title: Mathematical modeling of cancer invasion: the role of membrane-bound matrix metalloproteinases.
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.
authors.affiliation: Division of Mathematics, University of Dundee Dundee, UK.
authors.forename: Niall E
authors.initials: NE
authors.lastname: Deakin
authors.forename: Mark A J
authors.initials: MA
authors.lastname: Chaplain
keywords: cancer invasion; extracellular matrix; mathematical model; membrane-bound MMPs; metalloproteinases
references.citation: J Cell Sci. 2009 Jun 1;122(Pt 11):1788-99
references.pmid: 19435799
references.citation: J Biol Chem. 2000 Dec 29;275(52):41415-23
references.pmid: 10998420
references.citation: Mol Biol Cell. 2008 Aug;19(8):3221-33
references.pmid: 18495869
references.citation: J Biol Chem. 1995 Mar 10;270(10):5331-8
references.pmid: 7890645
references.citation: Int J Cancer. 2003 Nov 20;107(4):541-50
references.pmid: 14520690
references.citation: J Cell Biol. 2009 Apr 6;185(1):11-9
references.pmid: 19332889
references.citation: J Biol Chem. 1998 Jan 9;273(2):871-80
references.pmid: 9422744
references.citation: Invest Ophthalmol Vis Sci. 2013 Feb 05;54(2):1014-25
references.pmid: 23322569
references.citation: Cell. 2000 Jan 7;100(1):57-70
references.pmid: 10647931
references.citation: Exp Biol Med (Maywood). 2010 Apr;235(4):411-23
references.pmid: 20407073
references.citation: Bull Math Biol. 2004 Sep;66(5):1039-91
references.pmid: 15294418
references.citation: PLoS One. 2011;6(9):e24029
references.pmid: 21912660
references.citation: J Pathol. 2005 Mar;205(4):468-75
references.pmid: 15685705
references.citation: Cell. 2011 Mar 4;144(5):646-74
references.pmid: 21376230
references.citation: FEBS Lett. 2003 Oct 23;553(3):457-63
references.pmid: 14572669
references.citation: J Theor Biol. 2008 Feb 21;250(4):684-704
references.pmid: 18068728
references.citation: PLoS One. 2011;6(9):e24246
references.pmid: 21980344
references.citation: Growth. 1966 Jun;30(2):157-76
references.pmid: 5963695
references.citation: Cell. 2010 Apr 2;141(1):52-67
references.pmid: 20371345
references.citation: Bioinformatics. 2001 May;17(5):483-4
references.pmid: 11331245
references.citation: Nonlinearity. 2010;23(1):R1-R9
references.pmid: 20808719
references.citation: Semin Cell Dev Biol. 2009 Oct;20(8):931-41
references.pmid: 19682592
references.citation: PLoS Comput Biol. 2012;8(4):e1002479
references.pmid: 22511862
references.citation: Cancer Res. 2008 Nov 1;68(21):9096-104
references.pmid: 18974156
references.citation: Annu Rev Cell Dev Biol. 2009;25:567-95
references.pmid: 19575644
references.citation: Eur J Cell Biol. 2001 Jan;80(1):68-77
references.pmid: 11211937
references.citation: J Theor Biol. 2006 Jan 7;238(1):124-45
references.pmid: 16005020
references.citation: Cancer Chemother Pharmacol. 1999;43 Suppl:S42-51
references.pmid: 10357558
references.citation: Curr Opin Genet Dev. 2005 Feb;15(1):87-96
references.pmid: 15661538
references.citation: Eur J Biochem. 1997 Dec 15;250(3):751-7
references.pmid: 9461298
references.citation: J Biol Chem. 2004 Oct 8;279(41):43336-44
references.pmid: 15292230
references.citation: J Cell Sci. 1996 May;109 ( Pt 5):953-9
references.pmid: 8743942
references.citation: Cell. 1997 Nov 14;91(4):439-42
references.pmid: 9390552
references.citation: J Biol Chem. 1999 Jul 30;274(31):21491-4
references.pmid: 10419448
references.citation: BMC Med. 2008 Apr 28;6:11
references.pmid: 18442412
references.citation: J Biol Chem. 2001 Nov 9;276(45):42018-26
references.pmid: 11555661
references.citation: Br J Cancer. 1955 Dec;9(4):539-49
references.pmid: 13304213
references.citation: Front Pharmacol. 2012 Jul 17;3:140
references.pmid: 22822400
references.citation: J Biol Chem. 2004 Sep 10;279(37):39105-14
references.pmid: 15252025
references.citation: Biochem Soc Symp. 2003;(70):277-85
references.pmid: 14587300
references.citation: Nat Rev Mol Cell Biol. 2002 Jul;3(7):509-19
references.pmid: 12094217