Skip to content

Advertisement

Open Access

Non-renewal Markov models for spike-frequency adapting neural ensembles

BMC Neuroscience20078(Suppl 2):S12

https://doi.org/10.1186/1471-2202-8-S2-S12

Published: 6 July 2007

Keywords

Animal ModelMarkov ModelMarkov ProcessMaster EquationVariance Adaptation

We present a continuous Markov process model for spike-frequency adapting neural ensembles which synthesizes existing mean-adaptation approaches and inhomogeneous renewal theory. Unlike renewal theory, the Markov process can account for interspike interval correlations, and an expression for the first-order interspike interval correlation is derived. The Markov process in two dimensions is shown to accurately capture the firing-rate dynamics and interspike interval correlations of a spike-frequency adapting and relative refractory conductance-based integrate-and-fire neuron driven by Poisson spike trains. Using the Master equation for the proposed process, the assumptions of the standard mean-adaptation approach are clarified, and a mean+variance adaptation theory is derived which corrects the mean-adaptation firing-rate predictions for the biologically parameterized integrate-and-fire neuron model considered. An exact recipe for generating inhomogeneous realizations of the proposed Markov process is given.

Authors’ Affiliations

(1)
Kirchhoff Institute for Physics, University of Heidelberg, Heidelberg, Germany

Copyright

© Muller et al; licensee BioMed Central Ltd. 2007

This article is published under license to BioMed Central Ltd.

Advertisement