Abstract
Oscillations in the beta/low gamma range (10–45 Hz) are recorded in diverse neural structures. They have successfully been modeled as sparsely synchronized oscillations arising from reciprocal interactions between randomly connected excitatory (E) pyramidal cells and local interneurons (I). The synchronization of spatially distant oscillatory spiking E–I modules has been well-studied in the rate model framework but less so for modules of spiking neurons. Here, we first show that previously proposed modifications of rate models provide a quantitative description of spiking E–I modules of Exponential Integrate-and-Fire (EIF) neurons. This allows us to analyze the dynamical regimes of sparsely synchronized oscillatory E–I modules connected by long-range excitatory interactions, for two modules, as well as for a chain of such modules. For modules with a large number of neurons (> 105), we obtain results similar to previously obtained ones based on the classic deterministic Wilson-Cowan rate model, with the added bonus that the results quantitatively describe simulations of spiking EIF neurons. However, for modules with a moderate (~ 104) number of neurons, stochastic variations in the spike emission of neurons are important and need to be taken into account. On the one hand, they modify the oscillations in a way that tends to promote synchronization between different modules. On the other hand, independent fluctuations on different modules tend to disrupt synchronization. The correlations between distant oscillatory modules can be described by stochastic equations for the oscillator phases that have been intensely studied in other contexts. On shorter distances, we develop a description that also takes into account amplitude modes and that quantitatively accounts for our simulation data. Stochastic dephasing of neighboring modules produces transient phase gradients and the transient appearance of phase waves. We propose that these stochastically-induced phase waves provide an explanative framework for the observations of traveling waves in the cortex during beta oscillations.
Highlights
Rhythms and collective oscillations at different frequencies are ubiquitous in neural structures (Buzsaki, 2006)
An additional feature of our results as compared to the ones obtained with classical rate-models, is that, as we show, they quantitatively agree with simulations of spiking networks of large size
We choose the neurons in our spiking network simulations to be of the Exponential-Integrate-and-Fire type (EIF) (Fourcaud-Trocmé et al, 2003), which have been shown to describe well the dynamics of cortical neurons (Badel et al, 2008)
Summary
Rhythms and collective oscillations at different frequencies are ubiquitous in neural structures (Buzsaki, 2006). Gamma band oscillations (30–100 Hz) are for instance recorded in the visual cortex as well as several other structures and have been hypothesized to support various functional roles (Fries, 2009). An early study (Prechtl et al, 1997), using widefield imaging and voltage-sensitive dyes, reported that stimulus-induced oscillatory activity around 10 Hz and 20 Hz was organized in plane waves and spiral waves in the turtle cortex. This spiral-like organization was reported for pharmacologically induced 10 Hz oscillations in the rat visual cortex (Huang et al, 2010). The underlying mechanisms and specific cells involved in the synchronization of two distant regions have more recently been investigated using optogenetic manipulations in mice (Veit et al, 2017)
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