Abstract
AbstractWe present a time-dependent level-crossing theory for linear dynamical systems perturbed by colored Gaussian noise. We apply these results to approximate the firing statistics of conductance-based integrate-and-fire neurons receiving excitatory and inhibitory Poissonian inputs. Analytical expressions are obtained for three key quantities characterizing the neuronal response to time-varying inputs: the mean firing rate, the linear response to sinusoidally-modulated inputs, and the pairwise spike-correlation for neurons receiving correlated inputs. The theory yields tractable results that are shown to accurately match numerical simulations, and provides useful tools for the analysis of interconnected neuronal populations.
Highlights
We present a time-dependent level-crossing theory for linear dynamical systems perturbed by colored Gaussian noise
Synaptic input consists of discrete action potentials, which results in non-Gaussian voltage distributions and affects firing statistics [5,6,7,8]
The majority of theoretical studies include only one synaptic type and assume either fast (e.g., [9,10,11]) or slow [11, 12] kinetics compared with the membrane integration time, but experimental evidence suggests that these timescales are often comparable [13]
Summary
A neuron, with capacitance C and charged at a voltage V , obeys the current-balance equation. The synaptic current Isyn comprises excitatory and inhibitory conductances Isyn = Ge(Ee − V ) + Gi(Ei − V ) with reversals Ee = 0 and Ei = −80mV. Synaptic channels activate rapidly but close with a characteristic time particular to excitation (τe = 3ms) or inhibition (τi = 10ms). The assumption that these conductances are activated stochastically with a short autocταorGreαla=tionGαal−lowGsαa+Lσaαn√ge2vτiαnξαeqfuoartiαon to be written, ∈ {e, i}, where. The general form of this equation can be related to a family of underlying models; in our simulations a process is considered in which synaptic conductances increase by an amount.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
