Files in this item
Derivation and travelling wave analysis of phenotype-structured haptotaxis models of cancer invasion
Item metadata
dc.contributor.author | Lorenzi, Tommaso | |
dc.contributor.author | Macfarlane, Fiona R. | |
dc.contributor.author | Painter, Kevin J. | |
dc.date.accessioned | 2024-02-29T11:30:08Z | |
dc.date.available | 2024-02-29T11:30:08Z | |
dc.date.issued | 2024-02-27 | |
dc.identifier | 295497044 | |
dc.identifier | 704933dc-ed8d-4eb5-949d-9c77678188bd | |
dc.identifier | 85186238813 | |
dc.identifier.citation | Lorenzi , T , Macfarlane , F R & Painter , K J 2024 , ' Derivation and travelling wave analysis of phenotype-structured haptotaxis models of cancer invasion ' , European Journal of Mathematics , vol. FirstView . https://doi.org/10.1017/S0956792524000056 | en |
dc.identifier.issn | 2199-6768 | |
dc.identifier.other | ORCID: /0000-0003-2242-7745/work/154531464 | |
dc.identifier.uri | https://hdl.handle.net/10023/29385 | |
dc.description | Funding: TL gratefully acknowledges support from the Italian Ministry of University and Research (MUR) through the grant PRIN 2020 project (No. 2020JLWP23) “Integrated Mathematical Approaches to Socio-Epidemiological Dynamics” (CUP: E15F21005420006) and the grant PRIN2022-PNRR project (No. P2022Z7ZAJ) “A Unitary Mathematical Framework for Modelling Muscular Dystrophies” (CUP: E53D23018070001), from the CNRS International Research Project “Modelisation de la biomecanique cellulaire et tissulaire” (MOCETIBI), and from the Istituto Nazionale di Alta Matematica (INdAM) and the Gruppo Nazionale per la Fisica Matematica (GNFM). KJP is a member of INdAM-GNFM and acknowledges “Miur-Dipartimento di Eccellenza” funding to the Dipartimento di Scienze, Progetto e Politiche del Territorio (DIST). | en |
dc.description.abstract | 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. | |
dc.format.extent | 33 | |
dc.format.extent | 985187 | |
dc.language.iso | eng | |
dc.relation.ispartof | European Journal of Mathematics | en |
dc.subject | Individual-based models | en |
dc.subject | Partial integro-differential equation | en |
dc.subject | Travelling wave analysis | en |
dc.subject | Phenotypic diversity | en |
dc.subject | Haptotaxis models of cancer invasion | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject | SDG 3 - Good Health and Well-being | en |
dc.subject.lcc | QA | en |
dc.title | Derivation and travelling wave analysis of phenotype-structured haptotaxis models of cancer invasion | en |
dc.type | Journal article | en |
dc.contributor.institution | University of St Andrews. Applied Mathematics | en |
dc.identifier.doi | 10.1017/S0956792524000056 | |
dc.description.status | Peer reviewed | en |
This item appears in the following Collection(s)
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.