Understanding short-timescale neuronal firing sequences via bias matrices

The brain generates persistent neuronal firing sequences across varying timescales. The short-timescale (~100ms) sequences are believed to be crucial in the formation and transfer of memories. Large-amplitude local field potentials known as sharp-wave ripples (SWRs) occur irregularly in hippocampus when an animal has minimal interaction with its environment, such as during resting, immobility, or slow-wave sleep. SWRs have been long hypothesized to play a critical role in transferring memories from the hippocampus to the neocortex [1]. While sequential firing during SWRs is known to be biased by the previous experiences of the animal, the exact relationship of the short-timescale sequences during SWRs and longer-timescale sequences during spatial and nonspatial behaviors is still poorly understood. One hypothesis is that the sequences during SWRs are “replays” or “preplays” of “master sequences”, which are sequences that closely mimic the order of place fields on a linear track [2,3]. Rather than particular hard-coded “master” sequences, an alternative explanation of the observed correlations is that similar sequences arise naturally from the intrinsic biases of firing between pairs of cells. To distinguish these and other possibilities, one needs mathematical tools beyond the center-of-mass sequences and Spearman’s rank-correlation coefficient that are currently used