Pinning-depinning transition in a stochastic growth model for the evolution of cell colony fronts in a disordered medium

Abstract

We study a stochastic lattice model for cell colony growth, which takes into account proliferation, diffusion, and rotation of cells, in a culture medium with quenched disorder. The medium is composed both by sites that inhibit any possible change in the internal state of the cells, representing the disorder, as well as by active medium sites, that do not interfere with the cell dynamics. By means of Monte Carlo simulations we find that the velocity of the growing interface, which is taken as the order parameter of the model, strongly depends on the density of active medium sites (ρA). In fact, the model presents a (continuous) second-order pinning-depinning transition at a certain critical value of ρ ^crit A , such as for ρA &gt; ρ<sup>crit</sup A the interface moves freely across the disordered medium, but for ρA &lt; ρ^crit A the interface becomes irreversible pinned by the disorder. By determining the relevant critical exponents, our study reveals that within the depinned phase the interface can be rationalized in terms of the Kardar-Parisi-Zhang universality class, but when approaching the critical threshold, the non-linear term of the Kardar-Parisi-Zhang equation tends to vanish and then the pinned interface belongs to the quenched Edwards-Wilkinson universality class.