UC Merced

The mechanical micro-environment of cells significantly impacts their structure, function, and motility, influencing essential processes such as tissue development and cellular interactions. The actomyosin cytoskeleton is very important in controlling the shape and migration patterns of the cell.

Cells exert contractile forces on their substrates, leading to deformations that can mediate long-range cell-cell interactions and facilitate coordinated movements. To explore these dynamics, we propose and analyze a minimal biophysical model that integrates cell migration with mutual mechanical deformations of an elastic substrate. Our model evaluates key metrics including the number of cell-cell contacts, dispersion of cell trajectories, and probability of permanent cell contact, examining how these metrics vary with cell motility and substrate stiffness.

Inspired by cell mechanobiology, we model cells as self-propelling particles interacting through substrate-mediated forces. This active matter framework combines motility dynamics with linear elasticity to reveal emergent collective behaviors, such as the formation of flexible, motile chains and larger-scale structures with polar order. By varying elastic interaction strengths and motility, and considering confinement within a channel geometry, we identify different collective states and their implications for cell organization.

Additionally, we introduce a phenomenological model for durotaxis, the directed migration of cells towards stiffer substrate regions, incorporating elastic deformation-mediated interactions and stochastic motility. Our model demonstrates how cells reorient and migrate in response to substrate stiffness, with boundary conditions influencing accumulation or depletion. We quantify the effects of contractility and motility on durotaxis, presenting a phase diagram that characterizes distinct migration regimes.

Finally, we explore how orientational order in actively contractile elastic disks influences strain profiles. We analyze the 2D radial profiles displacement and strains and determine distribution of active stresses in the disk from an analysis of its strain. We also predict the out of plane deformations of active gels from its 2D dynamics. We further developed a simplistic continuum model, which combines elastic displacement with an orientational order parameter, provides analytic solutions for strain-induced alignment in filamentous gels. Comparative analysis with experimental data from actomyosin gel disks validates the model and enhances our understanding of active stress directionality in complex biological systems.

Overall, our work offers a framework for understanding mechanical interactions in cell migration and organization, applicable to both biological and synthetic active matter systems.