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

Biological microswimmers exhibit versatile strategies for sensing and navigating their environment, such as run-and-tumble and curvature modulation. Here, we report a striking phototactic behaviour of the microswimmer Euglena gracilis, where these eukaryotic 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. We find that this polygonal behaviour emerges from periodic switching between the flagellar beating patterns of helical swimming and spinning behaviours. We develop and experimentally validate a biophysical model that describes the phase relationship between the eyespot, cell orientation, light detection and cellular reorientation, accounting for all three behavioural states. Coordinated switching between these behaviours 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, such as edge avoidance and gradient descent. This feedback control links multiple system scales (flagellar beats, cellular behaviours and phototaxis strategies), with implications for other natural and synthetic microswimmers.