iaf_cond_alpha_mc – Multi-compartment conductance-based leaky integrate-and-fire neuron model

Description

THIS MODEL IS A PROTOTYPE FOR ILLUSTRATION PURPOSES. IT IS NOT YET FULLY TESTED. USE AT YOUR OWN PERIL!

iaf_cond_alpha_mc is an implementation of a multi-compartment spiking neuron using IAF dynamics with conductance-based synapses. It serves mainly to illustrate the implementation of multicompartment models in NEST.

The model has three compartments: soma, proximal and distal dendrite, labeled as s, p, and d, respectively. Compartments are connected through passive conductances as follows

\[ \begin{align}\begin{aligned}\begin{split}C_{m.s} d/dt V_{m.s} = \ldots - g_{sp} ( V_{m.s} - V_{m.p} ) \\\end{split}\\\begin{split}C_{m.p} d/dt V_{m.p} = \ldots - g_{sp} ( V_{m.p} - V_{m.s} ) - g_{pd} ( V_{m.p} - V_{m.d} ) \\\end{split}\\C_{m.d} d/dt V_{m.d} = \ldots \qquad - g_{pd} ( V_{m.d} - V_{m.p} )\end{aligned}\end{align} \]

A spike is fired when the somatic membrane potential exceeds threshold, \(V_{m.s} >= V_{th}\). After a spike, somatic membrane potential is clamped to a reset potential, :math:` V_{m.s} == V_{reset}`, for the refractory period. Dendritic membrane potentials are not manipulated after a spike.

There is one excitatory and one inhibitory conductance-based synapse onto each compartment, with alpha-function time course. The alpha function is normalized such that an event of weight 1.0 results in a peak current of 1 nS at \(t = \tau_{syn}\). Each compartment can also receive current input from a current generator, and an external (rheobase) current can be set for each compartment.

Synapses, including those for injection external currents, are addressed through the receptor types given in the receptor_types entry of the state dictionary. Note that in contrast to the single-compartment iaf_cond_alpha model, all synaptic weights must be positive numbers!

See also [1], [2].

Parameters

The following parameters can be set in the status dictionary. Parameters for each compartment are collected in a sub-dictionary; these sub-dictionaries are called “soma”, “proximal”, and “distal”, respectively. In the list below, these parameters are marked with an asterisk.

V_m*	mV	Membrane potential
E_L*	mV	Leak reversal potential
C_m*	pF	Capacity of the membrane
E_ex*	mV	Excitatory reversal potential
E_in*	mV	Inhibitory reversal potential
g_L*	nS	Leak conductance
tau_syn_ex*	ms	Rise time of the excitatory synaptic alpha function
tau_syn_in*	ms	Rise time of the inhibitory synaptic alpha function
I_e*	pA	Constant input current
g_sp	nS	Conductance connecting soma and proximal dendrite
g_pd	nS	Conductance connecting proximal and distal dendrite
t_ref	ms	Duration of refractory period
V_th	mV	Spike threshold in mV
V_reset	mV	Reset potential of the membrane

Sends

SpikeEvent

Receives

SpikeEvent, CurrentEvent, DataLoggingRequest

References

[1]

Meffin H, Burkitt AN, Grayden DB (2004). An analytical model for the large, fluctuating synaptic conductance state typical of neocortical neurons in vivo. Journal of Computational Neuroscience, 16:159-175. DOI: https://doi.org/10.1023/B:JCNS.0000014108.03012.81

[2]

Bernander O, Douglas RJ, Martin KAC, Koch C (1991). Synaptic background activity influences spatiotemporal integration in single pyramidal cells. Proceedings of the National Academy of Science USA, 88(24):11569-11573. DOI: https://doi.org/10.1073/pnas.88.24.11569

See also

Neuron, Integrate-And-Fire, Conductance-Based

Examples using this model

• Multi-compartment neuron example