Counting statistics of single molecule reaction events and reaction dynamics of a single molecule

We present an exact form for counting statistics of single-molecule (SM) reaction events for a molecule with arbitrary hidden dynamical processes coupled to the reaction, examples of which can be found in many single biopolymer experiments. The result suggests a novel SM experimental observable, Θ, which can serve as a sensitive measure of the slow dynamical processes coupled to the SM reaction. For a model biopolymer reaction coupled to a slow Gaussian process, we show that Θ is more directly related to the dynamics of those hidden processes than other more commonly used measures.