The role of thermal undulations in adhesion of a biological membrane

L. B. FreundDivisions of Engineering, Brown University,Providence, RI 02912Fibroblasts and other tissue secreting cells have the ability to adhere to extracellular matrix and to migrate in the course of tissue generation. Adhesion occurs through specific bonding of integrins, large transmembrane protein molecules in the cell wall, to ligands in the surrounding tissue. Integrins are mobile in the cell wall and diffuse randomly in a normal thermal environment. The mean density of integrins in the cell wall is normally too low for adhesion to occur casually upon contact. Instead, adhesions form gradually as a few integrins become immobilized in a small region. Such focal adhesion regions usually grow to about a micron or two in diameter.
Such adhesion patches have been studied at a coarse scale by means of a number of experimental approaches. In a departure from this trend, Arnold et al. [ChemPhysChem 5 (2004) 383] carried out experiments in which they were able to study the process of cell adhesion at the scale of individual binding sites. Among their observations was the discovery that there appeared to be an upper bound on spacing of integrin bond sites for tight adhesions to form. Furthermore, the critical value of this density was found to be essentially uniform among the four cell types examined. This raises the tantalizing question as to whether or not this remarkable finding can be understood in terms of a fundamental physical phenomenon across the cell types. In this presentation, the question will be examined from the point of view of classical statistical mechanics with bonding being represented by a well in the potential energy landscape of the system. It will be shown that thermal fluctuations arising from immersion of the membrane in a heat bath can account for the appearance of a critical bond site spacing.

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