Resumen de A theoretical and computational study of soft adhesion mediated by mobile binders
Dimitri Jean Antoine Kaurin
We examine a classical problem in soft-matter physics: the specific adhesion between deformable elastic objects, such as vesicles, mediated by mobile adhesion molecules. This problem is relevant to cell-cell adhesion. To understand this fundamental yet poorly understood problem, in Part I of the thesis we develop mechano-stochastic minimal models to examine the coupling between the stochastic nature of the binding/unbinding of the adhesion molecules, the mechanical environment and geometrical architecture of the adhesion patch. Building on previous works, we specifically investigate the stability of adhesion clusters under hydraulic interstitial pressure, relevant in various physiological cellular processes, and the role of surface tension at the boundary of the media bridged by the molecular bond cluster. Remarkably, we find that surface tension has a strong stabilizing effect because it increases the rebinding rate. We also discuss the influence of the mobility of these molecules. This first part lays the ground for the main contributions of the thesis in Part II. Here, we develop a continuum general approach of soft adhesion mediated by mobile binders. This approach relies on Onsager’s variational principle. We then apply this modelling framework to study the unbinding of adhering vesicles. We consider a membrane with bending rigidity, subject to a fixed tension and a separation force by a loading device, with mobile adhesion molecules. These molecules store elastic energy when deformed, diffuse, and react by attaching with partners in a neighbouring vesicle. The binding kinetics strongly depend on the distance to potential partners and the unbinding kinetics depends on the force experienced by the binders (slip bond behaviour). The equilibrium picture for this problem has has long been known but the dynamics have been barely explored. Based on our theoretical framework, we perform numerical calculations to explore previously anticipated qualitative scenarios. In particular, we characterize a diffusion-dominated regime in which, under an applied force, adhesion patches shrink in size and become increasingly concentrated in bond until a new equilibrium is reached. More interestingly, in an intermediate regime, motion of bonds by diffusion and bond-breaking compete during the remodelling of adhesion patches under force. This process always leads to full dissociation, but the lifetime depends very strongly on force, defining a critical force that delimits the threshold separating stability and instability. We show how this threshold depends on the physico-chemical properties of adhesion molecules and on molecular crowding. Since these properties can be controlled by cells, e.g. through calcium signalling, our study portrays soft adhesion mediated by mobile binders as a highly tuneable process allowing cells to strongly hold to each other or disengage to remodel. Finally, in a reaction-dominated limit, we identify a new unusual tear-out regime, in which an adhesion patch shrinks under force by progressive bond-breaking near its edge, but which is critically controlled by diffusion occurring in a small zone near the edge.
