Multi-stable oscillations in cortical networks with two classes of inhibition

In the classic view of cortical rhythms, the interaction between excitatory pyramidal neurons (E) and inhibitory parvalbumin neurons (I) has been shown to be sufficient to generate gamma and beta band rhythms. However, it is now clear that there are multiple inhibitory interneuron subtypes and that they play important roles in the generation of these rhythms. In this paper we develop a spiking network that consists of populations of E, I and an additional interneuron type, the somatostatin (S) internerons that receive excitation from the E cells and inhibit both the E cells and the I cells. These S cells are modulated by a third inhibitory subtype, VIP neurons that receive inputs from other cortical areas. We reduce the spiking network to a system of nine differential equations that characterize the mean voltage, firing rate, and synaptic conductance for each population and using this we find many instances of multiple rhythms within the network. Using tools from nonlinear dynamics, we explore the roles of each of the two classes of inhibition as well as the role of the VIP modulation on the properties of these rhythms.