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Coupled bulk-surface free boundary problems arising from a mathematical model of receptor-ligand dynamics

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Elliot_2016_Coupled_SIAMJMA_AAM.pdf (5.828Mb)
Date
08/02/2017
Author
Elliot, Charles M.
Ranner, Thomas
Venkataraman, Chandrasekhar
Keywords
QA Mathematics
QH301 Biology
T-NDAS
BDC
R2C
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Abstract
We consider a coupled bulk-surface system of partial differential equations with nonlinear coupling modeling 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 extracellular 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 spatiotemporal distributions of the receptors and ligands in a realistic geometry.
Citation
Elliot , C M , Ranner , T & Venkataraman , C 2017 , ' Coupled bulk-surface free boundary problems arising from a mathematical model of receptor-ligand dynamics ' , SIAM Journal on Mathematical Analysis , vol. 49 , no. 1 , pp. 360-397 . https://doi.org/10.1137/15M1050811
Publication
SIAM Journal on Mathematical Analysis
Status
Peer reviewed
DOI
https://doi.org/10.1137/15M1050811
ISSN
0036-1410
Type
Journal article
Rights
© 2017, Society for Industrial and Applied Mathematics. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at epubs.siam.org / https://dx.doi.org/10.1137/15M1050811
Description
This work was started whilst the authors were participants in the Isaac Newton Institute programme: “Free Boundary Problems and Related Topics” and finalised whilst the authors were participants in the Isaac Newton Institute programme: “Coupling Geometric PDEs with Physics for Cell Morphology, Motility and Pattern Formation” supported by EPSRC Grant Number EP/K032208/1. The work of CV received support from the Leverhulme Trust Research Project Grant (RPG-2014-149).
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  • University of St Andrews Research
URI
http://hdl.handle.net/10023/9779

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