Rate coefficients, binding probabilities, and related quantities for area reactivity models - Prüstel, Thorsten (J Chem Phys, 2014)
We further develop the general theory of the area reactivity model that describes the diffusion-influenced reaction of an isolated receptor-ligand pair in terms of a generalized Feynman-Kac equation and that provides an alternative to the classical contact reactivity model. Analyzing both the irreversible and reversible reaction, we derive the equation of motion of the survival probability as well as several relationships between single pair quantities and the reactive flux at the encounter distance. Building on these relationships, we derive the equation of motion of the many-particle survival probability for irreversible pseudo-first-order reactions. Moreover, we show that the usual definition of the rate coefficient as the reactive flux is deficient in the area reactivity model. Numerical tests for our findings are provided through Brownian Dynamics simulations. We calculate exact and approximate expressions for the irreversible rate coefficient and show that this quantity behaves differently from its classical counterpart. Furthermore, we derive approximate expressions for the binding probability as well as the average lifetime of the bound state and discuss on- and off-rates in this context. Throughout our approach, we point out similarities and differences between the area reactivity model and its classical counterpart, the contact reactivity model. The presented analysis and obtained results provide a theoretical framework that will facilitate the comparison of experiment and model predictions.