Analyzing Förster resonance energy transfer with fluctuation algorithms.

Fluorescence correlation spectroscopy (FCS) in combination with Förster resonance energy transfer (FRET) has been developed to a powerful statistical tool, which allows for the analysis of FRET fluctuations in the huge time of nanoseconds to seconds. FRET-FCS utilizes the strong distance dependence of the FRET efficiency on the donor (D)-acceptor (A) distance so that it developed to a perfect method for studying structural fluctuation in biomolecules involved in conformational flexibility, structural dynamics, complex formation, folding, and catalysis. Structural fluctuations thereby result in anticorrelated donor and acceptor signals, which are analyzed by FRET-FCS in order to characterize underlying structural dynamics. Simulated and experimental examples are discussed. First, we review experimental implementations of FRET-FCS and present theory for a two-state interconverting system. Additionally, we consider a very common case of FRET dynamics in the presence of donor-only labeled species. We demonstrate that the mean relaxation time for the structural dynamics can be easily obtained in most of cases, whereas extracting meaningful information from correlation amplitudes can be challenging. We present a strategy to avoid a fit with an underdetermined model function by restraining the D and A brightnesses of the at least one involved state, so that both FRET efficiencies and both rate constants (i.e., the equilibrium constant) can be determined. For samples containing several fluorescent species, the use of pulsed polarized excitation with multiparameter fluorescence detection allows for filtered FCS (fFCS), where species-specific correlation functions can be obtained, which can be directly interpreted. The species selection is achieved by filtering using fluorescence decays of individual species. Analytical functions for species auto- and cross-correlation functions are given. Moreover, fFCS is less affected by photophysical artifacts and often offers higher contrast, which effectively increases its time resolution and significantly enhances its capability to resolve multistate kinetics. fFCS can also differentiate between species even when their brightnesses are the same and thus opens up new possibilities to characterize complex dynamics. Alternative fluctuation algorithms to study FRET dynamics are also briefly reviewed.