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

Charles M. Elliot, Thomas Ranner, Chandrasekhar Venkataraman

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)360-397
Number of pages38
JournalSIAM Journal on Mathematical Analysis
Volume49
Issue number1
DOIs
Publication statusPublished - 8 Feb 2017

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