Visual cortical LFP in relation to the hippocampal theta rhythm in track running rats.

Theta oscillations in the primary visual cortex (VC) have been observed during running tasks, but the mechanism behind their generation is not well understood. Some studies have suggested that theta in the VC is locally generated, while others have proposed that it is volume conducted from the hippocampus. The present study aimed to investigate the relationship between hippocampal and VC LFP dynamics. Analysis of power spectral density revealed that LFP in the VC was similar to that in the hippocampus, but with lower overall magnitude. As running velocity increased, both the power and frequency of theta and its harmonics increased in the VC, similarly to what is observed in the hippocampus. Current source density analysis triggered to theta did not identify distinct current sources and sinks in the VC, supporting the idea that theta in the VC is conducted from the adjacent hippocampus. Phase coupling between theta, its harmonics, and gamma is a notable feature in the hippocampus, particularly in the lacunosum moleculare. While some evidence of coupling between theta and its harmonics in the VC was found, bicoherence estimates did not reveal significant phase coupling between theta and gamma. Similar results were seen in the cross-region bicoherence analysis, where theta showed strong coupling with its harmonics with increasing velocity. Thus, theta oscillations observed in the VC during running tasks are likely due to volume conduction from the hippocampus.

Nonlinear Theta-Gamma Coupling between the Anterior Thalamus and Hippocampus Increases as a Function of Running Speed.

The hippocampal theta rhythm strongly correlates to awake behavior leading to theories that it represents a cognitive state of the brain. As theta has been observed in other regions of the Papez circuit, it has been theorized that activity propagates in a reentrant manner. These observations complement the energy cascade hypothesis in which large-amplitude, slow-frequency oscillations reflect activity propagating across a large population of neurons. Higher frequency oscillations, such as gamma, are related to the speed with which inhibitory and excitatory neurons interact and distribute activity on the local level. The energy cascade hypothesis suggests that the larger anatomic loops, maintaining theta, drive the smaller loops. As hippocampal theta increases in power with running speed, so does the power and frequency of the gamma rhythm. If theta is propagated through the circuit, it stands to reason that the local field potential (LFP) recorded in other regions would be coupled to the hippocampal theta, with the coupling increasing with running speed. We explored this hypothesis using open-source simultaneous recorded data from the CA1 region of the hippocampus and the anterior dorsal and anterior ventral thalamus. Cross-regional theta coupling increased with running speed. Although the power of the gamma rhythm was lower in the anterior thalamus, there was an increase in the coupling of hippocampal theta to anterior thalamic gamma. Broadly, the data support models of how activity moves across the nervous system, suggesting that the brain uses large-scale volleys of activity to support higher cognitive processes.

Theta dominates cross-frequency coupling in hippocampal-medial entorhinal circuit during awake-behavior in rats.

Hippocampal theta and gamma rhythms are hypothesized to play a role in the physiology of higher cognition. Prior research has reported that an offset in theta cycles between the entorhinal cortex, CA3, and CA1 regions promotes independence of population activity across the hippocampus. In line with this idea, it has recently been observed that CA1 pyramidal cells can establish and maintain coordinated place cell activity intrinsically, with minimal reliance on afferent input. Counter to these observations is the contemporary hypothesis that CA1 neuron activity is driven by a gamma oscillation arising from the medial entorhinal cortex (MEC) that relays information by providing precisely timed synchrony between MEC and CA1. Reinvestigating this in rats during appetitive track running, we found that theta is the dominant frequency of cross-frequency coupling between the MEC and hippocampus, with hippocampal gamma largely independent of entorhinal gamma.

Spectrum Degradation of Hippocampal LFP During Euthanasia.

The hippocampal local field potential (LFP) exhibits a strong correlation with behavior. During rest, the theta rhythm is not prominent, but during active behavior, there are strong rhythms in the theta, theta harmonics, and gamma ranges. With increasing running velocity, theta, theta harmonics and gamma increase in power and in cross-frequency coupling, suggesting that neural entrainment is a direct consequence of the total excitatory input. While it is common to study the parametric range between the LFP and its complementing power spectra between deep rest and epochs of high running velocity, it is also possible to explore how the spectra degrades as the energy is completely quenched from the system. Specifically, it is unknown whether the 1/f slope is preserved as synaptic activity becomes diminished, as low frequencies are generated by large pools of neurons while higher frequencies comprise the activity of more local neuronal populations. To test this hypothesis, we examined rat LFPs recorded from the hippocampus and entorhinal cortex during barbiturate overdose euthanasia. Within the hippocampus, the initial stage entailed a quasi-stationary LFP state with a power-law feature in the power spectral density. In the second stage, there was a successive erosion of power from high- to low-frequencies in the second stage that continued until the only dominant remaining power was <20 Hz. This stage was followed by a rapid collapse of power spectrum toward the absolute electrothermal noise background. As the collapse of activity occurred later in hippocampus compared with medial entorhinal cortex, it suggests that the ability of a neural network to maintain the 1/f slope with decreasing energy is a function of general connectivity. Broadly, these data support the energy cascade theory where there is a cascade of energy from large cortical populations into smaller loops, such as those that supports the higher frequency gamma rhythm. As energy is pulled from the system, neural entrainment at gamma frequency (and higher) decline first. The larger loops, comprising a larger population, are fault-tolerant to a point capable of maintaining their activity before a final collapse.

