# Tripartite Synapse — Biological Reference (companion to v13 pseudocode)

> Companion to `tripartite_synapse_v13_pseudocode.md`. Explains the biology each variable and
> behavior conflates. Variable meanings are unchanged; v13 refined the model logic:
> per-spike calcium deposit (frequency emergent, not a parameter); BEHAVE now separates a FUEL
> shortfall (deposits endurance need) from an OCCUPANCY/structure shortfall (short-term
> depression — no endurance, since more fuel would not help); the endurance feedback term
> (retrograde NO) appears only at the presynapse, where such a signal actually arrives, while
> every other component's endurance proxy is own-state only; EVALUATE merged into TRACE
> (judging a behavior is maintaining a trace); shipment is modelled as a transit-delayed flow
> (axonal/dendritic transport takes a characteristic time, so distal targets receive later),
> reflecting the general principle that every flow has a timescale.

---

## The three synaptic components and their support structures

A SYNAPSE is composed of three first-class components:
- **PRE** — presynaptic bouton (the axon's terminal at this synapse)
- **POST** — postsynaptic spine (the dendrite's terminal at this synapse)
- **ASTRO** — astrosynapse, the perisynaptic astrocytic process (the astrocyte's terminal)

Each has an upstream support structure that supplies it:
- **AXON** supplies PRE (transmission + transport from soma)
- **DEND** supplies POST (integration + transport from soma)
- the **astrocyte cell body** supplies ASTRO (energy + ECM material)
- **SOMA** is the integrating center and the root of neuronal material

The compartment analogy: AXON:PRE = DEND:POST = astrocyte-body:ASTRO = supply line : terminal.

---

## Resource variables

### DAY budget (one per component)
Aggregates fast energy AND fast consumables — everything needed to run moment-to-moment.

- **pre_budget** — ATP for VGCC gating, vesicle fusion (SNARE), VATPase vesicle refill,
  plus fast consumables: vesicle membrane lipids, synaptotagmin recycling.
- **post_budget** — ATP for the NaK pump (membrane reset after current), NMDA current
  handling, plus fast actin monomers for transient spine changes and receptor-recycling lipids.
- **dend_budget** — ATP for bAP propagation (NaK reset along branch), local translation
  (ribosome running cost), SERCA Ca²⁺ resequestration, plus fast mRNA consumed by translation.
- **soma_budget** — ATP for AP generation (Na⁺/K⁺ currents + NaK reset), CREB
  phosphorylation, nuclear Ca²⁺ handling, plus shipping running costs.
- **axon_budget** — ATP for AP propagation at nodes of Ranvier, kinesin/dynein motor
  running cost, fast myelin maintenance.
- **astro_central_budget** — ATP from glycolysis at the astrocyte cell body; funds EAAT
  clearance, serine→D-serine synthesis, lactate export, fast process motility.

### astro_lactate[i]
Lactate exported from the astrocyte cell body to synapse i. Biologically: glucose →
(glycolysis) → lactate, released into extracellular space, absorbed by neuronal MCT2
transporters, converted to pyruvate → TCA → ATP in the neuron's mitochondria. The astrocyte
is the primary fast-energy supplier to pre, post, and dend.

### NIGHT energy (one per component) — NOT recoverable
ATP for structural assembly. Distinct from DAY budget because it is spent on building, and
the work of assembly is thermodynamically gone once done (cannot be recovered by disassembly).
- pre_energy: RIM/Munc13 incorporation, VGCC clustering.
- post_energy: CaMKII anchoring, actin polymerization, PSD scaffold remodeling.
- dend_energy: mitochondria incorporation, cytoskeletal reinforcement.
- soma_energy: ribosome biogenesis, ion-channel incorporation.
- axon_energy: myelination, microtubule stabilization.
- astro_energy: process retraction, ECM secretion, racemase upregulation.

