Two enhancements of the gravity algorithm for multiple spike train analysis

The gravity method for neuronal assembly analysis represents each neuron as a particle in N-space with a time varying charge that is a filtered version of the corresponding spike train, with appropriate rules for forces between and movements of the charged particles. Resulting trajectories reflect neuronal timing relationships. The usual short time constants in the filter restrict aggregation to highly synchronized neurons and reduce the sensitivity for delayed correlations; long time constants in the filter reduce selectivity. Here we describe an enhancement that modifies rules for assigning charge increment times to allow mixtures of short and long lag correlations. Charge increments for each pair are offset from the actual spike times by time lags defined by features in corresponding cross-correlograms; no such charge offsets are invoked if the correlogram is flat. Tuning increases charge products and aggregation of long lag correlated pairs. A second enhancement uses a new three-dimensional display of particle pair trajectories to parse the type of neuronal relationship. For each pair, we record and display the interparticle distance and the distance each particle moves from its original location in the N-space. The resulting trajectories cluster according to the type of interaction between the represented neurons. Results from simulated networks and in vivo multi-site recordings show that these modifications detect assembly properties not identified by the standard methods.