Theta-gamma coupling: a nonlinear dynamical model

Abstract

Cross-frequency coupling in the hippocampus has been hypothesized to support higher-cognition functions. While gamma modulation by theta is widely accepted, evidence of phase-coupling between the two frequency components is so far unconvincing. Our observations show that theta and gamma energy increases with rat speed, while the overall nonlinearity of the LFP trace also increases, suggesting that energy flow is fundamental for hippocampal dynamics. This contradicts current representations based on the Kuramoto phase model. Therefore, we propose a new approach, based on the three-wave equation, a universally-valid nonlinear-physics paradigm that synthesizes the effects of leading order, quadratic nonlinearity. The paradigm identifies bispectral analysis as the natural tool for investigating LFP cross-frequency coupling. Our results confirm the effectiveness of the approach by showing unambiguous coupling between theta and gamma. Bispectra features agree with predictions of the three-wave model, supporting the conclusion that cross-frequency coupling is a manifestation of nonlinear energy transfers.