A curved manifold orients rotational dynamics in motor cortex

Summary

Controlling 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.