The three compartments maintain distinct but coupled state variables across three time horizons. At the fast scale, the presynapse tracks residual calcium and its readily-releasable vesicle pool — both of which encode the very recent history of firing. The postsynapse tracks membrane voltage and the amplitude and speed of its calcium rise, which together encode the instruction for future change. The astrocyte tracks glutamate concentration both inside and outside the cleft, its own local and global calcium state, and its fuel output. At the intermediate scale, the shared signal layer tracks whether the mGluR overflow sensors have fired, and whether the neuromodulatory context gate has been set — specifically whether PKA has primed the AMPA insertion machinery, silenced the forgetting phosphatase, and enabled gene expression in the nucleus. At the slow scale, all three compartments track their own physical architecture: the postsynapse its receptor count and spine size, the presynapse its docking slot count and vesicle channel clustering, and the astrocyte its wall distance from the synapse, its matrix density, and its baseline co-agonist supply.

Fast scale: what happens spike by spike

Every action potential sets off a precise sequence across all three compartments simultaneously. The presynapse converts the electrical event into a chemical wavefront: calcium floods in, drives probabilistic vesicle release from the readily-releasable pool, and leaves a residual trace that biases the next release upward if spikes keep arriving and downward if they stop. The amount of glutamate released fills the cleft and begins diffusing outward.

The astrocyte responds in two parallel arms the moment glutamate spills beyond the cleft boundary. The first arm activates astrocytic mGluR5 receptors via a Gq cascade, triggering an internal calcium rise that is directly proportional to how much glutamate has escaped — this calcium rise drives D-serine release, widening the postsynaptic NMDA detection window. The second arm simultaneously activates presynaptic mGluR2/3 receptors via Gi, suppressing adenylyl cyclase and reducing vesicle release probability — a direct autoinhibitory brake on the very source of the overflow. These two arms run in opposite directions from the same trigger: the astrocyte brakes the presynapse while amplifying the postsynaptic learning window at the same time.

The postsynapse responds to the glutamate wavefront through its AMPA receptors, depolarizing the membrane. But full calcium entry through NMDA receptors only occurs if two conditions are met simultaneously: the membrane must be sufficiently depolarized to eject the magnesium block, and D-serine released by the astrocyte must be present as a co-agonist. This is the coincidence detection step — both conditions are required, and the astrocyte's D-serine supply is what makes it a three-party coincidence rather than a two-party one.

Once the spike is complete, the astrocyte vacuums up residual glutamate via its transporter proteins, and the harder it works at this clearance the faster it runs its glycolysis engine, converting blood glucose into lactate and pumping it into the extracellular space. Both the presynapse and postsynapse absorb this lactate to power their reset pumps — refilling the vesicle pool and restoring the resting membrane potential respectively. The energy supply is therefore coupled to activity: busier synapses generate more demand on the astrocyte, which in turn fuels faster recovery.

Intermediate scale: temporary tuning between spikes

If firing is sustained rather than isolated, the system begins temporary adjustments that do not yet commit to structural change. In the presynapse, sustained high-frequency firing keeps residual calcium elevated, progressively increasing release probability and mobilizing vesicles from deep reserve storage into the readily-releasable pool — a priming of the launchpad without permanently expanding it. If frequency is low and sparse, the reverse happens: the pool depletes faster than it refills and release probability falls.

In the postsynapse, sustained high-frequency input keeps the membrane depolarized long enough to hold the magnesium block off continuously, allowing calcium to accumulate gradually rather than in isolated pulses. This accumulation is the early signal for plasticity, but it is not yet sufficient on its own to commit a structural change.

In the astrocyte, sustained activity keeps mGluR5 activated and D-serine release elevated above its baseline pulse level, maintaining a wider NMDA detection window for as long as the high-frequency drive continues.

The neuromodulatory broadcast then sets the critical context gate. If dopamine or norepinephrine levels cross their respective thresholds — signaling that the current activity pattern is behaviorally significant — PKA activity rises and phosphorylates three targets in sequence. It lowers the threshold for AMPA receptor insertion by priming the GluA1 subunit at Ser845. It silences the LTD phosphatase PP1 by phosphorylating DARPP-32, effectively blocking the forgetting machinery from running while the save signal is present. And it translocates to the nucleus to phosphorylate CREB, enabling the gene expression needed to build new structural proteins. Acetylcholine from the basal forebrain acts in parallel, lowering the global LTP threshold — making the entire system more sensitive to incoming patterns during periods of high attention.

