A computational study of discrete 'cell-centre' approaches to modelling the evolution of a collection of cells is undertaken. The study focuses on the mechanical aspects of the tissue, in order to separate the passive mechanical response of the model from active effects such as cell-growth and cell division. Issues which arise when implementing these models are described, and a series of numerical mechanical experiments is performed. It is shown that discrete tissues modelled this way typically exhibit elastic-plastic behaviour under slow compression, and act as a brittle linear elastic solid under slow tension. Both overlapping spheres and Voronoi-tessellation-based models are examined, and the effect of different cell-cell interaction force laws on the bulk mechanical properties of the tissue is determined. This correspondence allows parameters in the cell-based model to be chosen to be compatible with bulk tissue measurements.

Multiscale modeling is emerging as one of the key challenges in mathematical biology. However, the recent rapid increase in the number of modeling methodologies being used to describe cell populations has raised a number of interesting questions. For example, at the cellular scale, how can the appropriate discrete cell-level model be identified in a given context? Additionally, how can the many phenomenological assumptions used in the derivation of models at the continuum scale be related to individual cell behavior? In order to begin to address such questions, we consider a discrete one-dimensional cell-based model in which cells are assumed to interact via linear springs. From the discrete equations of motion, the continuous Rouse [P. E. Rouse, J. Chem. Phys. 21, 1272 (1953)] model is obtained. This formalism readily allows the definition of a cell number density for which a nonlinear “fast” diffusion equation is derived. Excellent agreement is demonstrated between the continuum and discrete models. Subsequently, via the incorporation of cell division, we demonstrate that the derived nonlinear diffusion model is robust to the inclusion of more realistic biological detail. In the limit of stiff springs, where cells can be considered to be incompressible, we show that cell velocity can be directly related to cell production. This assumption is frequently made in the literature but our derivation places limits on its validity. Finally, the model is compared with a model of a similar form recently derived for a different discrete cell-based model and it is shown how the different diffusion coefficients can be understood in terms of the underlying assumptions about cell behavior in the respective discrete models.

Hair cycling is modulated by factors both intrinsic and extrinsic to hair follicles. Cycling defects lead to conditions such as aging-associated alopecia. Recently, we demonstrated that mouse skin exhibits regenerative hair waves, reflecting a coordinated regenerative behavior in follicle populations. Here, we use this model to explore the regenerative behavior of aging mouse skin. Old mice (>18 months) tracked over several months show that with progressing age, hair waves slow down, wave propagation becomes restricted, and hair cycle domains fragment into smaller domains. Transplanting aged donor mouse skin to a young host can restore donor cycling within a 3 mm range of the interface, suggesting that changes are due to extracellular factors. Therefore, hair stem cells in aged skin can be reactivated. Molecular studies show that extra-follicular modulators Bmp2, Dkk1, and Sfrp4 increase in early anagen. Further, we identify follistatin as an extra-follicular modulator, which is highly expressed in late telogen and early anagen. Indeed, follistatin induces hair wave propagation and its level decreases in aging mice. We present an excitable medium model to simulate the cycling behavior in aging mice and illustrate how the interorgan macroenvironment can regulate the aging process by integrating both “activator” and “inhibitor” signals.