Spontaneous variability in gamma dynamics described by a damped harmonic oscillator driven by noise

Circuits of excitatory and inhibitory neurons generate gamma-rhythmic activity (30–80 Hz). Gamma-cycles show spontaneous variability in amplitude and duration. To investigate the mechanisms underlying this variability, we recorded local-field-potentials (LFPs) and spikes from awake macaque V1. We developed a noise-robust method to detect gamma-cycle amplitudes and durations, which showed a weak but positive correlation. This correlation, and the joint amplitude-duration distribution, is well reproduced by a noise-driven damped harmonic oscillator. This model accurately fits LFP power-spectra, is equivalent to a linear, noise-driven E-I circuit, and recapitulates two additional features of gamma: (1) Amplitude-duration correlations decrease with oscillation strength; (2) amplitudes and durations exhibit strong and weak autocorrelations, respectively, depending on oscillation strength. Finally, longer gamma-cycles are associated with stronger spike-synchrony, but lower spike-rates in both (putative) excitatory and inhibitory neurons. In sum, V1 gamma-dynamics are well described by the simplest possible model of gamma: A damped harmonic oscillator driven by noise.