Comment on: "Characterization of subthreshold voltage fluctuations in   neuronal membranes" by M. Rudolph and A. Destexhe
  In two recent papers, Rudolph and Destexhe (Neural Comp. {\bf 15},   2577-2618, 2003; Neural Comp. in press, 2005) studied a leaky integrator model (i.e. an RC-circuit) driven by correlated (``colored'') Gaussian conductance noise and Gaussian current noise. In the first paper they derived an expression for the stationary probability density of the membrane voltage; in the second paper this expression was modified to cover a larger parameter regime. Here we show by standard analysis of solvable limit cases (white-noise limit of additive and multiplicative noise sources; only slow multiplicative noise; only additive noise) and by numerical simulations that their first result does not hold for the general colored-noise case and uncover the errors made in the derivation of a Fokker-Planck equation for the probability density. Furthermore, we demonstrate analytically (including an exact integral expression for the time-dependent mean value of the voltage) and by comparison to simulation results, that the extended expression for the probability density works much better but still does not solve exactly the full colored-noise problem. We also show that at stronger synaptic input the stationary mean value of the linear voltage model may diverge and give an exact condition relating the system parameters for which this takes place. 
Benjamin Lindner and Andre Longtin