Surface deformation and shear flow in ligand mediated cell adhesion

We present a unified, multiscale model to study the attachment/detachment dynamics of two deforming, charged, near spherical cells, coated with binding ligands and subject to a slow, homogeneous shear flow in a viscous, ionic fluid medium. The binding ligands on the surface of the cells experience both attractive and repulsive forces in an ionic medium and exhibit finite resistance to rotation via bond tilting. The microscale drag forces and couples describing the fluid flow inside the small separation gap between the cells, are calculated using a combination of methods in lubrication theory and previously published numerical results. For a selected range of material and fluid parameters, a hysteretic transition of the sticking probability curves (i.e., the function g∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g^*$$\end{document}) between the adhesion phase (when g∗>0.5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g^*>0.5$$\end{document}) and the fragmentation phase (when g∗<0.5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g^*<0.5$$\end{document}) is attributed to a nonlinear relation between the total nanoscale binding forces and the separation gap between the cells. We show that adhesion is favoured in highly ionic fluids, increased deformability of the cells, elastic binders and a higher fluid shear rate (until a critical threshold value of shear rate is reached). Within a selected range of critical shear rates, the continuation of the limit points (i.e., the turning points where the slope of g∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g^*$$\end{document} changes sign) predict a bistable region, indicating an abrupt switching between the adhesion and the fragmentation regimes. Although, bistability in the adhesion-fragmentation phase diagram of two deformable, charged cells immersed in an ionic aqueous environment has been identified by some in vitro experiments, but until now, has not been quantified theoretically.