Rotational dynamics in motor cortex are consistent with a feedback controller

Recent studies have identified rotational dynamics in motor cortex (MC) which many assume arise from intrinsic connections in MC. However, behavioural and neurophysiological studies suggest that MC behaves like a feedback controller where continuous sensory feedback and interactions with other brain areas contribute substantially to MC processing. We investigated these apparently conflicting theories by building recurrent neural networks that controlled a model arm and received sensory feedback from the limb. Networks were trained to counteract perturbations to the limb and to reach towards spatial targets. Network activities and sensory feedback signals to the network exhibited rotational structure even when the recurrent connections were removed. Furthermore, neural recordings in monkeys performing similar tasks also exhibited rotational structure not only in MC but also in somatosensory cortex. Our results argue that rotational structure may also reflect dynamics throughout the voluntary motor system involved in online control of motor actions.

Dynamics of freely rising spheres: the effect of moment of inertia

The goal of this study is to elucidate the effect the particle moment of inertia (MOI) has on the dynamics of spherical particles rising in a quiescent and turbulent fluid. To this end, we performed experiments with varying density ratios $\varGamma$ , the ratio of the particle density and fluid density, ranging from $0.37$ up to $0.97$ . At each $\varGamma$ the MOI was varied by shifting mass between the shell and the centre of the particle to vary $I^*$ (the particle MOI normalised by the MOI of a particle with the same weight and a uniform mass distribution). Helical paths are observed for low, and ‘three-dimensional (3-D) chaotic’ trajectories at higher values of $\varGamma$ . The present data suggest no influence of $I^*$ on the critical value for this transition $0.42<\varGamma _{{crit}}<0.52$ . For the ‘3-D chaotic’ rise mode, we identify trends of decreasing particle drag coefficient ( $C_d$ ) and amplitude of oscillation with increasing $I^*$ . Due to limited data it remains unclear if a similar dependence exists in the helical regime as well. Path oscillations remain finite for all cases studied and no ‘rectilinear’ mode is encountered, which may be the consequence of allowing for a longer transient distance in the present compared with earlier work. Rotational dynamics did not vary significantly between quiescent and turbulent surroundings, indicating that for the present configuration these are predominantly wake driven.

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.