Kinematic coordinates in which motor cortical cells encode movement direction

During goal-directed reaching in primates, a sensorimotor transformation generates a dynamical pattern of muscle activation. Within the context of this sensorimotor transformation, a fundamental question concerns the coordinate systems in which individual cells in the primary motor cortex (MI) encode movement direction. This article develops a mathematical framework that computes, as a function of the coordinate system in which an individual cell is hypothesized to operate, the spatial preferred direction (pd) of that cell as the arm configuration and hand location vary. Three coordinate systems are explicitly modeled: Cartesian spatial, shoulder-centered, and joint angle. The computed patterns of spatial pds are distinct for each of these three coordinate systems, and experimental approaches are described that can capitalize on these differences to compare the empirical adequacy of each coordinate hypothesis. One particular experiment involving curved motion was analyzed from this perspective. Out of the three coordinate systems tested, the assumption of joint angle coordinates best explained the observed cellular response properties. The mathematical framework developed in this paper can also be used to design new experiments that are capable of disambiguating between a given set of specified coordinate hypotheses.