Euglena gracilis is an interesting unicellular protist, also because it can adopt different motility strategies: swimming by flagellar propulsion, or crawling thanks to large amplitude shape changes of the whole body (a behavior known as “metaboly”, or “amoeboid motion”). Swimming trajectories are helical. The are powered by the beating of a single emerging flagellum, which spans non-planar waveforms in the shape of a twisted lasso. Finally the harmoniously coordinated shape changes that make metaboly possible, reminiscent of peristaltic waves, arise form the relative sliding of its pellicle strips, resulting in twisted helical bundles. We will report on the most recent findings on these interconnected topics, for which helical shapes provide a striking fil rouge.

The journey of development begins with sperm swimming through the female reproductive tract en-route to the egg. In order to successfully complete this journey sperm must beat a single flagellum, propelling themselves through a wide range of fluids, from liquified semen to viscous cervical mucus. It is well-known that the beating tail is driven by an array of 9 microtubule doublets surrounding a central pair, with interconnecting dynein motors generating shear forces and driving elastic wave propagation. Despite this knowledge, the exact mechanism by which coordination of these motors drives oscillating waves along the flagellum remains unknown; hypothesised mechanisms include curvature control, sliding control, and geometric clutch. In this talk we will discuss the mechanisms of flagellar bending, and present a simple model of active curvature that is able to produce many of the various sperm waveforms that are seen experimentally, including those in low and high viscosity fluids and after a cell has ‘hyperactivated’ (a chemical process thought to be key for fertilization). We will show comparisons between these simulated waveforms and sperm that have been experimentally tracked, and discuss methods for fitting simulated mechanistic parameters to these real cells.