Empirically constrained network models for contrast-dependent modulation of gamma rhythm in V1

Gamma oscillations are thought to play a key role in neuronal network function and neuronal communication, yet the underlying generating mechanisms have not been fully elucidated to date. At least partly, this may be due to the fact that even in simple network models of interconnected inhibitory (I) and excitatory (E) neurons, many parameters remain unknown and are set based on practical considerations or by convention. Here, we mitigate this problem by requiring PING (Pyramidal Interneuron Network Gamma) models to simultaneously satisfy a broad set of criteria for realistic behaviour based on empirical data spanning both the single unit (spikes) and local population (LFP) levels while unknown parameters are varied. By doing so, we were able to constrain the parameter ranges and select empirically valid models. The derived model constraints implied weak rather than strong PING as the generating mechanism for gamma, connectivity between E and I neurons within specific bounds, and variations of the external input to E but not I neurons. Constrained models showed valid behaviours, including gamma frequency increases with contrast and power saturation or decay at high contrasts. Using an empirically-validated model we studied the route to gamma instability at high contrasts. This involved increased heterogeneity of E neurons with increasing input triggering a breakdown of I neuron pacemaker function. Further, we illustrate the model's capacity to resolve disputes in the literature concerning gamma oscillation properties and GABA conductance proxies. We propose that the models derived in our study will be useful for other modelling studies, and that our approach to the empirical constraining of PING models can be expanded when richer empirical datasets become available. As local gamma networks are the building blocks of larger networks that aim to understand complex cognition through their interactions, there is considerable value in improving our models of these building blocks.