Single-molecule fluorescence spectroscopy can be used to estimate the rate constants for slow transitions between two states characterized by different lifetimes of a fluorescent probe. The fluorescence decay for this system is a biexponential, the coefficients of each exponential being the fraction of time spent by the system in each of the states. This paper explains how to estimate the rate constants for the transitions and derives the sampling error for the estimates on the assumption that the data are gathered on M molecules, each monitored for a time T. Results of the analysis indicate that the dominant factor in determining the precision of the rate constant is M and that the role of T is less significant.
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