Slow scale: the commit decision and structural rewriting

Once the fast and intermediate dynamics have run, the system evaluates a three-layer filter to decide whether to permanently rewrite its architecture. The first layer asks whether a genuine event occurred — specifically whether postsynaptic calcium rose above the high threshold at sufficient speed to activate the LTP kinase pathway. The second layer asks whether that event was excessive enough to saturate the cleft and trigger mGluR5 on the astrocyte. The third layer asks whether the neuromodulatory context validated the event as worth saving — whether PKA has primed the insertion machinery and silenced the forgetting machinery.

Only when all three conditions align does structural rewriting proceed, and when it does, all three compartments are rewritten simultaneously and in the same direction.

In the potentiation branch, the postsynapse anchors new AMPA receptors into the membrane via CaMKII — a process made easier because PKA has already lowered the insertion threshold — and the spine itself physically enlarges. The presynapse expands its active zone, clusters more calcium channels directly beneath the docking area to tighten the coupling between electrical events and vesicle release, and increases its baseline release probability. The astrocyte retracts its process walls inward toward the synapse, secretes structural matrix proteins to seal and stabilize the channel, upregulates its baseline D-serine synthesis for chronic NMDA priming, and reduces its glutamate clearance rate — meaning future signals will linger longer in the cleft rather than being vacuumed away immediately.

In the depression branch, the phosphatase PP1 wins instead of CaMKII, and all three changes run in reverse simultaneously. The postsynapse internalizes receptors and the spine shrinks. The presynapse removes docking slots, scatters its calcium channels away from the active zone, and pulls vesicles back into deep reserve storage. The astrocyte secretes matrix metalloproteinases to dissolve the structural scaffold, cuts its D-serine supply to starve the NMDA gate chronically, and extends its process walls outward away from the synapse, loosening the diffusion barrier so that future glutamate bleeds away faster rather than concentrating at the cleft.

If the calcium event occurred but the neuromodulatory save signal did not arrive, only transient changes happen — early receptor insertion and brief facilitation — both of which reverse within minutes without trace. If no threshold was crossed at all, nothing changes and the current structural state is simply held.

The critical asymmetry

The astrocyte's perisynaptic wall distance is the variable that makes both outcomes self-reinforcing rather than merely additive. When it moves inward during potentiation, it concentrates glutamate at the cleft, maintains D-serine near the postsynapse, and tightens the presynaptic feedback loop — making future high-frequency events even more likely to cross the threshold. When it moves outward during depression, it dilutes the signal, starves the NMDA gate, and loosens the presynaptic feedback — making future events even less likely to reach threshold. The astrocyte therefore does not simply mirror what the neurons decide: it actively deepens the valley the synapse has already rolled into, in whichever direction that happens to be.

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global state variables

── Fast (ms–s): wave propagation ─────────────────────────────

Presynapse

pre_Ca_residual // leftover Ca²⁺ between spikes — short-term trace vesicle_release_prob // P(0.1–1.0) per docking slot RRP_pool // readily-releasable vesicle pool reserve_pool // chained vesicles in deep storage

Postsynapse

membrane_potential // Vm — depolarization state NMDA_Mg_block // bool — mechanical clamp on/off post_Ca_amplitude // peak [Ca²⁺] rise in spine post_Ca_rise_speed // d(Ca)/dt — fast=LTP signal, slow=LTD signal

Astrocyte

glutamate_cleft // [glu] in synaptic cleft glutamate_spillover // extrasynaptic [glu] — saturates mGluRs astro_Ca_local // IP3-triggered local rise near synapse astro_Ca_global // soma-wide wave — network overload flag D_serine_release // gliotransmitter — NMDA co-agonist pulse lactate_output // fuel export rate to pre and post

── Intermediate (s–min): temporary tuning ────────────────────

mGluR2_3_activation // presynaptic Gi — autoinhibitory brake mGluR5_activation // astrocytic Gq — IP3→Ca²⁺→D-serine cascade cAMP_level // set by dopamine/NE via Gs → adenylyl cyclase PKA_activity // downstream of cAMP GluA1_Ser845_primed // bool — AMPA insertion threshold lowered by PKA DARPP32_phospho // bool — PP1 (LTD phosphatase) silenced by PKA CREB_active // bool — structural gene expression enabled

── Slow (h–weeks): structural architecture ───────────────────

AMPA_count // surface receptors — postsynaptic sensitivity spine_volume // physical size of dendritic spine active_zone_size // docking slot count RRP_pool_capacity // max readily-releasable pool VGCC_clustering // Ca²⁺ channels beneath active zone perisynaptic_distance // how close astrocyte walls are to synapse ECM_integrity // extracellular matrix density D_serine_tonic_level // baseline co-agonist supply (sustained) glutamate_clearance_rate // EAAT transporter density

fast time scale — wave propagation (ms → s)

function fire_action_potential(input_freq):

