Estimating membrane voltage correlations from extracellular spike trains.

The cross-correlation coefficient between neural spike trains is a commonly used tool in the study of neural interactions. Two well-known complications that arise in its interpretation are 1) modulations in the correlation coefficient may result solely from changes in the mean firing rate of the cells and 2) the mean firing rates of the neurons impose upper and lower bounds on the correlation coefficient whose absolute values differ by an order of magnitude or more. Here, we propose a model-based approach to the interpretation of spike train correlations that circumvents these problems. The basic idea of our proposal is to estimate the cross-correlation coefficient between the membrane voltages of two cells from their extracellular spike trains and use the resulting value as the degree of correlation (or association) of neural activity. This is done in the context of a model that assumes the membrane voltages of the cells have a joint normal distribution and spikes are generated by a simple thresholding operation. We show that, under these assumptions, the estimation of the correlation coefficient between the membrane voltages reduces to the calculation of a tetrachoric correlation coefficient (a measure of association in nominal data introduced by Karl Pearson) on a contingency table calculated from the spike data. Simulations of conductance-based leaky integrate-and-fire neurons indicate that, despite its simplicity, the technique yields very good estimates of the intracellular membrane voltage correlation from the extracellular spike trains in biologically realistic models.