The minimum endpoint variance trajectory depends on the profile of the signal-dependent noise

It has been proposed that the central nervous system determines reaching movement trajectories so as to minimize the positional variance of the endpoint in the presence of signal-dependent noise. The hypothesis well reproduces the empirical movement trajectories for noise to the control signal whose variance is proportional to the second power of the amplitude of the control signal. However, empirical studies do not necessarily exhibit such a simple signal-noise relationship. The studies exhibit a wide distribution of estimates of the value of the exponent. This discrepancy raises the question of how the minimum endpoint variance trajectory depends on the value of the exponent. To address this question, we calculated minimum endpoint variance trajectories in simulations in which the value of the exponent was varied from 0 to 3. We found that the optimal trajectories differed according to the value of the exponent, and the profiles of optimal trajectories gradually diverged from the empirical ones as the value approached 0, though this change was not remarkable for larger values. Moreover, the optimal trajectories failed to replicate Fitts' law when the value was not equal to 2. These results suggest that the acceptability of the minimum endpoint variance theory depends on the value of the exponent in our motor system.