An investigation into the nonlinear coupling between CA1 layers and the dentate gyrus.

Although the activity from the dentate gyrus is known to have strong connections with other hippocampal layers, the functionality of these connections, that is, the degree to which it drives activity in the downstream regions of the hippocampus, is not well understood. This question is particularly relevant for mesoscale localfield potential (LFP) rhythms such as gamma oscillations. Following the hypothesis that fundamental features of the LFP are consistent with turbulent dynamics, we investigate the crosslayer relationship between the CA1 layers and the dentate gyrus as a function of running speed. In agreement with previous studies, same-layer spectral and bispectral analyses show that increasing input (rat speed) results in an increase of power and nonlinearity (phase coupling) between theta and gamma. The effectiveness of the connection between the 2 regions is investigated using cross-bicoherence analysis. Based on the turbulence interpretation of the evolution of spectra and bispectra as a function of the power input rate, we propose a measure for estimating the strength of the cross-frequency, cross-layer nonlinear forcing, that compares the magnitude of bicoherence (same-layer) and cross-bicoherence (cross-layer). Our results suggest that at moderate speeds gamma in CA1 is mainly driven by local theta, while the coupling of the CA1 gamma to the dentate-gyrus gamma becomes significant. Overall, these data are consistent with the hypothesis of theta-to-gamma energy cascade model for the organization of hippocampal LFP, with theta playing the role of a global pacemaker across the entire hippocampus while gamma is a local oscillation generated by through local anatomical connections. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Wave Turbulence and Energy Cascade in the Hippocampus.

Mesoscale cortical activity can be defined as the organization of activity of large neuron populations into collective action, forming time-dependent patterns such as traveling waves. Although collective action may play an important role in the cross-scale integration of brain activity and in the emergence of cognitive behavior, a comprehensive formulation of the laws governing its dynamics is still lacking. Because collective action processes are macroscopic with respect to neuronal activity, these processes cannot be described directly with methods and models developed for the microscale (individual 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 field 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 non-linearity of collective action (e.g., theta and gamma rhythms) increase with increased speed. Our results show that collective-action dynamics are stochastic (the precise state of a single neuron is irrelevant), weakly non-linear, and weakly dissipative. These are the principles of the theory of weak turbulence. Therefore, we propose weak turbulence a theoretical framework for the description of mesoscopic activity in the hippocampus. The weak turbulence framework provides a complete description of the cross-scale energy exchange (the energy cascade). It uncovers the mechanism governing major features of LFP spectra and bispectra, such as the physical meaning of the exponent α of power-law LFP spectra (e.g., f -α, where f is the frequency), the strengthening of theta-gamma coupling with energy input into the hippocampus, as well as specific phase lags associated with their interaction. Remarkably, the weak turbulence framework is consistent with the theory of self organized criticality, which provides a simple explanation for the existence of the power-law background spectrum. Together with self-organized criticality, weak turbulence could provide a unifying approach to modeling the dynamics of mesoscopic activity.

Movement Enhances the Nonlinearity of Hippocampal Theta.

The nonlinear, metastable dynamics of the brain are essential for large-scale integration of smaller components and for the rapid organization of neurons in support of behavior. Therefore, understanding the nonlinearity of the brain is paramount for understanding the relationship between brain dynamics and behavior. Explicit quantitative descriptions of the properties and consequences of nonlinear neural networks, however, are rare. Because the local field potential (LFP) reflects the total activity across a population of neurons, nonlinearites of the nervous system should be quantifiable by examining oscillatory structure. We used high-order spectral analysis of LFP recorded from the dorsal and intermediate regions of the rat hippocampus to show that the nonlinear character of the hippocampal theta rhythm is directly related to movement speed of the animal. In the time domain, nonlinearity is expressed as the development of skewness and asymmetry in the theta shape. In the spectral domain, nonlinear dynamics manifest as the development of a chain of harmonics statistically phase coupled to the theta oscillation. This evolution was modulated across hippocampal regions, being stronger in the dorsal CA1 relative to more intermediate areas. The intensity and timing of the spiking activity of pyramidal cells and interneurons was strongly correlated to theta nonlinearity. Because theta is known to propagate from dorsal to ventral regions of the hippocampus, these data suggest that the nonlinear character of theta decreases as it travels and supports a hypothesis that activity dissipates along the longitudinal axis of the hippocampus. SIGNIFICANCE STATEMENT: We describe the first explicit quantification regarding how behavior enhances the nonlinearity of the nervous system. Our findings demonstrate uniquely how theta changes with increasing speed due to the altered underlying neuronal dynamics and open new directions of research on the relationship between single-neuron activity and propagation of theta through the hippocampus. This work is significant because it will encourage others to consider the nonlinear nature of the nervous system and higher-order spectral analyses when examining oscillatory interactions.