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Coupled bulk-surface free boundary problems arising from a mathematical model of receptor-ligand dynamics
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Elliott, Charles M., Ranner, Thomas and Venkataraman, Chandrasekhar (2017) Coupled bulk-surface free boundary problems arising from a mathematical model of receptor-ligand dynamics. SIAM Journal on Mathematical Analysis, 49 (1). pp. 360-397. ISSN 0036-1410.
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Official URL: http://dx.doi.org/10.1137/15M1050811
Abstract
We consider a coupled bulk-surface system of partial differential equations with nonlinear coupling modelling receptor-ligand dynamics. The model arises as a simplification of a mathematical model for the reaction between cell surface resident receptors and ligands present in the extra-cellular medium. We prove the existence and uniqueness of solutions. We also consider a number of biologically relevant asymptotic limits of the model. We prove convergence to limiting problems which take the form of free boundary problems posed on the cell surface. We also report on numerical simulations illustrating convergence to one of the limiting problems as well as the spatio-temporal distributions of the receptors and ligands in a realistic geometry.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Library of Congress Subject Headings (LCSH): | Differential equations, Partial, Finite element method | ||||||
Journal or Publication Title: | SIAM Journal on Mathematical Analysis | ||||||
Publisher: | Society for Industrial and Applied Mathematics | ||||||
ISSN: | 0036-1410 | ||||||
Official Date: | 8 February 2017 | ||||||
Dates: |
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Volume: | 49 | ||||||
Number: | 1 | ||||||
Page Range: | pp. 360-397 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Date of first compliant deposit: | 10 November 2016 | ||||||
Date of first compliant Open Access: | 22 May 2017 | ||||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC), Royal Society (Great Britain). Wolfson Research Merit Award (RSWRMA), Leverhulme Trust (LT). Research Fellowship | ||||||
Grant number: | EP/K032208/1 (EPSRC), EP/J004057/1 (EPSRC), RPG-2014-149 (LT) | ||||||
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