Mathematical modelling of cancer invasion: The multiple roles of TGF-β pathway on tumour proliferation and cell adhesion

Bitsouni, Vasiliki; Chaplain, M. A. J.; Eftimie, Raluca

doi:10.1142/s021820251750035x

Cited by 32 publications

(32 citation statements)

References 67 publications

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“…Let g i (υ (x + r,t) , c (x,t)) , i = 1, 2, describe the nature of the cell-cell and cell-matrix adhesive forces created at x due to signalling with cell/ECM components at x + r. These functions increase when the cell density and ECM density increase, and accordingly they decrease when the cell density and ECM density decrease. The functions g i , i = 1, 2, are chosen as in Bitsouni et al (2017) to be given by g 1 (υ (x + r,t) , c (x,t)) := S 1 (c (x,t)) u 1 (x + r,t) + S (c (x,t)) u 2 (x + r,t) +C 1 (c (x,t)) f (x + r,t) , (2.3) and g 2 (υ (x + r,t) , c (x,t)) := S 2 (c (x,t)) u 2 (x + r,t) + S (c (x,t)) u 1 (x + r,t) +C 2 (c (x,t)) f (x + r,t) , (2.4) 6 of 36 Vasiliki Bitsouni et al where S i (c (x,t)) is the cell-cell self-adhesion strength function for populations u i , S (c (x,t)) is the cell-cell cross-adhesion strength function between the two populations, and C i (c (x,t)) is the adhesion strength function between population u i and ECM. We should mention here that a similar term was considered before by Chaplain et al (2011).…”

Section: Derivation Of the Modelmentioning

confidence: 99%

Lyapunov–Schmidt and Centre Manifold Reduction Methods for Nonlocal PDEs Modelling Animal Aggregations

Buono

Eftimie

2016

Springer Proceedings in Mathematics &Amp; Statistics

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[Date] Cells adhere to each other and to the extracellular matrix (ECM) through protein molecules on the surface of the cells. The breaking and forming of adhesive bonds, a process critical in cancer invasion and metastasis, can be influenced by the mutation of cancer cells. In this paper, we develop a nonlocal mathematical model describing cancer cell invasion and movement as a result of integrin-controlled cell-cell adhesion and cell-matrix adhesion, for two cancer cell populations with different levels of mutation. The partial differential equations for cell dynamics are coupled with ordinary differential equations describing the extracellular matrix (ECM) degradation and the production and decay of integrins. We use this model to investigate the role of cancer mutation on the possibility of cancer clonal competition with alternating dominance, or even competitive exclusion (phenomena observed experimentally). We discuss different possible cell aggregation patterns, as well as travelling wave patterns. In regard to the travelling waves, we investigate the effect of cancer mutation rate on the speed of cancer invasion.

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Section: Derivation Of the Modelmentioning

confidence: 99%

Lyapunov–Schmidt and Centre Manifold Reduction Methods for Nonlocal PDEs Modelling Animal Aggregations

Buono

Eftimie

2016

Springer Proceedings in Mathematics &Amp; Statistics

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“…2013) as well as those exploring the direct effects of chemotaxis, proliferation and adhesion on tumour invasion (Bitsouni et al. 2017; Chauviere et al. 2007; Domschke et al.…”

Section: Introductionmentioning

confidence: 99%

Multiscale Modelling of Fibres Dynamics and Cell Adhesion within Moving Boundary Cancer Invasion

