Fig. 3

Optokinetic set-point adaptation model predicts the recorded SPV in larval zebrafish

(A) The mathematical model of set-point adaptation. Retinal slip velocity (V_r) is the difference between the stimulus velocity (V_s) and the eye velocity (V_e). During habituation, V_r is rectified and filtered with a time constant of T_h and gain of k_h (blue shaded area), and then scaled with h, to give a filtered V_r. In the sensory habituation operator, |u|, which produces the absolute value of the input (orange shaded area), together with a sign switch of output lead to a continuous habituating effect regardless of stimulus direction. The filtered V_r passes through a nonlinear gain (T-N gain) that captures the T-N asymmetry. The error between the filtered V_r and the set point is scaled by oculomotor gain (g) and added to the velocity storage mechanism (VSM) to control V_e. VSM contains a leaky integrator with a time constant of T_vsm and a gain of k_vsm that contributes to the eye velocity. V_e is then integrated with a time constant of T_a and a gain of k_a to adjust the set point.

(B–G) The model predicted population-median SPV (colored lines) superimposed on the median ± median absolute deviation (black line with gray shadow) of empirical SPVs during 10/10 symmetric alternating stimulations (SA, n = 29) (B–D) and 20/5 asymmetric alternating stimulations (AA, n = 18) (E–G). Considering the starting direction of alternating stimulation was randomized, we aligned the first stimulus direction as positive instead of left or right. Therefore, the plots show one eye started with a nasalward movement (blue trace) and another eye started with a temporalward movement (red trace). The stimulus image pattern (darkness or gratings) and the stimulus velocity are shown on the top as horizontal bars and lines, respectively.