# 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 ref:multicompartment models <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!

## 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

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