## Characterization of subthreshold voltage fluctuations in neuronal
membranes

#### Michael Rudolph and Alain Destexhe

* Neural Computation* 15: 2577-2618 (2003).

## Abstract

Synaptic noise due to intense network activity can significantly impact on the
electrophysiological properties of individual neurons. This is the case for the
cerebral cortex, where ongoing activity leads to strong barrages of synaptic
inputs, which act as the main source of synaptic noise impacting on neuronal
dynamics. Here, we characterize the subthreshold behavior of neuronal models in
which synaptic noise is represented by either additive or multiplicative noise,
described by Ornstein-Uhlenbeck processes. We derive and solve the Fokker-Planck
equation for this system, which describes the time evolution of the probability
density function for the membrane potential. We obtain an analytic expression
for the membrane potential distribution at steady-state and compare this analytic
expression with the subthreshold activity obtained in Hodgkin-Huxley type models
with stochastic synaptic inputs. The differences between multiplicative and
additive noise models suggest that multiplicative noise is adequate to describe
the high-conductance states similar to *in vivo* conditions. Because the
steady-state membrane potential distribution is easily obtained experimentally,
this approach provides a possible method to estimate the mean and variance of
synaptic conductances in real neurons.

See also the following related papers:
Rudolph M and Destexhe A. An extended
analytic expression for the membrane potential distribution of
conductance-based synaptic noise. *Neural Computation* 17:
2301-2315, 2005.

This paper is a follow-up of the
above article. We proposed an "extended" analytic expression which
matches the numerical simulations over a much larger parameter space.

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 so far is the
"extended" analytic expression proposed in the 2005 paper.

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