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

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.