Polygonal motion and adaptable phototaxis via flagellar beat switching in Euglena gracilis

Biological microswimmers exhibit versatile strategies for sensing and navigating their environment 1-7, e.g., run-and-tumble 2 and curvature modulation 3. Here we report a striking behavior of Euglena gracilis, where Euglena cells swim in polygonal trajectories due to exposure to increasing light intensities. While smoothly curved trajectories are common for microswimmers 3, 8, such quantized ones have not been reported previously. This polygonal behavior emerges from periodic switching between the flagellar beating patterns of helical swimming 6, 9 and spinning 10 behaviors. We develop and experimentally validate a biophysical model that describes the phase relationship between the eyespot, cell orientation, light detection, and cellular reorientation, that accounts for all three behavioral states. Coordinated switching between these behaviors allows ballistic, superdiffusive, diffusive, or subdiffusive motion 11,12 (i.e., the tuning of the diffusion constant over 3 orders of magnitude) and enables navigation in structured light fields, e.g., edge avoidance and gradient descent. This feedback-control links multiple system scales (flagellar beats, cellular behaviors, phototaxis strategies) with implications for other natural and synthetic microswimmers 13.