An Information-Theoretic Framework to Measure the Dynamic Interaction between Neural Spike Trains

Objective: While understanding the interaction patterns among simultaneous recordings of spike trains from multiple neuronal units is a key topic in neuroscience, existing methods either do not consider the inherent point-process nature of spike trains or are based on parametric assumptions. This work presents an information-theoretic framework for the model-free, continuous-time estimation of both undirected (symmetric) and directed (Granger-causal) interactions between spike trains. Methods: The framework computes the mutual information rate (MIR) and the transfer entropy rate (TER) for two point processes X and Y, showing that the MIR between X and Y can be decomposed as the sum of the TER along the directions X Y and Y X. We present theoretical expressions and introduce strategies to estimate efficiently the two measures through nearest neighbor statistics. Results: Using simulations of independent and coupled spike train processes, we show the accuracy of MIR and TER to assess interactions even for weakly coupled and short realizations, and prove the superiority of continuous-time estimation over the standard discrete-time approach. In a real data scenario of recordings from in-vitro preparations of spontaneously-growing cultures of cortical neurons, we show the ability of MIR and TER to describe how the functional organization of the networks of spike train interactions emerges through maturation of the neuronal cultures. Conclusion and Significance: the proposed framework provides principled measures to assess undirected and directed spike train interactions with more efficiency and flexibility than previous discrete-time or parametric approaches, opening new perspectives for the analysis of point-process data in neuroscience and many other fields.