Abstract

Eukaryotic cells are made up of protein filaments (such as actins) which can be polarized at the macroscopic level. These actin filaments can polymerize in the direction of polarization causing protrusion in the cell. Furthermore, these filaments are also crosslinked by motor proteins (called myosin), which pull the filaments together causing contraction. Several eukaryotic cells employ these mechanisms for different types of cellular motility such as crawling, swimming or tumbling. Here we consider a droplet of actomyosin as a minimal model for cellular motility with two active ingredients: 1) self-propulsion in the direction of polarisation to represent actin polymerisation, and 2) contractile stress to represent actomyosin contraction. In particular, self-propulsion can create protrusion during cell crawling. Cell swimming, on the other hand, is due to spontaneous symmetry breaking of actomyosin contraction. Finally, we also consider the effects of chirality (such as twisted actin filaments). A tumbling motility is a consequence of chiral symmetry breaking. Some organisms (e.g. Toxoplasma gondii) might employ a combination of swimming and tumbling motility to give rise to a spiral trajectory.