Equilibrium and Response Properties of the Integrate-and-Fire Neuron in Discrete Time.

Frontiers in Computational Neuroscience
Moritz HeliasS Rotter

Abstract

The integrate-and-fire neuron with exponential postsynaptic potentials is a frequently employed model to study neural networks. Simulations in discrete time still have highest performance at moderate numerical errors, which makes them first choice for long-term simulations of plastic networks. Here we extend the population density approach to investigate how the equilibrium and response properties of the leaky integrate-and-fire neuron are affected by time discretization. We present a novel analytical treatment of the boundary condition at threshold, taking both discretization of time and finite synaptic weights into account. We uncover an increased membrane potential density just below threshold as the decisive property that explains the deviations found between simulations and the classical diffusion approximation. Temporal discretization and finite synaptic weights both contribute to this effect. Our treatment improves the standard formula to calculate the neuron's equilibrium firing rate. Direct solution of the Markov process describing the evolution of the membrane potential density confirms our analysis and yields a method to calculate the firing rate exactly. Knowing the shape of the membrane potential distribution near ...Continue Reading

Citations

Oct 4, 2011·Journal of Computational Neuroscience·Moritz DegerStefan Rotter
Sep 22, 2010·PLoS Computational Biology·Moritz HeliasMarkus Diesmann
Apr 18, 2013·PLoS Computational Biology·Matthias Schultze-KraftMoritz Helias
Nov 10, 2013·PLoS Computational Biology·Ramakrishnan IyerStefan Mihalas
Jun 1, 2016·Neural Networks : the Official Journal of the International Neural Network Society·Thomas Saaty
Nov 8, 2012·PLoS Computational Biology·Tom TetzlaffMarkus Diesmann
Jan 15, 2011·Physical Review Letters·Magnus J E Richardson, Rupert Swarbrick
Aug 8, 2019·Journal of the Royal Society, Interface·Marie LevakovaRyota Kobayashi
Jun 7, 2017·Journal of Computational Neuroscience·Felix Droste, Benjamin Lindner

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