Cross frequency coupling in next generation inhibitory neural mass models

Abstract

Coupling among neural rhythms is one of the most important mechanisms at the basis of cognitive processes in the brain. In this study we consider a neural mass model, rigorously obtained from the microscopic dynamics of an inhibitory spiking network with exponential synapses, able to autonomously generate collective oscillations (COs). These oscillations emerge via a super-critical Hopf bifurcation, and their frequencies are controlled by the synaptic time scale, the synaptic coupling and the excitability of the neural population. Furthermore, we show that two inhibitory populations in a master-slave configuration with different synaptic time scales can display various collective dynamical regimes: namely, damped oscillations towards a stable focus, periodic and quasi-periodic oscillations, and chaos. Finally, when bidirectionally coupled the two inhibitory populations can exhibit different types of{theta} -{gamma} cross-frequency couplings (CFCs): namely, phase-phase and phase-amplitude CFC. The coupling between{theta} and{gamma} COs is enhanced in presence of a external{theta} forcing, reminiscent of the type of modulation induced in Hippocampal and Cortex circuits via optogenetic drive.\n\nIn healthy conditions, the brains activity reveals a series of intermingled oscillations, generated by large ensembles of neurons, which provide a functional substrate for information processing. How single neuron properties influence neuronal population dynamics is an unsolved question, whose solution could help in the understanding of the emergent collective behaviors arising during cognitive processes. Here we consider a neural mass model, which reproduces exactly the macroscopic activity of a network of spiking neurons. This mean-field model is employed to shade some light on an important and ubiquitous neural mechanism underlying information processing in the brain: the{theta} -{gamma} cross-frequency coupling. In particular, we will explore in detail the conditions under which two coupled inhibitory neural populations can generate these functionally relevant coupled rhythms.