17 KiB
17 KiB
Tripartite Synapse — Full Budget-Aware Pseudocode
Color key: PRE = presynapse · POST = postsynapse · ASTRO = astrocyte · SIG = signal/neuromodulator · BUD = budget/resource pool
Shared Resource Pools — one per territory
// ── Axonal arbor: shared across all boutons on one axon ───────────────
BUD axon_vesicle_protein_pool // RIM, Munc13, VGCC subunits for AZ expansion
BUD axon_mitochondria_capacity // ATP ceiling for vesicle release and refill
BUD axon_tagged_boutons // set of boutons competing for drifting proteins
// ── Dendritic segment: shared across all spines on one branch ─────────
BUD dendrite_receptor_reserve // local endosomal AMPA pool — not instantly replenished
BUD dendrite_actin_machinery // Rac1/RhoA + actin monomers for spine enlargement
BUD dendrite_protein_flux // plasticity proteins arriving from soma via CREB
BUD dendrite_tagged_spines // set of spines competing for protein flux
// ── Astrocyte territory: shared across all wrapped synapses ───────────
BUD astro_serine_racemase_cap // enzyme ceiling for D-serine synthesis rate
BUD astro_EAAT_pool // transporter protein for glutamate clearance
BUD astro_ECM_protein_pool // Glypicans, Thrombospondins for sealing
BUD astro_process_extensions // finite perisynaptic processes — selectively allocated
BUD astro_ATP_budget // total ATP — drives clearance, synthesis, motility
BUD astro_lactate_ceiling // hard cap set by capillary glucose supply
// ── Soma: shared across the entire neuron ─────────────────────────────
BUD soma_protein_synthesis_rate // CREB-driven — peaks during sleep
BUD soma_receptor_synthesis_rate // new AMPA subunits per hour
Global State Variables
// ── Fast (ms–s): wave propagation ─────────────────────────────────────
// Presynapse
PRE pre_Ca_residual // leftover Ca²⁺ between spikes — short-term trace
PRE vesicle_release_prob // P(0.1–1.0) per docking slot
PRE RRP_pool // readily-releasable vesicle pool
PRE reserve_pool // chained vesicles in deep storage
// Postsynapse
POST membrane_potential // Vm — depolarization state
POST NMDA_Mg_block // bool — mechanical clamp on/off
POST post_Ca_amplitude // peak [Ca²⁺] rise in spine
POST post_Ca_rise_speed // d(Ca)/dt — fast=LTP signal, slow=LTD signal
// Astrocyte
ASTRO glutamate_cleft // [glu] in synaptic cleft
ASTRO glutamate_spillover // extrasynaptic [glu] — saturates mGluRs
ASTRO astro_Ca_local // IP3-triggered local rise near synapse
ASTRO astro_Ca_global // soma-wide wave — network overload flag
ASTRO D_serine_release // gliotransmitter — NMDA co-agonist pulse
ASTRO lactate_out // fuel export rate to pre and post
// ── Intermediate (s–min): temporary tuning ────────────────────────────
SIG mGluR2_3_activation // presynaptic Gi — autoinhibitory brake
SIG mGluR5_activation // astrocytic Gq — IP3→Ca²⁺→D-serine cascade
SIG cAMP_level // set by dopamine/NE via Gs → adenylyl cyclase
SIG PKA_activity // downstream of cAMP
SIG GluA1_Ser845_primed // bool — AMPA insertion threshold lowered by PKA
SIG DARPP32_phospho // bool — PP1 (LTD phosphatase) silenced by PKA
SIG CREB_active // bool — structural gene expression enabled
// ── Slow (h–weeks): structural architecture ───────────────────────────
POST AMPA_count // surface receptors — postsynaptic sensitivity
POST spine_volume // physical size of dendritic spine
PRE active_zone_size // docking slot count
PRE RRP_pool_capacity // max readily-releasable pool
PRE VGCC_clustering // Ca²⁺ channels beneath active zone
ASTRO perisynaptic_distance // how close astrocyte walls are to synapse
