Treffer: Phenotype structuring in collective cell migration: a tutorial of mathematical models and methods.

Title:
Phenotype structuring in collective cell migration: a tutorial of mathematical models and methods.
Authors:
Lorenzi T; Department of Mathematical Sciences 'G. L. Lagrange', Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129, Torino, Italy., Painter KJ; Dipartimento Interateneo di Scienze, Progetto e Politiche del Territorio, Politecnico di Torino, Viale Pier Andrea Mattioli, 39, 10125, Torino, Italy. kevin.painter@polito.it., Villa C; Sorbonne Université, CNRS, Université de Paris, Inria, Laboratoire Jacques-Louis Lions UMR 7598, 75005, Paris, France.; Université Paris-Saclay, Inria, Centre Inria de Saclay, 91120, Palaiseau, France.
Source:
Journal of mathematical biology [J Math Biol] 2025 May 16; Vol. 90 (6), pp. 61. Date of Electronic Publication: 2025 May 16.
Publication Type:
Journal Article; Review
Language:
English
Journal Info:
Publisher: Springer Verlag Country of Publication: Germany NLM ID: 7502105 Publication Model: Electronic Cited Medium: Internet ISSN: 1432-1416 (Electronic) Linking ISSN: 03036812 NLM ISO Abbreviation: J Math Biol Subsets: MEDLINE
Imprint Name(s):
Publication: Berlin : Springer Verlag
Original Publication: Wien, New York, Springer-Verlag.
MeSH Terms:
Cell Movement*/physiology , Models, Biological*, Phenotype ; Humans ; Mathematical Concepts ; Computer Simulation ; Animals ; Neoplasms/pathology
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Grant Information:
E15F21005420006 Ministero dell'Istruzione e del Merito; E53D23018070001 Ministero dell'Istruzione e del Merito; MOCETIBI Centre National de la Recherche Scientifique; MOCETIBI Centre National de la Recherche Scientifique
Contributed Indexing:
Keywords: Cell movement; Collective cell dynamics; Concentration phenomena; Non-local PDEs; Phenotype-structured populations; Travelling waves
Entry Date(s):
Date Created: 20250516 Date Completed: 20250516 Latest Revision: 20250603
Update Code:
20250603
PubMed Central ID:
PMC12084280
DOI:
10.1007/s00285-025-02223-y
PMID:
40377698
Database:
MEDLINE

Weitere Informationen

Populations are heterogeneous, deviating in numerous ways. Phenotypic diversity refers to the range of traits or characteristics across a population, where for cells this could be the levels of signalling, movement and growth activity, etc. Clearly, the phenotypic distribution - and how this changes over time and space - could be a major determinant of population-level dynamics. For instance, across a cancerous population, variations in movement, growth, and ability to evade death may determine its growth trajectory and response to therapy. In this review, we discuss how classical partial differential equation (PDE) approaches for modelling cellular systems and collective cell migration can be extended to include phenotypic structuring. The resulting non-local models - which we refer to as phenotype-structured partial differential equations (PS-PDEs) - form a sophisticated class of models with rich dynamics. We set the scene through a brief history of structured population modelling, and then review the extension of several classic movement models - including the Fisher-KPP and Keller-Segel equations - into a PS-PDE form. We proceed with a tutorial-style section on derivation, analysis, and simulation techniques. First, we show a method to formally derive these models from underlying agent-based models. Second, we recount travelling waves in PDE models of spatial spread dynamics and concentration phenomena in non-local PDE models of evolutionary dynamics, and combine the two to deduce phenotypic structuring across travelling waves in PS-PDE models. Third, we discuss numerical methods to simulate PS-PDEs, illustrating with a simple scheme based on the method of lines and noting the finer points of consideration. We conclude with a discussion of future modelling and mathematical challenges.
(© 2025. The Author(s).)

Declarations. Ethical statement: Not applicable. Competing interests: The authors have no competing interests to declare that are relevant to the content of this article. Consent for publication: All authors have given approval for publication. Materials availability: Not applicable. Code availability: Python code is available on the GitHub repository https://github.com/ChiaraVilla/LorenziEtAl2025Phenotype under GNU General Public License ( https://www.gnu.org/licenses/ ).