VOLUME 87, NUMBER 17 PHYSICAL REVIEW LETTERS 22 OCTOBER 2001 From Macroscopic Adhesion Energy to Molecular Bonds: A Test of the Theory Frédéric Pincet, 1, * Eric Perez, 1 Jean-Christophe Loudet, 1 and Luc Lebeau 2 1 Laboratoire de Physique Statistique de l’Ecole Normale Supérieure, associé au CNRS et aux universités Paris VI et Paris VII, 24, rue Lhomond, 75231 Paris Cedex 05, France 2 Laboratoire de Synthèse Bio-organique, CNRS, Unité de Recherche Associée 1386, Faculté de Pharmacie, 74 Route du Rhin, 67401 Illkirch, France (Received 5 July 2000; published 9 October 2001) We present a statistical mechanical treatment relating the macroscopic adhesion energy of two surfaces, which can be obtained by micropipette aspiration studies, to the microscopic adhesion energy between individual bonds. The treatment deals with the case of weak reversible bonds, so that the equilibrium partition function has significance. This description is coherent with previous theories. Experiment and theory are compared to probe the nature of weak bonds in membranes, where local equilibria can be obtained. The case of a bead and a vesicle decorated by nucleosides was considered. DOI: 10.1103/PhysRevLett.87.178101 PACS numbers: 87.15.Kg, 68.35.Md, 87.15.By Biological media provide a great variety of physico- chemical phenomena through molecular recognition. Ev- erything biological is accomplished with weak interactions and bonds. Strong interactions would stop the dynamical processes which are indispensable to life. The adhesion of surfaces exhibiting binding sites has been widely investi- gated theoretically [1 – 4]. Because of the diffusion pro- cess, the adhesion sites are attracted to the contact zone. A previous pioneering work [5] has indeed analyzed and confirmed the kinetics of the enrichment in the contact zone of two vesicles. In contrast, the experimental test of the theory was hindered by the lack of available weak binding sites with reversible adhesion. Recently designed lipid molecules and end-functionalized polymers now al- low such experiments. The aim of this paper is to ex- tend the equilibrium models and test them with these new molecular tools: the static adhesion energy was measured between a lipid vesicle and a polymer bead both functional- ized with nucleosides that provide weak binding sites. The lipid vesicle can act as a reservoir of adhesion molecules which equilibrate with the contact zone while the adhe- sion groups on the bead are relatively immobile. Experi- ment and theory are compared to probe the nature of weak bonds in membranes, where local equilibria can be ob- tained. These are limiting physical behaviors, of general interest in biological and nonbiological applications. The adhesion measurements are carried out by the micropipette aspiration technique developed by Evans [6]. Observations are made by differential interferometric contrast microscopy in order to see the vesicle (Fig. 1). To measure their adhesion, the osmotically controlled vesicle and the bead are aspirated in micropipettes and micromanipulated into contact. The (negative) pressure DP in the pipette controls the (positive) hydrostatic pressure in the vesicle and thus the mechanical tension t m in its membrane [5], t m  DP 2 1 r p 2 1 r y  , (1) where r p and r y are, respectively, the radius of the micropipette and of the vesicle. The adherent vesicle is held with low pressure and remains deformable. The adhesion free energy W adh is obtained by determining the contact angle u c (Fig. 1) and the tension t m of the flaccid vesicle membrane, W adh  t m 1 2 cosu c  . (2) By combining (1) and (2), it is easy to relate DP to W adh , FIG. 1. (a) Functionalized bead with an end-grafted polyethyl- ene glycol (PEG) bearing biotin at one end and one nucleoside at the other. (b) Micromanipulated vesicle in contact with a bead held by a micropipette. The bar represents 5 mm. 178101-1 0031-9007 01 87(17) 178101(4)$15.00 © 2001 The American Physical Society 178101-1