Maximum Likelihood Analysis of Diffusing Molecules with Conformational Dynamics in Single-Molecule FRET

In single-molecule Förster resonance energy transfer (FRET) experiments, characterizing conformational dynamics from photon bursts emitted by diffusing molecules can be challenging due to the interplay of molecular transitions, translational diffusion, and background noise. This paper extends the maximum likelihood analysis of photon bursts (burstML) to incorporate both conformational dynamics and diffusion through the laser spot, offering a comprehensive analysis of photon bursts from single diffusing molecules. The new approach integrates two previously developed methods: one accounting for diffusion without conformational dynamics and the other addressing conformational dynamics without diffusion. By combining these approaches, the extended burstML method allows determination of brightness, diffusion time, FRET efficiency in each state, and transition rates, even under challenging conditions, such as fast (comparable to photon count rates) and slow (one transition per several bursts) transition rates, high background noise, and unequal brightness or diffusivity of the states. The performance of burstML was demonstrated on simulated data of a two-state diffusing molecule and compared with the colorML method, which simplifies analysis by excluding translational diffusion. While colorML is computationally efficient and performs well under ideal conditions (low background noise and equal brightness and diffusivity of states), its accuracy diminishes when these conditions are not met. In contrast, burstML remains accurate across a broader range of experimental scenarios. Both burstML and colorML were applied to analyze folding of several proteins (Pin1 WW domain, FiP35 WW domain, FBP28 WW domain, villin, and a synthetic protein α₃D) under various experimental conditions, highlighting where colorML differs from burstML and providing insights into the applicability of the methods in diverse experimental settings.