Abstract
The Wilson-Cowan model can emulate gamma oscillations, and thus is extensively used to research the generation of gamma oscillations closely related to cognitive functions. Previous studies have revealed that excitatory and inhibitory inputs to the model can modulate its gamma oscillations. Inhibitory and excitatory self-feedback loops are important structural features of the model, however, its functional role in the regulation of gamma oscillations in the model is still unclear. In the present study, bifurcation analysis and spectrum analysis are employed to elucidate the regulating mechanism of gamma oscillations underlined by the inhibitory and excitatory self-feedback loops, especially how the two self-feedback loops cooperate to generate the gamma oscillations and regulate the oscillation frequency. The present results reveal that, on one hand, the inhibitory self-feedback loop is not conducive to the generation of gamma oscillations, and increased inhibitory self-feedback strength facilitates the enhancement of the oscillation frequency. On the other hand, the excitatory self-feedback loop promotes the generation of gamma oscillations, and increased excitatory self-feedback strength leads to the decrease of oscillation frequency. Finally, theoretical analysis is conducted to provide explain on how the two self-feedback loops play a crucial role in the generation and regulation of neural oscillations in the model. To sum up, Inhibitory and excitatory self-feedback loops play a complementary role in generating and regulating the gamma oscillation in Wilson-Cowan model, and cooperate to bidirectionally regulate the gamma-oscillation frequency in a more flexible manner. These results might provide testable hypotheses for future experimental research.
Highlights
Gamma oscillation is a rhythmic electrical activity ranged from 30 to 80 Hz (Buzsáki, 2009; Wang et al, 2011), which is widely present in the thalamus, cortex and hippocampus of animal and human brains (Womelsdorf and Fries, 2007), and is closely related to the cognitive function of animals and humans (Gevins et al, 1997; Engel et al, 2001; Bartos et al, 2007; Cabral et al, 2014)
In the section “Results,” by combining bifurcation analysis and spectrum analysis, we explore how inhibitory and excitatory self-feedback loops regulate gamma oscillations, respectively, and especially focus on elucidating the synergistic regulating mechanism underlined by the interaction of the two self-feedback loops
We conduct a one-parameter bifurcation to determine the ranges of inhibitory and excitatory self-feedback strength generating limit cycle oscillations, probing how inhibitory and excitatory self-feedback loops generate gamma oscillations in the Wilson-Cowan model
Summary
Gamma oscillation is a rhythmic electrical activity ranged from 30 to 80 Hz (Buzsáki, 2009; Wang et al, 2011), which is widely present in the thalamus, cortex and hippocampus of animal and human brains (Womelsdorf and Fries, 2007), and is closely related to the cognitive function of animals and humans (Gevins et al, 1997; Engel et al, 2001; Bartos et al, 2007; Cabral et al, 2014). The synaptic connection strength between neurons plays an important role in the generation of gamma oscillations. Ray and Maunsell (2011) recorded local field potential (LPF) in the V1 brain area of rhesus monkeys to detect the origin of oscillations in different gamma bands. Ray et al (2013) studied the effect of excitation and inhibition balance on gamma oscillations by recording the local field potential (LPF) in the MT area of rhesus monkeys, and found that visual stimuli would change the balance of excitability and inhibitory activity, and adjust the gamma oscillations. Recent experimental studies have shown that visual stimuli plays an important role in inducing gamma oscillations and frequency modulation (Chen et al, 2017, 2020; Saleem et al, 2017; Veit et al, 2017; Welle and Contreras, 2017). Veit et al (2017) used optogenetic technology to conduct mouse experiments and found that SOM (somatostatin) cells were stimulated to induce gamma oscillations, and inhibitory SOM cells would decrease the energy of gamma oscillations
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