The most likely voltage path and large deviations approximations for integrate-and-fire neurons.

Journal of Computational Neuroscience
Liam Paninski

Abstract

We develop theory and numerical methods for computing the most likely subthreshold voltage path of a noisy integrate-and-fire (IF) neuron, given observations of the neuron's superthreshold spiking activity. This optimal voltage path satisfies a second-order ordinary differential (Euler-Lagrange) equation which may be solved analytically in a number of special cases, and which may be solved numerically in general via a simple "shooting" algorithm. Our results are applicable for both linear and nonlinear subthreshold dynamics, and in certain cases may be extended to correlated subthreshold noise sources. We also show how this optimal voltage may be used to obtain approximations to (1) the likelihood that an IF cell with a given set of parameters was responsible for the observed spike train; and (2) the instantaneous firing rate and interspike interval distribution of a given noisy IF cell. The latter probability approximations are based on the classical Freidlin-Wentzell theory of large deviations principles for stochastic differential equations. We close by comparing this most likely voltage path to the true observed subthreshold voltage trace in a case when intracellular voltage recordings are available in vitro.

References

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Citations

May 12, 2007·Journal of Computational Neuroscience·Liam PaninskiGabor Szirtes
Jan 12, 2011·Journal of Computational Neuroscience·Remi Monasson, Simona Cocco
Nov 18, 2011·Journal of Computational Neuroscience·Liam PaninskiDaniel Gil Ferreira
Sep 21, 2010·Nature Neuroscience·Jean-Pascal PfisterMáté Lengyel
Aug 12, 2009·Proceedings of the National Academy of Sciences of the United States of America·Simona CoccoRémi Monasson
Apr 23, 2011·Journal of Neurophysiology·Yashar AhmadianLiam Paninski
Jan 27, 2012·Journal of Neurophysiology·Deepankar MohantyNicholas J Priebe
Nov 20, 2009·Neural Computation·Michael Famulare, Adrienne Fairhall
Feb 9, 2011·Neural Computation·Robert Rosenbaum, Krešimir Josić
Jan 7, 2011·The Journal of Neuroscience : the Official Journal of the Society for Neuroscience·Rick L JenisonMatthew A Howard
Nov 17, 2009·Computational Intelligence and Neuroscience·Anne C SmithEmery N Brown
Aug 4, 2015·Frontiers in Cellular Neuroscience·Corina S Drapaca
Nov 11, 2017·Journal of Integrative Neuroscience·Antonio CapolupoGiuseppe Vitiello
Dec 8, 2006·Journal of Neurophysiology·Martin PospischilAlain Destexhe
Feb 1, 2008·Physical Review Letters·G Bard ErmentroutNathaniel N Urban
Sep 4, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Laurent BadelMagnus J E Richardson
Jun 23, 2012·Journal of Neurophysiology·Sungho HongErik De Schutter
Mar 5, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·M T Wilson, D A Steyn-Ross

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