The function of biological macromolecules involves large-scale conformational dynamics spanning multiple time scales, from microseconds to seconds. Such conformational motions, which may involve whole domains or subunits of a protein, play a key role in allosteric regulation. There is an urgent need for experimental methods to probe the fastest of these motions. Single-molecule fluorescence experiments can in principle be used for observing such dynamics, but there is a lack of analysis methods that can extract the maximum amount of information from the data, down to the microsecond time scale. To address this issue, we introduce HMM, a maximum likelihood estimation algorithm for photon-by-photon analysis of single-molecule fluorescence resonance energy transfer (FRET) experiments. HMM is based on analytical estimators for model parameters, derived using the Baum-Welch algorithm. An efficient and effective method for the calculation of these estimators is introduced. HMM is shown to accurately retrieve the reaction times from ∼1 s to ∼10 μs and even faster when applied to simulations of freely diffusing molecules. We further apply this algorithm to single-molecule FRET data collected from Holliday junction molecules and show that at low magnesium concentrations their kinetics are as fast as ∼10 s. The new algorithm is particularly suitable for experiments on freely diffusing individual molecules and is readily incorporated into existing analysis packages. It paves the way for the broad application of single-molecule fluorescence to study ultrafast functional dynamics of biomolecules.

Among the advantages of the single-molecule approach when used to study biomolecular structural dynamics and interaction is its ability to distinguish between and independently observe minor subpopulations. In a single-molecule Förster resonance energy transfer (FRET) and alternating laser excitation diffusion experiment, the various populations are apparent in the resultant histograms. However, because histograms are calculated based on the per-burst mean FRET and stoichiometry ratio and not on the internal photon distribution, much of the acquired information is lost, thereby reducing the capabilities of the method. Here we suggest what to our knowledge is a novel statistical analysis tool that significantly enhances these capabilities, and we use it to identify and isolate static and dynamic subpopulations. Based on a kernel density estimator and a proper photon distribution analysis, for each individual burst, we calculate scores that reflect properties of interest. Specifically, we determine the FRET efficiency and brightness ratio distributions and use them to reveal 1), the underlying structure of a two-state DNA-hairpin and a DNA hairpin that is bound to DNA origami; 2), a minor doubly labeled dsDNA subpopulation concealed in a larger singly labeled dsDNA; and 3), functioning DNA origami motors concealed within a larger subpopulation of defective motors. Altogether, these findings demonstrate the usefulness of the proposed approach. The method was developed and tested using simulations, its rationality is described, and a computer algorithm is provided.

While numerous DNA-based molecular machines have been developed in recent years, high operational yield and speed remain a major challenge. To understand the reasons for the limited performance, and to find rational solutions, we applied single-molecule fluorescence techniques and conducted a detailed study of the reactions involved in the operation of a model system comprised of a bipedal DNA walker that strides on a DNA origami track powered by interactions with fuel and antifuel strands. Analysis of the kinetic profiles of the leg-lifting reactions indicates a pseudo-first-order antifuel binding mechanism leading to a rapid and complete leg-lifting, indicating that the fuel-removal reaction is not responsible for the 1% operational yield observed after six steps. Analysis of the leg-placing reactions showed that although increased concentrations of fuel increase the reaction rate, they decrease the yield by consecutively binding the motor and leading to an undesirable trapped state. Recognizing this, we designed asymmetrical hairpin-fuels that by regulating the reaction hierarchy avoid consecutive binding. Motors operating with the improved fuels show 74% yield after 12 consecutive reactions, a dramatic increase over the 1% observed for motors operating with nonhairpin fuels. This work demonstrates that studying the mechanisms of the reactions involved in the operation of DNA-based molecular machines using single-molecule fluorescence can facilitate rationally designed improvements that increase yield and speed and promote the applicability of DNA-based machines.

The dynamics of two DNA hairpins (5'-TCGCCT-A31-AGGCGA-3' and 5'-TCGCCG-A31-CGGCGA-3') were studied using immobilization-based and diffusion-based single-molecule fluorescence techniques. The techniques enabled separated and detailed investigation of the states and of the transition reactions. Only two states, open and closed, were identified from analysis of the FRET histograms; metastable states with lifetimes longer than the technique resolution (0.3 ms) were not observed. The opening and closing reaction rates were determined directly from the FRET time trajectories, and the Gibbs free energies of these states and of the transition state were calculated using the Kramer theory. The rates, which are undoubtedly of transitions between the fully closed and the fully open states and ranged from 2 to 90 s(-1), were lower (∼10-fold) than the rates previously determined from fluorescence correlation spectroscopy. The heights of the barriers for closing were almost identical for the two hairpins. The barrier for opening the hairpin with the stronger stem was higher (4.3 kJ/mol) than that for the hairpin with the weaker stem, in very good agreement with the difference in stability calculated by the nearest-neighbor method. The barrier for closing the hairpin decreased (∼8 kJ/mol) and the barrier for opening increased (∼4 kJ/mol) with increasing NaCl concentration (10-100 mM), indicating that higher ionic strength stabilizes the folded state with respect to the transition state and stabilizes the transition state relative to the unfolded state. The very good agreements in the dynamics measured for free hairpins, for hairpins anchored to origami, and for hairpins anchored to the coverslip and the very good agreement between the two single-molecule techniques demonstrate that neither the origami nor the coverslip influence the hairpin dynamics, supporting a previous demonstration that origami can serve as a platform for biophysical investigations.

Here we provide high resolution study of DNA hairpin dynamics achieved by probability distribution analysis (PDA) of diffusion-based single-molecule Förster resonance energy transfer (sm-FRET) histograms. The opening and closing rates of three hairpins both free and attached to DNA origami were determined. The agreement with rates previously obtained using the total internal reflection (TIRF) technique and between free hairpins and hairpins attached to origami validated the PDA and demonstrated that the origami had no influence on the hairpin dynamics. From comparison of rates of four DNA hairpins, differing only in stem sequence, and from comparison with rates calculated using nearest-neighbor method and standard transition state theory, we conclude that the unfolding reaction resembles that of melting of DNA duplex with a corresponding sequence and that the folding reaction depends on counterion concentration and not on stem sequence. Our validation and demonstration of the PDA method will encourage its implementation in future high-resolution dynamic studies of freely diffusing biomolecules.