### NIGHT material (one per component) — RECOVERABLE
Slow structural proteins. Recoverable because disassembly (LTD) returns the proteins to a
reusable pool (ubiquitin-proteasome → amino acids; internalized receptors → endosomal reserve).
- **soma_material** (root) — all neuronal structural proteins from CREB-driven synthesis:
  AMPA subunits, PSD scaffold, AZ scaffold, mRNA transcripts (Arc, BDNF), organelles.
- **dend_material** — from soma: Arc/plasticity mRNA, mitochondria, cytoskeletal proteins,
  AMPA subunits in transit to spines.
- **post_material** — from dend: AMPA receptor subunits (GluA1/2), PSD scaffold (PSD-95,
  SHANK, Homer), structural actin, CaMKII.
- **axon_material** — from soma: kinesin/dynein motors, microtubule components, myelin proteins.
- **pre_material** — from axon: RIM, Munc13, VGCC subunits, structural vesicle proteins.
- **astro_material** (root: astrocyte cell body) — EAAT proteins, serine racemase, ECM
  proteins (Glypicans, Thrombospondins), process cytoskeleton.

**Why energy and material are separate in NIGHT but combined in DAY:** during DAY both are
fast consumables replenished on the same timescale, so one `budget` variable suffices. During
NIGHT they diverge — material is recoverable after LTD, energy is not — so they must be two
variables. This asymmetry (material returns to the pool, energy is gone) is what makes one
synapse's depression genuinely fund another's potentiation.

---

## Structural variables (strength ceilings — written in NIGHT)

Each aggregates several correlated structural properties into one capacity.

- **pre_structure** — active zone capacity:
  slot_ceiling (number of vesicle docking slots) + VGCC_coupling (Ca²⁺-channel proximity to
  slots, sets release efficiency) + refill_ceiling (max RRP replenishment rate).
- **post_structure** — spine sensitivity capacity:
  slot_ceiling (number of PSD anchoring slots for AMPA) + spine_volume (local reserve and
  actin machinery) + reserve_ceiling (endosomal AMPA pool size).
- **dend_structure** — branch capacity:
  bAP_fidelity(position) (mitochondrial density sets propagation strength, attenuates with
  distance) + translation_ceiling (local mRNA capacity) + transport_speed (cytoskeletal integrity).
- **soma_structure** — somatic output capacity:
  baseline_threshold (inverse: ion-channel density at axon initial segment) + AP_reliability
  (Na⁺ channel density) + synthesis_ceiling (ribosome density + CREB machinery).
- **axon_structure** — axonal capacity:
  propagation reliability (myelination density) + transport_ceiling (motor density + microtubule
  integrity) + mitochondrial density.
- **astro_structure** — astrosynaptic environmental capacity:
  perisynaptic_distance⁻¹ (wall proximity — closer = more glutamate contained) + EAAT_density
  (clearance ceiling) + Dserine_tonic (baseline co-agonist) + ECM_integrity.
  **Self-reinforcing both directions:** tighter wrap + more tonic D-serine make future
  potentiation easier; looser wrap + zero tonic D-serine make future depression easier.

---

## Budget ceilings (endurance ceilings — written in NIGHT)

- **{component}_budget_ceiling** — the maximum fuel the component can hold / the maximum
  duration of sustained behavior. Biologically: mitochondrial density and local fuel-storage
  capacity. Built by activity-driven mitochondrial biogenesis; lost by mitophagy when idle.
  Parallel to structure: structure is strength capacity, budget_ceiling is endurance capacity.

---

## Trace variables

### fast_trace (one per component) — DAY only, decays automatically
The local record of recent activity that biases the next behavior.
- **pre_fast_trace** — residual presynaptic Ca²⁺ after spikes (τ≈100ms). Biases NT release
  (facilitation) and provides tagging eligibility.
- **post_fast_trace** — spine Ca²⁺ amplitude × rise-speed (τ≈tens ms). Encodes the LTP-vs-LTD
  instruction (fast rise → CaMKII → potentiation; slow rise → phosphatase → depression).
- **dend_fast_trace** — branch Ca²⁺ from bAP + spine spillover (τ≈300ms). Integrates branch co-activity.
- **soma_fast_trace** — nuclear Ca²⁺ from each AP (τ≈seconds). Drives toward CREB activation.
- **axon_fast_trace** — propagation load (τ≈seconds). High load → Na⁺ inactivation at branch
  points → propagation failure (this is axonal short-term depression).
- **astro_fast_trace** — perisynaptic Ca²⁺ from mGluR5 activation by glutamate spillover
  (τ≈seconds). Drives D-serine release.

