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General theory of area reactivity models: rate coefficients, binding probabilities and all that

We further develop the general theory of the area reactivity model that provides an alternative description of the diffusion-influenced reaction of an isolated receptor-ligand pair in terms of a generalized Feynman-Kac equation. We analyze both the irreversible and reversible reaction and derive the equation of motion for the survival and separation probability. Furthermore, we discuss the notion of a time-dependent rate coefficient within the alternative model and obtain a number of relations between the rate coefficient, the survival and separation probabilities and the reaction rate. Finally, we calculate asymptotic and approximate expressions for the (irreversible) rate coefficient, the binding probability, the average lifetime of the bound state and discuss on- and off-rates in this context. Throughout our treatment, we will point out similarities and differences between the area and the classical contact reactivity model. The presented analysis and obtained results provide a theoretical framework that will facilitate the comparison of experiment and model predictions.