  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.
