Unraveling Burst Selection Bias in Single-Molecule FRET of Species with Unequal Brightness and Diffusivity

Single-molecule free diffusion experiments enable accurate quantification of coexisting species or states. However, unequal brightness and diffusivity introduce a burst selection bias and affect the interpretation of experimental results. We address this issue with a photon-by-photon maximum likelihood method, burstML, which explicitly considers burst selection criteria. BurstML accurately estimates parameters, including photon count rates, diffusion times, Förster resonance energy transfer (FRET) efficiencies, and population, even in cases where species are poorly distinguished in FRET efficiency histograms. We develop a quantitative theory that determines the fraction of photon bursts corresponding to each species and thus obtain accurate species populations from the measured burst fractions. In addition, we provide a simple approximate formula for burst fractions and establish the range of parameters where unequal brightness and diffusivity can significantly affect the results obtained by conventional methods. The performance of the burstML method is compared with that of a maximum likelihood method that assumes equal species brightness and diffusivity, as well as standard Gaussian fitting of FRET efficiency histograms, using both simulated and real single-molecule data for cold-shock protein, protein L, and protein G. The burstML method enhances the accuracy of parameter estimation in single-molecule fluorescence studies.