Reconciling Information Directionality with Negative Time Lag in Neuronal Circuits

Synchronization has been extensively studied in the brain, where it has been hypothesized to be relevant to issues such as the binding problem, temporal coding, deployment of spatial attention, higher cognitive functions, and many others. Among the tools available to assess the coordinated activity of two or more areas, correlation functions are probably the most widely employed. However, correlations do not detect the directionality of the connection. Granger causality (GC) has shed light into the directional influences and the time arrow of the information flow. A positive GC from an area A to an area B would indicate that the activity of area A causes the activity of area B. Intuitively, one tends to assume that a positive GC is accompanied by a positive time delay (relative phase) between the activities of areas A and B, signaling that activity in A precedes that of B. But, would it be possible to compute a positive GC and a negative time delay? This is precisely the scenario we study in this work, motivated by experiments reported in monkeys while performing a visual task