Modeling cellular self-organization in strain-stiffening hydrogels

Abstract

We develop a three-dimensional mathematical model framework for the collective evolution of cell populations by an agent-based model (ABM) that mechanically interacts with the surrounding extra-cellular matrix (ECM) modeled as a hydrogel. We derive effective two-dimensional models for the geometrical set-up of a thin hydrogel sheet to study cell-cell and cell-hydrogel mechanical interactions for a range of external conditions and intrinsic material properties. We show that without any stretching of the hydrogel sheets, cells show the well-known tendency to form long chains with varying orientations. Our results further show that external stretching of the sheet produces the expected nonlinear strain-softening or stiffening response, with, however, little qualitative variation of the over-all cell dynamics for all the materials considered. The behavior is remarkably different when solvent is entering or leaving from strain softening or stiffening hydrogels, respectively.