### soma timing traces (emergent refractory + adaptation + alignment)
- **soma_Na_inactivation** (τ≈ms) — sodium-channel inactivation after an AP. Its recovery IS
  the refractory period (emergent, not a hardcoded timer). High → absolute refractory; decaying
  → relative refractory; recovered → normal.
- **soma_adaptation** (τ≈100s of ms) — slow K⁺ channel (SK/M-type) activation accumulating
  over a spike train, raising threshold. This is spike-frequency adaptation.
- **soma_refractory_alignment** — deposited when a suprathreshold input arrives during
  refractoriness (a missed coincidence). Speeds future recovery so the soma aligns to its input
  rhythm. Bottom-up: no rhythm is represented; alignment emerges from accumulated local
  mismatches and decays when mismatches stop (self-limiting).

### possible_tag (one per component) — intermediate, τ≈s–min
Graded accumulation of tagging eligibility. For POST, this is the CANDIDATE tag lifetime.

### endurance_need (one per component) — intermediate, τ≈s–min
Deposited when budget depletion interrupts a behavior that was on a LOCALLY successful
trajectory. Records that fuel — not structure, not significance — was the binding constraint
on a forming success. Requires NO dopamine (homeostatic, not associative).
**Local success proxy per component** (each uses only its own state + arrived signals):
- PRE: own fast_trace high (was releasing strongly), optionally amplified by retrograde
  messenger (endocannabinoid / NO / BDNF) that has arrived.
- POST: own Ca²⁺ climbing toward tagging threshold (naturally local).
- DEND: own branch strongly active (high branch voltage/Ca²⁺) when propagation fell short.
- SOMA: own nuclear Ca²⁺ climbing toward CREB.
- AXON: own propagation load high (was carrying a strong train).
- ASTRO: own local glutamate/Ca²⁺ high (was under heavy clearance/D-serine demand).

### tag (one per component) — DAY→NIGHT bridge, τ≈hours
The validated record of significance that survives to NIGHT and gates strength commits.
Formed by coincidence of local eligibility + non-local validation (dopamine).
**POST is special — two-phase, three coincidences:**
- CANDIDATE: local Ca²⁺ above threshold + astrosynapse D-serine present (coincidence 1).
- amplified when bAP confirms soma fired (coincidence 2).
- STABLE: CANDIDATE + dopamine within stabilization window (coincidence 3).
Biologically: early CaMKII creates a labile tag (early-LTP); PKA driven by dopamine via D1R
stabilizes it (late-LTP). Without dopamine, the candidate degrades — early-LTP reverses.

---

## Behaviors — biological meaning

### PRE | AP — neurotransmitter release
`NT_flux = RRP × sat(pre_fast_trace, K_release)` models continuous NT release proportional to
the readily-releasable pool and a saturating Ca²⁺ drive (synaptotagmin's cooperative Ca²⁺
sensitivity, simplified to a saturating curve). RRP depletes as released (short-term depression
as a consequence) and refills via VATPase (energy-throttled, so low budget deepens depression).
The mGluR2/3 brake is presynaptic autoinhibition by spillover (Gi → reduced VGCC opening).

### POST | NOT_bAP — three calcium sources, two plasticity cases
- **Source 1 (AMPA):** glutamate opens AMPA → depolarizing current + small Ca²⁺; the
  depolarization begins ejecting the NMDA Mg²⁺ block.
- **Source 2 (NMDA):** if depolarized enough (Mg²⁺ ejected) AND D-serine present (astrocyte
  co-agonist) AND glutamate bound → large Ca²⁺ influx. This is the coincidence detector.
- **Source 3 (bAP, separate context):** back-propagating AP adds depolarization + Ca²⁺,
  amplifying an existing signal supralinearly.
- **Case 1 (STP):** high Ca²⁺ drives AMPA receptors from the local reserve to the surface,
  bounded by the anchoring-slot ceiling. Fast, reversible, NO dopamine. When Ca²⁺ falls,
  receptors drift back — short-term depression as a passive consequence, never signaled.
- **Case 2 (LTP tag):** high Ca²⁺ + (later) dopamine sets the tag that NIGHT uses to raise the
  slot ceiling. NIGHT builds slots; DAY fills them.

### DEND | bAP — bidirectional signaling
Propagates the bAP from soma toward spines (fidelity attenuates with distance — distal spines
get weaker confirmation, are harder to potentiate) and integrates spine signals toward the soma.

