The ability to extract the regular pulse in music and to respond in synchrony to this pulse is called beat synchronization and is a natural human behavior exhibited during dancing and musical ensemble playing. In this study we recorded the simultaneous activity of hundreds of cells in the medial premotor areas during a rhythmic tapping task where monkeys synchronized their movements to a visual or auditory metronome whose tempo changed from trial to trial. The aim was to determine how the geometry and kinematics of state-space neural population trajectories controlled the rhythmic timing behavior.

We found that more than half of the recorded neurons were engaged in the task, showing selective responses that multiplexed the sequential and temporal structure of rhythmic tapping. Notably, we also found subpopulations of neurons that were selective to the metronome’s modality. These complex and time-varying single-cell response profiles produced rotatory population neural trajectories that showed the following properties. First, a complete circular loop was formed for each produced interval, converging to a similar state-space point close to the tapping time. Second, these oscillatory trajectories did not overlap across durations, a signature of temporal scaling; instead, they showed a linear increase in their radius and a constant linear speed as a function of the target interval. In fact, the amplitude of the neural trajectories was closely related to the produced intervals on a trial by trial basis. Finally, the geometry of neural trajectories was consistent with a mechanism where the initial condition of the cortical dynamics is adjusted by the modality of the metronome, so that the trajectories evolved with similar kinematics but in different state space coordinates for the auditory and visual conditions. These results support the notion that the premotor areas work as dynamic system to represent different aspects of rhythmic timing behaviors.

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