Non-Local Effects and Surface-Bound Reactions in Cancer Invasion Model Development, Analysis and Numerical Simulation
Bioinformatics and Theoretical Biology
Final Report Abstract
Cancer invasion, recognised as one of the hallmarks of cancer, is a complex, multiscale phenomenon involving many inter-related genetic, biochemical, cellular and tissue processes at different spatial and temporal scales. Central to invasion is the ability of cancer cells to alter and degrade the extracellular matrix. Combined with abnormal excessive proliferation and migration which is enabled and enhanced by altered cell–cell and cell–matrix adhesion, the cancerous mass can invade the neighbouring tissue. Along with tumourinduced angiogenesis, invasion is a key component of metastatic spread, ultimately leading to the formation of secondary tumours in other parts of the host body. In a first project part, we explored the spatio-temporal dynamics of a model of cancer invasion, where cell–cell and cell–matrix adhesion is accounted for through non-local interaction terms in a system of partial integro-differential equations. The change of adhesion properties during cancer growth and development is investigated here through timedependent adhesion characteristics within the cell population as well as those between the cells and the components of the extracellular matrix. The temporal arrangement of changes in the adhesive properties is crucial. Our computational simulation results demonstrate a range of heterogeneous dynamics which are qualitatively similar to the invasive growth patterns observed in a number of different types of cancer, such as tumour infiltrative growth patterns (INF). In a second project part, we have investigated the role exerted by the dynamic interplay between collective cell movement and the various molecules involved in the accompanying cell signalling mechanisms occurring within the process of cancer invasion. Information about the various structures embedded within this process enables a detailed exploration of the binding of molecular species to cell-surface receptors within the evolving cell population. To this end, we established a general spatio-temporal-structural framework that enables the description of surface-bound reaction processes coupled with the cell population dynamics. We first provided a general theoretical description for this approach and then illustrated it with two concrete examples arising from cancer invasion.
Publications
- Mathematical modelling of cancer invasion: Implications of cell adhesion variability for tumour infiltrative growth patterns. Journal of Theoretical Biology, 361:41–60, 2014
P. Domschke, D. Trucu, A. Gerisch, and M. A. J. Chaplain
(See online at https://doi.org/10.1016/j.jtbi.2014.07.010)
