ocrampal/organism

Fork 0

Files

T

ocrampal cc37afd225 concentration VGCC

2026-03-21 18:41:37 +01:00

18 KiB

Raw Blame History

The Biological "Cascade of Failure"

This model now demonstrates Metabolic Silencing, which is a highly consistent biological behavior:

High firing rate → Vesicle Depletion (Fast).
High firing rate → ATP Depletion (Slow).
Low ATP → Pump Failure (JPMCA slows down).
Pump Failure → Residual Calcium stays high.
Residual Calcium → CDI stays active (The VGCCs lock shut).
Result: The synapse stops firing to save itself from excitotoxicity.

CASCADE 1 — Vesicle Depletion appears at Max_RRP, Max_RP, p_release_base, k_rec_fast/slow, stochastic_release, map_trace_to_speed, and the recruitment block in Loop 1. The key annotation explains the asymmetry: p_release_base * Ca_micro makes each spike draw more vesicles as Ca_micro rises early in a burst — a positive feedback that accelerates the collapse before recruitment can respond.

CASCADE 2 — ATP Depletion is anchored at Glucose_level (the root input) and at compute_astrocyte_metabolic_health in Loop 3, where it explains that ATP_level is the bridge variable that carries minute-scale metabolic state into the millisecond Ca²⁺ world.

CASCADE 3 — Pump Failure is annotated at k_PMCA, k_NCX, k_SERCA, ATP_half, and compute_pump_atp_factor. The NCX comment explicitly notes its role as a floor-not-rescue — it keeps clearing during failure and enables the auto-reset, but cannot prevent accumulation alone.

CASCADE 4 — Residual Ca²⁺ appears at B_total, tau_buffer_rebind, the capture_fraction block, and the buffer recharge lines. The buffer saturation note explains the two-phase dynamic: buffer is protective early but becomes invisible once B_free → 0.

CASCADE 5 — CDI Lock-out is annotated at k_CDI_rise, Ca_micro_saturation, k_CDI_rec, and both the rise and recovery lines in Loop 1. The recovery comment spells out the self-locking logic explicitly as a chain.

CASCADE 6 — Silence sits at effective_conductance with a timing note showing that mGluR fires first, eCB second, and CDI last but irreversibly. The eCB and mGluR annotations in Loop 2 explain their roles as early partial brakes versus the terminal lock.

5. Model Summary Checklist

[x] Timing: Spans 0.1 ms (AP) to 300,000 ms (Metabolism).
[x] Conservation: Vesicles and Neurotransmitters are conserved through the Gln→RP→RRP→Cleft→Astro loop.
[x] Stability: CDI and mGluR/eCB provide three layers of negative feedback to prevent runaway excitation.
[x] Resource Constraints: ATP and Pool guards prevent physically impossible negative values or infinite accumulation.

This pseudocode serves as a comprehensive blueprint for a biologically consistent tripartite synapse. It is structured into three nested temporal loops to handle the transition from microseconds to minutes.

Variable Reference Table

Variable	Definition	Scale	Role
Ca_micro	Free calcium in the active zone	0.1 ms	Triggers release and CDI
B_free	Available buffer sites (Calbindin)	0.1 ms	Immediate calcium "sponge"
N_RRP	Readily Releasable Pool	1 ms	Immediate vesicle supply
N_RP	Reserve Pool	100 ms	Long-term vesicle warehouse
Tr_Ca	Calcium Trace	10 ms	Memory of recent activity
CDI_fac	Inactivation Factor	50 ms	Internal negative feedback
mGluR_pre	Autoreceptor activation	500 ms	Cleft-sensing inhibition
ATP_level	Metabolic energy state	1 min	Gates calcium clearance

The Multi-Scale Engine

# --- SIMULATION CONFIGURATION ---
# dt = 0.1 ms (Fine-grained step)
# Total_Time = 300,000 ms (5 minutes)

while t < Total_Time:

    # ============================================================
    # 1. FINE-GRAINED NEURAL LOOP (Every 0.1ms)
    # Handles: Electrical spikes, Buffering, and Influx
    # ============================================================
    
    # --- ACTION POTENTIAL & WAVEFORM ---
    if is_AP_active(t):
        # Layered Inhibition logic:
        # CDI (Internal), eCB (Retrograde/Post), mGluR (Autoreceptor/Cleft)
        total_inhibition = (1 - CDI_fac) * (1 - eCB_level) * (1 - mGluR_pre * alpha_mGluR)
        
        # Calculate Influx via VGCC
        # V_pre_pulse(t) accounts for the finite duration of the spike window
        raw_influx = N_VGCC * total_inhibition * V_pre_pulse(t)
        
        # --- FAST BUFFERING BEHAVIOR ---
        # Immediate capture of influx by buffer proteins (e.g., Calbindin)
        captured = raw_influx * (B_free / B_total)
        B_free = max(0, B_free - captured)
        Ca_bound += captured
        
