Tensor Analysis Reveals Distinct Population Structure that Parallels the Different Computational Roles of Areas M1 and V1.

Cortical firing rates frequently display elaborate and heterogeneous temporal structure. One often wishes to compute quantitative summaries of such structure-a basic example is the frequency spectrum-and compare with model-based predictions. The advent of large-scale population recordings affords the opportunity to do so in new ways, with the hope of distinguishing between potential explanations for why responses vary with time. We introduce a method that assesses a basic but previously unexplored form of population-level structure: when data contain responses across multiple neurons, conditions, and times, they are naturally expressed as a third-order tensor. We examined tensor structure for multiple datasets from primary visual cortex (V1) and primary motor cortex (M1). All V1 datasets were 'simplest' (there were relatively few degrees of freedom) along the neuron mode, while all M1 datasets were simplest along the condition mode. These differences could not be inferred from surface-level response features. Formal considerations suggest why tensor structure might differ across modes. For idealized linear models, structure is simplest across the neuron mode when responses reflect external variables, and simplest across the condition mode when responses reflect population dynamics. This same pattern was present for existing models that seek to explain motor cortex responses. Critically, only dynamical models displayed tensor structure that agreed with the empirical M1 data. These results illustrate that tensor structure is a basic feature of the data. For M1 the tensor structure was compatible with only a subset of existing models.

Motor Cortex Embeds Muscle-like Commands in an Untangled Population Response.

Primate motor cortex projects to spinal interneurons and motoneurons, suggesting that motor cortex activity may be dominated by muscle-like commands. Observations during reaching lend support to this view, but evidence remains ambiguous and much debated. To provide a different perspective, we employed a novel behavioral paradigm that facilitates comparison between time-evolving neural and muscle activity. We found that single motor cortex neurons displayed many muscle-like properties, but the structure of population activity was not muscle-like. Unlike muscle activity, neural activity was structured to avoid "tangling": moments where similar activity patterns led to dissimilar future patterns. Avoidance of tangling was present across tasks and species. Network models revealed a potential reason for this consistent feature: low tangling confers noise robustness. Finally, we were able to predict motor cortex activity from muscle activity by leveraging the hypothesis that muscle-like commands are embedded in additional structure that yields low tangling.

Behaviorally Selective Engagement of Short-Latency Effector Pathways by Motor Cortex.

Blocking motor cortical output with lesions or pharmacological inactivation has identified movements that require motor cortex. Yet, when and how motor cortex influences muscle activity during movement execution remains unresolved. We addressed this ambiguity using measurement and perturbation of motor cortical activity together with electromyography in mice during two forelimb movements that differ in their requirement for cortical involvement. Rapid optogenetic silencing and electrical stimulation indicated that short-latency pathways linking motor cortex with spinal motor neurons are selectively activated during one behavior. Analysis of motor cortical activity revealed a dramatic change between behaviors in the coordination of firing patterns across neurons that could account for this differential influence. Thus, our results suggest that changes in motor cortical output patterns enable a behaviorally selective engagement of short-latency effector pathways. The model of motor cortical influence implied by our findings helps reconcile previous observations on the function of motor cortex.

The Largest Response Component in the Motor Cortex Reflects Movement Timing but Not Movement Type.

Neural activity in monkey motor cortex (M1) and dorsal premotor cortex (PMd) can reflect a chosen movement well before that movement begins. The pattern of neural activity then changes profoundly just before movement onset. We considered the prediction, derived from formal considerations, that the transition from preparation to movement might be accompanied by a large overall change in the neural state that reflects when movement is made rather than which movement is made. Specifically, we examined "components" of the population response: time-varying patterns of activity from which each neuron's response is approximately composed. Amid the response complexity of individual M1 and PMd neurons, we identified robust response components that were "condition-invariant": their magnitude and time course were nearly identical regardless of reach direction or path. These condition-invariant response components occupied dimensions orthogonal to those occupied by the "tuned" response components. The largest condition-invariant component was much larger than any of the tuned components; i.e., it explained more of the structure in individual-neuron responses. This condition-invariant response component underwent a rapid change before movement onset. The timing of that change predicted most of the trial-by-trial variance in reaction time. Thus, although individual M1 and PMd neurons essentially always reflected which movement was made, the largest component of the population response reflected movement timing rather than movement type.