A curved manifold orients rotational dynamics in motor cortex
During reaching, neurons in motor cortex exhibit complex, time-varying activity patterns. Though single-neuron activity correlates with movement parameters, movement correlations explain neural activity only partially. Neural responses also reflect population-level dynamics thought to generate outputs. These dynamics have previously been described as "rotational", such that activity orbits in neural state space. Here, we find two essential features previously missed. First, the planes in which rotations occur differ for different reaches. Second, this variation in planes reflects the overall location of activity in neural state space. Our "location-dependent rotations" model fits nearly all motor cortex activity during reaching and enables higher-quality decoding of reach kinematics from single-trial spiking. Varying rotational planes allows motor cortex to more simply produce richer outputs than possible under previous models. Finally, our model links representational and dynamical ideas: a representation-like signal is present as the state space location, which dynamics then convert into time-varying command signals.