  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.
