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2026-04-08 10:58:25 +02:00
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2 changed files with 27 additions and 29 deletions
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@@ -40,10 +40,14 @@ In this model we decide to simplify:
The simplifications imply that: The simplifications imply that:
- Removing channel kinetics means the AP has no temporal profile at the soma — it is a binary event that either occurs or does not at each timestep. The shaping of firing patterns by sodium inactivation and potassium activation is absent. Removing the axon hillock as a separate compartment means the threshold comparison is applied directly to V_soma rather than to a spatially distinct zone with its own channel density. In biology the hillock has a lower threshold than the soma body because of its higher Na⁺ channel density — this gradient is absent here. A single fixed threshold applied to V_soma is a reasonable approximation for a single-compartment model, but it means the model cannot capture phenomena that depend on the hillock's spatial separation from the dendritic integration zone, such as the ability of strong distal dendritic inputs to bypass somatic inhibition.
- Removing the refractory period means the soma could theoretically fire at 1000 Hz (one spike per ms) if given sufficient input. In practice the external `soma_spike_train` constrains this, but the biological ceiling on firing rate is not enforced by the model itself. Removing neuromodulatory inputs means the threshold and gain of the soma are fixed across the entire simulation. In biology dopamine, serotonin, and acetylcholine continuously adjust V_soma_threshold and the shape of the f-I curve in response to behavioural state. A neuron in an attentive animal fires more readily to the same input than the same neuron in a drowsy animal. This state-dependence is entirely absent — the soma responds identically to a given V_dend at all times.
- Removing neuromodulation means the soma's threshold is fixed across the entire simulation. The ability of global brain states to shift the neuron's responsiveness is absent.
- Making firing external means V_soma is computed as a read-only variable that reflects the integrated dendritic input, but the threshold crossing that would generate a bAP and a presynaptic AP is provided externally rather than emerging from the model dynamics. This is consistent with how the presynapse currently treats its own AP — also driven by an external spike train. The architecture is therefore symmetric: both the presynaptic AP and the somatic AP are external inputs in this version of the model, and both could be internalised in a future extension. Removing subthreshold oscillations means V_soma behaves as a simple leaky integrator between APs. In some neuron types, voltage-gated channels produce rhythmic subthreshold fluctuations that bias the timing of AP generation toward specific phases of network oscillations. These are not modelled — V_soma decays smoothly toward rest between threshold crossings.
Removing the f-I curve as an explicit target means the relationship between input intensity and output firing rate is not directly controlled. Instead, firing rate emerges naturally from the interplay of V_soma integration, threshold, and the refractory period. A sustained V_dend above threshold will produce repeated APs at a rate limited by t_refractory_rel — the maximum firing rate is approximately 1000 / t_refractory_rel Hz. This emergent f-I behaviour is biologically plausible even if it is not calibrated to a specific neuron type.
Sharing the postsynaptic ATP pool rather than maintaining a separate somatic pool means Na/K-ATPase costs at the soma are not distinguished from those at the spine. In biology the soma and its proximal dendrites have a large Na/K-ATPase demand that is metabolically distinct from the spine compartment. Here both costs accumulate into ATP_demand_post and are replenished from the same glucose budget. This is a simplification of convenience — the total metabolic load is accounted for, but its spatial origin within the postsynaptic compartment is not resolved.
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@@ -51,39 +55,34 @@ The simplifications imply that:
— ms: — ms:
- V_soma integrates V_dend each ms - VDB is integrated (each Dendratites acts as leaky integrator)
V_soma += V_dend * soma_weight - Threshold check (only when not in AP waveform phase and not in absolute refractory)
soma_weight scales the dendritic contribution to somatic potential - condition VDB fullness
-- AP
-- bAP
-- tau_AP_rise = 0.5 ms - Na⁺ channels open — explosive depolarisation
-- (tau_AP_fall = 1.5 ms) - V_soma falls toward V_AHP - K⁺ channels open — repolarisation
-- (tau_AHP = 5.0 ms) - V_soma recovers from V_AHP toward V_soma_reset - K⁺ channels close — after-hyperpolarisation
- V_soma decays passively each ms (leaky integrator) - V_bAP decays each ms (from dendrite loop)
V_soma *= (1 - dt / tau_soma) V_bAP += (0 - V_bAP) * dt / tau_bAP
tau_soma is the somatic membrane time constant decay runs independently of soma state
- Threshold check (read-only in simplified model)
if V_soma > V_soma_threshold:
— would fire in a closed-loop model
— in this version firing is read from soma_spike_train
- If soma fires this ms (step in soma_spike_train):
AP_fired = True
V_soma resets toward rest (instantaneous reset)
V_soma = V_soma_reset
— AP propagates forward: feeds presynaptic spike_train of next neuron
— AP propagates backward: sets V_bAP = V_bAP_peak in dendrite loop
— seconds: — seconds:
- nothing in the simplified model - nothing — no slow integration in the soma
(firing rate statistics could be computed here if needed) (firing rate statistics could be computed here as a diagnostic
but they do not feed back into any other variable)
— mins: — mins:
- nothing in the simplified model - nothing in the simplified model
(homeostatic threshold regulation would live here if added: (homeostatic threshold regulation would live here if added:
sustained low firing threshold decreases sustained low firing rate → V_soma_threshold decreases
sustained high firing threshold increases sustained high firing rate → V_soma_threshold increases
this is the somatic equivalent of postsynaptic AMPA scaling) this is the somatic equivalent of postsynaptic AMPA scaling
the neuron adjusts its own excitability to maintain a target
firing rate in the face of changing input statistics)
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@@ -26,7 +26,6 @@ bAP
AP AP
Based on the computational model provided, here is the complete breakdown of all simulated behaviors, categorized by functional compartment. Based on the computational model provided, here is the complete breakdown of all simulated behaviors, categorized by functional compartment.
## 1. Presynaptic Behaviors ## 1. Presynaptic Behaviors