An information-theoretic framework to measure the dynamic interaction between neural spike trains

Understanding the interaction patterns among simultaneous recordings of spike trains from multiple neuronal units is a key topic in neuroscience. However, an optimal approach of assessing these interactions has not been established, as existing methods either do not consider the inherent point process nature of spike trains or are based on parametric assumptions that may lead to wrong inferences if not met. This work presents a framework, grounded in the field of information dynamics, for the model-free, continuous-time estimation of both undirected (symmetric) and directed (causal) interactions between pairs of spike trains. The framework decomposes the overall information exchanged dynamically between two point processes X and Y as the sum of the dynamic mutual information (dMI) between the histories of X and Y, plus the transfer entropy (TE) along the directions X->Y and Y->X. Building on recent work which derived theoretical expressions and consistent estimators for the TE in continuous time, we develop algorithms for estimating efficiently all measures in our framework through nearest neighbor statistics. These algorithms are validated in simulations of independent and coupled spike train processes, showing the accuracy of dMI and TE in the assessment of undirected and directed interactions even for weakly coupled and short realizations, and proving the superiority of the continuous-time estimator over the discrete-time method. Then, the usefulness of the framework is illustrated in a real data scenario of recordings from in-vitro preparations of spontaneously-growing cultures of cortical neurons, where we show the ability of dMI and TE to identify how the networks of undirected and directed spike train interactions change their topology through maturation of the neuronal cultures.