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.