Efficient evaluation of neuron populations receiving colored-noise current based on a refractory density method.
The expected firing probability of a stochastic neuron is approximated by a function of the expected subthreshold membrane potential, for the case of colored noise. We propose this approximation in order to extend the recently proposed white noise model [A. V. Chizhov and L. J. Graham, Phys. Rev. E 75, 011924 (2007)] to the case of colored noise, applying a refractory density approach to conductance-based neurons. The uncoupled neurons of a single population receive a common input and are dispersed by the noise. Within the framework of the model the effect of noise is expressed by the so-called hazard function, which is the probability density for a single neuron to fire given the average membrane potential in the presence of a noise term. To derive the hazard function we solve the Kolmogorov-Fokker-Planck equation for a mean voltage-driven neuron fluctuating due to colored noisy current. We show that a sum of both a self-similar solution for the case of slow changing mean voltage and a frozen stationary solution for fast changing mean voltage gives a satisfactory approximation for the hazard function in the arbitrary case. We demonstrate the quantitative effect of a temporal correlation of noisy input on the neuron dynamics in the case of leaky integrate-and-fire and detailed conductance-based neurons in response to an injected current step.
Chizhov
Anton V
AV
A.F. Ioffe Physico-Technical Institute of RAS, 26 Politekhnicheskaya Street, 194021 St. Petersburg, Russia. Anton.Chizhov@mail.ioffe.ru
Graham
Lyle J
LJ
D000200:Action Potentials / Q000502:physiology*; D001921:Brain / Q000502:physiology*; D003198:Computer Simulation; D008959:Models, Neurological; D015233:Models, Statistical; D009415:Nerve Net / Q000502:physiology*; D009474:Neurons / Q000502:physiology*; D012032:Refractory Period, Electrophysiological / Q000502:physiology*; D013269:Stochastic Processes