Firing-rate response properties of spiking neurons: beyond the diffusion limit

Abstract

Event Abstract Back to Event Firing-rate response properties of spiking neurons: beyond the diffusion limit Eilen Nordlie1*, Tom Tetzlaff1 and Gaute T. Einevoll1 1 Norwegian University of Life Sciences, Department of Mathematical Sciences and Technology, Norway Instantaneous firing rates are often used to describe either the compound spiking activity of neuron ensembles (population rate) or the trial-averaged response of individual neurons to multiple repetitions of the same stimulus. For the case of weak synapses and high input firing rates (diffusion limit), the (linear) rate response of an ensemble of independent neurons has been derived in previous studies for several integrate-and-fire (IaF) neuron models [1-5]. The assumption of weak synapses can however not always be justified: in the early visual pathway, for example, single action potentials emitted by retinal ganglion cells initiate response spikes in postsynaptic thalamic cells with a high probability [6]. Also within the cortex, a considerable fraction of synapses has moderately strong weights [7,8]. It is unclear to what extent the results obtained under the diffusion approximation can be generalised to these cases.Here, we numerically investigate the response properties of leaky IaFneurons receiving input spikes through arbitrarily strong excitatory (current-based alpha-) synapses. The input spike trains are modelled as Poisson point-processes with sinusoidal intensity. Modulation amplitudes and phases of the trial-averaged spike responses are measured for a broad range of stimulus modulation frequencies and synaptic weights.We show that the input-output rate transmission can be well modelled by a simple first-order low-pass filter (Fig.A). The dependence of the cutoff frequency fcon the synaptic weight w (Fig.B) is dominated by a sharp increase of fc at a critical weight wc (the minimal weight for which a single presynaptic action potential leads to a threshold crossing in the postsynaptic cell; dashed vertical line in Fig.B). In general, the cutoff frequencies are determined by the time constants τm and τs of both the membrane and the postsynaptic currents. The dependence on τm disappears if the synaptic weights are normalised by wc. The remaining dependence on τs is most prominent in the supercritical regime (w>wc). Acknowledgements:We acknowledge partial support by the Research Council of Norway (eNEURO, NOTUR) and the Honda Research Institute Europe. All simulations were carried out with the NEST simulation tool (see http://www.nest-initiative.org).