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Interspike Interval Statistics in the Stochastic Hodgkin-Huxley Model: Coexistence of Gamma Frequency Bursts and Highly Irregular Firing

prowat{at}ucsd.edu Institute for Neural Computation, University of California at San Diego, La Jolla, CA 92093, U.S.A.

When the classical Hodgkin-Huxley equations are simulated with Na- and K-channel noise and constant applied current, the distribution of interspike intervals is bimodal: one part is an exponential tail, as often assumed, while the other is a narrow gaussian peak centered at a short interspike interval value. The gaussian arises from bursts of spikes in the gamma-frequency range, the tail from the interburst intervals, giving overall an extraordinarily high coefficient of variation—up to 2.5 for 180,000 Na channels when I 7µA/cm². Since neurons with a bimodal ISI distribution are common, it may be a useful model for any neuron with class 2 firing. The underlying mechanism is due to a subcritical Hopf bifurcation, together with a switching region in phase-space where a fixed point is very close to a system limit cycle. This mechanism may be present in many different classes of neurons and may contribute to widely observed highly irregular neural spiking.

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