Spike-response model

1. The Spike Response Model 1 ABSTRACT A description of neuronal activity on the level of ion channels, as in the Hodgkin-Huxley model, leads to a set of coupled nonlinear diier-ential equations which are diicult to analyze. In this paper, we present a conceptual framework for a reduction of the nonlinear spike dynamics to a threshold process. Spikes occur if the membrane potential u(t) reaches a threshold #. The voltage response to spike input is described by the postsy-naptic potential. Postsynaptic potentials of several input spikes are added linearly until u reaches #. The output pulse itself and the reset/refractory period which follow the pulse are described by a function. Since and can be interpreted as response kernels, the resulting model is called the Spike Response Model (SRM). After a short review of the Hodgkin-Huxley model we show that (i) Hodgkin-Huxley dynamics with time-dependent input can be reproduced to a high degree of accuracy by the SRM; (ii) the simple integrate-and-re neuron is a special case of the Spike Response Model; (iii) compartmental neurons with a passive dendritic tree and a threshold process for spike generation can be treated in SRM-framework; (iv) small nonlinearities lead to interactions between spikes to be described by higher-order kernels.

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