Mathematical modelling of cell migration: stiffness dependent jump rates result in durotaxis.
Advection–diffusion equation
Cell migration
Durotaxis
Jump process
Stochastic model
Journal
Journal of mathematical biology
ISSN: 1432-1416
Titre abrégé: J Math Biol
Pays: Germany
ID NLM: 7502105
Informations de publication
Date de publication:
06 2019
06 2019
Historique:
received:
05
06
2018
revised:
25
01
2019
pubmed:
12
4
2019
medline:
12
9
2020
entrez:
12
4
2019
Statut:
ppublish
Résumé
Durotaxis, the phenomena where cells migrate up a gradient in substrate stiffness, remains poorly understood. It has been proposed that durotaxis results from the reinforcement of focal adhesions on stiff substrates. In this paper we formulate a mathematical model of single cell migration on elastic substrates with spatially varying stiffness. We develop a stochastic model where the cell moves by updating the position of its adhesion sites at random times, and the rate of updates is determined by the local stiffness of the substrate. We investigate two physiologically motivated mechanisms of stiffness sensing. From the stochastic model of single cell migration we derive a population level description in the form of a partial differential equation for the time evolution of the density of cells. The equation is an advection-diffusion equation, where the advective velocity is proportional to the stiffness gradient. The model shows quantitative agreement with experimental results in which cells tend to cluster when seeded on a matrix with periodically varying stiffness.
Identifiants
pubmed: 30972438
doi: 10.1007/s00285-019-01344-5
pii: 10.1007/s00285-019-01344-5
pmc: PMC6534528
doi:
Types de publication
Journal Article
Research Support, Non-U.S. Gov't
Langues
eng
Sous-ensembles de citation
IM
Pagination
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