pp_pop_psc_delta – Population of point process neurons with leaky integration of delta-shaped PSCs¶

Description¶

pp_pop_psc_delta is an effective model of a population of neurons. The N component neurons are assumed to be spike response models with escape noise, also known as generalized linear models. We follow closely the nomenclature of 1. The component neurons are a special case of pp_psc_delta (with purely exponential rate function, no reset and no random dead_time). All neurons in the population share the inputs that it receives, and the output is the pooled spike train.

The instantaneous firing rate of the N component neurons is defined as

\[rate(t) = \rho_0 * \exp( (h(t) - \eta(t))/\delta_u ),\]

where h(t) is the input potential (synaptic delta currents convolved with an exponential kernel with time constant tau_m), eta(t) models the effect of refractoriness and adaptation (the neuron’s own spike train convolved with a sum of exponential kernels with time constants tau_eta), and delta_u sets the scale of the voltages.

To represent a (homogeneous) population of N inhomogeneous renewal process neurons, we can keep track of the numbers of neurons that fired a certain number of time steps in the past. These neurons will have the same value of the hazard function (instantaneous rate), and we draw a binomial random number for each of these groups. This algorithm is thus very similar to ppd_sup_generator and gamma_sup_generator, see also 2.

However, the adapting threshold eta(t) of the neurons generally makes the neurons non-renewal processes. We employ the quasi-renewal approximation 1, to be able to use the above algorithm. For the extension of [1] to coupled populations see 3.

In effect, in each simulation time step, a binomial random number for each of the groups of neurons has to be drawn, independent of the number of represented neurons. For large N, it should be much more efficient than simulating N individual pp_psc_delta models.

pp_pop_psc_delta emits spike events like other neuron models, but no more than one per time step. If several component neurons spike in the time step, the multiplicity of the spike event is set accordingly. Thus, to monitor its output, the multiplicity of the spike events has to be taken into account. Alternatively, the internal variable n_events gives the number of spikes emitted in a time step, and can be monitored using a multimeter.

EDIT Nov 2016: pp_pop_psc_delta is now deprecated, because a new and presumably much faster population model implementation is now available, see gif_pop_psc_exp.

Parameters¶

The following parameters can be set in the status dictionary.

N	integer	Number of represented neurons
tau_m	ms	Membrane time constant
C_m	pF	Capacitance of the membrane
rho_0	1/s	Base firing rate
delta_u	mV	Voltage scale parameter
I_e	pA	Constant input current
tau_eta	list of ms	Time constants of post-spike kernel
val_eta	list of mV	Amplitudes of exponentials in post-spike-kernel
len_kernel	real	Post-spike kernel eta is truncated after max(tau_eta) * len_kernel

The parameters correspond to the ones of pp_psc_delta as follows.

c_1	0.0
c_2	rho_0
c_3	1/delta_u
q_sfa	val_eta
tau_sfa	tau_eta
I_e	I_e
dead_time	simulation resolution
dead_time_random	False
with_reset	False
t_ref_remaining	0.0

References¶

1(1,2): Naud R, Gerstner W (2012). Coding and decoding with adapting neurons: a population approach to the peri-stimulus time histogram. PLoS Compututational Biology 8: e1002711. DOI: https://doi.org/10.1371/journal.pcbi.1002711
2: Deger M, Helias M, Boucsein C, Rotter S (2012). Statistical properties of superimposed stationary spike trains. Journal of Computational Neuroscience 32:3, 443-463. DOI: https://doi.org/10.1007/s10827-011-0362-8
3: Deger M, Schwalger T, Naud R, Gerstner W (2014). Fluctuations and information filtering in coupled populations of spiking neurons with adaptation. Physical Review E 90:6, 062704. DOI: https://doi.org/10.1103/PhysRevE.90.062704

Sends¶

SpikeEvent

Receives¶

SpikeEvent, CurrentEvent, DataLoggingRequest