Spike-Frequency Adapting Neural Ensembles: Beyond Mean Adaptation and Renewal Theories

We propose a Markov process model for spike-frequency adapting neural ensembles which synthesizes existing mean-adaptation approaches, population density methods, and inhomogeneous renewal theory, resulting in a unified and tractable framework which goes beyond renewal and mean-adaptation theories by accounting for correlations between subsequent interspike intervals. A method for efficiently generating inhomogeneous realizations of the proposed Markov process is given, numerical methods for solving the population equation are presented, and an expression for the first-order interspike interval correlation is derived. Further, we show that the full five-dimensional master equation for a conductance-based integrate-and-fire neuron with spike-frequency adaptation and a relative refractory mechanism driven by Poisson spike trains can be reduced to a two-dimensional generalization of the proposed Markov process by an adiabatic elimination of fast variables. For static and dynamic stim...

• Type: Journal
• Year: 2007
• Where: NECO
• Authors: Eilif Mueller, Lars Buesing, Johannes Schemmel, Karlheinz Meier
• Keywords: Interspike Interval, Markov Process, Markov Process Model, NECO 2007