post
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@@ -1,91 +1,299 @@
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## BEH-POST-UNIFIED: The Integrated Postsynaptic Model
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---
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### **ms: behaviors (Fast Kinetics & Gate Logic)**
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**What needs adjustment**
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#### **Voltage-Context: Episode**
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`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.
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*Determines the total depolarization level (Vpost) available to clear the NMDA Mg-block.*
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`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.
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- **Vpost_Maximum: Episode**
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- — `V_bAP` full OR (`g_AMPA` full AND `V_bAP` medium)
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- — Result: Vpost is high enough for complete Mg-block removal.
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- **Vpost_Attenuated: Episode**
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- — `g_AMPA` medium AND `V_bAP` empty/low
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- — Result: Vpost is sub-threshold; Mg-block partially remains.
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- **Vpost_Passive: Episode**
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- — `g_AMPA` empty AND `V_bAP` empty
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- — Result: Vpost at rest; Mg-block fully intact.
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`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.
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#### **NMDA-Coincidence: Context**
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`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.
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- **NMDA_Open: Episode**
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- — `NT_cleft` full AND `V_post` maximum
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- — Result: Capost surges; triggers high ATP demand for clearance.
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- **NMDA_LogicBlocked: Episode**
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- — `NT_cleft` full BUT `V_post` attenuated/passive
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- — Result: Mg-block prevents Ca2+ influx despite NT presence.
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- **NMDA_LigandBlocked: Episode**
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- — `V_post` maximum BUT `NT_cleft` empty
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- — Result: No glutamate to open the channel; Ca2+ entry zero.
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`Astrocyte_Supply_Crises` has a typo (Crises → Crisis).
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#### **Ca-Dynamics & ATP-Drain: Context**
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- **Clearance_Optimal: Episode**
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- — `ATP_level_post` full
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- — Result: Pumps flush Ca2+ rapidly; `ATP_demand_post` increases.
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- **Clearance_Failing: Episode**
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- — `ATP_level_post` low/empty
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- — Result: Ca2+ remains elevated (residual floor); creates "False Trigger" conditions.
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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.
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---
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### **sec: behaviors (Signal Integration & Fate)**
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**Final restructured specification**
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#### **Synaptic-Weight-Decision (Plasticity)**
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```
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BEH-POST-UNIFIED: The Integrated Postsynaptic Model
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=====================================================
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Three loops, three timescales, one shared astrocyte supply.
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Each loop feeds the next: V_post enables NMDA, NMDA drives
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Ca_post, Ca_post determines plasticity and eCB, ATP sustains
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all three. Failure of ATP does not silence the postsynapse
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(unlike the presynapse) — it corrupts it, triggering false
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retrograde signals and risking excitotoxic Ca2+ accumulation.
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- **Plasticity_LTP: Episode**
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- — `Ca_post_history` (recent 2s) is **Full**
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- — Result: High-frequency/High-amplitude coincidence detected; tags synapse for AMPA increase.
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- **Plasticity_LTD: Episode**
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- — `Ca_post_history` is **Medium**
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- — Result: Low-frequency or poorly timed coincidence; tags synapse for AMPA removal.
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Variables:
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V_bAP — back-propagating AP amplitude (0→1)
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[GAP — requires bAP_train input,
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analogous to presynaptic spike_train]
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g_AMPA — AMPA receptor conductance (= receptor_conductance)
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V_post — total postsynaptic membrane potential (0→1)
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NT_cleft — glutamate in cleft (from presynapse)
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Desensitization — fraction of AMPA receptors desensitized (0→1)
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Ca_post — free Ca2+ in postsynaptic spine (0→...)
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Ca_post_history — 2 s rolling mean of Ca_post
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ATP_level_post — normalised postsynaptic ATP (0→1)
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ATP_demand_post — accumulated ATP cost since last metabolic cycle
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g_AMPA_baseline — long-term AMPA receptor density set by plasticity
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[GAP — not yet in model; LTP/LTD would write this]
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eCB_level — endocannabinoid retrograde signal (0→1)
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written here, read by presynapse Loop 1
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#### **Retrograde-Feedback (eCB)**
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━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
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ms: behaviors — Fast Kinetics and Gate Logic
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━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
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- **eCB_Synthesis_Active: Episode**
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- — `Ca_post_history` > threshold (0.7)
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- — **Logic A (Protection):** Response to genuine NMDA over-activity.
