Transition between Swimming and Crawling: A Model of Eukaryotic Cell Motility

Abstract

Eukaryotic cells can migrate spontaneously or in response to external stimuli such as chemical gradients and may travel either individually or collectively. Eukaryotic cell motility is crucial during development, wound healing, the immune response, and cancer metastasis. In liquids, eukaryotic cells can swim by pushing on the surrounding fluid, but they more often crawl along the extracellular matrix. We are interested in studying the relationships between hydrodynamics and adhesion that regulate a cell's transition between swimming and crawling. Therefore, we develop a simple model of a cell capable of both kinds of motion based on the three-sphere swimmer proposed by Najafi and Golestanian. The model includes additional adhesive friction terms, geometry motivated by cells crawling on fibers, substrate surface hydrodynamic effects, and parameters from experimental data. Hydrodynamic effects diminish in the high adhesion limit, and the crawling cell can achieve significant center-of-mass velocity compared to its swimming counterpart. The crawling cell maintains the same net displacement per cycle regardless of its sequence of motions, including reciprocal cycles that would be unproductive in the frictionless limit, which constrains cell motion by the Scallop Theorem of low-Reynolds number hydrodynamics. The center-of-mass velocity of the cell plateaus at a maximum value as adhesion increases until the frictional drag exceeds the largest force the cell can generate, after which velocity decreases with increasing adhesion. This recapitulates the common experimental observation that cell speed is not monotonic with adhesion strength.