Reliability theory for receptor–ligand bond dissociation

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Abstract
Cell adhesion in the presence of hydrodynamic forces is a critical factor in inflammation, cancermetastasis, and blood clotting. A number of assays have recently been developed to apply forces to small numbers of the receptor–ligand bonds responsible for adhesion. Examples include assays using hydrodynamic shear in flow chambers or elastic probe deflection assays such as the atomic force microscope or the biomembrane force probe. One wishes to use the data on the time distribution of dissociation from these assays to derive information on the force dependence of reaction rates, an important determinant of cell adhesive behavior. The dissociation process can be described using the theory developed for reliability engineering of electronic components and networks. We use this framework along with the Bell model for the reverse reaction rate (k r =k r 0 exp [r 0 f/kT], where f is the applied force and k r 0 and r 0 are Bell model parameters) to write closed form expressions for the probability distribution of break-up with multiple independent or interacting bonds. These expressions show that the average lifetime of nbonds scales with the n th harmonic number multiplied by the lifetime of a single bond. Results from calculation and simulations are used to describe the effect of experimental procedures in forced unbinding assays on the estimation of parameters for the force dependence of reverse reaction rates.