Mean first passage times for bond formation for a Brownian particle in linear shear flow above a wall

TL;DR

This paper models the bond formation process between a Brownian particle and a wall under shear flow, deriving a Langevin equation with multiplicative noise, and explores different regimes of receptor-ligand binding relevant to cell adhesion.

Contribution

It introduces a Langevin equation with position-dependent mobility for simulating bond formation under shear flow, including receptor geometry effects, and provides exact solutions for homogeneous cases.

Findings

Derived a Langevin equation with multiplicative noise for the system

Developed a high-accuracy numerical simulation scheme

Identified scaling regimes relevant to biological cell adhesion

Abstract

Motivated by cell adhesion in hydrodynamic flow, here we study bond formation between a spherical Brownian particle in linear shear flow carrying receptors for ligands covering the boundary wall. We derive the appropriate Langevin equation which includes multiplicative noise due to position-dependent mobility functions resulting from the Stokes equation. We present a numerical scheme which allows to simulate it with high accuracy for all model parameters, including shear rate and three parameters describing receptor geometry (distance, size and height of the receptor patches). In the case of homogeneous coating, the mean first passage time problem can be solved exactly. In the case of position-resolved receptor-ligand binding, we identify different scaling regimes and discuss their biological relevance.