The first step towards the mathematical understanding of the role of matrix metalloproteinase-8 in cancer invasion

Anna Wilson, Thomas Williams, Nikolaos Sfakianakis*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution


The role of matrix metalloproteinases-8 (MMP-8) in the cancer progression is quite complex, with contradictory indications as to whether it suppresses or assists the local growth of cancer. In addition, while other types of MMPs appear in either soluble or (cancer cell) membrane-bound form MMP-8 seems to appear in both. We take the first step in unravelling this dual nature of MMP-8 by shedding some mathematical light into its properties. To this end, we develop a mathematical model to investigate the impact of both soluble and membrane-bound MMPs in the early stages of local invasion of cancer cells. We propose an extension to a previously developed three-dimensional, hybrid atomistic-collective, cancer invasion model that allows the description of individual cancer cells along side with macroscopic tissue representations, and for the natural transition between these phases. We further assume that the soluble MMPs are produced by polymorphonuclear neutrophils, that pre-exist in the environment, and that they get activated by the cancer cells. The membrane-bound MMPs are expressed on the membrane of the cancer cells and along with the soluble MMPs, participate in the degradation of the extracellular matrix and, in effect, directly influence the migration of the cancer cells in what is understood to be a self-generated haptotaxis invasion strategy. With a series of numerical experiments and simulations we investigate the potential of the model in producing various invasion patterns, some resembling, qualitatively, to experimental invasion assays.
Original languageEnglish
Title of host publicationMethods of mathematical oncology
Subtitle of host publicationfusion of mathematics and biology, Osaka, Japan, October 26–28, 2020
EditorsTakashi Suzuki, Clair Poignard, Mark Chaplain, Vito Quaranta
Place of PublicationSingapore
Number of pages20
ISBN (Electronic)9789811648663
ISBN (Print)9789811648656, 9789811648687
Publication statusPublished - 22 Aug 2021
EventInternational Conference by Center for Mathematical Modeling and Data Science - Osaka University, Japan
Duration: 26 Oct 202028 Oct 2020

Publication series

NameSpringer proceedings in mathematics & statistics
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017


ConferenceInternational Conference by Center for Mathematical Modeling and Data Science
Abbreviated titleMMDS 2020
Internet address


  • Cancer invasion
  • Metalloproteinases
  • Plymorphonuclear neutrophils
  • Mathematical models
  • Partial differential equations
  • Stochastic differential equations
  • Genuinely hybrid models


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