aeif_cond_exp – Conductance based exponential integrate-and-fire neuron model

Description

aeif_cond_exp is the adaptive exponential integrate and fire neuron according to Brette and Gerstner (2005), with post-synaptic conductances in the form of truncated exponentials.

This implementation uses the embedded 4th order Runge-Kutta-Fehlberg solver with adaptive stepsize to integrate the differential equation.

The membrane potential is given by the following differential equation:

\[\begin{split}C dV/dt= -g_L(V-E_L)+g_L*\Delta_T*\exp((V-V_T)/\Delta_T)-g_e(t)(V-E_e) \\ -g_i(t)(V-E_i)-w +I_e\end{split}\]

and

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

Note that the spike detection threshold V_peak is automatically set to \(V_th+10 mV\) to avoid numerical instabilites that may result from setting V_peak too high.

Parameters:

The following parameters can be set in the status dictionary.

Dynamic state variables:

V_m

mV

Membrane potential

g_ex

nS

Excitatory synaptic conductance

g_in

nS

Inhibitory synaptic conductance

w

pA

Spike-adaptation current

Membrane Parameters

C_m

pF

Capacity of the membrane

t_ref

ms

Duration of refractory period

V_reset

mV

Reset value for V_m after a spike

E_L

mV

Leak reversal potential

g_L

nS

Leak conductance

I_e

pA

Constant external input current

Spike adaptation parameters

a

nS

Subthreshold adaptation

b

pA

Spike-triggered adaptation

Delta_T

mV

Slope factor

tau_w

ms

Adaptation time constant

V_th

mV

Spike initiation threshold

V_peak

mV

Spike detection threshold

Synaptic parameters

E_ex

mV

Excitatory reversal potential

tau_syn_ex

ms

Exponential decay time constant of excitatory synaptic conductance kernel

E_in

mV

Inhibitory reversal potential

tau_syn_in

ms

Exponential decay time constant of inhibitory synaptic conductance kernel

Integration parameters

gsl_error_tol

real

This parameter controls the admissible error of the GSL integrator. Reduce it if NEST complains about numerical instabilities.

Sends

SpikeEvent

Receives

SpikeEvent, CurrentEvent, DataLoggingRequest

References

1

Brette R and Gerstner W (2005). Adaptive Exponential Integrate-and-Fire Model as an Effective Description of Neuronal Activity. J Neurophysiol 94:3637-3642. DOI: https://doi.org/10.1152/jn.00686.2005