Epithelial monolayers are the foundation of many mammalian organs and have a significant impact on numerous biological processes, including the secretion of cytokines, absorption of waste products and barrier function. During organ development epithelia are subject to many external forces due to the growth of the surrounding tissues. They exhibit complex responses to such forces, with deformation occurring on short timescales (seconds), and relaxation and remodelling occurring on longer timescales (minutes or hours). Existing mathematical and computational models do not typically account for subcellular remodelling, assuming instead that the response to an applied force or strain acts on a single timescale. In this paper we extend an off-lattice, cell-centre modelling framework to account for subcellular and tissue remodelling by introducing a Dynamic Reference Frame (DRF). The DRF provides a discrete, cell-based analogue of morpho-elasticity: it decouples the evolution of each cell's mechanical reference configuration from its instantaneous deformation, providing a phenomenological description of subcellular remodelling processes - cytoskeletal reorganisation, myosin turnover and adhesion bond remodelling - at the cellular scale. Using this extended multicellular model, we reproduce multiscale responses to external mechanical forces, including creep and stress relaxation experiments, and demonstrate that the history of applied deformation influences tissue recovery upon release. Additionally we identify and quantify where and how these multiscale responses occur. The resulting framework allows for more detailed descriptions and analyses of the development and function of biological tissues.
Osborne, J. M., Van Ammers, R., Davit, Y., Gavaghan, D. J., Byrne, H.
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