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- — **Logic B (Error):** Response to pump failure (Ca2+ accumulation due to low ATP).
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- **eCB_Synthesis_Idle: Episode**
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- — `Ca_post_history` < threshold; eCB level decays.
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Voltage-Context: Context
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Determines the total depolarisation (V_post) available to
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lift the NMDA Mg block. Two independent sources contribute:
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AMPA-driven local depolarisation (g_AMPA) and the somatic
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back-propagating AP (V_bAP). Either alone can partially
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depolarise; both together reach maximum.
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---
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Vpost_Maximum: Episode
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— V_bAP full OR
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— g_AMPA full AND V_bAP medium
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— Result: V_post high enough for complete Mg block removal.
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NMDA gate can open fully.
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Both ATP costs charged at maximum rate.
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### **min: behaviors (Bioenergetics & Structural Change)**
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Vpost_Attenuated: Episode
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— g_AMPA medium AND V_bAP empty/low OR
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— g_AMPA low AND V_bAP medium
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— Result: V_post sub-threshold.
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Mg block partially remains.
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NMDA gate opens partially or not at all.
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This is the most common state during low-rate firing
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without a coincident bAP.
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#### **Metabolic-Recovery**
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Vpost_Passive: Episode
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— g_AMPA empty AND V_bAP empty
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— Result: V_post at rest.
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Mg block fully intact.
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No Ca_post entry possible.
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Na/K-ATPase cost minimal.
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- **Astrocyte_Supply_Active: Episode**
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- — `Glucose_level` full; `ATP_level_post` is replenished.
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- **Astrocyte_Supply_Crises: Episode**
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- — `Glucose_level` low; `ATP_level_post` remains empty; Ca2+ pumps fail.
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Desensitization-Context: Context
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Modulates g_AMPA independently of NT_cleft.
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Sustained NT exposure drives receptors into a closed state
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that persists even when NT remains present.
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#### **Structural-Update**
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DesensitizationRising: Episode
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— NT_cleft sustained high (multiple consecutive ms)
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— Desensitization rises each ms
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— g_AMPA effectively reduced despite NT presence
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— attenuates Vpost_Maximum toward Vpost_Attenuated
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- **AMPA_Population_Increase: Episode**
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- — Triggered by `Plasticity_LTP` AND `ATP_level_post` NOT empty.
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- — Result: `g_AMPA_baseline` shifts higher for next cycle.
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- **AMPA_Population_Decrease: Episode**
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- — Triggered by `Plasticity_LTD`.
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- — Result: `g_AMPA_baseline` shifts lower.
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DesensitizationRecovering: Episode
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— NT_cleft low or empty
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— Desensitization decays with tau_desensitization = 500 ms
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— g_AMPA ceiling restored gradually
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---
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NMDA-Coincidence: Context
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Strict AND gate: both NT (ligand) and V_post (voltage) must
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be simultaneously non-zero for Ca_post to rise.
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Unlike presynaptic VGCCs which open with any spike, NMDA
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requires coincidence. This makes Ca_post a detector of
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coordinated pre+post activity, not just input rate.
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### **Key Structural Observations**
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NMDA_Open: Episode
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— NT_cleft full AND V_post maximum (Vpost_Maximum active)
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— Mg block fully lifted
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— Ca_post surges — LTP territory
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— ATP_demand_post rises sharply (PMCA must clear Ca_post)
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— if sustained → Ca_post_history crosses eCB threshold
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1. **The Vpost Priority:** Vpost is now the "sum" of local input and global feedback. This allows the model to simulate both **Hebbian learning** (needs a bAP) and **Homeostatic Scaling** (where enough local AMPA activity can eventually trigger the NMDA gate alone).
