Polygonal swimming via coordinated flagellar beat switching in microswimmer Euglena gracilis

Biological microswimmers exhibit versatile strategies for sensing and navigating their environment, e.g., run-and-tumble and curvature modulation. Here we report a striking behavior of Euglena gracilis, where Euglena cells swim in polygonal trajectories due to a sudden increase in light intensity. While smoothly curved trajectories are common for microswimmers, such quantized ones have not been reported previously. This polygonal behavior emerges from periodic switching between the flagellar beating patterns of helical swimming and spinning behaviors. We develop and experimentally validate a biophysical model that captures all three behavioral states. Coordinated switching between these behaviors selects for ballistic, superdiffusive, diffusive, or subdiffusive motion (including tuning the effective diffusion constant over several orders of magnitude), thereby enabling navigation in spatially 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.