aeif_psc_exp – Current-based exponential integrate-and-fire neuron model

Description

aeif_psc_exp is the adaptive exponential integrate and fire neuron according to [1], with postsynaptic currents in the form of truncated exponentials.

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

The membrane potential is given by the following differential equation:

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

where I_syn (t) is the sum of the synaptic currents modeled as truncated exponentials with time constant tau_syn.

The differential equation for the spike-adaptation current w is:

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

Note

As mentioned in the Differences between NEST GPU and NEST, all the aeif neuron models in NEST GPU are multisynapse models. 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. 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
I_syn	pA	Synaptic current
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
tau_syn	ms	Exponential decay time constant of synaptic current

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. J Neurophysiol 94:3637-3642. DOI: https://doi.org/10.1152/jn.00686.2005

See also

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