An adapting Markov process: Beyond renewal descriptions of neuronal firing

Eilif Müller

Ecole Polytechnique Fédérale de Lausanne, Computational Neuroscience Laboratory, Lausanne, Switzerland

Spike-Frequency Adaptation is ubiquitous in the central nervous systems of diverse species. While adaptation has prominent consequences for neuronal firing dynamics, it is often neglected in the community when considering, for example, the dynamic nature of the neural code, the propagation of synchrony in networks, or the function of spike-time-based learning rules, probably due to the added difficulty in accounting for it. We present a new and powerful tool for treating Spike-Frequency Adaptation: an adapting continuous Markov process. This adapting Markov process in two dimensions can be shown to accurately capture the firing-rate dynamics and inter-spike interval correlations of a spike-frequency adapting and relative refractory conductance-based integrate-and-fire neuron driven by Poisson spike trains.

[1] E. Muller, L. Buesing, J. Schemmel, K. Meier (2007). Spike-Frequency Adapting Neural Ensembles: Beyond Mean Adaptation and Renewal Theories. Neural Computation 19:2958-3010.

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