The first step towards the mathematical understanding of the role of matrix metalloproteinase-8 in cancer invasion

The role of matrix metalloproteinases-8 (MMP-8) in the cancer progression is quite complex, with contradictory indications as to whether it suppresses or assists the local growth of cancer. In addition, while other types of MMPs appear in either soluble or (cancer cell) membrane-bound form MMP-8 seems to appear in both. We take the first step in unravelling this dual nature of MMP-8 by shedding some mathematical light into its properties. To this end, we develop a mathematical model to investigate the impact of both soluble and membrane-bound MMPs in the early stages of local invasion of cancer cells. We propose an extension to a previously developed three-dimensional, hybrid atomistic-collective, cancer invasion model that allows the description of individual cancer cells along side with macroscopic tissue representations, and for the natural transition between these phases. We further assume that the soluble MMPs are produced by polymorphonuclear neutrophils, that pre-exist in the environment, and that they get activated by the cancer cells. The membrane-bound MMPs are expressed on the membrane of the cancer cells and along with the soluble MMPs, participate in the degradation of the extracellular matrix and, in effect, directly influence the migration of the cancer cells in what is understood to be a self-generated haptotaxis invasion strategy. With a series of numerical experiments and simulations we investigate the potential of the model in producing various invasion patterns, some resembling, qualitatively, to experimental invasion assays.