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Cholecystokinin-expressing (CCK+) basket cells are key controllers of theta-gamma coupled rhythms in the hippocampus

It has been shown that different inhibitory cell types underlie brain rhythmic and cross-frequency coupling output, but exactly how inhibitory cell types manifest their contributions to these outputs is far from clear. Brain rhythms and their couplings are functionally important in cognition and behaviour, and thus it is essential that we determine and understand these contributions. To do this, one needs simultaneous access to multiple cell types and population brain output in functionally relevant states. This is extremely challenging to do with experiments alone, and here we use mathematical models of different types to gain insight into the contributions of the different inhibitory cell types. We focus on theta and gamma rhythms in the hippocampus and use a previously developed detailed model to develop precise hypotheses of how these rhythms are generated and coupled. We find critical contributions by four different cell types - pyramidal cells, parvalbumin-expressing (PV+) basket cells (BCs), cholecystokinin-expressing (CCK+) BCs and bistratified cells. We develop a reduced population rate model (PRM) based on these hypotheses and do extensive explorations and visualizations of the PRM to obtain testable predictions. We find that CCK+BCs exhibit a much higher degree of control relative to PV+BCs for theta or gamma rhythm dominance and thus their coupling, and that coupling from PV+BCs to CCK+BCs more strongly affects theta frequencies relative to coupling from CCK+BCs to PV+BCs. As it is now possible to target these specific inhibitory cell types in the behaving animal, experimentally testing these hypotheses and predictions would be possible. Moreover, our work shows that a variety of mathematical model types creates new insights that would not be revealed with a single model type.