A model of movement coordinates in the motor cortex: Posture-dependent changes in the gain and direction of single cell tuning curves

This article outlines a methodology for investigating the coordinate systems by which movement variables are encoded in the firing rates of individual motor cortical neurons. Recent neurophysiological experiments have probed the issue of underlying coordinates by examining how cellular preferred directions (as determined by the center-out task) change with posture. Several key experimental findings have resulted that constrain hypotheses about how motor cortical cells encode movement information. But while the significance 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 - that is, gain changes - have not been similarly identified as a means of coordinate inference. This article develops a vector field framework in which the preferred direction and the gain of a cell's tuning curve are viewed as dual components of a unitary response vector. The formalism can be used to compute how each aspect of call response covaries with posture as a function of the coordinate system in which a given cell is hypothesized to encode its movement information. Such an integrated approach leads to a model of motor cortical cell activity that codifies the following four observations: (i) cell activity correlates with hand movement direction; (ii) call activity correlates with hand movement speed; (iii) preferred directions vary with posture; and (iv) the modulation depth of tuning curves varies with posture. Finally, the model suggests general methods for testing coordinate hypotheses at the single-call level and simulates an example protocol for three possible coordinate systems: Cartesian spatial, shoulder-centered, and joint angle.