We consider the early carcinogenesis model originally proposed as a deterministic
reaction-diffusion system. The model has been conceived to explore the spatial effects
stemming from growth regulation of pre-cancerous cells by diffusing growth factor
molecules. The model exhibited Turing instability producing transient spatial spikes in
cell density, which might be considered a model counterpart of emerging foci of malignant
cells. However, the process of diffusion of growth factor molecules is by its nature a
stochastic random walk. An interesting question emerges to what extent the dynamics of the
deterministic diffusion model approximates the stochastic process generated by the model.
We address this question using simulations with a new software tool called sbioPN (spatial
biological Petri Nets). The conclusion is that whereas single-realization dynamics of the
stochastic process is very different from the behavior of the reaction diffusion system,
it is becoming more similar when averaged over a large number of realizations. The degree
of similarity depends on model parameters. Interestingly, despite the differences, typical
realizations of the stochastic process include spikes of cell density, which however are
spread more uniformly and are less dependent of initial conditions than those produced by
the reaction-diffusion system.