Vasiliki Bitsouni, Dumitru Trucu, Mark A J Chaplain, Raluca Eftimie
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Aggregation and travelling wave dynamics in a two-population model of cancer cell growth and invasion.
Cells adhere to each other and to the extracellular matrix (ECM) through protein molecules on the surface of the cells. The breaking and forming of adhesive bonds, a process critical in cancer invasion and metastasis, can be influenced by the mutation of cancer cells. In this paper, we develop a nonlocal mathematical model describing cancer cell invasion and movement as a result of integrin-controlled cell-cell adhesion and cell-matrix adhesion, for two cancer cell populations with different levels of mutation. The partial differential equations for cell dynamics are coupled with ordinary differential equations describing the ECM degradation and the production and decay of integrins. We use this model to investigate the role of cancer mutation on the possibility of cancer clonal competition with alternating dominance, or even competitive exclusion (phenomena observed experimentally). We discuss different possible cell aggregation patterns, as well as travelling wave patterns. In regard to the travelling waves, we investigate the effect of cancer mutation rate on the speed of cancer invasion.
期刊介绍:
Formerly the IMA Journal of Mathematics Applied in Medicine and Biology.
Mathematical Medicine and Biology publishes original articles with a significant mathematical content addressing topics in medicine and biology. Papers exploiting modern developments in applied mathematics are particularly welcome. The biomedical relevance of mathematical models should be demonstrated clearly and validation by comparison against experiment is strongly encouraged.
The journal welcomes contributions relevant to any area of the life sciences including:
-biomechanics-
biophysics-
cell biology-
developmental biology-
ecology and the environment-
epidemiology-
immunology-
infectious diseases-
neuroscience-
pharmacology-
physiology-
population biology