Turbulence in the Hippocampus: An Ansatz for the Energy Cascade Hypothesis

Abstract

A. Mesoscopic neural activity may play an important role in the cross-scale integration of brain activity and in the emergence of cognitive behavior. Mesoscale activity in the cortex can be de ined as the organization of activity of large populations of neurons into collective actions, such as traveling waves in the hippocampus. A comprehensive description of collective activity is still lacking, in part because it cannot be built directly with methods and models developed for the microscale (individual neurons): the laws governing mesoscale dynamics are different from those governing a few neurons. To identify the characteristic features of mesoscopic dynamics, and to lay the foundations for a theoretical description of mesoscopic activity in the hippocampus, we conduct a comprehensive examination of observational data of hippocampal local ield potential (LFP) recordings. We use the strong correlation between rat running-speed and the LFP power to parameterize the energy input into the hippocampus, and show that both the power, and the nonlinearity of mesoscopic scales of collective action (e.g., theta and gamma rhythms) increase as with energy input. Our results point to a few fundamental characteristics: collective-action dynamics are stochastic (the precise state of a single neuron is irrelevant), weakly nonlinear, and weakly dissipative. These are the principles of the theory of weak turbulence. Therefore, we propose weak turbulence as an ansatz for the development of a theoretical description of mesoscopic activity. The perspective of weak turbulence provides simple and meaningful explanations for the major features observed in the evolution of LFP spectra and bispectra with energy input, such as spectral slopes and their evolution, the increased nonlinear coupling observed between theta and gamma, as well as speci ic phase lags associated with their interaction. The weak turbulence ansatz is consistent with the theory of self organized criticality, which provides a simple explanation for the existence of the powerlaw background spectrum, and could provide a unifying approach to modeling the dynamics of mesoscopic activity.