Waveform of Ca²⁺ signals determines path shape. (A–C, top graphs) Ca²⁺ signals and changes in path curvature κ evoked by release of cGMP at t = 0 (dashed lines) in three cells. Cyan dots on the Ca²⁺ signals correspond to local maxima of dF_r/dt. (middle graphs) dF_r/dt and curvature κ superimpose on each other. (bottom illustrations) Swimming paths of the same cells before (green) and after (red) release of cGMP (black arrows and yellow bars). Green and red arrows indicate the swimming direction of the cell before and after release of resact, respectively. From left A to right C, cells vary from fast and symmetric Ca²⁺ oscillations to slower and skewed oscillations. Correspondingly, path curvature varies from fast oscillations (on a high [Ca²⁺]_i) to slow and asymmetric oscillations with brief episodes of steep peaks (turns) and long episodes of low curvature (runs). Swimming paths for the respective cells vary from short turn and run episodes with almost symmetrical but opposite curving (A) to sharp turns and long runs (C). Cyan dots indicate local maxima of dF_r/dt.