Time derivative of [Ca²⁺]_i controls curvature of swimming path. (A) Changes in [Ca²⁺]_i and path curvature κ. (B) Color-coded F_r along the swimming path of a cell. The blue arrow indicates the swimming direction. After photorelease of cGMP (black arrow), the cell displays Ca²⁺ oscillations and abandons swimming in closed circles. Of note, [Ca²⁺]_i was still rising even after the curvature peaked. (C) Time course of the time derivative dF_r/dt and κ superimposes. (A and C) Photolysis of caged cGMP was at t = 0 (dashed lines). (D) Color-coded dF_r/dt along the path of the same cell as in B. (E) Detail of the swimming path. F_r is maximal while the cell swims straight, whereas dF_r/dt is maximal when the cell turns. (F) Pearson correlation between path curvature and dF_r/dt or F_r. Individual data points are displayed as black circles (n = 27), mean correlation is in red, and SD is in blue (box length is twice the SD).