Theta-gamma cross-frequency coupling enables covariance between distant brain regions

Cross-frequency coupling (CFC) is thought to play an important role in communication across distant brain regions. However, neither the mechanism of its generation nor the influence on the underlying spiking dynamics is well understood. Here, we investigate the dynamics of two interacting distant neuronal modules coupled by inter-regional long-range connections. Each neuronal module comprises an excitatory and inhibitory population of quadratic integrate-and-fire neurons connected locally with conductance-based synapses. The two modules are coupled reciprocally with delays that represent the long-range conduction time. We applied the Ott-Antonsen ansatz to reduce the spiking dynamics to the corresponding mean field equations as a small set of delay differential equations. Bifurcation analysis on these mean field equations shows inter-regional conduction delay is sufficient to produce CFC via a torus bifurcation. Spike correlation analysis during the CFC revealed that several local clusters exhibit synchronized firing in gamma-band frequencies. These clusters exhibit locally decorrelated firings between the cluster pairs within the same population. In contrast, the clusters exhibit long-range gamma-band cross-covariance between the distant clusters that have similar firing frequency. The interactions of the different gamma frequencies produce a beat leading to population-level CFC. We analyzed spike counts in relation to the phases of the macroscopic fast and slow oscillations and found population spike counts vary with respect to macroscopic phases. Such firing phase preference accompanies a phase window with high spike count and low Fano factor, which is suitable for a population rate code. Our work suggests the inter-regional conduction delay plays a significant role in the emergence of CFC and the underlying spiking dynamics may support long-range communication and neural coding.