aeif_cond_alpha_multisynapse – Conductance-based adaptive exponential integrate-and-fire neuron model

Description

aeif_cond_alpha_multisynapse is a conductance-based adaptive exponential integrate-and-fire neuron model according to [1] with multiple synaptic time constants, and synaptic conductance modeled by an alpha function.

This implementation uses the 5th order Runge-Kutta solver with adaptive step size to integrate the differential equation.

It allows an arbitrary number of synaptic time constants. Synaptic conductance is modeled by an alpha function, as described in [2].

The membrane potential is given by the following differential equation:

\[C_m \frac{dV}{dt} = -g_L(V-E_L) + g_L\Delta_T \exp\left(\frac{V-V_{th}}{\Delta_T}\right) + I_{syn_{tot}}(V, t)- w + I_e\]

where

\[I_{syn_{tot}}(V,t) = \sum_i g_i(t) (V - E_{rev,i}) ,\]

the synapse i is excitatory or inhibitory depending on the value of \(E_{rev,i}\) and the differential equation for the spike-adaptation current w is

\[\tau_w dw/dt = a(V - E_L) - w\]

When the neuron fires a spike, the adaptation current \(w <- w + b\).

Note

The number of receptor ports must be specified at neuron creation (default value is 1) and the receptor index starts from 0 (and not from 1 as in NEST multisynapse models). The time constants are supplied by an array, tau_syn, and the pertaining synaptic reversal potentials are supplied by the array E_rev. Port numbers are automatically assigned in the range 0 to n_receptors-1. During connection, the ports are selected with the synapse property receptor.

Parameters

The following parameters can be set in the status dictionary.

Dynamic state variables:
V_m	mV	Membrane potential
w	pA	Spike-adaptation current

Membrane Parameters
V_th	mV	Spike initiation threshold
Delta_T	mV	Slope factor
g_L	nS	Leak conductance
E_L	mV	Leak reversal potential
C_m	pF	Capacity of the membrane
I_e	pA	Constant external input current
V_peak	mV	Spike detection threshold
V_reset	mV	Reset value for V_m after a spike
t_ref	ms	Duration of refractory period
den_delay	ms	Dendritic delay

Spike adaptation parameters
a	ns	Subthreshold adaptation
b	pA	Spike-triggered adaptation
tau_w	ms	Adaptation time constant

Synaptic parameters
E_rev	list of mV	Reversal potential
tau_syn	list of ms	Time constant of synaptic conductance

Integration parameters
h0_rel	real	Starting step in ODE integration relative to time resolution
h_min_rel	real	Minimum step in ODE integration relative to time resolution

References

[1]

Brette R and Gerstner W (2005). Adaptive exponential integrate-and-fire model as an effective description of neuronal activity. Journal of Neurophysiology. 943637-3642 DOI: https://doi.org/10.1152/jn.00686.2005

[2]

A. Roth and M. C. W. van Rossum, Computational Modeling Methods for Neuroscientists, MIT Press 2013, Chapter 6. DOI: https://doi.org/10.7551/mitpress/9780262013277.003.0007

See also

Neuron, Integrate-And-Fire, Adaptive Threshold, Conductance-Based