The modulation index for neuronal direction tuning was calculated using a tuning index, (Preferred – Null) / (Preferred + Null). All indices were determined using the average firing rate responses to the indicated stimulus conditions with the indicated stimuli at 100% contrast. Equation 3 was fit using four free parameters (LP, LN, σ, α; see Results for definitions). A fifth parameter (β) was fixed at 2.75, the average β determination when β was allowed to be a free parameter, for all of the neurons. The model parameters were fit via unconstrained nonlinear optimizing that minimized the sum-of-squares error. The model parameters were constrained in the fit to be greater than 0, but there were no

other constraints on check details the model fits. The goodness of fit of the model was calculated for each neuron as the total explained variance, which was determined by taking the square of the correlation coefficient BKM120 molecular weight between the estimated firing rates from the model and the firing rates of the neuron across the stimulus conditions fit by the model. For the main experiment, nine stimulus conditions were fit by the model to determine the free parameter estimations: five conditions with spatial attention directed outside of the receptive field, four conditions with spatial attention

directed inside of the receptive field. As a control to ensure that the α term estimations were not biased by the four stimulus conditions with spatial attention directed to the receptive field (see Results), eight stimulus conditions with spatial attention directed outside of the receptive field and to the intermediate direction of motion were fit to the model to determine Mannose-binding protein-associated serine protease α term estimations without the influence of attention. These conditions were: Preferred 50% contrast, Preferred 100% contrast, Null 50% contrast, Null 100% contrast, Preferred 50% contrast + Null 50% contrast, Preferred 100% contrast + Null 50% contrast, Preferred 50% contrast + Null 100% contrast, Preferred 100% contrast + Null 100% contrast. A value of β = 2.75 was applied according to Equation 3

to the α, LP, LN, and σ determinations from these eight sensory interaction conditions, to determine how well the free parameters determined by the eight stimulus interaction conditions alone fit the data collected during the attention conditions. The model provided an excellent fit of the attention conditions using a value of β = 2.75 and the predetermined α, LP, LN, and σ estimations. p values were computed for Pearson’s linear correlation coefficients using a Student’s t distribution, unless it was noted that a Spearman’s rho was determined instead, in which case the p values were computed using large-sample approximations. A Bonferroni correction was applied in the case of multiple comparisons. We thank Marlene R. Cohen, Incheol Kang, and J. Patrick Mayo for helpful comments and discussions.