshold oscillations — VSOMA is a simple leaky integrator - We do not model somatic ATP The simplifications imply that: -Removing the axon hillock as a separate compartment means the threshold comparison is applied directly to V_soma rather than to a spatially distinct zone with its own channel density. In biology the hillock has a lower threshold than the soma body because of its higher Na⁺ channel density — this gradient is absent here. A single fixed threshold applied to V_soma is a reasonable approximation for a single-compartment model, but it means the model cannot capture phenomena that depend on the hillock's spatial separation from the dendritic integration zone, such as the ability of strong distal dendritic inputs to bypass somatic inhibition. +Removing the axon hillock as a separate compartment means the threshold comparison is applied directly to VSOMA rather than to a spatially distinct zone with its own channel density. In biology the hillock has a lower threshold than the soma body because of its higher Na⁺ channel density — this gradient is absent here. A single fixed threshold applied to VSOMA is a reasonable approximation for a single-compartment model, but it means the model cannot capture phenomena that depend on the hillock's spatial separation from the dendritic integration zone, such as the ability of strong distal dendritic inputs to bypass somatic inhibition. -Removing neuromodulatory inputs means the threshold and gain of the soma are fixed across the entire simulation. In biology dopamine, serotonin, and acetylcholine continuously adjust V_soma_threshold and the shape of the f-I curve in response to behavioural state. A neuron in an attentive animal fires more readily to the same input than the same neuron in a drowsy animal. This state-dependence is entirely absent — the soma responds identically to a given V_dend at all times. +Removing neuromodulatory inputs means the threshold and gain of the soma are fixed across the entire simulation. In biology dopamine, serotonin, and acetylcholine continuously adjust VSOMA_threshold and the shape of the f-I curve in response to behavioural state. A neuron in an attentive animal fires more readily to the same input than the same neuron in a drowsy animal. This state-dependence is entirely absent — the soma responds identically to a given VDB at all times. -Removing subthreshold oscillations means V_soma behaves as a simple leaky integrator between APs. In some neuron types, voltage-gated channels produce rhythmic subthreshold fluctuations that bias the timing of AP generation toward specific phases of network oscillations. These are not modelled — V_soma decays smoothly toward rest between threshold crossings. +Removing subthreshold oscillations means VSOMA behaves as a simple leaky integrator between APs. In some neuron types, voltage-gated channels produce rhythmic subthreshold fluctuations that bias the timing of AP generation toward specific phases of network oscillations. These are not modelled — VSOMA decays smoothly toward rest between threshold crossings. ATP is a simplification of convenience — at this stage we do not comprehend the total metabolic load. --- -**Appunti**: - -The reason the pump isn't the "timer" for the refractory period is scale. - -A single action potential only changes the internal sodium concentration by a fraction of 1% (approx. 0.0001 mM). - -The neuron does not need to "pump out" that sodium to fire again. It has enough "buffer" to fire hundreds or even thousands of times before the internal sodium concentration becomes a problem. - -Peer Correction: If the neuron had to wait for the pump to reset the concentration before every spike, our brains would run at about 1 Hz (1 spike per second) instead of 100–500 Hz. The pump is the "slow recharger," not the "instant reset." - ---- - **Simplified behaviors**: — ms: @@ -71,8 +66,8 @@ Peer Correction: If the neuron had to wait for the pump to reset the concentrati -- bAP -- VSOMA --- tau_AP_rise = 0.5 ms - Na⁺ channels open — explosive depolarisation ---- (tau_AP_fall = 1.5 ms) - V_soma falls toward V_AHP - K⁺ channels open — repolarisation ---- (tau_AHP = 5.0 ms) - V_soma recovers from V_AHP toward V_soma_reset - K⁺ channels close — after-hyperpolarisation +--- (tau_AP_fall = 1.5 ms) - VSOMA falls toward V_AHP - K⁺ channels open — repolarisation +--- (tau_AHP = 5.0 ms) - VSOMA recovers from V_AHP toward VSOMA_reset - K⁺ channels close — after-hyperpolarisation - V_bAP as a context is active during ? @@ -94,8 +89,8 @@ Peer Correction: If the neuron had to wait for the pump to reset the concentrati - nothing in the simplified model (homeostatic threshold regulation would live here if added: - sustained low firing rate → V_soma_threshold decreases - sustained high firing rate → V_soma_threshold increases + sustained low firing rate → VSOMA_threshold decreases + sustained high firing rate → VSOMA_threshold increases this is the somatic equivalent of postsynaptic AMPA scaling — the neuron adjusts its own excitability to maintain a target firing rate in the face of changing input statistics) diff --git a/neuron/appunti/2026-04-09-threshold-refractory-period.md b/neuron/appunti/2026-04-09-threshold-refractory-period.md index e69de29..4b007f6 100644 --- a/neuron/appunti/2026-04-09-threshold-refractory-period.md +++ b/neuron/appunti/2026-04-09-threshold-refractory-period.md @@ -0,0 +1,222 @@ +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?** \ No newline at end of file