ASTRO ECM_integrity // extracellular matrix density
ASTRO D_serine_tonic_level // baseline co-agonist supply (sustained)
ASTRO glutamate_clearance_rate // EAAT transporter density
Budget Allocation Functions
function request_axon_resources(bouton_id, req_AZ):
available = axon_vesicle_protein_pool × tag_priority(bouton_id, axon_tagged_boutons)
granted = min(req_AZ, available)
axon_vesicle_protein_pool -= granted
if granted < req_AZ:
trigger(heterosynaptic_depression, neighbors(bouton_id)) // passive depletion
return granted
function request_dendrite_resources(spine_id, req_AMPA, req_actin):
priority = tag_priority(spine_id, dendrite_tagged_spines)
g_AMPA = min(req_AMPA, dendrite_receptor_reserve × priority)
g_actin = min(req_actin, dendrite_actin_machinery × priority)
dendrite_receptor_reserve -= g_AMPA
dendrite_actin_machinery -= g_actin
if g_AMPA < req_AMPA:
queue(spine_id, deficit, dendrite_protein_flux) // wait for soma delivery
trigger(heterosynaptic_depression, neighbors(spine_id))
return (g_AMPA, g_actin)
function request_astro_resources(syn_id, req_Ds, req_ECM, req_proc):
g_Ds = min(req_Ds, astro_serine_racemase_cap)
g_ECM = min(req_ECM, astro_ECM_protein_pool)
g_proc = min(req_proc, astro_process_extensions)
ATP_cost = compute_ATP(g_Ds, g_ECM, g_proc)
if ATP_cost > astro_ATP_budget:
scale_down(g_Ds, g_ECM, g_proc) // proportional rationing
astro_serine_racemase_cap -= g_Ds
astro_ECM_protein_pool -= g_ECM
astro_process_extensions -= g_proc
astro_ATP_budget -= ATP_cost
return (g_Ds, g_ECM, g_proc)
function replenish_budgets(Δt):
// Pools recover over time — rates set by metabolic and synthetic capacity
axon_vesicle_protein_pool += protein_transport_rate(axon) × Δt
dendrite_receptor_reserve += soma_receptor_synthesis_rate × delivery_fraction() × Δt
dendrite_actin_machinery += actin_recovery_rate() × Δt
dendrite_protein_flux = soma_protein_synthesis_rate // set by CREB, peaks during sleep
astro_serine_racemase_cap += enzyme_synthesis_rate() × Δt
astro_ECM_protein_pool += ECM_synthesis_rate() × Δt
astro_process_extensions += process_recovery_rate() × Δt // slow — hours timescale
astro_ATP_budget += glycolysis(astro_lactate_ceiling) × Δt
astro_lactate_ceiling = capillary_glucose_supply() // vascular hard ceiling
soma_protein_synthesis_rate = CREB_driven_expression() // elevated during sleep replay
Fast Time Scale — Wave Propagation (ms → s)
function fire_action_potential(input_freq):
// Presynapse: release gated by ATP budget
if axon_mitochondria_capacity > release_ATP_cost:
pre_Ca_residual += spike_influx(input_freq)
pre_Ca_residual *= decay(τ ≈ 100ms)
vesicle_release_prob *= facilitation(pre_Ca_residual)
released = binomial(RRP_pool, vesicle_release_prob)
glutamate_cleft = released × quantal_content
RRP_pool -= released
axon_mitochondria_capacity -= release_ATP_cost
else:
suppress(release) // ATP-depleted bouton goes silent
// Astrocyte: overflow sensing — D-serine draw budget-checked
glutamate_spillover = extrasynaptic_diffusion(glutamate_cleft)
if glutamate_spillover > spillover_threshold:
mGluR5_activation = True
astro_Ca_local += IP3_cascade(PLC)
(g_Ds, _, _) = request_astro_resources(syn_id, proportional_to(astro_Ca_local), 0, 0)
D_serine_release += g_Ds // may be less than ideal if budget low
mGluR2_3_activation = True // Gi arm: brake presynapse regardless
cAMP_level -= Gi_inhibition(adenylyl_cyclase)
vesicle_release_prob -= VGCC_suppression()
// Astrocyte: global overload check
astro_Ca_global = soma_wave(astro_Ca_local > OVERLOAD_threshold)
