The most likely voltage path and large deviations approximations for integrate-and-fire neurons |
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Authors: | Liam Paninski |
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Institution: | (1) Department of Statistics, Columbia University, Columbia |
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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.
Action Editor: Peter Latham |
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Keywords: | Likelihood Stochastic dynamics Freidlin-Wentzell Calculus of variations Intracellular recordings |
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