Presynapse: launch wavefront

pre_Ca_residual += spike_influx(input_freq) pre_Ca_residual *= decay(τ ≈ 100ms) // fades unless spikes keep arriving vesicle_release_prob *= facilitation(pre_Ca_residual) released_vesicles = binomial(RRP_pool, vesicle_release_prob) glutamate_cleft = released_vesicles × quantal_content RRP_pool -= released_vesicles

Astrocyte: overflow sensing and co-agonist release

glutamate_spillover = extrasynaptic_diffusion(glutamate_cleft) if glutamate_spillover > spillover_threshold: mGluR5_activation = True // Gq arm → IP3 → Ca²⁺ → D-serine astro_Ca_local += IP3_cascade(PLC) D_serine_release += proportional_to(astro_Ca_local) mGluR2_3_activation = True // Gi arm → brake presynapse cAMP_level -= Gi_inhibition(adenylyl_cyclase) vesicle_release_prob -= VGCC_suppression() // autoinhibitory brake

Astrocyte: check for network overload

astro_Ca_global = soma_wave(astro_Ca_local > OVERLOAD_threshold) if astro_Ca_global: trigger(shockwave_lockdown)

Postsynapse: wavefront strikes resonator

AMPA_current = glutamate_cleft × AMPA_count membrane_potential += AMPA_current

NMDA gate: coincidence check

if membrane_potential > -40mV and D_serine_release > threshold: NMDA_Mg_block = False // Mg²⁺ ejected post_Ca_amplitude += NMDA_influx(glutamate_cleft) post_Ca_rise_speed = d(post_Ca_amplitude) / dt

Astrocyte: vacuum trailing echoes + fuel pipeline

glutamate_cleft -= glutamate_clearance_rate × Δt lactate_output += glycolysis_rate(glutamate_clearance_rate) membrane_potential restored by NaK_ATPase(lactate_output) RRP_pool refilled by VATPase(lactate_output)

intermediate time scale — temporary tuning (s → min)

function short_term_plasticity(input_freq, duration):

Presynapse: facilitate or depress based on Ca²⁺ history

if input_freq > 20Hz: vesicle_release_prob *= 1.3 // residual Ca²⁺ primes launchpad mobilize(reserve_pool → RRP_pool) // break storage chains elif input_freq < 5Hz: vesicle_release_prob *= 0.7 // RRP depleted faster than refill

Postsynapse: NMDA gate primed if frequency sustained

if input_freq >= 50Hz and duration > 1s: NMDA_Mg_block = False // sustained depolarization post_Ca_amplitude accumulates // early-LTP signal rises

Astrocyte: sustained volume → escalate co-agonist

if astro_Ca_local > local_threshold: D_serine_release += gliotransmitter_pulse() // widens NMDA window

Neuromodulators: set context gate via Gs protein

if dopamine_level > D1_threshold or NE_level > β_threshold: cAMP_level += Gs_activation(adenylyl_cyclase) PKA_activity = proportional_to(cAMP_level) phosphorylate(GluA1, site=Ser845) GluA1_Ser845_primed = True // lowers CaMKII threshold phosphorylate(DARPP32) DARPP32_phospho = True // silences PP1 — blocks LTD translocate(PKA → nucleus) → phosphorylate(CREB) CREB_active = True // enables structural gene expression

Acetylcholine: lower LTP threshold globally

LTP_threshold *= (1 / (1 + ACh_level × mAChR_gain))

slow time scale — structural commit (h → weeks)

function commit_to_structural_change():

Hierarchical filter: three conditions must align

event_detected = post_Ca_amplitude > Ca_HIGH // layer 1: did something happen? overflow_sensed = mGluR5_activation == True // layer 2: was it excessive? context_validated = DARPP32_phospho and GluA1_Ser845_primed // layer 3: worth saving?

── Branch 1: LTP — potentiation ──────────────────────────────

if event_detected and overflow_sensed and context_validated:

Postsynapse: anchor receptors, enlarge spine

activate(CaMKII) AMPA_count += receptor_insertion(CaMKII, GluA1_Ser845_primed) spine_volume *= 1.5

Presynapse: expand launchpad, increase output reliability

active_zone_size *= 1.4 // more docking slots RRP_pool_capacity += pool_expansion(active_zone_size) VGCC_clustering += cluster_beneath_AZ() // tighter Ca²⁺ coupling vesicle_release_prob += 0.1 // driven by VGCC clustering

