Elastic interactions compete with persistent cell motility to drive durotaxis

Many animal cells crawling on elastic substrates exhibit durotaxis and have implications in several biological processes including tissue development, and tumor progression. Here, we introduce a phenomenological model for durotactic migration incorporating both elastic deformation-mediated cell-substrate interactions and the stochasticity of cell migration. Our model is motivated by the key observation in one of the first demonstrations of durotaxis: a single contractile cell at an interface between a softer and a stiffer region of an elastic substrate reorients and migrates towards the stiffer region. We model migrating cells as self-propelling, persistently motile agents that exert contractile, dipolar traction forces on the underlying elastic substrate. The resulting substrate deformations induce elastic interactions with mechanical boundaries, captured by an elastic potential that depends on cell position and orientation relative to the boundary. The potential is attractive or repulsive depending on whether the mechanical boundary condition is clamped or free, which represents the cell being on the softer or stiffer side, respectively, of a confining boundary. The forces and torques from the interactions drive cells to orient perpendicular (parallel) to the boundary and accumulate (deplete) at the clamped (free) boundary, extent of which is determined by elastic potential (A) and motility (Pe). While the elastic interaction drives durotaxis, cell migratory movements such as random reorientation and self-propulsion enable the cell from the attractive potential thereby reducing durotaxis. We define metrics quantifying boundary accumulation and durotaxis and present a phase diagram that identifies three possible regimes: durotaxis, adurotaxis without accumulation and adurotaxis with motility-induced accumulation at a confining boundary.Comment: 14 figures, 28 page

Matrix Stiffness Modulates Mechanical Interactions and Promotes Contact between Motile Cells.

The mechanical micro-environment of cells and tissues influences key aspects of cell structure and function, including cell motility. For proper tissue development, cells need to migrate, interact, and form contacts. Cells are known to exert contractile forces on underlying soft substrates and sense deformations in them. Here, we propose and analyze a minimal biophysical model for cell migration and long-range cell-cell interactions through mutual mechanical deformations of the substrate. We compute key metrics of cell motile behavior, such as the number of cell-cell contacts over a given time, the dispersion of cell trajectories, and the probability of permanent cell contact, and analyze how these depend on a cell motility parameter and substrate stiffness. Our results elucidate how cells may sense each other mechanically and generate coordinated movements and provide an extensible framework to further address both mechanical and short-range biophysical interactions

Matrix Stiffness Modulates Mechanical Interactions and Promotes Contact between Motile Cells.

The mechanical micro-environment of cells and tissues influences key aspects of cell structure and function, including cell motility. For proper tissue development, cells need to migrate, interact, and form contacts. Cells are known to exert contractile forces on underlying soft substrates and sense deformations in them. Here, we propose and analyze a minimal biophysical model for cell migration and long-range cell-cell interactions through mutual mechanical deformations of the substrate. We compute key metrics of cell motile behavior, such as the number of cell-cell contacts over a given time, the dispersion of cell trajectories, and the probability of permanent cell contact, and analyze how these depend on a cell motility parameter and substrate stiffness. Our results elucidate how cells may sense each other mechanically and generate coordinated movements and provide an extensible framework to further address both mechanical and short-range biophysical interactions