Polarization of cells and soft objects driven by mechanical interactions: consequences for migration and chemotaxis.

We study a generic model for the polarization and motility of self-propelled soft objects, biological cells, or biomimetic systems, interacting with a viscous substrate. The active forces generated by the cell on the substrate are modeled by means of oscillating force multipoles at the cell-substrate interface. Symmetry breaking and cell polarization for a range of cell sizes naturally "emerge" from long range mechanical interactions between oscillating units, mediated both by the intracellular medium and the substrate. However, the harnessing of cell polarization for motility requires substrate-mediated interactions. Motility can be optimized by adapting the oscillation frequency to the relaxation time of the system or when the substrate and cell viscosities match. Cellular noise can destroy mechanical coordination between force-generating elements within the cell, resulting in sudden changes of polarization. The persistence of the cell's motion is found to depend on the cell size and the substrate viscosity. Within such a model, chemotactic guidance of cell motion is obtained by directionally modulating the persistence of motion, rather than by modulating the instantaneous cell velocity, in a way that resembles the run and tumble chemotaxis of bacteria.