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

Abstract

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.

Neural Manifolds for the Control of Movement

“…The experimental data were best reproduced by the simplest RNN connectivity that allowed the network to output the measured muscle activity. A similar result was subsequently achieved with an RNN trained to output the x and y components of hand velocity for a delayed center-out reach task (Michaels et al, 2016). …”

“…The concept of the neural manifold and its associated latent variables has been used in a series of recent studies that replace the search for movement representation by single neurons to consider instead movement planning and execution based on the activation of a few neural modes (Ahrens et al, 2012; Bruno et al, 2015; Churchland et al, 2012, 2010a, 2010b; Churchland and Shenoy, 2007; Elsayed et al, 2016; Kaufman et al, 2016, 2014; Michaels et al, 2016; Overduin et al, 2015; Sadtler et al, 2014; Santhanam et al, 2009; Sussillo et al, 2015). …”

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

“…Recent physiological and theoretical investigations suggest that the neural state in motor cortex obeys smooth dynamics 20,24,26,27,29,58,59 . Smooth dynamics imply that neural trajectories should not be ‘tangled’: similar neural states, either during different movements or at different times for the same movement, should not be associated with different derivatives.…”

“…Yet responses of motor cortical neurons can differ from what would be expected if they encode muscle force, motivating the hypothesis that motor cortex primarily encodes movement velocity or direction 3,17–19 . Alternatively, it has been proposed that non-muscle-like response features may be explained by network or feedback dynamics 20–30 . Many studies, largely focused on reaching, have produced little consensus 31–42 .…”

Cerebellar neurodynamics during motor planning predict decision timing and outcome on single-trial level

“…These observations are incompatible with static and trial-averaged tuning frameworks for representation of motor responses, as averaging can mask the inherent trial-to-trial variability of neuronal activity and motor response, and thus their relationship on a trial-by-trial basis (Afshar et al, 2011;Briggman et al, 2005;Churchland and Kiani, 2016;Wei et al, 2019). Frameworks based on dynamical systems-in which the movement-related neuronal dynamics are described by differential equations whose initial conditions are set by the preparatory activity-have been shown to provide a better model than trial-averaged representation frameworks for how motor behavior emerges from pre-motor neuronal population dynamics (Churchland et al, 2010;Mante et al, 2013;Michaels et al, 2016;Pandarinath et al, 2018;Shenoy et al, 2013).…”