Single-molecule kinetics with time-dependent rates: A generating function approach

A theoretical strategy for calculating the statistical properties of time series generated by single molecule measurements is presented. Emphasis is placed on the case where observable states interconvert via rate "constants" exhibiting stochastic time dependence. Such is the case for measurements of single fluorophores coupled to biomolecules undergoing conformational fluctuations [H. P. Lu, L. Xun, and X. S. Xie, Science 282, 1877 (1998)]. In contrast to previous studies, we focus on the number of fluorophore blinking events occurring within a given amount of time as our stochastic variable. This formulation allows for an elementary analysis within the generating function framework.