Gradient descent decomposition of force-field motor primitives optogenetically elicited for motor mapping of the murine lumbosacral spinal cord

Generating diverse motor behaviors critical for survival is a challenge that confronts the central nervous system (CNS) of all animals. During movement execution, the CNS performs complex calculations to control a large number of neuromusculoskeletal elements. The theory of modular motor control proposes that spinal interneurons are organized in discrete modules that can be linearly combined to generate a variety of behavioral patterns. These modules have been previously represented as stimulus-evoked force fields (FFs) comprising isometric limb-endpoint forces across workspace locations. Here, we ask whether FFs elicited by different stimulations indeed represent the most elementary units of motor control or are themselves the combination of a limited number of even more fundamental motor modules. To probe for potentially more elementary modules, we optogenetically stimulated the lumbosacral spinal cord of intact and spinalized Thy1-ChR2 transgenic mice (n=21), eliciting FFs from as many single stimulation loci as possible (20-70 loci per mouse) at minimally necessary power. We found that the resulting varieties of FFs defied simple categorization with just a few clusters. We used gradient descent to further decompose the FFs into their underlying basic force fields (BFFs), whose linear combination explained FF variability. Across mice, we identified 4-5 BFFs with partially localizable but overlapping representations along the spinal cord. The BFFs were structured and topographically distributed in such a way that a rostral-to-caudal traveling wave of activity across the lumbosacral spinal cord may generate a swing-to-stance gait cycle. These BFFs may represent more rudimentary submodules that can be flexibly merged to produce a library of motor modules for building different motor behaviors.