Coupled bulk-surface free boundary problems arising from a mathematical model of receptor-ligand dynamics
Date
08/02/2017Metadata
Show full item recordAbstract
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
ISSN
0036-1410Type
Journal article
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).Collections
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