Abstract
One of the hallmarks of cancer growth and metastatic spread is the process of local invasion of the surrounding tissue. Cancer cells achieve protease-dependent invasion by the secretion of enzymes involved in proteolysis. These overly expressed proteolytic enzymes then proceed to degrade the host tissue allowing the cancer cells to disseminate throughout the microenvironment by active migration and interaction with components of the extracellular matrix (ECM) such as collagen. In this paper we develop a mathematical model of cancer invasion which consider the role of matrix metalloproteinases (MMPs). Specifically our model will focus on two distinct types of MMP, i.e., soluble, diffusible MMPs (e.g., MMP-2) and membrane-bound MMPs (e.g., MT1-MMP), and the roles each of these plays in cancer invasion. The implications of MMP-2 activation by MMP-14 and the tissue inhibitor of metalloproteinases-2 are considered alongside the effect the architecture of the matrix may have when applied to a model of cancer invasion. Elements of the ECM architecture investigated include pore size of the matrix, since in some highly dense collagen structures such as breast tissue, the cancer cells are unable to physically fit through a porous region, and the crosslinking of collagen fibers. In this scenario, cancer cells rely on membrane-bound MMPs to forge a path through which degradation by other MMPs and movement of cancer cells becomes possible.
Highlights
For metastasis to occur, cancer cells must exhibit invasion through a variety of structured media such as the highly dense collagen constitution of some peritumoral stroma (Hanahan and Weinberg, 2000, 2011)
Mathematical modeling has continued to develop to investigate a number of topics in cancer progression and invasion, including models taking into account: oxygen/nutrient driven dynamics, the immune response, the acidity of the environment, forcebased pressure, the microenvironment in general, and proteasedependent invasion using the techniques of partial differential equations for densities of cells, individual-based models including cellular automaton models and multi-scale models as outlined in the review papers of Araujo and McElwain (2004), Rejniak and McCawley (2010), and Lowengrub et al (2010) and the references therein
We focus on a continuum, deterministic approach to protease-dependent invasion where matrix degrading enzymes cleave collagen fibrils and other extracellular matrix (ECM) components rather than protease-independent invasion where mechanical forces physically displace matrix fibrils and cancer cells adopt an amoeboid-like shape
Summary
Cancer cells must exhibit invasion through a variety of structured media such as the highly dense collagen constitution of some peritumoral stroma (Hanahan and Weinberg, 2000, 2011). This means that tissue degradation in advance of the cancer cells is the result of the soluble MMPs. While MT1MMP activity is restricted in range, it has an advantage in its capability of overcoming environments of higher collagen density such as exists in some peritumoral stroma.
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