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2. **The ATP Bottleneck for LTP:** Note that in the `min` behaviors, I’ve added a constraint: LTP requires `ATP_level_post` to be healthy. Moving receptors into the membrane is a physical "work" process. If the synapse is energy-starved, it might "decide" to do LTP in the `sec` loop but fail to **execute** it in the `min` loop.
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3. **The Coincidence Hierarchy:**
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- **LTP** = Perfect Timing (NT + bAP).
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- **LTD** = Misaligned Timing (Low NT or Out-of-sync bAP).
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- **False eCB** = Metabolic Failure (No NT, No bAP, just Low ATP).
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NMDA_LogicBlocked: Episode
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— NT_cleft full BUT V_post attenuated or passive
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— Mg block partially or fully intact
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— Ca_post does not rise despite NT presence
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— Result: presynapse fired but postsynapse was not ready
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No plasticity signal generated
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This is the mechanism for input selectivity:
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only synapses active during postsynaptic firing
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produce a Ca_post signal
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NMDA_LigandBlocked: Episode
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— V_post maximum BUT NT_cleft empty
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— No glutamate to open the channel
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— Ca_post entry zero despite full depolarisation
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— Result: bAP arrived but presynapse was silent
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Again no plasticity signal
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The AND logic enforces true coincidence
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Ca-Dynamics-Context: Context
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Ca_post clearance rate depends entirely on ATP_level_post.
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This is the bridge from the ATP loop into the Ca2+ loop.
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When ATP fails, Ca_post clearance fails, and the Ca2+ loop
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becomes corrupted — Ca_post reflects pump state rather
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than genuine coincidence events.
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Clearance_Optimal: Episode
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— ATP_level_post full → pump_scale_post near 1
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— PMCA (ATP-gated) + NCX (always on) both clearing
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— Ca_post returns to baseline between events
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— Each coincidence event is temporally isolated
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— ATP_demand_post increases proportionally to Ca_post load
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Clearance_Reduced: Episode
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— ATP_level_post medium → pump_scale_post reduced
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— Ca_post clears more slowly
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— Residual elevation begins accumulating between events
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— Ca_post_history starts drifting upward
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— eCB threshold may be approached during heavy firing
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Clearance_Failing: Episode
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— ATP_level_post low or empty → pump_scale_post near 0
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— Only NCX clearing (floor, not rescue)
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— Ca_post accumulates regardless of coincidence activity
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— False Trigger conditions: Ca_post_history crosses eCB
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threshold without genuine NMDA overactivity
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— Excitotoxicity risk if Ca_post elevation is sustained
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━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
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sec: behaviors — Signal Integration and Fate
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━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
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Synaptic-Weight-Decision: Context
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Ca_post_history (2 s rolling mean of Ca_post) determines
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the plasticity signal. The threshold logic is graded:
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the same variable produces opposite outcomes depending
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on whether it is above or below the LTP/LTD boundary.
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ATP_level_post gates LTP expression but not LTD —
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strengthening requires energy, weakening does not.
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Plasticity_LTP: Episode
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— Ca_post_history full (above Ca_post_LTP threshold)
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— High-frequency or high-amplitude coincidence detected
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— Tags synapse for AMPA receptor insertion
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— Requires ATP_level_post NOT empty for expression
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(CaMKII phosphorylation and receptor trafficking are
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ATP-dependent — energy failure blocks LTP even if
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the Ca_post signal is correct)
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— [GAP] LTP expression writes g_AMPA_baseline upward
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in the minutes loop
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Plasticity_Boundary: Episode
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— Ca_post_history medium
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— Poorly timed or low-frequency coincidence
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— Neither LTP nor LTD threshold crossed
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— Synapse weight unchanged this cycle
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Plasticity_LTD: Episode
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— Ca_post_history low but non-zero
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— Weak or mistimed coincidence — presynapse fired
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but postsynapse was not sufficiently depolarised
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— Tags synapse for AMPA receptor removal
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— Less ATP-dependent than LTP; can proceed under
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mild energy stress
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— [GAP] LTD expression writes g_AMPA_baseline downward
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in the minutes loop
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Plasticity_Silent: Episode
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— Ca_post_history empty (prolonged absence of activity)
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— Homeostatic depression: unused synapses weaken
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— [GAP] not yet modelled; would require Ca_post_trace
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integration over hours
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Retrograde-Feedback: Context
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eCB synthesis is triggered by Ca_post_history, not V_post.
