Experimental and theoretical studies demonstrate that neuronal gamma oscillations crucially depend on interneurons, but current models do not consider the diversity of known interneuron subtypes. Moreover, in CA1 of the hippocampus, experimental evidence indicates the presence of multiple gamma oscillators, two of which may be coordinated by differing interneuron populations. In this article, we show that models of networks with competing interneuron populations with different postsynaptic effects are sufficient to generate, within CA1, distinct oscillatory regimes. We find that strong mutual inhibition between the interneuron populations permits distinct fast and slow gamma states, whereas weak mutual inhibition generates mixed gamma states. We develop idealized firing rate models to illuminate dynamic properties of these competitive gamma networks, and reinforce these concepts with basic spiking models. The models make several explicit predictions about gamma oscillators in CA1. Specifically, interneurons of different subtype phase-lock to different gamma states, and one population of interneurons is silenced and the other active during fast and slow gamma events. Finally, mutual inhibition between interneuron populations is necessary to generate distinct gamma states. Previous experimental studies indicate that fast and slow gamma oscillations reflect different information processing modes, although it is unclear whether these rhythms are intrinsic or imposed. The models outlined demonstrate that basic architectures can locally generate these oscillations, as well as capture other features of fast and slow gamma, including theta-phase preference and spontaneous transitions between gamma states. These models may extend to describe general dynamics in networks with diverse interneuron populations. The oscillatory coordination of neural signals is crucial to healthy brain function. We have developed an idealized neuronal model that generates distinct fast and slow gamma oscillations, a known feature of the rodent hippocampus. Our work provides a mechanism of this phenomenon, as well as a theoretical framework for future experiments concerning hippocampal gamma. It moreover offers a tractable model of competitive gamma oscillations that is generalizable across the nervous system.

Gamma oscillations are readily observed in a variety of brain regions during both waking and sleeping states. Computational models of gamma oscillations typically involve simulations of large networks of synaptically coupled spiking units. These networks can exhibit strongly synchronized gamma behavior, whereby neurons fire in near synchrony on every cycle, or weakly modulated gamma behavior, corresponding to stochastic, sparse firing of the individual units on each cycle of the population gamma rhythm. These spiking models offer valuable biophysical descriptions of gamma oscillations; however, because they involve many individual neuronal units they are limited in their ability to communicate general network-level dynamics. Here we demonstrate that few-variable firing rate models with established synaptic timescales can account for both strongly synchronized and weakly modulated gamma oscillations. These models go beyond the classical formulations of rate models by including at least two dynamic variables per population: firing rate and synaptic activation. The models’ flexibility to capture the broad range of gamma behavior depends directly on the timescales that represent recruitment of the excitatory and inhibitory firing rates. In particular, we find that weakly modulated gamma oscillations occur robustly when the recruitment timescale of inhibition is faster than that of excitation. We present our findings by using an extended Wilson-Cowan model and a rate model derived from a network of quadratic integrate-and-fire neurons. These biophysical rate models capture the range of weakly modulated and coherent gamma oscillations observed in spiking network models, while additionally allowing for greater tractability and systems analysis. NEW & NOTEWORTHY Here we develop simple and tractable models of gamma oscillations, a dynamic feature observed throughout much of the brain with significant correlates to behavior and cognitive performance in a variety of experimental contexts. Our models depend on only a few dynamic variables per population, but despite this they qualitatively capture features observed in previous biophysical models of gamma oscillations that involve many individual spiking units.

Highlights d Compass-like MEC head-direction cell tuning can degrade during effective navigation d MEC head-direction cells encode a consistent, internally organized direction sense d The MEC-encoded direction sense inconsistently registers to environmental landmarks d MEC-based navigation operates like an etak (variably oriented) system rather than a GPS

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