The reaction-limited kinetics of membrane-to-surface adhesion and detachment

Abstract

Biological adhesion is frequently mediated by specific membrane proteins (adhesion molecules). Starting with the notion of adhesion molecules, we present a simple model of the physics of membrane-to-surface attach­ment and detachment. This model consists of coupling the equations for deformation of an elastic membrane with equations for the chemical kinetics of the adhesion molecules. We propose a set of constitutive laws relating bond stress to bond strain and also relating the chemical rate constants of the adhesion molecules to bond strain. We derive an exact formula for the critical tension. We also describe a fast and accurate finite difference algorithm for generating numerical solutions of our model. Using this algorithm, we are able to compute the transient behaviour during the initial phases of adhesion and detachment as well as the steady-state geometry of adhesion and the velocity of the contact. An unexpected consequence of our model is the predicted occurrence of states in which adhesion cannot be reversed by application of tension. Such states occur only if the adhesion molecules have certain constitutive properties (catch-bonds). We discuss the rational for such catch-bonds and their possible biological significance. Finally, by analysis of numeri­cal solutions, we derive an accurate and general expression for the steady-state velocity of attachment and detachment. As applications of the theory, we discuss data on the rolling velocity of granulocytes in post-capillary venules and data on lectin-mediated adhesion of red cells.

Rolling and transient tethering of leukocytes on antibodies reveal specializations of selectins

“…7). To characterize quantitatively the effect of force on k off , the data were fit to Bell's model of k off as an exponential function of F b (20) and a Hookean spring model of k off as an exponential function of F b 2 as proposed by Dembo et al (21). 2 analysis showed that the fits were good for the Bell model ( 2 ϭ 56.2, with 112 df) and the Hookean spring model ( 2 ϭ 82.4, with 112 df) for the combined data from HL-60 cells and neotrophils.…”

“…Rolling and firmly adherent populations of cells often coexisted. These are the types of results that are predicted based on dynamic simulations of cell adhesive interactions in shear flow (12) or by some peeling models (21) and contrast with results with selectins. One remarkable property of selectins is the lack of development of firm adhesion in the absence of shear flow.…”

Liaisons « accrocheuses » et mécanique moléculaire

“…Ce travail démontre la réalité d'un concept imaginé par un théoricien, Micah Dembo, quinze ans auparavant [2]. Il marque aussi une étape supplémentaire dans un domaine de recherche qui s'est montré très actif au cours de la dernière décennie: l'observation directe des liaisons moléculaires individuelles [3].…”

“…Cette rupture constitue un événement aléatoire que l'on peut comparer, en quelque sorte, à la désin-tégration d'une substance radioactive. Quelques années plus tard, M. Dembo et al [2] glissantes» (slip bonds) dont la constante de dissociation était -conformément à l'intuition -augmentée par une force de séparation, d'hypothétiques «liaisons accrocheuses» (catch bonds) qui présenteraient un comportement opposé. Bien sûr, le comportement du rapport k on /k off est le même pour les deux types de liaisons, puisque ce rapport est déterminé par les lois de la thermodynamique.…”

Deformation Model for Thioredoxin Catalysis of Disulfide Bond Dissociation by Force

“…The catch-slip binding transitions were discovered recently in a number of receptor-ligand biological complexes. 2,3,7,8,10,17,18,[21][22][23][24]26,27,32 The disulfide bond presents the first example of a chemical catch-bond, i.e., a system in which the increased lifetimes are associated with breaking a covalent bond.…”