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It is Ca2+ in the spine — not voltage — that activates the
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enzymes (DAGL, PLC) that produce endocannabinoids.
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The model cannot distinguish internally between the two
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causes of elevated Ca_post_history (genuine vs pump failure)
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but the consequences differ: one is communication,
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the other is survival.
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eCB_Synthesis_Active: Episode
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— Ca_post_history > eCB_threshold (0.7)
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— Logic A (Genuine Protection):
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Cause : sustained NMDA_Open events — real overactivity
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Effect : appropriate retrograde stop signal
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Outcome : presynapse reduces NT → NT_cleft falls →
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NMDA closes → Ca_post load drops →
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Ca_post_history falls → eCB synthesis subsides
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Loop closes correctly
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— Logic B (False Trigger — Excitotoxic Protection):
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Cause : Clearance_Failing — Ca_post elevated by
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pump failure, not genuine coincidence
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Effect : presynapse silenced without real overactivity
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Outcome : NT_cleft falls → NMDA closes → Ca_post
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load drops → ATP_demand_post falls →
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ATP_level_post recovers → pumps restart →
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Ca_post clears → Ca_post_history falls →
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eCB synthesis subsides
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Desperate survival loop — buys time for
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metabolic recovery
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eCB_Synthesis_Idle: Episode
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— Ca_post_history < eCB_threshold
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— eCB_level decays with tau_eCB_decay = 10000 ms
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— Presynaptic suppression lifts gradually
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— 10 s decay means suppression outlasts the trigger —
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prevents immediate re-engagement before Ca_post
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has stabilised
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━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
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min: behaviors — Bioenergetics and Structural Change
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━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
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Metabolic-Recovery: Context
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ATP_level_post is computed from Glucose_level (shared
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supply) minus ATP_demand_post (postsynaptic-specific cost).
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The shared supply creates the coupling: both pre and post
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deplete the same astrocyte glucose budget simultaneously.
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Presynaptic silence is therefore metabolically beneficial
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to the postsynapse — less NT means less NMDA activation
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means less Ca_post means less PMCA cost.
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Astrocyte_Supply_Active: Episode
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— Glucose_level full
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— ATP_demand_post within supply capacity
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— ATP_level_post replenished each cycle
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— All three loops operating normally
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Astrocyte_Supply_Stressed: Episode
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— Glucose_level medium OR ATP_demand_post elevated
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— ATP_level_post partially reduced
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— Clearance_Reduced begins
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— Plasticity_LTP at risk (ATP dependency)
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Astrocyte_Supply_Crisis: Episode
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— Glucose_level low OR ATP_demand_post chronically high
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— ATP_level_post near empty
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— Clearance_Failing — only NCX clearing Ca_post
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— False Trigger likely → eCB_Synthesis_Active (Logic B)
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— Presynaptic silence indirectly reduces postsynaptic
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ATP demand — the coupled protection mechanism
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Structural-Update: Context
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Long-term changes to AMPA receptor density.
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These are the physical substrate of learning and memory.
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[GAP] g_AMPA_baseline not yet implemented in the model.
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Would be written in Loop 3 and read by Loop 1 as the
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ceiling of receptor_conductance.
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AMPA_Population_Increase: Episode
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— Triggered by Plasticity_LTP
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— AND ATP_level_post NOT empty
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— g_AMPA_baseline shifts higher for next cycle
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— More AMPA receptors → stronger Vpost_Maximum
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— Easier to reach NMDA_Open in future events
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— Positive feedback: LTP makes future LTP more likely
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AMPA_Population_Decrease: Episode
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— Triggered by Plasticity_LTD or Plasticity_Silent
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— g_AMPA_baseline shifts lower
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— Fewer AMPA receptors → Vpost_Attenuated more common
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— Harder to reach NMDA_Open → weakens synapse further
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— Negative feedback: LTD stabilises by reducing
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future coincidence probability
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```
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Reference in New Issue
Block a user