if astro_Ca_global: trigger(shockwave_lockdown)
// Postsynapse: AMPA current + NMDA coincidence gate
membrane_potential += glutamate_cleft × AMPA_count
if membrane_potential > -40mV and D_serine_release > threshold:
NMDA_Mg_block = False
post_Ca_amplitude += NMDA_influx(glutamate_cleft)
post_Ca_rise_speed = d(post_Ca_amplitude) / dt
// Astrocyte: clearance + fuel — capped at vascular ceiling
glutamate_cleft -= glutamate_clearance_rate × Δt
lactate_out = min(glycolysis_rate(glutamate_clearance_rate), astro_lactate_ceiling)
membrane_potential restored by NaK_ATPase(lactate_out)
RRP_pool refilled by VATPase(lactate_out)
astro_ATP_budget -= clearance_ATP_cost(glutamate_clearance_rate)
Intermediate Time Scale — Temporary Tuning (s → min)
function short_term_plasticity(input_freq, duration):
// Presynapse: facilitate or depress — pool-limited
if input_freq > 20Hz:
vesicle_release_prob *= 1.3
mobilize(reserve_pool → RRP_pool) // only if reserve_pool > 0
elif input_freq < 5Hz:
vesicle_release_prob *= 0.7 // pool depletes faster than refill
// Postsynapse: NMDA priming + plant synaptic tag
if input_freq >= 50Hz and duration > 1s:
NMDA_Mg_block = False
post_Ca_amplitude accumulates
dendrite_tagged_spines.add(spine_id) // enters competition for drifting proteins
// Astrocyte: escalate D-serine — budget-checked
if astro_Ca_local > local_threshold:
(g_Ds, _, _) = request_astro_resources(syn_id, gliotransmitter_pulse(), 0, 0)
D_serine_release += g_Ds
// Neuromodulators: set context gate + plant axonal tag
if dopamine_level > D1_threshold or NE_level > β_threshold:
cAMP_level += Gs_activation(adenylyl_cyclase)
PKA_activity = proportional_to(cAMP_level)
phosphorylate(GluA1, Ser845) → GluA1_Ser845_primed = True
phosphorylate(DARPP32) → DARPP32_phospho = True
translocate(PKA → nucleus) → CREB_active = True
axon_tagged_boutons.add(bouton_id) // captures drifting axonal proteins
LTP_threshold *= (1 / (1 + ACh_level × mAChR_gain))
Slow Time Scale — Structural Commit (h → weeks)
function commit_to_structural_change(bouton_id, spine_id, syn_id):
// Three-layer hierarchical filter
event_detected = post_Ca_amplitude > Ca_HIGH
overflow_sensed = mGluR5_activation == True
context_validated = DARPP32_phospho and GluA1_Ser845_primed
// ── Branch 1: LTP — all budgets requested simultaneously ──────────
if event_detected and overflow_sensed and context_validated:
g_AZ = request_axon_resources(bouton_id, AZ_expansion_cost)
(g_AMPA, g_actin) = request_dendrite_resources(spine_id, AMPA_cost, actin_cost)
(g_Ds, g_ECM, g_pr) = request_astro_resources(syn_id, Ds_cost, ECM_cost, proc_cost)
// Postsynapse: commit proportional to granted resources
activate(CaMKII)
AMPA_count += receptor_insertion(CaMKII, g_AMPA)
spine_volume *= (1 + spine_scale(g_actin))
// Presynapse: commit proportional to granted resources
active_zone_size += g_AZ
RRP_pool_capacity += pool_expansion(active_zone_size)
VGCC_clustering += cluster_beneath_AZ(g_AZ)
vesicle_release_prob += scale_with(g_AZ)
// Astrocyte: commit proportional to granted resources
perisynaptic_distance -= g_pr // walls IN → tighter wrap
ECM_integrity += g_ECM
D_serine_tonic_level += g_Ds
glutamate_clearance_rate *= (1 - clearance_scale(g_pr))
// Partial grants: queue deficit — fulfilled when soma replenishes pools
if g_AMPA < AMPA_cost or g_AZ < AZ_expansion_cost:
queue(bouton_id, spine_id, deficit, dendrite_protein_flux)
axon_tagged_boutons.remove(bouton_id)
dendrite_tagged_spines.remove(spine_id)
return "potentiated" // may be partial if budgets constrained
