The reaching task: evidence for vector arithmetic in the motor system?

During a reaching task, the population vector is an encoding of direction based on cells with cosine response functions. Scaling the response by a magnitude factor produces a vector encoding, enabling vector arithmetic to be performed by the summation of firing rates. We show that the response properties of selected populations of cells in the primary motor cortex and area 5 can be explained in terms of arithmetic relationships among load, goal, and motor command vectors. Our computer simulations show good agreement with single-cell recording data.