Reach-dependent reorientation of rotational dynamics in motor cortex

Abstract

Controlling arm movements requires complex, time-varying patterns of muscle activity. Accordingly, the responses of neurons in motor cortex are complex, time-varying, and heterogeneous during reaching. When examined at the population level, patterns of neural activity evolve over time according to dynamical rules. During reaching, these rules have been argued to be "rotational" or variants thereof, 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.

Motor cortex activity across movement speeds is predicted by network-level strategies for generating muscle activity

“…These findings are consistent with suggestions regarding how a circuit can generate multiple behaviors ( Briggman and Kristan, 2008 ) and with empirical and network solutions across distinct behaviors such as forward and backward cycling ( Russo et al, 2018 ) or cycling with one arm versus the other ( Ames and Churchland, 2019 ). The present results indicate that the same principle – ‘tilting’ into different dimensions to alter motor output – is operative when continuously adjusting a specific behavior (also see [ Sabatini and Kaufman, 2021 ]). Yet while the separation across individual-speed trajectories was sufficient to aid low tangling, it was modest enough to allow solutions to remain related.…”

Irrational choices via a curvilinear representational geometry for value

“…The idea that curvature can exist even in a circumstance where it compromises behavior lends credence to the notion that curvature is a ubiquitous feature of the population encoding of any linear variable. This study stands alongside growing evidence for curved representational geometries across several brain structures for several linear variables, including those underlying perceptual decisions (Okazawa et al 2021), motor control (Sabatini and Kaufman 2021) and interval reproduction (Sohn et al 2019). Given a bounded dynamic range of neuronal firing rates, curvature could be a powerful way to maximize information coding (Okazawa et al 2021).…”

“…Curvature emerges naturally from fundamental constraints on the dynamic range of neuronal firing rates (i.e. the absolute lower bound at zero and an upper bound at the neuron’s metabolic limits; Okazawa et al 2021) and appears even in tasks where there is no natural alignment with any difficulty axis (Sohn et al 2019; Sabatini and Kaufman 2021). Further, even when the axis of curvature aligns with task difficulty, position along the “difficulty” axis does not appear to predict animals’ self-reported confidence in their decisions (Okazawa et al 2021).…”

Emergent neural dynamics and geometry for generalization in a transitive inference task

“…While a non-rotational solution may also be possible, constraints relevant to neurobiology (e.g. metabolic efficiency or the dimensionality of outputs) may favor rotational solutions [103, 128, 117, 129]. Notably, we used the generalized idea of rotational transformation during the delay to identify an additional neural prediction distinguishing RNN variants (mean angle change, Fig.…”