Astrocyte: seal and insulate the channel

perisynaptic_distance -= process_retraction() // walls move IN → tighter wrap ECM_integrity += secrete(Glypicans, Thrombospondins) D_serine_tonic_level += upregulate_synthesis() // sustained NMDA priming glutamate_clearance_rate *= 0.85 // tighter wrap → slower diffusion away return "potentiated"

── Branch 2: temporary only — Ca²⁺ rose, no save signal ─────

elif event_detected and not context_validated: AMPA_count += transient_insertion() // early-LTP only — reverses in minutes vesicle_release_prob += transient_facilitation()

No astrocyte structural change

return "temporary facilitation only"

── Branch 3: LTD — active forgetting ─────────────────────────

elif event_detected and not overflow_sensed and not context_validated:

Postsynapse: internalize receptors, shrink spine

activate(PP1) AMPA_count -= receptor_internalization(PP1) spine_volume *= 0.7

Presynapse: dismantle launchpad

active_zone_size -= docking_slot_removal() RRP_pool_capacity -= pool_contraction() VGCC_clustering -= scatter_VGCCs() // decouple Ca²⁺ from AZ vesicle_release_prob *= 0.6

Astrocyte: dissolve matrix, pull away, cut support

ECM_integrity -= secrete(MMPs) // molecular scissors D_serine_tonic_level = 0 // co-agonist supply cut perisynaptic_distance += process_extension() // walls move OUT → loose wrap glutamate_clearance_rate *= 1.2 // looser wrap → faster spillover return "depressed"

── Branch 4: baseline ────────────────────────────────────────

else:

All structural variables unchanged — system holds current state

return "baseline — no change"

special case — shockwave lockdown (>100Hz uncoordinated)

function shockwave_lockdown(): astro_Ca_global = GLOBAL_WAVE // soma-level flood release(GABA, ATP) // gel floods postsynapse AMPA_count -= mass_internalization() membrane_potential = HYPERPOLARIZED cluster(VGCC → beneath_active_zone) // ensures signal survives chaos

energy supply chain — metabolic gating (continuous)

function metabolic_loop(Δt):

Astrocyte: glucose → lactate pipeline

glucose_uptake = blood_capillary_supply() lactate_output = glycolysis(glucose_uptake, glutamate_clearance_rate) lactate_output *= load_factor(glutamate_clearance_rate)

Pre + post absorb lactate → power their pumps

RRP_pool refill rate ∝ VATPase(lactate_output) membrane_potential reset ∝ NaK_ATPase(lactate_output)

key asymmetry — perisynaptic distance is bidirectional

// LTP: astrocyte moves IN → tighter diffusion barrier // → glutamate_clearance_rate ↓ (signal contained, not diluted) // → D_serine_tonic_level ↑ (NMDA gate chronically primed)

// LTD: astrocyte moves OUT → looser diffusion barrier // → glutamate_clearance_rate ↑ (signal bleeds away faster) // → D_serine_tonic_level = 0 (NMDA gate chronically starved)

// Result: astrocyte amplifies both directions simultaneously // potentiation becomes self-reinforcing; depression becomes self-reinforcing

Neuromodulators

These are produced by small, anatomically concentrated nuclei that broadcast widely across the brain:

dopamine_level // "save button" — validates LTP norepinephrine_level // arousal / signal-to-noise gain acetylcholine_level // attention — lowers LTP threshold

Dopamine

Dopamine is produced primarily by neurons in the Substantia Nigra pars compacta (projecting to the striatum, relevant for motor learning and habit formation) and the Ventral Tegmental Area (VTA) (projecting to the prefrontal cortex and limbic system via the mesolimbic and mesocortical pathways, relevant for reward, motivation, and the "save button" function in your model).

Norepinephrine

Norepinephrine is produced almost exclusively by the Locus Coeruleus, a tiny nucleus in the brainstem pons. Despite its small size it projects diffusely across virtually the entire brain — cortex, hippocampus, cerebellum, spinal cord. It's essentially the brain's arousal and signal-to-noise broadcaster, firing tonically at low rates during calm wakefulness and phasically during novel or stressful events.

Acetylcholine

Acetylcholine has two main sources: the basal forebrain nuclei (including the nucleus basalis of Meynert) projecting to the cortex and hippocampus — relevant for attention and learning gating — and the medial septum projecting specifically to the hippocampus, where it strongly modulates theta rhythms and memory encoding.

What's striking in the context of your model is that all three systems share the same architectural logic: a tiny, localized cell population broadcasts a global contextual signal that shifts the operational threshold of millions of synapses simultaneously — none of them carrying specific content, all of them modulating how content gets written.

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Intro

Global state: what each compartment tracks