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