// ── Branch 2: temporary only — no structural budget drawn ─────────
elif event_detected and not context_validated:
AMPA_count += transient_insertion() // reverses — reserve not permanently drawn
vesicle_release_prob += transient_facilitation()
dendrite_tagged_spines.remove(spine_id) // tag expires without save signal
axon_tagged_boutons.remove(bouton_id)
return "temporary facilitation only"
// ── Branch 3: LTD — resources returned to pool ────────────────────
elif event_detected and not overflow_sensed and not context_validated:
// Postsynapse: internalize receptors — returned to reserve
activate(PP1)
rec_AMPA = receptor_internalization(PP1)
AMPA_count -= rec_AMPA
dendrite_receptor_reserve += rec_AMPA // returned to local pool
spine_volume *= 0.7
dendrite_actin_machinery += actin_depolymerization() // freed actin returned
// Presynapse: dismantle launchpad — proteins returned to axonal pool
rec_AZ = docking_slot_removal()
active_zone_size -= rec_AZ
axon_vesicle_protein_pool += rec_AZ // returned for reuse elsewhere
RRP_pool_capacity -= pool_contraction()
VGCC_clustering -= scatter_VGCCs()
vesicle_release_prob *= 0.6
// Astrocyte: dissolve matrix — resources partially recycled
rec_ECM = secrete(MMPs)
ECM_integrity -= rec_ECM
astro_ECM_protein_pool += rec_ECM × recycling_fraction // partial recovery
D_serine_tonic_level = 0
perisynaptic_distance += process_extension()
astro_process_extensions += freed_process // process freed for reallocation
glutamate_clearance_rate *= 1.2
return "depressed"
// ── Branch 4: baseline ────────────────────────────────────────────
else:
return "baseline — no change"
Heterosynaptic Depression — Passive Resource Depletion
function heterosynaptic_depression(neighbor_ids):
// Triggered when a tagged synapse exhausts the shared pool
// No active signal required — purely a consequence of budget depletion
for n in neighbor_ids:
if n not in dendrite_tagged_spines and n not in axon_tagged_boutons:
AMPA_count[n] -= passive_depletion_rate()
vesicle_release_prob[n] -= passive_depletion_rate()
Special Case — Shockwave Lockdown (>100Hz uncoordinated)
function shockwave_lockdown():
astro_Ca_global = GLOBAL_WAVE
release(GABA, ATP) // emergency flood — bypasses normal budget gate
rec_AMPA = mass_internalization()
AMPA_count -= rec_AMPA
dendrite_receptor_reserve += rec_AMPA // receptors returned to reserve
membrane_potential = HYPERPOLARIZED
cluster(VGCC → beneath_active_zone) // overdrive — bypasses normal budget gate
astro_ATP_budget -= emergency_response_cost() // rapid budget depletion
Energy Supply Chain — Metabolic Gating (continuous)
function metabolic_loop(Δt):
glucose_uptake = blood_capillary_supply() // hard vascular ceiling
lactate_out = min(glycolysis(glucose_uptake, glutamate_clearance_rate),
astro_lactate_ceiling)
lactate_out *= load_factor(glutamate_clearance_rate)
RRP_pool refill rate ∝ VATPase(lactate_out)
membrane_potential reset ∝ NaK_ATPase(lactate_out)
astro_ATP_budget += glycolysis(lactate_out) × Δt
replenish_budgets(Δt)
Key Asymmetry — Perisynaptic Distance Amplifies Both Directions
// LTP: walls IN → clearance_rate ↓, D_serine_tonic ↑ — self-reinforcing
// LTD: walls OUT → clearance_rate ↑, D_serine_tonic = 0 — self-reinforcing
// Both directions cost astro_process_extensions budget.
// A budget-depleted astrocyte delivers partial changes only — until replenish_budgets runs.
// This is why sleep matters: soma_protein_synthesis_rate peaks during slow-wave sleep,
// replenishing all pools and completing deferred structural commits held in the queue.