Representation of cooperative firing activity among simultaneously recorded neurons

Simultaneous and separable extracellular recording of substantial populations of neurons under chronic and behavioral conditions is becoming experimentally feasible. We have recently described a conceptual transformation of such multiple spike train data that allows the experimenter to analyze the entire network of observed neurons as an entity rather than as a summation of neuron pairs. The basic transformation represents each of N neurons as a particle in an N-space. Each particle is given a "charge" that is related to the spike train of the corresponding neuron. The resulting forces on the N particles cause aggregation of those particles that represent neurons with time-related firing. The present paper extends the visualization and possibilities of this way of analyzing properties of neuronal assemblies. Data are taken from computer-simulated neuronal networks in order to provide known properties. We demonstrate projection of particle positions from the N space to a plane. Under the right conditions the spatial arrangement of the particles forms a Venn diagram of functional relationships in the entire neural network. We introduce revised force rules in the transformation that allow detection and study of inhibitory connections among the observed neurons. Sensitivity is lower than for excitatory connections. We introduce revised "charge" rules that improve "signal-to-noise" properties and in addition allow inference of directed connectivity. The original transformation only allows identification of neurons with time-related firing. The two-charge transformation allows explicit identification of presynaptic and postsynaptic neurons. Finally we examine sensitivity of the transformation to individual and near-coincident firing rates. Some criteria are presented for choice of charge normalization rules in the transformation.