Fluorophore-quencher distance correlation functions from single-molecule photon arrival trajectories

We generalize and simplify the method of Yang and Xie (J. Chem. Phys. 2002, 117, 10965) to obtain distance correlation functions from photon arrival trajectories of single fluorophores whose lifetime, [k(r)](-1), depends on the distance to a quencher. It is assumed that this distance does not change during the fluorescence lifetime. The experimental trajectory is first transformed by replacing the delay time (i.e., the interval between the photon arrival and the nearest laser pulse) by a certain function of this delay time. This function is the inverse Laplace transform of r(k), which is the solution of k(r) = 1. The correlation function of the transformed data then directly gives the distance correlation function. Illustrative examples include Forster energy transfer and quenching due to electron transfer.