## 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.

## Abstract

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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