Model dependence in quantification of spike interdependence by joint peri-stimulus time histogram

Multineuronal recordings have enabled us to examine context-dependent changes in the relationship between the activities of multiple cells. The joint peri-stimulus time histogram (JPSTH) is a much-used method for investigating the dynamics of the interdependence of spike events between pairs of cells. Its results are often taken as an estimate of interaction strength between cells, independent of modulations in the cells' firing rates. We evaluate the adequacy of this estimate by examining the mathematical structure of how the JPSTH quantifies an interaction strength after excluding the contribution of firing rates. We introduce a simple probabilistic model of interacting point processes to generate simulated spike data and show that the normalized JPSTH incorrectly infers the temporal structure of variations in the interaction parameter strength. This occurs because, in our model, the correct normalization of firing-rate contributions is different than that used in Aertsen, Gerstein, Habib, and Palm's (1989) effective connectivity model. This demonstrates that firing-rate modulations cannot be corrected for in a model-independent manner, and therefore the effective connectivity does not represent a universal characteristic that is independent of modulation of the firing rates. Aertsen et al.'s (1989) effective connectivity may still be used in the analysis of experimental data, provided we are aware that this is simply one of many ways of describing the structure of interdependence. We also discuss some measure-independent characteristics of the structure of interdependence.