Last modified: 2014-03-31
Abstract
Cancer invasion is a complex process occurring across several spatial and temporal scales, perhaps the three most important being the intracellular, cellular and tissue scales. Key biological processes occurring during invasion are the secretion of matrix degrading enzymes, cell proliferation, the loss of cell-cell adhesion on one hand and enhanced cell-matrix adhesion on the other hand, as well as active migration. The ability of cancer cells to alter or degrade the surrounding tissue enables the cancer cells to locally invade the neighbouring region. The movement of cancer cells occurs through chemotaxis as well as haptotaxis and is supported by the binding and unbinding of molecules on the cell surface to other cells and/or the extracellular matrix (ECM). The number and strength of these binding proteins define the magnitude of cell-cell and cell-matrix adhesion and are modified by the cell’s microenvironment. Hence, the movement of the cells is not only determined locally but depends on the neighbourhood of the cell.
We explore the spatio-temporal dynamics of a mathematical model of cancer invasion, where cell-cell and cell-matrix adhesion are accounted for through non-local interaction terms. A non-local model of cancer invasion for a single cancer cell population [1] is extended to a structured-population model with n cancer cell sub-populations, which may mutate into each other. The change of adhesion properties during the growth of the cancer is investigated through time-dependent adhesion parameters within the cancer cell sub-populations as well as those between the cancer cells and the components of the extracellular matrix. We focus on one and two cancer cell sub-population models in two spatial dimensions, which show heterogeneous dynamics in our computational simulation results.
[1] A. Gerisch and M. A. J. Chaplain. Mathematical modelling of cancer cell invasion of tis- sue: Local and non-local models and the effect of adhesion. Journal of Theoretical Biology, 250(4):684 – 704, 2008.