Coupled bulk-surface free boundary problems arising from a mathematical model of receptor-ligand dynamics
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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.
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 . DOI: 10.1137/15M1050811
SIAM Journal on Mathematical Analysis
© 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
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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