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 postsynaptic 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:

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

and

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

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

For implementation details see the aeif_models_implementation notebook.

Note

The default refractory period for aeif models is zero, consistent with the model definition in Brette & Gerstner [1]. Thus, an aeif neuron with default parameters can fire multiple spikes in a single time step, which can lead to exploding spike numbers and extreme slow-down of simulations.

To avoid such unphysiological behavior, you should set a refractory time t_ref > 0.

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

See also

iaf_cond_exp, aeif_cond_alpha

Examples using this model

• IF curve example

• Testing the adapting exponential integrate and fire model in NEST (Brette and Gerstner Fig 3D)