Auto and crosscorrelograms for the spike response of LIF neurons with slow synapses

An analytical description of the response properties of simple but realistic neuron models in the presence of noise is still lacking. We determine completely up to the second order the firing statistics of a single and a pair of leaky integrate-and-fire neurons (LIFs) receiving some common slowly filtered white noise. In particular, the auto-and cross-correlation functions of the output spike trains of pairs of cells are obtained from an improvement of the adiabatic approximation introduced in [1]. These two functions define the firing variability and firing synchronization between neurons, and are of much importance for understanding neuron communication. The variability of the spike trains of cortical neurons and their correlations might constraint the coding capabilities of the brain [2], but they can also reflect the strategies the brain uses to decipher the stimuli arriving from the world [3]. Neurons in cortex fire with high variability resembling Poisson spike trains [4], and nearby pairs of cortical neurons fire in a correlated fashion [2], reflecting the presence of some common source of noise. These variability and correlation of the spike trains affect the firing statistics of a neuron receiving those inputs [5, 6]. It has been shown that the large variability observed in vivo can be accounted for by neuron models operating in a regime in which the membrane time constant , τ m , becomes shorter or comparable to the synaptic decay constants, τ s , due to spontaneous background activity (τ s ≥ τ m) [7, 8]. However, very little progress has been made in providing analytical tools to describe such variability and correlations found in cortex. In this Letter we study analytically the variability and correlations in the firing responses of pairs of LIF neurons receiving both common and independent sources of white noise input filtered by synapses in the regime τ s ≥ τ m. For a single neuron we obtain the firing rate, the auto-correlation function of its output spike train (ACF), the Fano factor of the spike count, F N. For a pair of cells, we obtain the crosscorrelation function of their output spike trains (CCF) and the correlation coefficient of their spike counts, ρ. These results characterize completely the firing response of these spiking neurons up to second order, and open the possibility for a principled way of including synchrony effects in the modeling of biologically plausible spiking neural networks. The neuron and input models. …