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

Charles M. Elliot; Thomas Ranner; Chandrasekhar Venkataraman

doi:10.1137/15M1050811

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

Charles M. Elliot, Thomas Ranner, Chandrasekhar Venkataraman

Applied Mathematics

Research output: Contribution to journal › Article › peer-review

16 Citations (Scopus)

4 Downloads (Pure)

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 language	English
Pages (from-to)	360-397
Number of pages	38
Journal	SIAM Journal on Mathematical Analysis
Volume	49
Issue number	1
DOIs	https://doi.org/10.1137/15M1050811
Publication status	Published - 8 Feb 2017

Access to Document

10.1137/15M1050811

Elliot_2016_Coupled_SIAMJMA_AAM
© 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
Accepted author manuscript, 5.83 MB

Cite this

@article{e4b0310ff06d4f64a01b352ff99eff47,

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

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.",

author = "Elliot, {Charles M.} and Thomas Ranner and Chandrasekhar Venkataraman",

note = "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).",

year = "2017",

month = feb,

day = "8",

doi = "10.1137/15M1050811",

language = "English",

volume = "49",

pages = "360--397",

journal = "SIAM Journal on Mathematical Analysis",

issn = "0036-1410",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "1",

}

TY - JOUR

T1 - Coupled bulk-surface free boundary problems arising from a mathematical model of receptor-ligand dynamics

AU - Elliot, Charles M.

AU - Ranner, Thomas

AU - Venkataraman, Chandrasekhar

N1 - 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).

PY - 2017/2/8

Y1 - 2017/2/8

N2 - 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.

AB - 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.

U2 - 10.1137/15M1050811

DO - 10.1137/15M1050811

M3 - Article

SN - 0036-1410

VL - 49

SP - 360

EP - 397

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 1

ER -

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

Abstract

Access to Document

Fingerprint

Cite this