Toggling between gamma-frequency activity and suppression of cell assemblies.

ABSTRACT

Gamma (30-80 Hz) rhythms in hippocampus and neocortex resulting from the interaction of excitatory and inhibitory cells (E- and I-cells), called Pyramidal-Interneuronal Network Gamma (PING), require that the I-cells respond to the E-cells, but don't fire on their own. In idealized models, there is a sharp boundary between a parameter regime where the I-cells have weak-enough drive for PING, and one where they have so much drive that they fire without being prompted by the E-cells. In the latter regime, they often de-synchronize and suppress the E-cells; the boundary was therefore called the "suppression boundary" by Börgers and Kopell (2005). The model I-cells used in the earlier work by Börgers and Kopell have a "type 1" phase response, i.e., excitatory input always advances them. However, fast-spiking inhibitory basket cells often have a "type 2" phase response Excitatory input arriving soon after they fire delays them. We study the effect of the phase response type on the suppression transition, under the additional assumption that the I-cells are kept synchronous by gap junctions. When many E-cells participate on a given cycle, the resulting excitation advances the I-cells on the next cycle if their phase response is of type 1, and this can result in suppression of more E-cells on the next cycle. Therefore, strong E-cell spike volleys tend to be followed by weaker ones, and vice versa. This often results in erratic fluctuations in the strengths of the E-cell spike volleys. When the phase response of the I-cells is of type 2, the opposite happens strong E-cell spike volleys delay the inhibition on the next cycle, therefore tend to be followed by yet stronger ones. The strengths of the E-cell spike volleys don't oscillate, and there is a nearly abrupt transition from PING to ING (a rhythm involving I-cells only).