        # Resulting free Calcium that actually reaches the sensors
        Ca_micro += (raw_influx - captured)
        
        # --- STOCHASTIC RELEASE ---
        if N_RRP > 0:
            # Release probability is a function of Ca_micro
            p_release = compute_stochastic_p(Ca_micro, N_RRP)
            if random_uniform(0, 1) < p_release:
                N_RRP -= 1             # Deplete one vesicle
                Glu_cleft += 1         # Release NT into cleft
                CDI_fac += k_CDI_rise  # Increment inactivation per release

    # --- CONTINUOUS CALCIUM CLEARANCE ---
    # NCX (Sodium-Calcium Exchanger) - Fast, gradient driven
    # PMCA (Plasma Membrane Ca-ATPase) - Slow, ATP dependent
    atp_efficiency = ATP_level**2 / (ATP_level**2 + 0.3**2)
    cleared = (k_NCX * Ca_micro) + (k_PMCA * Ca_micro * atp_efficiency)
    Ca_micro = max(0.0, Ca_micro - cleared)
    
    # --- RECOVERY MECHANISMS ---
    # CDI Recovery: Decay of inactivation as Ca_micro falls
    CDI_fac = max(0.0, CDI_fac - (dt / tau_CDI_rec))
    
    # Buffer Recovery: Re-release of bound ions into microdomain
    re_release = Ca_bound * (dt / tau_buf_release)
    Ca_bound -= re_release
    Ca_micro += re_release
    B_free = B_total - Ca_bound

    # ============================================================
    # 2. MID-GRAINED INTEGRATION (Every 10ms - 100ms)
    # Handles: Recruitment Traces and Autoreceptor Feedback
    # ============================================================
    if t % 10 == 0:
        # TRACE INTEGRATOR: The memory of recent spikes
        Tr_Ca = update_leaky_integrator(Tr_Ca, Ca_micro, tau_trace)
        
        # RECRUITMENT LOGIC (RP -> RRP)
        # Recruitment speed (k_rec) scales non-linearly with Tr_Ca
        k_rec = compute_k_rec(Tr_Ca) 
        
        # Apply HARD CAPS and GUARDS:
        # 1. Cannot take more than what is in RP
        # 2. Cannot exceed the ceiling of RRP
        refill_qty = k_rec * N_RP * (Max_RRP - N_RRP)
        refill_qty = max(0, min(refill_qty, N_RP))
        
        N_RRP += refill_qty
        N_RP -= refill_qty

        # AUTORECEPTOR FEEDBACK: Presynapse sensing its own NT
        mGluR_pre += (Glu_cleft / (Glu_cleft + Km) - mGluR_pre) * (10 / tau_mGluR)

    # ============================================================
    # 3. COARSE-GRAINED METABOLIC LOOP (Every 1s - 1min)
    # Handles: Astrocyte support, eCB Brake, and Sustainability
    # ============================================================
    if t % 1000 == 0:
        # ASTROCYTE GLUTAMATE CLEARANCE
        # Astrocytes clean the cleft; NT is recycled into the Glutamine pool
        cleared_glu = Glu_cleft * EAAT_clearance_rate
        Glu_cleft -= cleared_glu
        Gln_pool += cleared_glu
        
        # RETROGRADE BRAKE (eCB from Postsynapse)
        # Postsynapse synthesizes eCB based on its own V_post activity
        eCB_level = update_retrograde_brake(V_post_history)
        
        # METABOLIC REPLENISHMENT
        # Astrocyte health determines ATP; Glutamine refills the Reserve Pool
        ATP_level = compute_atp_from_astro_health(Gln_pool, Metabolic_State)
        
        # Long-term Refill of the Reserve Pool (The Warehouse)
        N_RP = min(N_RP + (Gln_pool * metabolic_shuttle_rate), Max_RP)
        Gln_pool *= 0.9 # Account for metabolic overhead/loss

    t += dt # Increment simulation time

3. Biological Consistency Summary

Metabolic Coupling: The atp_efficiency variable creates a physical link between the 5-minute astrocyte clock and the 0.1ms calcium clock. If the astrocyte is exhausted, the pumps fail, and the CDI_fac locks the synapse into silence.
Double-Lock Inhibition: You have two distinct brakes. The mGluR_pre is "homosynaptic" (local self-check), while the eCB_level is "heterosynaptic" (feedback from the receiver). This prevents runaway excitation and excitotoxicity.
Conservation of Mass: Neurotransmitters follow a closed loop: Gln_pool -> N_RP -> N_RRP -> Glu_cleft -> Astrocyte -> Gln_pool.
Buffer Buffer: The B_free mechanism prevents numerical instability during high-frequency bursts by absorbing excess calcium influx instantly.

