Cell Motility and Locomotion by Shape Control

Mathematical modeling and quantitative study of biological motility is producing new biophysical insight and opportunities for discoveries at the level of both fundamental science and technology. One example is the elucidation of how complex behavior of simple organisms emerges from specific (and sophisticated) body architectures, and how this is affected by environmental cues. Moreover, the two-directional interaction between biology and mechanics is promoting new approaches to problems in engineering and in the life sciences: understand biology by constructing bio-inspired machines, build new machines thanks to bio-inspiration. This article contains an introduction to the mathematical study of swimming locomotion of unicellular organisms (e.g., unicellular algae). We use the tools of geometric control theory to identify some general principles governing life at low Reynolds numbers, that can guide the design of engineered devices trying to replicate the successes of their biological counterparts. Locomotion strategies employed by biological organism are, in fact, a rich source of inspiration for studying mechanisms for shape control. We focus on morphing mechanisms based on Gauss’ theorema egregium, which shows that the curvature of a thin shell can be controlled through lateral modulations of stretches induced in its mid-surface. We discuss some examples of this Gaussian morphing principle both in nature and technology.