Movement Enhances the Nonlinearity of Hippocampal Theta

Abstract

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.

Discriminating Valid from Spurious Indices of Phase-Amplitude Coupling

“…This would produce a saw-tooth like shape (Fig. 2 e ), which indeed has been observed in the rat hippocampus (Terrazas et al, 2005; Belluscio et al, 2012; Sheremet et al, 2016) and in electrocorticography recordings in the human motor cortex (Cole et al, 2016). Another possibility is pulses of neuronal activity repeated at a fixed frequency.…”

“…However, the reliability of PAC has recently been questioned since the measure is sensitive to nonsinusoidal properties of the neuronal oscillations (Kramer et al, 2008; Aru et al, 2015). Indeed, recent articles have reported PAC, which can fully be explained by the lower-frequency oscillation, as having a saw-tooth like shape (Cole et al, 2016; Sheremet et al, 2016; Cole and Voytek, 2017). Although these concerns are valid, they do not exclude the existence of a true measure of PAC that is associated with neuronal activity in different frequency bands.…”

“…Therefore, great care must be taken when interpreting measures of PAC, in particular in the frequency bands of the higher harmonics, additionally taking into account the effective frequency smoothing (Kramer et al, 2008; Aru et al, 2015; Cole et al, 2016; Jones, 2016; Lozano-Soldevilla et al, 2016). In particular, Cole et al (2016) and Sheremet et al (2016) provide concrete examples from respective intracranial human and hippocampal rat recordings in which nonsinusoidal oscillations contribute to estimates of PAC.…”

On cross-frequency phase-phase coupling between theta and gamma oscillations in the hippocampus

“…Due to the non-sinusoidal shape of theta (Belluscio et al, 2012; Sheremet et al, 2016), the LFP also exhibited spectral peaks at harmonic frequencies (Figure 7A). We constructed phase–phase plots using LFP components narrowly filtered at theta and its harmonics: 14, 21, 28 and 35 Hz.…”

Mechanisms underlying memory enhancement in humans

“…Furthermore nonstationary processes, such as most neural signals in general, would exhibit spectral correlations missed by a stationary Fourier expansion that could be misinterpreted (Lii & Rosenblatt, 2002). Also recent studies (Cole et al, 2016;Sheremet, Burke, & Maurer, 2016) provided concrete examples of human and rat hippocampal recordings with nonsinusoidal oscillations contributing to PAC estimates. Lower frequency periodic but non sinusoidal signals can be expressed, by their Fourier decompositions, as a weighted sum of harmonics.…”