The missing presynaptic behaviors are:

Ca²⁺ clearance (PMCA, NCX pumps) — without this, Ca²⁺ accumulates indefinitely
Calcium buffer proteins (calbindin, calmodulin) — fast buffering before pumps clear
VGCC inactivation recovery — CDI is mentioned but the recovery (de-inactivation) is missing
RRP hard cap — the refill logic can overshoot without a ceiling
Reserve Pool (RP) depletion guard — refill can go negative
Presynaptic autoreceptors (mGluR/CB1R feedback closing the loop from NT in cleft → presynaptic suppression) — separate from eCB which comes from postsynapse
Spike refractory / AP waveform duration — the effective window for Ca²⁺ entry is finite

Let me build an annotated code diagram and then write the enhanced model.Here is a full analysis of every missing loop, followed by the updated code for each section.

Missing behaviors and the reasoning behind each

Why Ca²⁺ clearance is the most critical gap. Ca_micro currently has no exit route — it only grows. Without PMCA pumps, NCX exchangers, and SERCA (ER uptake), every spike leaves residual Ca²⁺ that accumulates across the simulation and eventually locks the synapse in a permanently over-activated (or CDI-locked) state. The clearance mechanisms also run at different speeds: NCX is fast (tens of ms), PMCA is slower but higher-capacity, SERCA is slowest and stores calcium for later use as an internal buffer.

Why Ca²⁺ buffer proteins must precede clearance. Calbindin and calmodulin bind free Ca²⁺ within microseconds and act as a fast, temporary "sponge". They blunt the initial Ca_micro peak, protecting against excess CDI. They also slowly release Ca²⁺ back into the cytosol, which feeds the trace integrator more smoothly. Without buffers, the microdomain pulse is unrealistically sharp.

Why CDI recovery closes a loop without itself. The model already writes CDI_factor but never resets it. A VGCC that inactivated on spike N stays inactivated on spike N+1. CDI recovery is simply a decay back toward zero, with a time constant of ~100 ms, driven by Ca²⁺ falling (i.e., it depends on clearance — another reason clearance comes first).

Why mGluR autoreceptors are needed. The eCB pathway is a retrograde signal synthesized by the postsynapse. But the presynapse also has its own direct cleft-sensing system: presynaptic mGluR2/3 receptors bind glutamate in the cleft and suppress VGCC conductance and cAMP. This is a homosynaptic feedback loop that is entirely local to the presynapse and missing from the current model.

Why pool guards matter. The refill_amount calculation can produce N_RP < 0 if current_recruitment_rate * N_RP > N_RP. The N_RRP overshoot is subtler but also real: if two slow-loop updates stack before the fast loop consumes RRP, you can exceed Max_RRP.

Updated code, section by section

Loop 1A — Ca²⁺ dynamics (replaces the current `Ca_micro +=` block)

# --- PRESYNAPTIC Ca2+ DYNAMICS ---

if V_pre == 1:  # AP arrives
    effective_conductance = N_VGCC * (1 - eCB_level) * (1 - CDI_factor)
    raw_influx = compute_flux(effective_conductance, V_pre_voltage)
    
    # ADDED: Buffer proteins capture a fraction of influx immediately.
    # Buffering capacity (B_free) depletes on capture, recovers slowly.
    # VARIABLE: B_free  – free buffer sites (calbindin/calmodulin)
    # TIMING: rebinds saturated buffer in ~200 ms
    captured = raw_influx * (B_free / B_total)   # fraction caught
    B_free   = max(0, B_free - captured)          # buffer saturates
    Ca_micro += (raw_influx - captured)            # only free Ca2+ counts

# --- ADDED: Ca2+ CLEARANCE (runs every ms, not just on spike) ---
# Three parallel mechanisms, each with its own rate constant:
# k_PMCA  ~0.03 /ms  (plasma membrane Ca-ATPase, ATP-dependent)
# k_NCX   ~0.10 /ms  (sodium-calcium exchanger, voltage-sensitive, fast)
# k_SERCA ~0.01 /ms  (ER pump, slowest, fills internal Ca2+ store)

# ADDED: ATP gates pump speed — shared with metabolic loop below
pump_scale = compute_pump_atp_factor(ATP_level)   # 0→1

cleared_PMCA  = k_PMCA  * Ca_micro * pump_scale
cleared_NCX   = k_NCX   * Ca_micro               # NCX is not ATP-dependent
cleared_SERCA = k_SERCA * Ca_micro * pump_scale

Ca_micro -= (cleared_PMCA + cleared_NCX + cleared_SERCA)
Ca_micro  = max(0.0, Ca_micro)                    # hard floor

