# gif_pop_psc_exp – Population of generalized integrate-and-fire neurons with exponential postsynaptic currents and adaptation¶

## Description¶

This model simulates a population of spike-response model neurons with multi-timescale adaptation and exponential postsynaptic currents, as described by Schwalger et al. (2017) 1.

The single neuron model is defined by the hazard function

$h(t) = \lambda_0 \exp\frac{V_m(t) - E_{\text{sfa}}(t)}{\Delta_V}$

After each spike, the membrane potential $$V_m$$ is reset to $$V_{\text{reset}}$$. Spike frequency adaptation is implemented by a set of exponentially decaying traces, the sum of which is $$E_{\text{sfa}}$$. Upon a spike, each of the adaptation traces is incremented by the respective $$q_{\text{sfa}}$$ and decays with the respective time constant $$\tau_{\text{sfa}}$$.

The corresponding single neuron model is available in NEST as gif_psc_exp. The default parameters, although some are named slightly different, are not matched in both models for historical reasons. See below for the parameter translation.

Connecting two population models corresponds to full connectivity of every neuron in each population. An approximation of random connectivity can be implemented by connecting populations through a spike_dilutor.

## Parameters¶

The following parameters can be set in the status dictionary.

 V_reset mV Membrane potential is reset to this value after a spike V_T_star mV Threshold level of the membrane potential E_L mV Resting potential Delta_V mV Noise level of escape rate C_m pF Capacitance of the membrane tau_m ms Membrane time constant t_ref ms Duration of refractory period I_e pA Constant input current N integer Number of neurons in the population len_kernel integer Refractory effects are accounted for up to len_kernel time steps lambda_0 1/s Firing rate at threshold tau_syn_ex ms Time constant for excitatory synaptic currents tau_syn_in ms Time constant for inhibitory synaptic currents tau_sfa list of ms vector Adaptation time constants q_sfa list of ms Adaptation kernel amplitudes BinoRand boolean If True, binomial random numbers are used, otherwise we use Poisson distributed spike counts
 Parameter translation to gif_psc_exp gif_pop_psc_exp gif_psc_exp relation tau_m g_L tau_m = C_m / g_L N — use N gif_psc_exp neurons

## References¶

1

Schwalger T, Deger M, Gerstner W (2017). Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size. PLoS Computational Biology. https://doi.org/10.1371/journal.pcbi.1005507

SpikeEvent