Modelling biological and bio-inspired swimming at microscopic scales: Recent results and perspectives

Some recent results on biological and bio-inspired swimming at microscopic scales are reviewed, and used to identify promising research directions for the future. We focus on broad conceptual principles such as looping in the space of shapes, loss of controllability of systems in which shape is only partially controlled, and steering by modulating the actuation rate. Moreover, we discuss propulsion mechanism that are most common for unicellular swimmers, such as flagellar and ciliary beating, and we examine amoeboid motion and flagellar propulsion in Euglena. The Helix Theorem, a universal law characterising orbits traced by ciliated and flagellated unicellular swimmers propelled by the periodic beating of cilia and flagella, is proved and discussed as a principle of self-assembly for helical structures.