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

Circuits of excitatory and inhibitory neurons can generate rhythmic activity in the gamma frequency-range (30-80Hz). Individual gamma-cycles show spontaneous variability in amplitude and duration. The mechanisms underlying this variability are not fully understood. We recorded local-field-potentials (LFPs) and spikes from awake macaque V1, and developed a noise-robust method to detect gamma-cycle amplitudes and durations. Amplitudes and durations showed a weak but positive correlation. This correlation, and the joint amplitude-duration distribution, is well reproduced by a dampened harmonic oscillator driven by stochastic noise. We show that this model accurately fits LFP power spectra and is equivalent to a linear PING (Pyramidal Interneuron Network Gamma) circuit. The model recapitulates two additional features of V1 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 linear harmonic oscillator driven by noise.