Abstract
The direction and speed tuning of MT neurons has been well characterized physiologically. Direction tuning curves are generally Gaussian, whereas speed tuning curves are typically skewed toward higher speeds on a linear axis.
We show that the speed tuning curves of MT neurons are well fit (median R2 = 0.97) by a Gaussian in log speed, q(|v|) = ln((|v|+v0)|v0), with center position q(v_c) and standard deviation sigma_s. Speed is denoted by |v|, v0 is a constant, and v_c denotes the preferred speed. The fits produced tightly clustered values for sigma_s (mean =1.22) and v0 (mean = 0.30 deg/sec) across a population of 501 MT neurons. Fixing both of these parameters causes only a modest reduction in the quality of the fits (median R2 = 0.92), leaving only the preferred speed, v_c, and amplitude of the tuning curve to vary across neurons. Thus, the speed tuning curves of the MT neurons are well-described by a single function that is simply shifted along the log speed axis by q(v_c).
We next generalized the expression for the velocity tuning of MT neurons in two dimensions by adopting a log-polar model (similar to that used to model the retinotopic map in V1) in which the 2D mapping from v to q is locally isotropic. The tuning curves are modeled as a Gaussian in q, with variance sigma_s along the preferred direction and sigma_d in the orthogonal direction. This model provided good simultaneous fits to the direction and speed tuning curves of MT neurons (median R2 = 0.94), with the values of sigma_s and sigma_d tightly clustered around their means of 1.3 and 0.80. Theoretical analysis predicts sigma_d should be less than sigma_s.
Thus, our modeling shows the shape of the velocity tuning of the majority of MT neurons can be fit by a single function parameterized solely by the preferred direction and speed. For speeds > v0=0.3deg/sec, which is quite small, the representation is scale invariant and supports a Weber-Fechner law for speed discrimination.