### SOMA | AP — integration, firing, emergent timing
Fires when integrated branch input exceeds a threshold that is the baseline (from structure)
raised by adaptation and modulated by neuromodulators, gated by the emergent refractory state.
Each AP deposits three traces (inactivation → refractory, adaptation → threshold rise, nuclear
Ca²⁺ → plasticity). The soma is the coincidence detector at the cellular scale (nuclear Ca²⁺ +
dopamine → CREB), and the production bottleneck: its tag gates how much material all downstream
components get in NIGHT.

### AXON | AP — reliable propagation with frequency-dependent failure
Propagation reliability is set by myelination and degraded by high-frequency load (Na⁺
inactivation at branch points = axonal STD). The axon also transports material to boutons and
sets the timescale of presynaptic structural commits.

### ASTRO | CONTINUOUS — gatekeeper and energy hub
Clears glutamate (EAAT), supplies D-serine (the NMDA co-agonist that gates postsynaptic LTP),
and distributes lactate to the territory by demand-weighting (active synapses generating more
clearance load pull more fuel; slow synapses get less). The same spillover that excites the
astrocyte (mGluR5 → Ca²⁺ → D-serine) also brakes the presynapse (mGluR2/3 → Gi) — one signal,
opposite effects via different receptors. The astrocyte is the energy root and the gain control
of the whole synapse.

---

## NIGHT operations — biological meaning

- **Step 1 (replenish/distribute):** overnight protein synthesis peaks (CREB-driven, gated by
  soma_tag — corresponds to slow-wave-sleep replay). Soma material flows to branches/axon then
  spines/boutons; astrocyte material flows to astrosynapses, tag-weighted.
- **Step 2 (strength commits):** tagged components build structure — more slots, tighter
  coupling, tighter astrosynaptic wrap. Coherence bonus when pre+post+astro all tagged (the
  whole synapse agrees). astro_structure self-reinforces.
- **Step 2b (endurance commits):** components with high endurance_need build budget_ceiling —
  mitochondrial biogenesis. Competes with step 2 for the same material/energy.
- **Step 3 (passive decay):** both ceilings decay; maintenance from the remaining pool resists
  decay only where sufficient. Depotentiation and endurance-loss are both by neglect — no
  signal weakens anything; unmaintained capacity simply drifts down. Recovered material (not
  energy) returns to pools.
- **Step 4 (homeostatic scaling):** if the soma fired too much overall, all synapses scale down
  proportionally (sleep-associated global downscaling), preserving relative differences.
- **Step 5 (clear traces):** fast traces, possible tags, endurance needs, and soma timing traces
  reset; tags below expiry clear, above-expiry tags carry forward (multi-night consolidation);
  structure and budget_ceiling persist.

### Shockwave lockdown
Emergency global astrocytic Ca²⁺ wave → GABA + ATP release → mass AMPA internalization and
hyperpolarization. Bypasses budget gates. A circuit breaker against runaway excitation.

---

## Pool-filling: private reserve vs contested supply

The pseudocode uses two filling primitives, distinguished by where the resource comes from.

**`fill` (private reserve).** The pool is replenished from a source the component owns
outright, uncontested by siblings, bounded by the component's own ceiling and a rate cap.
- RRP refill — vesicles mobilized from the bouton's own reserve pool toward the docking-slot
  ceiling, rate-limited by VATPase. The reserve is private to the bouton.
- SOMA self-replenish — the soma fuels itself from its own mitochondria toward its budget
  ceiling. No other component draws on it.

**`refill` (contested supply).** The pool is replenished from a supply that multiple
components compete for, rationed by demand (gap to ceiling).
- pre/post/dend/axon budgets — drawn from astrocytic lactate (shared across all synapses the
  astrocyte wraps) plus shipment from soma/axon/dendrite (shared across downstream targets).

**Neither primitive (their own forms).** Some inflows are not fills toward a ceiling:
- AMPA surface insertion — Ca²⁺-driven rate from the spine's private endosomal reserve, with
  an explicit passive drift-back (short-term depression) when Ca²⁺ is low. Not a steady fill.
- D-serine release — demand-driven (saturating in astro Ca²⁺) and budget-limited, like NT
  release; a release process, not a pool top-up.
- Root productions — `glycolysis(glucose)` at the astrocyte and `CREB_synth(soma_tag)` at the
  soma are the system's energy and material roots: raw inflows capped only by the external
  vascular supply, not fills toward an internal ceiling.

