Time-scale matching in the response of a leaky integrate-and-fire neuron model to periodic stimulus with additive noise

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Abstract
We study the response of a leaky integrate-and-fire neuron model to subthreshold periodic stimulus with additive noise. Previous works have shown that the interspike interval distribution at the modulation period goes through a maximum with increasing either the noise intensity or the period. This maximum appears when the stimulation period is close to the mode of the interspike interval distribution in the absence of the modulation. This phenomenon is called time-scale matching. In this paper, we examine time-scale matching in the response to periodic signals with and without resetting of the input phase at each firing. For the case without resetting, we calculate the phase distribution by iterating a stochastic phase transition operator. This operator extends the phase transition curve commonly used in the analysis of the response of deterministic oscillators to periodic stimulation. We also examine the dependence of the time-scale matching on the input amplitude. Furthermore, we consider the response of the system in the frequency domain. It is known that the signal-to-noise ratio derived from the power spectral density goes through a maximum with increasing noise intensity. We show that the signal-to-noise ratio also has a hump as a function of the period, and discuss its relation to time-scale matching. This work helps in clarifying conditions whereby noise can improve the detection of a weak periodic signal by neurons through time-scale matching.