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.Comment: 13 pages, 4 figure

Phase Dependent Sign Changes of GABAergic Synaptic Input Explored In-Silicio and In-Vitro

Abstract. Inhibitory interactions play a crucial role in the synchronization of neuronal activity. Here we investigate the effect of GABAergic PSPs on spike timing in cortical neurons that exhibit an oscillatory modulation of their membrane potential. To this end we combined numerical simulations with in-vitro patch-clamp recordings from layer II/III pyramidal cells of the rat visual cortex. Special emphasis was placed on exploring how the reversal potential of the GABAergic synaptic currents (EGABA) and the phase relations of the PSPs relative to the oscillation cycles affect the timing of spikes riding on the depolarizing peaks of the oscillations. The simulations predicted: (1) With EGABA more negative than the oscillation minima PSPs are hyperpolarizing at all phases and thus delay or prevent spikes. (2) With EGABA being more positive than the oscillation maxima PSPs are depolarizing in a phase-independent way and lead to a phase advance of spikes. (3) In the intermediate case where EGABA lies within oscillation maxima and minima PSPs are either hyper- or depolarizing depending on their phase relations to the Vm oscillations and can therefore either delay or advance spikes. Experiments conducted in this most interesting last configuration with biphasic PSPs agreed with the model predictions. Additional theoretical investigations revealed the effect of these PSP induced shifts in spike timing on synchronization in neuronal circuits. The results suggest that GABAergic mechanisms can assume highly specific timing functions in oscillatory networks