Characterizing neuronal activity by describing the membrane potential as a stochastic process

Cortical neurons behave similarly to stochastic processes, as a consequence of their irregularity and dense connectivity. Their firing pattern is close to a Poisson process, and their membrane potential (Vm)(Vm) is analogous to colored noise. One way to characterize this activity is to identify VmVm to a multidimensional stochastic process. We review here this approach and how it can be used to extract important statistical signatures of neuronal activity. The “VmD method” consists of fitting the VmVm distribution obtained intracellularly to analytic expressions derived from stochastic processes, and thereby deduce synaptic conductance parameters. However, this method requires at least two levels of VmVm, which prevents applications to single-trial measurements. We also discuss methods that can be applied to single VmVm traces, such as power spectral analysis and the “STA method” to calculate spike-triggered average conductances based on a maximum likelihood procedure. A recently proposed method, the “VmT method”, is based on the fusion of these two concepts. This method is analogous to the VmD method and estimates the mean excitatory and inhibitory conductances and their variances. However, it does so by using a maximum-likelihood estimation, and can thus be applied to single VmVm traces. All methods were tested using controlled conductance injection in dynamic-clamp experiments.