An extended analytic expression for the membrane potential distribution of conductance-based synaptic noise

Michael Rudolph and Alain Destexhe

Neural Computation 17: 2301-2315, 2005.

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Synaptically generated subthreshold membrane potential (Vm) fluctuations can be characterized within the framework of stochastic calculus. It is possible to obtain analytic expressions for the steady-state Vm distribution, even in the case of conductance-based synaptic currents. However, as we show here, the analytic expressions obtained may substantially deviate from numerical solutions if the stochastic membrane equations are solved exclusively based on expectation values of differentials of the stochastic variables, hence neglecting the spectral properties of the underlying stochastic processes. We suggest a simple solution that corrects these deviations, leading to extended analytic expressions of the Vm distribution valid for a parameter regime that covers several orders of magnitude around physiologically realistic values. These extended expressions should enable finer characterization of the stochasticity of synaptic currents by analyzing experimentally recorded Vm distributions and may be applicable to other classes of stochastic processes as well.

Supplementary Material

In the Supplementary Material page, we provide (a) a NEURON program to simulate the model and compare it to the extended analytic expression; (b) several supplementary figures which compare the Vm distributions obtained from numerical simulations, with the extended analytic expression for extreme parameter sets; (c) a discussion of the limits of this approach.
See also the following related papers:
Rudolph M and Destexhe A. Characterization of subthreshold voltage fluctuations in neuronal membranes. Neural Computation 15: 2577-2618, 2003.
This is the original contribution proposing an analytic expression for the steady-state voltage distribution of passive membranes subject to conductance-based synaptic noise sources.
Rudolph M and Destexhe A. On the use of analytic expressions for the voltage distribution to analyze intracellular recordings. Neural Computation 18: 2917-2922, 2006.
In this later article, we compared different approximations for the steady-state voltage distribution with conductance-based synaptic noise, and show that the most accurate expression for physiological parameters is the "extended" analytic expression.
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