Rate dynamics of leaky integrate-and-fire neurons with strong synapses

Abstract

Firing-rate models provide a practical tool for studying the dynamics of trial- or population-averaged neuronal signals. A wealth of theoretical and experimental studies has been dedicated to the derivation or extraction of such models by investigating the firing-rate response characteristics of ensembles of neurons. The majority of these studies assumes that neurons receive input spikes at a high rate through weak synapses (diffusion approximation). For many biological neural systems, however, this assumption cannot be justified. So far, it is unclear how time-varying presynaptic firing rates are transmitted by a population of neurons if the diffusion assumption is dropped. Here, we numerically investigate the stationary and non-stationary firing-rate response properties of leaky integrate-and-fire neurons receiving input spikes through excitatory synapses with alpha-function shaped postsynaptic currents for strong synaptic weights. Input spike trains are modeled by inhomogeneous Poisson point processes with sinusoidal rate. Average rates, modulation amplitudes, and phases of the period-averaged spike responses are measured for a broad range of stimulus, synapse, and neuron parameters. Across wide parameter regions, the resulting transfer functions can be approximated by a linear first-order low-pass filter. Below a critical synaptic weight, the cutoff frequencies are approximately constant and determined by the synaptic time constants. Only for synapses with unrealistically strong weights are the cutoff frequencies significantly increased. To account for stimuli with larger modulation depths, we combine the measured linear transfer function with the nonlinear response characteristics obtained for stationary inputs. The resulting linear–nonlinear model accurately predicts the population response for a variety of non-sinusoidal stimuli.

Stability of Bumps in a Two Population Neural Field Model

“…which are derived by means of the Linear Chain Trick (LCT) [29]. It is also possible to obtain a system of rate equations from (4) by the LCT when the temporal kernels are given by quasipower functions (3). In this case, we get a system of (k e + k i + 2) coupled equations with (k e + k i ) auxiliary variables.…”

“…Let us consider the case when the temporal kernels are given as (3). The Laplace transforms are computed as…”

“…However, under simplifying assumptions, they can be derived or extracted from the single-neuron dynamics (see e.g. [3] and the references therein).…”

“…The temporal kernel α mn (t) denotes the impulse response (Green's function) of the target population n given a deltashaped input from population m. 1 Several experimental [10][11][12][13][14] and theoretical studies [2,3,[15][16][17][18][19][20][21][22][23][24] have shown that populations of (unconnected) neurons typically exhibit low-pass characteristics (at least if one takes into account that incoming spikes are low-pass filtered by the synapses): while the neuron ensembles can reliably track low-frequency fluctuations in the input, high-frequency components are damped. Most previous studies on neural-field models have taken this into account by considering exponential temporal kernels α mn (t) = exp(−t/τ n )/τ n with time constants τ n , i.e.…”

Firing-rate models for neurons with a broad repertoire of spiking behaviors

“…To this end, we extend previous work on simple integrate-and-fire neurons [1,2] to the multi-timescale adaptive threshold (MAT) [3] and the Izhikevich model [4]. The model neurons are probed by spike trains modeled as realizations of inhomogeneous Poisson or Gamma point processes with sinusoidally modulated intensity.…”