Searching for cell assemblies: how many electrodes do I need?

Two methods were derived to estimate the probability of recording cell assemblies using multiple simultaneous electrode recordings. The derivations are independent of the definition of a cell assembly, and require only a statistic for evaluating cell assembly membership from spike train data. The resulting equations are functions of 1) the size of the search area, 2) the smallest expected assembly size, 3) the number of recorded neurons, and 4) the predicted spatial distribution of assembly neurons. The equations can be used to estimate the following three quantities. First, the equations directly calculate the probability of detecting i or more cells of an hypothesized assembly. Second, by making several such calculations, one can estimate when sufficient sampling has been performed to claim, at any desired confidence level, that a posited type of cell assembly does not exist. Third, the probability of detecting one out of several active assemblies can be calculated, given assumptions about assembly-assembly interactions.