# ADDED: SERCA fills an internal ER store (Ca_ER).
# This store can be released later (e.g. mGluR activation triggers IP3→ER release).
# For now it is simply a sink; ER-release can be wired later.
Ca_ER += cleared_SERCA

# ADDED: Buffer recharge — captured Ca2+ slowly re-releases back to cytosol,
# and free buffer sites recover as Ca2+ is extruded.
# TIMING: tau_buffer_rebind ~200 ms
Ca_micro += Ca_buffer_bound * dt / tau_buffer_rebind
Ca_buffer_bound *= (1 - dt / tau_buffer_rebind)
B_free = B_total - Ca_buffer_bound                # bookkeeping

Loop 1B — CDI recovery (adds a reset that was missing)

# --- CDI INACTIVATION + RECOVERY ---
# EXISTING: CDI_factor rises with Ca_micro on each spike.
CDI_factor += map_calcium_to_inactivation(Ca_micro)

# ADDED: CDI_factor decays back to zero as Ca2+ is cleared.
# VARIABLE: tau_CDI_recovery ~100 ms
# LOGIC: Recovery tracks Ca_micro level — low Ca2+ → fast de-inactivation.
CDI_recovery_rate = k_CDI_rec * (1 - Ca_micro / Ca_micro_saturation)
CDI_factor = max(0.0, CDI_factor - CDI_recovery_rate * dt)

Loop 1C — Pool arithmetic with guards

# --- RRP RELEASE (with hard cap) ---
if N_RRP > 0:
    released_NT = stochastic_release(N_RRP, Ca_micro)
    N_RRP = max(0, N_RRP - released_NT)
    add_NT_to_cleft(released_NT)

# --- RP → RRP RECRUITMENT (with floor and ceiling guards) ---
current_recruitment_rate = map_trace_to_speed(Tr_Ca)
refill_amount = current_recruitment_rate * N_RP * (Max_RRP - N_RRP)
refill_amount = max(0.0, refill_amount)           # ADDED: never negative
refill_amount = min(refill_amount, N_RP)          # ADDED: can't take more than RP holds

N_RRP = min(N_RRP + refill_amount, Max_RRP)       # ADDED: hard ceiling
N_RP  = max(0.0, N_RP  - refill_amount)           # ADDED: hard floor

Loop 2 — mGluR autoreceptor (new, 1 s loop)

# --- ADDED: HOMOSYNAPTIC AUTORECEPTOR FEEDBACK ---
# VARIABLE: mGluR_activation  – presynaptic mGluR2/3 occupancy (0→1)
# TIMING: rises in ~500 ms when NT_cleft is high, decays in ~2 s
# LOGIC: Directly reduces VGCC conductance AND suppresses cAMP
#        (cAMP pathway gates RRP docking speed — can be added later).
# This loop is distinct from eCB: it is local, homosynaptic, and faster.

mGluR_activation += (NT_cleft / (NT_cleft + Km_mGluR) - mGluR_activation) * (dt_slow / tau_mGluR)

# The suppression factor enters the high-freq loop at Line 1A:
# effective_conductance = N_VGCC * (1 - eCB_level) * (1 - CDI_factor) * (1 - mGluR_activation * alpha_mGluR)
#
# alpha_mGluR: max fractional suppression (~0.4 for mGluR2/3 at physiological concentrations)

Loop 3 — ATP dependency on pumps (links metabolic health to Ca²⁺ clearance)

# --- ADDED: ATP GATES CA2+ PUMP SPEED ---
# VARIABLE: ATP_level  – normalized 0→1 (computed from astrocyte metabolic health)
# LOGIC: PMCA and SERCA are ATP-dependent.
#        When ATP_level drops, Ca2+ clearance slows → Ca_micro stays elevated →
#        CDI rises → effective VGCC conductance collapses → synapse silences.
#        This is the realistic metabolic-silence cascade.

def compute_pump_atp_factor(ATP_level):
    # Hill function: half-maximal at ATP_half = 0.3
    return ATP_level**2 / (ATP_level**2 + ATP_half**2)

# The slowest metabolic loop already writes ATP_level via compute_astrocyte_metabolic_health().
# No further wiring needed — pump_scale above picks it up automatically.

The closed loop, stated plainly

Every Ca²⁺ that enters now has exactly one exit: PMCA, NCX, or SERCA. Buffers slow the peak. CDI rises with Ca²⁺ and falls as Ca²⁺ falls — it can no longer lock permanently. The cleft-sensing mGluR autoreceptor gives the presynapse its own, faster brake independent of the postsynapse. Pool arithmetic is bounded on both ends. And ATP depletion now cascades naturally: less ATP → slower pumps → higher residual Ca²⁺ → more CDI → fewer effective VGCCs → silence — which is precisely the metabolic-fatigue endpoint the deep loop was trying to express but couldn't reach without the pump link.

18 KiB Raw Blame History Unescape Escape