Neural Population Dynamics during Reaching Are Better Explained by a Dynamical System than Representational Tuning

Recent models of movement generation in motor cortex have sought to explain neural activity not as a function of movement parameters, known as representational models, but as a dynamical system acting at the level of the population. Despite evidence supporting this framework, the evaluation of representational models and their integration with dynamical systems is incomplete in the literature. Using a representational velocity-tuning based simulation of center-out reaching, we show that incorporating variable latency offsets between neural activity and kinematics is sufficient to generate rotational dynamics at the level of neural populations, a phenomenon observed in motor cortex. However, we developed a covariance-matched permutation test (CMPT) that reassigns neural data between task conditions independently for each neuron while maintaining overall neuron-to-neuron relationships, revealing that rotations based on the representational model did not uniquely depend on the underlying condition structure. In contrast, rotations based on either a dynamical model or motor cortex data depend on this relationship, providing evidence that the dynamical model more readily explains motor cortex activity. Importantly, implementing a recurrent neural network we demonstrate that both representational tuning properties and rotational dynamics emerge, providing evidence that a dynamical system can reproduce previous findings of representational tuning. Finally, using motor cortex data in combination with the CMPT, we show that results based on small numbers of neurons or conditions should be interpreted cautiously, potentially informing future experimental design. Together, our findings reinforce the view that representational models lack the explanatory power to describe complex aspects of single neuron and population level activity.Author Summary: The question of how the brain generates movement has been extensively studied, yet multiple competing models exist. Representational approaches relate the activity of single neurons to movement parameters such as velocity and position, approaches useful for the decoding of movement intentions, while the dynamical systems approach predicts that neural activity should evolve in a predictable way based on population activity. Existing representational models cannot reproduce the recent finding in monkeys that predictable rotational patterns underlie motor cortex activity during reach initiation, a finding predicted by a dynamical model in which muscle activity is a direct combination of neural population rotations. However, previous simulations did not consider an essential aspect of representational models: variable time offsets between neurons and kinematics. Whereas these offsets reveal rotational patterns in the model, these rotations are statistically different from those observed in the brain and predicted by a dynamical model. Importantly, a simple recurrent neural network model also showed rotational patterns statistically similar to those observed in the brain, supporting the idea that dynamical systems-based approaches may provide a powerful explanation of motor cortex function.