Proliferation of cells with aggregation and communication

Cell proliferation is often considered to occur via front propagation with constant velocity. This scenario proposed by Fisher, Kolmogorov, Petrovsky, and Piskunov is based on the solution of the corresponding mean-field reaction-diffusion equations and does not take into account that due to adhesion the cells have tendency to aggregate and that the rate of cell division may depend on the cell-cell communication. Herein, the author presents extensive Monte Carlo simulations taking both these factors into account and illustrating that the former factor can dramatically modify the spatio-temporal kinetics of cell proliferation. In particular, the conventional relation between the front velocity and diffusion coefficient may fail, the front velocity may appreciably increase with increasing time, and/or the front may be partly or fully smeared on the realistic length scales.