Mathematical Modelling of Cancer Invasion: The Multiple Roles of TGF-β Pathway on Tumour Proliferation and Cell Adhesion

Vasiliki Bitsouni; Mark Chaplain; Raluca Eftimie

doi:10.1142/S021820251750035X

Mathematical Modelling of Cancer Invasion: The Multiple Roles of TGF-β Pathway on Tumour Proliferation and Cell Adhesion

Vasiliki Bitsouni (Lead / Corresponding author), Mark Chaplain, Raluca Eftimie

Research output: Contribution to journal › Article › peer-review

24 Citations (Scopus)

227 Downloads (Pure)

Abstract

In this paper, we develop a non-local mathematical model describing cancer cell invasion and movement as a result of integrin-controlled cell-cell adhesion and cell-matrix adhesion, and transforming growth factor-beta (TGF-β) effect on cell proliferation and adhesion, for two cancer cell populations with different levels of mutation. The model consists of partial integro-differential equations describing the dynamics of two cancer cell populations, coupled with ordinary differential equations describing the extracellular matrix (ECM) degradation and the production and decay of integrins, and with a parabolic PDE governing the evolution of TGF-β concentration. We prove the global existence of weak solutions to the model. We then use our model to explore numerically the role of TGF-β in cell aggregation and movement.

Original language	English
Pages (from-to)	1929-1962
Number of pages	34
Journal	Mathematical Models and Methods in Applied Sciences
Volume	27
Issue number	10
DOIs	https://doi.org/10.1142/S021820251750035X
Publication status	Published - 6 Jul 2017

Keywords

Non-local model of cancer progression
Existence
Boundedness of solution
Cell heterogeneity
TGF-β
Cell-cell and cell-matrix adhesion

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1142/S021820251750035XLicence: CC BY

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This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC-BY) License. Further distribution of this work is permitted, provided the original work is properly cited.
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Mathematical Investigation into the Role of Cell-cell Communication Pathways on Collective Cell Migration (First Grant Scheme)
Eftimie, R. (Investigator)
Engineering and Physical Sciences Research Council
1/11/13 → 31/10/15
Project: Research

Nonlinear Nonlocal Parabolic-Hyperbolic Coupled Systems for Cancer Cell Movement and Aggregation
Bitsouni, V. (Author), Eftimie, R. (Supervisor) & Chaplain, M. (Supervisor), 2017
Student thesis: Doctoral Thesis › Doctor of Philosophy

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title = "Mathematical Modelling of Cancer Invasion: The Multiple Roles of TGF-β Pathway on Tumour Proliferation and Cell Adhesion",

abstract = "In this paper, we develop a non-local mathematical model describing cancer cell invasion and movement as a result of integrin-controlled cell-cell adhesion and cell-matrix adhesion, and transforming growth factor-beta (TGF-β) effect on cell proliferation and adhesion, for two cancer cell populations with different levels of mutation. The model consists of partial integro-differential equations describing the dynamics of two cancer cell populations, coupled with ordinary differential equations describing the extracellular matrix (ECM) degradation and the production and decay of integrins, and with a parabolic PDE governing the evolution of TGF-β concentration. We prove the global existence of weak solutions to the model. We then use our model to explore numerically the role of TGF-β in cell aggregation and movement.",

keywords = "Non-local model of cancer progression, Existence, Boundedness of solution, Cell heterogeneity, TGF-β, Cell-cell and cell-matrix adhesion",

author = "Vasiliki Bitsouni and Mark Chaplain and Raluca Eftimie",

note = "The authors would like to thank Dr. D. Trucu for fruitful discussions. VB acknowledges support from an Engineering and Physical Sciences Research Council (UK) grant number EP/L504932/1. RE was partially supported by an Engineering and Physical Sciences Research Council (UK) grant number EP/K033689/1.",

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doi = "10.1142/S021820251750035X",

language = "English",

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Mathematical Modelling of Cancer Invasion: The Multiple Roles of TGF-β Pathway on Tumour Proliferation and Cell Adhesion. / Bitsouni, Vasiliki (Lead / Corresponding author); Chaplain, Mark; Eftimie, Raluca.
In: Mathematical Models and Methods in Applied Sciences, Vol. 27, No. 10, 06.07.2017, p. 1929-1962.

Research output: Contribution to journal › Article › peer-review

TY - JOUR

T1 - Mathematical Modelling of Cancer Invasion

T2 - The Multiple Roles of TGF-β Pathway on Tumour Proliferation and Cell Adhesion

AU - Bitsouni, Vasiliki

AU - Chaplain, Mark

AU - Eftimie, Raluca

N1 - The authors would like to thank Dr. D. Trucu for fruitful discussions. VB acknowledges support from an Engineering and Physical Sciences Research Council (UK) grant number EP/L504932/1. RE was partially supported by an Engineering and Physical Sciences Research Council (UK) grant number EP/K033689/1.

PY - 2017/7/6

Y1 - 2017/7/6

N2 - In this paper, we develop a non-local mathematical model describing cancer cell invasion and movement as a result of integrin-controlled cell-cell adhesion and cell-matrix adhesion, and transforming growth factor-beta (TGF-β) effect on cell proliferation and adhesion, for two cancer cell populations with different levels of mutation. The model consists of partial integro-differential equations describing the dynamics of two cancer cell populations, coupled with ordinary differential equations describing the extracellular matrix (ECM) degradation and the production and decay of integrins, and with a parabolic PDE governing the evolution of TGF-β concentration. We prove the global existence of weak solutions to the model. We then use our model to explore numerically the role of TGF-β in cell aggregation and movement.

AB - In this paper, we develop a non-local mathematical model describing cancer cell invasion and movement as a result of integrin-controlled cell-cell adhesion and cell-matrix adhesion, and transforming growth factor-beta (TGF-β) effect on cell proliferation and adhesion, for two cancer cell populations with different levels of mutation. The model consists of partial integro-differential equations describing the dynamics of two cancer cell populations, coupled with ordinary differential equations describing the extracellular matrix (ECM) degradation and the production and decay of integrins, and with a parabolic PDE governing the evolution of TGF-β concentration. We prove the global existence of weak solutions to the model. We then use our model to explore numerically the role of TGF-β in cell aggregation and movement.

KW - Non-local model of cancer progression

KW - Existence

KW - Boundedness of solution

KW - Cell heterogeneity

KW - TGF-β

KW - Cell-cell and cell-matrix adhesion

U2 - 10.1142/S021820251750035X

DO - 10.1142/S021820251750035X

M3 - Article

SN - 0218-2025

VL - 27

SP - 1929

EP - 1962

JO - Mathematical Models and Methods in Applied Sciences

JF - Mathematical Models and Methods in Applied Sciences

IS - 10

ER -

Mathematical Modelling of Cancer Invasion: The Multiple Roles of TGF-β Pathway on Tumour Proliferation and Cell Adhesion

Abstract

Keywords

UN SDGs

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Projects

Mathematical Investigation into the Role of Cell-cell Communication Pathways on Collective Cell Migration (First Grant Scheme)

Student theses

Nonlinear Nonlocal Parabolic-Hyperbolic Coupled Systems for Cancer Cell Movement and Aggregation

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