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Stochastic resonance in thalamic neurons and resonant neuron models Reinker, Stefan

Abstract

Neurons of the thalamus are major participants in gating sensory information for relay to the neocortex. Thalamic neurons are crucially involved in rhythmogenesis which determines the sleep/wake cycle. These roles require critical involvement of a T-type calcium current, conferring a frequency preference in response to subthreshold signals. We examine the interactions of this membrane resonance and noise using whole-cell patch clamp recordings in thalamocortical and reticular neurons of rat brain slices. We perform Monte-Carlo simulations and mathematical analysis using Hodgkin-Huxley-type and polynomial models of resonant neurons. We demonstrate stochastic resonance (SR) as maximal coherence between the input and stochastic output at intermediate noise levels. SR is measured by determining the signal-to-noise ratio under sine wave inputs, and from the reliability of detection measure under a-function inputs. In the experiments and neuron models with T-current, we demonstrate subthreshold resonance at 2-3 Hz, as well as noise dependent frequency dependence of SR for sine wave inputs. The simpler Hindmarsh-Rose model has a similar SR. This model also shows improved detection when the delay of consecutive EPSPs matches the preferred frequency. We show that the preferred frequency of the subthreshold and stochastic resonances depends on the time scale of the slow variable. The stochastic frequency preference arises from modulation of the firing probability of the fast subsystem. We develop a simple linear integrate-and-fire model with subthreshold resonance, which retains the main features of the more complicated models. An analytical solution of the stochastic equations shows that the eigenvalues determine frequency preferences in subthreshold resonance and stochastic resonance. SR can occur even with only noise. This autonomous SR depends on the resonance in our experiments and models. We demonstrate that preferred stochastic firing in the single neuron model translates into synchronized behaviour in a noisy network of resonant neuron models. With inhibitory synaptic coupling, noise can extend the parameter range of oscillations. With excitatory synaptic coupling, noise produces synchronized oscillations of the quiescent deterministic network. We speculate that combined subthreshold membrane resonance and stochastic resonance have physiological utility in coupling synaptic activity to preferred firing frequency, and in network synchronization under noise.

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