  In order to grasp the features arising from cellular discreteness and
individuality, in large parts of cell tissue modelling agent-based models are
favoured. The subclass of off-lattice models allows for a physical motivation
of the intercellular interaction rules. 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. The cell cycle time
of keratinocytes is controlled by a diffusible substance provided by the
dermis. Its concentration is calculated from a diffusion equation with
time-dependent boundary conditions and varying diffusion coefficients. The
dynamics of a nutrient is also taken into account by a reaction-diffusion
equation. It turns out that the analysed control mechanism suffices to explain
several characteristics of epidermal homoeostasis formation. In addition, we
examine the question of how {\em in silico} melanoma with decreased basal
adhesion manage to persist within the steady-state flow-equilibrium of the
skin.Interestingly, even for melanocyte cell cycle times being substantially
shorter than for keratinocytes, tiny stochastic effects can lead to completely
different outcomes. The results demonstrate that the understanding of initial
states of tumour growth can profit significantly from the application of
off-lattice agent-based models in computer simulations.

Biological Physics