2019

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Recognised as one of the hallmarks of cancer, local cancer cell invasion is a complex multiscale process that combines the secretion of matrix-degrading enzymes with a series of altered key cell processes (such as abnormal cell proliferation and changes in cell–cell and cell–matrix adhesion leading to enhanced migration) to degrade important components of the surrounding extracellular matrix (ECM) and this way spread further in the human tissue. In order to gain a deeper understanding of the invasion process, we pay special attention to the interacting dynamics between the cancer cell population and various constituents of the surrounding tumour microenvironment. To that end, we consider the key role that ECM plays within the human body tissue, and in particular we focus on the special contribution of its fibrous proteins components, such as collagen and fibronectin, which play an important part in cell proliferation and migration. In this work, we consider the two-scale dynamic cross-talk between cancer cells and a two-component ECM (consisting of both a fibre and a non-fibre phase). To that end, we incorporate the interlinked two-scale dynamics of cell–ECM interactions within the tumour support that contributes simultaneously both to cell adhesion and to the dynamic rearrangement and restructuring of the ECM fibres. Furthermore, this is embedded within a multiscale moving boundary approach for the invading cancer cell population, in the presence of cell adhesion at the tissue scale and cell-scale fibre redistribution activity and leading edge matrix-degrading enzyme molecular proteolytic processes. The overall modelling framework will be accompanied by computational results that will explore the impact on cancer invasion patterns of different levels of cell adhesion in conjunction with the continuous ECM fibres rearrangement.

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“…Biological and mathematical models of both in vivo and in vitro experiments have given us a deeper insight into many processes involved during tumour invasion. Great focus has been placed on modelling the effects of cell-cell and cell-matrix adhesion (Painter et al, 2010;Armstrong et al, 2006;Anderson, 2005;Turner and Sherratt, 2002;Gerisch and Chaplain, 2008;Domschke et al, 2014;Bitsouni et al, 2017). On the other hand, recent works such as (Chauviere et al, 2007;Painter, 2008;Hillen et al, 2010;Schluter et al, 2012;Hillen et al, 2013;Engwer et al, 2015) have highlighted the vital importance that the composition of the ECM has on the overall invasion of cancer.…”

Section: Introductionmentioning

confidence: 99%

Multiscale dynamics of a heterotypic cancer cell population within a fibrous extracellular matrix

Shuttleworth

Trucu

2020

Journal of Theoretical Biology

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Local cancer cell invasion is a complex process involving many cellular and tissue interactions and is an important prerequisite for metastatic spread, the main cause of cancer related deaths. Occurring over many different temporal and spatial scales, the first stage of local invasion is the secretion of matrixdegrading enzymes (MDEs) and the resulting degradation of the extra-cellular matrix (ECM). This process creates space in which the cells can invade and thus enlarge the tumour. As a tumour increases in malignancy, the cancer cells adopt the ability to mutate into secondary cell subpopulations giving rise to a heterogeneous tumour. This new cell subpopulation often carries higher invasive qualities and permits a quicker spread of the tumour.Building upon the recent multiscale modelling framework for cancer invasion within a fibrous ECM introduced in Shuttleworth and Trucu (2019), in this paper we consider the process of local invasion by a heterotypic tumour consisting of two cancer cell populations mixed with a two-phase ECM. To that end, we address the double feedback link between the tissue-scale cancer dynamics and the cell-scale molecular processes through the development of a two-part modelling framework that crucially incorporates the multiscale dynamic redistribution of oriented fibres occurring within a two-phase extra-cellular matrix and combines this with the multiscale leading edge dynamics exploring key matrix-degrading enzymes molecular processes along the tumour interface that drive the movement of the cancer boundary. The modelling framework will be accompanied by computational results that explore the effects of the underlying fibre network on the overall pattern of cancer invasion.

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Mathematical modelling of cancer invasion: The multiple roles of TGF-β pathway on tumour proliferation and cell adhesion

Cited by 32 publications

References 67 publications

Lyapunov–Schmidt and Centre Manifold Reduction Methods for Nonlocal PDEs Modelling Animal Aggregations

Lyapunov–Schmidt and Centre Manifold Reduction Methods for Nonlocal PDEs Modelling Animal Aggregations

Multiscale Modelling of Fibres Dynamics and Cell Adhesion within Moving Boundary Cancer Invasion

Multiscale dynamics of a heterotypic cancer cell population within a fibrous extracellular matrix

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