Characterization of subthreshold voltage fluctuations in neuronal membranes.
Michael Rudolph and Alain Destexhe

Neural Computation 15: 2577-2618, 2003.

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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 neuron.
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.