[Statistical analysis of the activity of pyramidal cells in the dorsal hippocampus of the rabbit]

Interspike interval statistics in the stochastic Hodgkin-Huxley model: coexistence of gamma frequency bursts and highly irregular firing

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 approximately 7 microA/cm(2). 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.

Dendritic transformations on random synaptic inputs as measured from a neuron's spike train--modeling and simulation

Extracellular spike trains recorded from central nervous system neurons reflect the random activations from a multitude of presynaptic cells making contacts mainly on the extensive dendritic trees. The dendritic potential variations are propagated towards the trigger zone where action potentials are generated. In this paper, two dendritic propagation modes are modeled: passive and quasi-active. Synaptic bombardments are modeled as being applied apically, somatically, or distributed over the dendritic tree. The resulting simulated neuronal spike trains are analyzed by point process techniques. Dendritic inputs resulted in a tendency for random bursting, interspike interval histograms with a long tail and coefficients of variation larger than one. The autocorrelation histograms reflected dynamics of the dendritic tree and they were able to discriminate between a passive or a quasi-active propagation mode and between dendritic and somatic synaptic inputs.

A theoretical basis for large coefficient of variation and bimodality in neuronal interspike interval distributions

We consider the classic Stein (1965) model for stochastic neuronal firing under random synaptic input. Our treatment includes the additional effect of synaptic reversal potentials. We develop and employ two numerical methods (in addition to Monte Carlo simulations) to study the relation of the various parameters of the model to the shape of the theoretical interspike interval distribution. Contrary to the results of Tuckwell (1979) we are unable to account, on the basis of substantial synaptic inhibition and with parameter settings in the known physiologic range, for experimental interspike interval distributions which exhibit large coefficients of variation or bimodality. We therefore introduce a time varying threshold into the model, which readily allows for such distributions and which has physiological justification.