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:

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

where I_syn_ex and I_syn_in are the synaptic currents modeled as truncated exponentials with time constants tau_syn_ex and tau_syn_in respectively.

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

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

Note

Although this model is not multisynapse, the port (excitatory or inhibitory) to be chosen must be specified using the synapse property receptor. The excitatory port has index 0, whereas the inhibitory one has index 1. Differently from NEST, the connection weights related to the inhibitory port must be positive.

Parameters

The following parameters can be set in the status dictionary.

Dynamic state variables:
V_m	mV	Membrane potential
I_syn_ex	pA	Excitatory synaptic current
I_syn_in	pA	Inhibitory 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_ex	ms	Exponential decay time constant of excitatory synaptic current
tau_syn_in	ms	Exponential decay time constant of inhibitory 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