The distinction matters biologically: a private reserve guarantees a component some autonomy
(the bouton can refill its RRP from its own vesicles even when lactate is scarce), while a
contested supply couples a component's fate to its neighbours' demands (operational budget
fails first where many active synapses compete for the same lactate).

---

## PRE ↔ POST interaction: local computation, message-only coupling

The presynapse and postsynapse never read each other's internal state. They interact only
by writing to and reading from shared cleft channels. Each side computes entirely locally on
what it has: its own variables plus whatever signals have arrived in the cleft. This is the
message-passing realization of the locality principle.

**Forward channel — glutamate (PRE → POST and ASTRO).** The presynapse writes glutamate via
NT_flux. The postsynapse reads it (AMPA, NMDA) and the astrosynapse reads it (clearance,
mGluR5). The astrosynapse clears it. PRE never knows whether POST responded — it only emits.

**Gate channel — astro_Dserine (ASTRO → POST).** The astrosynapse writes D-serine; the
postsynapse reads it as the obligatory NMDA co-agonist. POST cannot open NMDA without this
arrived signal, but it does not read the astrocyte's state — only the delivered D-serine.

**Backward channel + — retro_NO (POST → PRE).** When the postsynapse's NMDA opens (Mg²⁺
ejected, D-serine present, glutamate bound), nNOS — physically tethered to the NMDA receptor
through PSD-95 — synthesises nitric oxide (and, on a slower timescale, BDNF is released).
These diffuse retrogradely to the presynapse. Biologically this is the classic retrograde
messenger of LTP: it tells the bouton that its release landed on a postsynapse that genuinely
responded. In the model, POST emits `retro_NO` proportional to its own NMDA-driven calcium —
computed purely from POST's local state — and PRE reads it as `retro_NO_local`.

  `retro_NO_local` is exactly the grounding of the presynaptic endurance signal. The
  presynapse's local success proxy is "I was releasing strongly" (`pre_fast_trace` high). On
  its own that only says the bouton was working hard, not that the work mattered. `retro_NO`
  adds the missing confirmation — that the postsynapse responded — without PRE ever reading
  POST's calcium. So PRE deposits endurance need as `pre_fast_trace × (1 + retro_NO_local)`:
  strong release that was confirmed effective makes the strongest claim that fuel, not
  futility, was what interrupted a forming success. retro_NO is short-lived (NO degrades and
  diffuses within seconds), so the channel decays fast — confirmation must be recent to count.

**Backward channel − — retro_eCB (POST → PRE).** When the postsynapse is strongly
depolarised, it synthesises endocannabinoids (2-AG, anandamide) that diffuse retrogradely and
bind presynaptic CB1 receptors, suppressing release. This is depolarisation-induced
suppression of excitation (DSE) — a homeostatic negative feedback: an over-driven postsynapse
tells the presynapse to release less. In the model, POST emits `retro_eCB` from its own
membrane potential, and PRE reads it as `retro_eCB_local`, which reduces the release drive
`sat(...) × (1 - retro_eCB_local)`. Again POST computes from its own state; PRE adjusts from
the arrived signal; neither reads the other's interior.

The two backward channels are opposite-signed messages the postsynapse sends about its own
condition: retro_NO says "your input was effective — worth sustaining," retro_eCB says "I am
saturated — ease off." Together with the forward glutamate and the D-serine gate, they make
the synapse a fully message-coupled system of locally-computing components.

**Why RRP refill is in NOT_AP only.** During an AP the bouton releases — RRP depletes. Refill
(VATPase reloading vesicles from the reserve pool) is a recovery process that proceeds between
spikes. Placing `fill(RRP, ...)` only in the NOT_AP context makes the AP context pure
depletion and the NOT_AP context pure recovery. A consequence falls out for free: during
sustained high-frequency firing there are many AP steps and few NOT_AP steps, so RRP depletes
faster than it recovers — short-term depression deepens with frequency, with no explicit
depression rule. The release itself is throttled further when budget is low (VATPase refill
is energy-limited), coupling metabolic state to the depth of depression.
