A Model of Movement Coordinates in Motor Cortex: Posture-Dependent Changes in the Gain and Direction of Single Cell Tuning Curves
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Central to the problem of elucidating the cortical mechanisms that mediate movement behavior is an investigation of the coordinate systems by which movement variables are encoded in the firing rates of individual motor cortical neurons. In the last decade, neurophysiologists have probed how the preferred direction of an individual motor cortical cell (as determined by a center-out task) will change with posture because such changes are useful for inferring underlying cordinates. However, while the importance of shifts in preferred direction is well-known and widely accepted, posture-dependent changes in the depth of modulation of a cell's tuning curve, i.e. gain changes, have not been similarly identified as a means of coordinate inference. This paper develops a vector field framework which, by viewing the preferred direction and the gain of a cell's tuning curve as dual components of a unitary response vector, can compute how each aspect of cell response covaries with posture as a function of the coordinate system in which a given cell is hypothesized to encode its movement information. This integrated approach leads to a model of motor cortical cell activity that codifies the following four observations: 1) cell activity correlates with hand movement direction, 2) cell activity correlates with hand movement speed, 3) preferred directions vary with posture, and 4) the modulation depth of tuning curves varies with posture. Finally, the model suggests general methods for testing coordinate hypotheses at the single cell level and example protocols arc simulated for three possible coordinate systems: Cartesian spatial, shoulder-centered, and joint angle.