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The Reaction-Limited Kinetics of Membrane-to-Surface Adhesion and Detachment
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...
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Published in: | Proceedings of the Royal Society of London. Series B, Biological sciences Biological sciences, 1988-06, Vol.234 (1274), p.55-83 |
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Main Authors: | , , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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Summary: | 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. |
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ISSN: | 0962-8452 0080-4649 0950-1193 1471-2954 2053-9193 |
DOI: | 10.1098/rspb.1988.0038 |