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 in Schwalger et al. (2017) 1.

The single neuron model is defined by the hazard function:

\[\lambda_0 * \exp\left(( V_m - E_{sfa} ) / \Delta_V\right)\]

After each spike, the membrane potential V_m is reset to V_reset. Spike frequency adaptation is implemented by a set of exponentially decaying traces, the sum of which is E_sfa. Upon a spike, all adaptation traces are incremented by the respective q_sfa each and decay with the respective time constant tau_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 due to historical reasons. See below for the parameter translation.

As gif_pop_psc_exp represents many neurons in one node, it may send a lot of spikes. In each time step, it sends at most one spike though, the multiplicity of which is set to the number of emitted spikes. Postsynaptic neurons and devices in NEST understand this as several spikes, but communication effort is reduced in simulations.

This model uses a new algorithm to directly simulate the population activity (sum of all spikes) of the population of neurons, without explicitly representing each single neuron. The computational cost is largely independent of the number N of neurons represented. The algorithm used here is fundamentally different from and likely much faster than the one used in the previously added population model pp_pop_psc_delta.

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

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

Sends

SpikeEvent

Receives

SpikeEvent, CurrentEvent, DataLoggingRequest

See also

Neuron, Integrate-And-Fire, Current-Based