On the use of analytic expressions for the voltage distribution to analyze intracellular recordings.
Michelle Rudolph and Alain Destexhe

Neural Computation 18: 2917-2922, 2006.

Copy of the full paper (PDF)
Different analytic expressions for the membrane potential distribution of membranes subject to synaptic noise have been proposed, and can be very helpful to analyze experimental data. However, all of these expressions are either approximations or limit cases, and it is not clear how they compare, and which expression should be used in a given situation. In this note, we provide a comparison of the different approximations available, with an aim to delineate which expression is most suitable for analyzing experimental data.
Supplementary Material
In the Supplementary Material page, we provide

(a) a NEURON program to simulate the model and compare it to different analytic expressions;

(b) several supplementary figures which compare the Vm distributions obtained from numerical simulations, with different analytic expressions for various parameter sets.

See also the following previous papers on the same subject:

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. An extended analytic expression for the membrane potential distribution of conductance-based synaptic noise. Neural Computation 17:2301-2315, 2005.

In this paper, we proposed an “extended” analytic expression which matches the numerical simulations over a much larger parameter space. As shown in the 2006 paper above, this extended expression is the most accurate expression for physiological parameters.