Mathematical Modeling of Metastatic Cancer Migration through a Remodeling Extracellular Matrix

Edalgo, Yen T. Nguyen; Versypt, Ashlee N. Ford

doi:10.3390/pr6050058

Cited by 19 publications

(7 citation statements)

References 61 publications

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“…Another key purpose of mathematical models in biology is in elucidating unexplained processes, for example, the role of the ECM remodeling enzyme LOX during cancer cell migration (Nguyen Edalgo and Ford Versypt, 2018). This particular model provides predictions that could guide therapeutic treatments, such as inhibiting LOX production to slow down ECM remodeling, thus preventing the spread of cancer.…”

Section: Discussionmentioning

confidence: 99%

Modeling the extracellular matrix in cell migration and morphogenesis: a guide for the curious biologist

Crossley,

Johnson,

Tsingos

et al. 2024

Front. Cell Dev. Biol.

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The extracellular matrix (ECM) is a highly complex structure through which biochemical and mechanical signals are transmitted. In processes of cell migration, the ECM also acts as a scaffold, providing structural support to cells as well as points of potential attachment. Although the ECM is a well-studied structure, its role in many biological processes remains difficult to investigate comprehensively due to its complexity and structural variation within an organism. In tandem with experiments, mathematical models are helpful in refining and testing hypotheses, generating predictions, and exploring conditions outside the scope of experiments. Such models can be combined and calibrated with in vivo and in vitro data to identify critical cell-ECM interactions that drive developmental and homeostatic processes, or the progression of diseases. In this review, we focus on mathematical and computational models of the ECM in processes such as cell migration including cancer metastasis, and in tissue structure and morphogenesis. By highlighting the predictive power of these models, we aim to help bridge the gap between experimental and computational approaches to studying the ECM and to provide guidance on selecting an appropriate model framework to complement corresponding experimental studies.

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Section: Discussionmentioning

confidence: 99%

Modeling the extracellular matrix in cell migration and morphogenesis: a guide for the curious biologist

Crossley,

Johnson,

Tsingos

et al. 2024

Front. Cell Dev. Biol.

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“…Numerical simulations have also been used to investigate models of the form of (1) [28]. Further models extend systems of this form, for example, to include more detailed mechanisms of ECM remodelling and enzyme activities [3,15,47], or through the inclusion of non-local terms to incorporate the effects of cell-cell adhesion [29,51]. Models have also been formulated to include detailed cell mechanics -e.g.…”

Section: Mathematical Modelling Backgroundmentioning

confidence: 99%

Derivation and travelling wave analysis of phenotype-structured haptotaxis models of cancer invasion

Lorenzi,

Macfarlane,

Painter

2024

Eur. J. Appl. Math

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We formulate haptotaxis models of cancer invasion wherein the infiltrating cancer cells can occupy a spectrum of states in phenotype space, ranging from ‘fully mesenchymal’ to ‘fully epithelial’. The more mesenchymal cells are those that display stronger haptotaxis responses and have greater capacity to modify the extracellular matrix (ECM) through enhanced secretion of matrix-degrading enzymes (MDEs). However, as a trade-off, they have lower proliferative capacity than the more epithelial cells. The framework is multiscale in that we start with an individual-based model that tracks the dynamics of single cells, which is based on a branching random walk over a lattice representing both physical and phenotype space. We formally derive the corresponding continuum model, which takes the form of a coupled system comprising a partial integro-differential equation for the local cell population density function, a partial differential equation for the MDE concentration and an infinite-dimensional ordinary differential equation for the ECM density. Despite the intricacy of the model, we show, through formal asymptotic techniques, that for certain parameter regimes it is possible to carry out a detailed travelling wave analysis and obtain invading fronts with spatial structuring of phenotypes. Precisely, the most mesenchymal cells dominate the leading edge of the invasion wave and the most epithelial (and most proliferative) dominate the rear, representing a bulk tumour population. As such, the model recapitulates similar observations into a front to back structuring of invasion waves into leader-type and follower-type cells, witnessed in an increasing number of experimental studies over recent years.

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“…ABMs have been widely used to simulate the dynamics of diverse immune 34 , 35 , 36 and cancer cells populations. 37 , 38 , 39 Specifically, models have investigated properties of tumor morphology, 40 , 41 adaptation of cancer cells in the TME, 42 mutations and phenotype diversity, 43 the role of the extracellular matrix, 44 , 45 and the effect of drugs and nutrition on tumor survival and proliferation. 46 , 47 , 48 Recent works focusing more specifically on macrophages in the TME of solid tumors have mostly exploited ordinary differential equation approaches.…”

Section: Introductionmentioning

confidence: 99%

An agent-based model of monocyte differentiation into tumour-associated macrophages in chronic lymphocytic leukemia

et al. 2023

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Mathematical Modeling of Metastatic Cancer Migration through a Remodeling Extracellular Matrix

Cited by 19 publications

References 61 publications

Modeling the extracellular matrix in cell migration and morphogenesis: a guide for the curious biologist

Modeling the extracellular matrix in cell migration and morphogenesis: a guide for the curious biologist

Derivation and travelling wave analysis of phenotype-structured haptotaxis models of cancer invasion

An agent-based model of monocyte differentiation into tumour-associated macrophages in chronic lymphocytic leukemia

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