Two-Cell to N-Cell Heterogeneous, Inhibitory Networks: Precise Linking of Multistable and Coherent Properties

Inhibitory networks are now recognized as being the controllers of several brain rhythms. However, experimental work with inhibitory cells is technically difficult not only because of their smaller percentage of the neuronal population, but also because of their diverse properties. As such, inhibitory network models with tight links to the experimental data are needed to understand their contributions to population rhythms. However, mathematical analyses of network models with more than two cells is challenging when the cellular models involve biophysical details. We use bifurcation analyses and simulations to show that two-cell analyses can quantitatively predict N-cell (N = 20, 50, 100) network dynamics for heterogeneous, inhibitory networks. Interestingly, multistable states in the two-cell system are manifest as different and distinct coherent network patterns in the N-cell networks for the same parameter sets.