Active remodelling of tissues to describe biphasic rheological responses

Tissues form from collections of cells that interact together mechanically via cell-to-cell adhesion, mediated by transmembrane cell adhesion molecules. Under a sufficiently large amount of induced stress, these tissues can undergo elastic deformation in the direction of tension, where they then elongate without any topological changes, and experience plastic deformation within the tissue. In this work, we present a novel mathematical model describing the deformation of cells, where tissues are elongated in a controlled manner. In doing so, the cells are able to undergo remodelling through elastic and then plastic deformation, in accordance with experimental observation. Our model describes bistable sizes of a cell that actively deform under stress to elongate the cell. In the absence of remodelling, the model reduces to the standard linear interaction model. In the presence of instant remodelling, we provide a bifurcation analysis to describe the existence of the bistable cell sizes. In the case of general remodelling, we show numerically that cells within a tissue may populate both the initial and elongated cell sizes, following a sufficiently large degree of stress.