One of the main steps in solid cancers to invade surrounding tissues is degradation of tissue barriers in the extracellular matrix. This operation that leads to initiate, angiogenesis and metastasis to other organs, is essentially consequence of collapsing dynamic balance between matrix metalloproteinases (MMP) and tissue inhibitors of metalloproteinases (TIMP). In this work, we model the MMP-TIMP interaction in both normal tissue and invasive cancer using evolutionary game theory. Our model explains how invasive cancer cells get the upper hand in MMP-TIMP imbalance scenarios. We investigate dynamics of them over time and discuss stable and nonstable states in the population. Numerical simulations presented here provide the identification of key genotypic features in the tumor invasion and a natural description for phenotypic variability. The simulation results are consistent with the experimental results in vitro observations presented in medical literature. Finally, by the provided results the necessary conditions to inhibit cancer invasion or prolong its course are explained. In this way, two therapeutic approaches with respect to how they could meet the required conditions are considered.
Keywords: Evolutionary game theory; Invasive cancer; MMP–TIMP interaction; Replicator dynamic.
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