A curved manifold orients rotational dynamics in motor cortex

SummaryControlling arm movements requires complex, time-varying patterns of muscle activity 1,2. Accordingly, the responses of neurons in motor cortex are complex, time-varying, and heterogeneous during reaching 2–4. When examined at the population level, patterns of neural activity evolve over time according to dynamical rules 5,6. During reaching, these rules have been argued to be “rotational” 7 or variants thereof 8,9, containing coordinated oscillations in the spike rates of individual neurons. While these models capture key aspects of the neural responses, they fail to capture others – accounting for only 20-50% of the neural response variance. Here, we consider a broader class of dynamical models. We find that motor cortex dynamics take an unexpected form: there were 3-4 rotations at fixed frequencies in M1 and PMd explaining more than 90% of neural responses, but these rotations occurred in different portions of state space when movements differ. These rotations appear to reflect a curved manifold of fixed points in state space, around which dynamics are locally rotational. These fixed-frequency rotations obeyed a simple relationship with movement: the orientation of rotations in motor cortex activity were related almost linearly to the movement the animal made, allowing linear decoding of reach kinematic time-courses on single trials. This model constitutes a fundamentally novel way to consider pattern generation: like placing a record player in a large bowl, the frequency of activity is fixed, but the location of motor cortex activity on a curved manifold sets the orientation of locally-rotational dynamics. This system simplifies motor control, helps reconcile conflicting frameworks for interpreting motor cortex, and enables greatly improved neural decoding.