Extended Data Fig. 2: Design space for scale-free vertical tracking using a “hydrodynamic treadmill”: Effect of stage and fluid dynamics.
a, When an object accelerates vertically to achieve a maximum velocity uobj over a behavioral timescale τobj, its motion is compensated by the stage. b, Left, velocity time traces of the object (green dotted line), stage (blue solid line) and fluid (cyan dash-dotted line), showing the viscous delay (τvisc) between stage and fluid movements. Tracking success can be quantified by the difference (Δτ) between two sets of time-scales, one related to the object (τobj+τFOV) and the other related to the stage plus fluid system (τstage+τvisc), where τFOV=LFOV/uobj and LFOV is the optical field-of-view (FOV) size. (b) Right, successful tracking is when the object’s movements can be compensated so that its distance from the center of the optical FOV (red dashed line) never exceeds half the FOV size (solid red line). c, Plots of Δτ with respect to the chamber width (W) and object speed (uobj) for τobj = 0 (instantaneous velocity changes). The tracking limits (zero-crossing of Δτ) are shown for different behavioral timescales τobj (solid, dashed and dot-dashed contour lines). Symbols (mean) and whiskers (standard deviation) correspond to various organisms (see Supplementary Table 1) which were successfully tracked for chamber widths of 3.2,3.5 and 4 mm.
