aeif_psc_alpha – Current-based exponential integrate-and-fire neuron model¶

Description¶

aeif_psc_alpha is the adaptive exponential integrate and fire neuron according to Brette and Gerstner (2005). Synaptic currents are modelled as alpha-functions.

This implementation uses the embedded 4th order Runge-Kutta-Fehlberg solver with adaptive step size 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

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

For implementation details see the aeif_models_implementation notebook.

Parameters¶

The following parameters can be set in the status dictionary.

Dynamic state variables:
V_m	mV	Membrane potential
I_ex	pA	Excitatory synaptic current
dI_ex	pA/ms	First derivative of I_ex
I_in	pA	Inhibitory synaptic current
dI_in	pA/ms	First derivative of I_in
w	pA	Spike-adaptation current
g	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
tau_syn_ex	ms	Rise time of excitatory synaptic conductance (alpha function)
tau_syn_in	ms	Rise time of the inhibitory synaptic conductance (alpha function)

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