18 KiB
18 KiB
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
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ms: behaviors — Fast Kinetics and Gate Logic
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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
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sec: behaviors — Signal Integration and Fate
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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
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min: behaviors — Bioenergetics and Structural Change
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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
Behaviors:
— ms:
- NT arrives in cleft → AMPA receptors bind NT, gated by Desensitization_level
- V_post rises with AMPA conductance, decays passively each ms
- bAP arrives → V_post receives additional depolarisation boost
- NMDA gate checks coincidence: NT_cleft AND V_post both non-zero
- Ca²⁺ enters spine via NMDA — amount determined by NT_cleft × Mg_block_removal
- Ca²⁺ cleared slowly from spine (single decay term, ATP detail not modelled)
- V_post history updated every ms (rolling buffer, feeds seconds loop)
- Desensitization_level rises with NT_cleft exposure, recovers during silence
- ATP cost charged per V_post level (Na/K-ATPase recharge, continuous)
- ATP cost charged per unit Ca²⁺ cleared (PMCA cost, continuous)
— seconds:
- Ca_post_history computed (2 s rolling mean of Ca_post)
- eCB synthesised when Ca_post_history exceeds threshold
- eCB_level decays when Ca_post_history falls below threshold
- eCB_level written → read by presynapse as retrograde brake on VGCCs
- Ca_post_history compared to LTP/LTD thresholds → plasticity tag set
- Desensitization recovery continues passively
— mins:
- ATP_demand_post (accumulated from ms loop) reduces ATP_level_post
- ATP_demand_post resets to zero
- Glucose level (shared with presynapse) sets ATP_level_post
- If ATP_level_post low → Ca²⁺ clearance slows → false eCB trigger risk
- If Plasticity_LTP tagged AND ATP_level_post not empty → AMPA density increases
- If Plasticity_LTD tagged → AMPA density decreases
- AMPA density feeds back into receptor_conductance ceiling for next cycle
Simplified comprehension:
In this comprehension we decide to simplify:
- We do not model ATP — the postsynaptic energy loop is removed
- We do not model Desensitization_level — receptor availability is assumed constant
- We do not model Ca²⁺ clearance detail — Ca_post decays with a single slow term
The simplification implies that:
- Removing ATP removes the false eCB trigger mechanism entirely. The retrograde signal remains but it is always genuine — driven by real Ca_post elevation from NMDA coincidence, not pump failure. The synapse cannot enter the excitotoxic protection cascade.
- Removing Desensitization_level means the postsynapse cannot fatigue under sustained NT exposure. Receptor availability is always at maximum, so the tenth burst produces the same AMPA response as the first. This preserves the short-term dynamics of V_post without the adaptation layer.
- Removing Ca²⁺ clearance detail means Ca_post reflects the cumulative history of coincidence events with a single decay constant rather than the interplay of PMCA, NCX speed, and ATP availability. Ca_post will still accumulate under high-frequency coincident firing if the decay is slow relative to the event rate, which preserves the eCB trigger dynamic even without the full pump machinery.
Simplified Behaviors:
— ms:
- NT arrives in cleft → AMPA receptors bind NT (receptor availability constant, no desensitization)
- V_post rises with AMPA conductance, decays passively each ms
- bAP arrives → V_post receives additional depolarisation boost
- NMDA gate checks coincidence: NT_cleft AND V_post both non-zero
- Mg_block_removal = V_post / (V_post + V_NMDA_half) — sigmoid of V_post
- Ca²⁺ enters spine via NMDA: Ca_post += k_NMDA × NT_cleft × Mg_block_removal
- Ca_post decays slowly each ms (single exponential, no pump detail)
- Ca_post_history updated every ms (feeds seconds loop)
- V_post_history updated every ms (retained for reference)
— seconds:
- Ca_post_history mean computed over past 2 s
- eCB synthesised when Ca_post_history mean exceeds eCB threshold
- eCB_level decays when Ca_post_history mean falls below threshold
- eCB_level written → read by presynapse as retrograde brake on VGCCs
- Ca_post_history compared to LTP/LTD thresholds → plasticity tag set
— mins:
- If Plasticity_LTP tagged → AMPA density increases
- If Plasticity_LTD tagged → AMPA density decreases
- AMPA density feeds back into receptor_conductance ceiling for next cycle