Epidermal homeostasis control in an off-lattice agent-based model

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Abstract
We apply an improved version of a previously introduced off-lattice agent-based model to the steady-state flow equilibrium of skin. The dynamics of cells is determined by conservative and drag forces, supplemented with delta-correlated random forces. Cellular adjacency is detected by a weighted Delaunay triangulation. We analyze a simple control mechanism: The cell cycle time of keratinocytes is controlled by a diffusible substance provided by the dermis, in particular we consider the local water concentration. This concentration is calculated from a diffusion equation with time-dependent boundary conditions and varying diffusion coefficients. It turns out that this simple control mechanism suffices to explain several characteristics of epidermal growth. The dynamics of a nutrient is also taken into account by a reaction-diffusion equation. In addition, we ask the simple question of how melanoma with decreased basal adhesion manage to persist within the steady-state flow-equilibrium of the skin. It turns out that there exist physiological parameter sets, where stochastic effects have important consequences.

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