403 lines
20 KiB
Markdown
403 lines
20 KiB
Markdown
---
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**What needs adjustment**
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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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`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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`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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`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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`Astrocyte_Supply_Crises` has a typo (Crises → Crisis).
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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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**Final restructured specification**
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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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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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━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
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ms: behaviors — Fast Kinetics and Gate Logic
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━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
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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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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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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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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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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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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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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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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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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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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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---
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---
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## short term
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Short-term potentiation (STP) and short-term depression (STD) are distinct from LTP/LTD in a fundamental way: they are **temporary** changes that last seconds to minutes and leave no lasting structural trace. They do not require the postsynapse at all — they are entirely presynaptic phenomena in most cases, and they operate on a completely different mechanism.
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---
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**What they are and where they live**
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Short-term plasticity is driven by the **history of presynaptic Ca²⁺** and **vesicle pool state**, not by postsynaptic coincidence detection. The table we just built describes long-term plasticity — structural changes to AMPA density driven by Ca_post. Short-term plasticity describes transient changes to **how much NT the presynapse releases** on the next spike, driven by what happened on the last few spikes.
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There are two opposing forms:
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**Short-term potentiation / facilitation** — if a spike arrives shortly after the previous one, residual Ca²⁺ from the first spike has not fully cleared. The next spike adds to this residual, producing a larger Ca_post microdomain and therefore a higher release probability. The synapse releases more NT on the second spike than the first. This is already partially captured in the presynaptic model through `Tr_Ca` — elevated calcium trace from recent activity speeds up RRP recruitment and effectively increases release efficiency.
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**Short-term depression** — if spikes arrive rapidly, the RRP depletes faster than it can be refilled. Each successive spike releases fewer vesicles because there are fewer available. NT release drops with each spike in a burst. This is already the core of CASCADE 1 in the presynaptic model — RRP depletion under high firing rate.
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---
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**Where they fit in the model**
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Both are already implicitly present in the presynaptic ms and seconds loops:
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```
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Short-term facilitation:
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Residual Ca_micro from spike N
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→ elevated Ca_micro at spike N+1
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→ higher release fraction in deterministic_release (Hill curve)
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→ more NT per spike
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→ decays as Ca_micro clears between spikes (tau ~100-200 ms)
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Short-term depression:
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Rapid firing depletes N_RRP
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→ fewer vesicles available per spike
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→ released_NT falls
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→ recovers as RP→RRP recruitment refills (seconds timescale)
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```
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The timescale of each depends on parameters already in the model:
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| Form | Timescale | Driven by | Recovery |
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|--------------|------------|-------------------|-------------------------|
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| Facilitation | 100-500 ms | residual Ca_micro | Ca²⁺ clearance rate |
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| Depression | seconds | RRP depletion | RP→RRP recruitment rate |
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---
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**What is missing from the current model**
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The model captures both implicitly but does not name them as behaviours. Two things are genuinely absent:
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**Augmentation** — a slower form of facilitation lasting 5-10 seconds, driven by residual Ca²⁺ accumulating in the presynaptic terminal across many spikes. It is distinct from spike-by-spike facilitation and would require a second, slower Ca²⁺ trace with `tau ~5000 ms`. The current `Tr_Ca` with `tau = 1000 ms` is between the two — it captures some augmentation but not cleanly.
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**Post-tetanic potentiation (PTP)** — an even slower presynaptic enhancement lasting minutes after a high-frequency burst, driven by protein kinase C activation from sustained Ca²⁺ elevation. This is a presynaptic phenomenon that looks like LTP from the outside but has no postsynaptic component and no structural change. It would require a third, very slow trace variable.
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---
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**How they interact with the LTP/LTD table**
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Short-term and long-term plasticity operate on the same synapse simultaneously but independently:
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```
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Spike arrives
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→ short-term: how much NT releases THIS spike (presynaptic, ms-seconds)
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→ long-term: does the synapse get stronger or weaker PERMANENTLY (postsynaptic, mins-hours)
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```
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A synapse can be undergoing LTD (slowly losing AMPA receptors over minutes) at the same time as it is showing short-term facilitation (releasing more NT per spike due to residual Ca²⁺). The two processes do not interfere — they act on different variables through different mechanisms.
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The important implication for your model is that **the LTP/LTD table we built describes what happens to** `g_AMPA_baseline` **over minutes**. Short-term potentiation/depression describes what happens to `released_NT` over milliseconds to seconds. They are different outputs of the same synapse, running in parallel.
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If you want to add short-term plasticity explicitly to the behaviour specification it would live entirely in the presynaptic ms and seconds loops as named episodes of existing variables:
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```
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— ms (presynapse, short-term plasticity):
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ShortTermFacilitation: Episode
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— residual Ca_micro > 0 at next spike arrival
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— release_frac in deterministic_release elevated above baseline
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— decays as Ca_micro clears (tau ~100-500 ms)
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— more NT per spike than at rest
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ShortTermDepression: Episode
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— N_RRP depleted by rapid successive spikes
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— release_frac unchanged but N_RRP reduced
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— fewer absolute vesicles released per spike
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— recovers via RP→RRP recruitment (seconds)
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— seconds (presynapse, short-term plasticity):
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Augmentation: Episode [GAP — not yet modelled]
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— requires second slow Ca2+ trace (tau ~5000 ms)
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— elevated release probability for 5-10 s after burst
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— distinct from spike-by-spike facilitation
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PostTetanicPotentiation: Episode [GAP — not yet modelled]
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— requires very slow trace (tau ~minutes)
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— elevated release probability for minutes after tetanus
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— presynaptic only, no postsynaptic component
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``` |