Numerical study of coding of the movement direction by a population in the motor cortex

The fundamental statistical aspects of population coding of the movement direction in the motor cortex are studied numerically. The activity of neurons in a population is simulated using pseudorandom numbers so that the directional selectivity of the neurons is similar to that observed experimentally. Accuracy of the coding, which is evaluated by the root-mean-square (rms) error, is analyzed for various population sizes, degrees of variability of neuronal activity, and degrees of nonuniformity of distribution of the preferred directions. The dependence of the rms error on the population size shows a good fit to the inverse square-root law, from which it is estimated that a single population must contain around 10 000 neurons in order to attain the accuracy that allows 1 deg rms error, for example. The coding is studied further for populations with different types of tuning function. The results support the hypothesis proposed by Georgopoulos et al. (1988) except that the tuning function must be tuned in the sense that the average value of the function for movements with components in the preferred direction is larger than for movements away from the preferred direction.