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

TL;DR

This paper analyzes a coupled bulk-surface PDE system modeling receptor-ligand interactions, proving solution existence, exploring asymptotic limits leading to free boundary problems, and providing numerical simulations in realistic geometries.

Contribution

It introduces a simplified coupled PDE model for receptor-ligand dynamics, proves its well-posedness, and investigates biologically relevant asymptotic limits with numerical validation.

Findings

Existence and uniqueness of solutions established.

Convergence to free boundary problems in asymptotic limits.

Numerical simulations demonstrate model behavior in realistic geometries.

Abstract

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.