Reliability and accuracy of single-molecule FRET studies for characterization of structural dynamics and distances in proteins.

Single-molecule Förster-resonance energy transfer (smFRET) experiments allow the study of biomolecular structure and dynamics in vitro and in vivo. We performed an international blind study involving 19 laboratories to assess the uncertainty of FRET experiments for proteins with respect to the measured FRET efficiency histograms, determination of distances, and the detection and quantification of structural dynamics. Using two protein systems with distinct conformational changes and dynamics, we obtained an uncertainty of the FRET efficiency ≤0.06, corresponding to an interdye distance precision of ≤2 Å and accuracy of ≤5 Å. We further discuss the limits for detecting fluctuations in this distance range and how to identify dye perturbations. Our work demonstrates the ability of smFRET experiments to simultaneously measure distances and avoid the averaging of conformational dynamics for realistic protein systems, highlighting its importance in the expanding toolbox of integrative structural biology.

Publisher Correction: Precision and accuracy of single-molecule FRET measurements-a multi-laboratory benchmark study.

This paper was originally published under standard Springer Nature copyright. As of the date of this correction, the Analysis is available online as an open-access paper with a CC-BY license. No other part of the paper has been changed.

Precision and accuracy of single-molecule FRET measurements-a multi-laboratory benchmark study.

Single-molecule Förster resonance energy transfer (smFRET) is increasingly being used to determine distances, structures, and dynamics of biomolecules in vitro and in vivo. However, generalized protocols and FRET standards to ensure the reproducibility and accuracy of measurements of FRET efficiencies are currently lacking. Here we report the results of a comparative blind study in which 20 labs determined the FRET efficiencies (E) of several dye-labeled DNA duplexes. Using a unified, straightforward method, we obtained FRET efficiencies with s.d. between ±0.02 and ±0.05. We suggest experimental and computational procedures for converting FRET efficiencies into accurate distances, and discuss potential uncertainties in the experiment and the modeling. Our quantitative assessment of the reproducibility of intensity-based smFRET measurements and a unified correction procedure represents an important step toward the validation of distance networks, with the ultimate aim of achieving reliable structural models of biomolecular systems by smFRET-based hybrid methods.

Single molecule FRET investigation of pressure-driven unfolding of cold shock protein A.

We demonstrate that fused silica capillaries are suitable for single molecule fluorescence resonance energy transfer (smFRET) measurements at high pressure with an optical quality comparable to the measurement on microscope coverslips. Therefore, we optimized the imaging conditions in a standard square fused silica capillary with an adapted arrangement and evaluated the performance by imaging the focal volume, fluorescence correlation spectroscopy benchmarks, and FRET measurements. We demonstrate single molecule FRET measurements of cold shock protein A unfolding at a pressure up to 2000 bars and show that the unfolded state exhibits an expansion almost independent of pressure.

Single Molecule 3D Orientation in Time and Space: A 6D Dynamic Study on Fluorescently Labeled Lipid Membranes.

Interactions between single molecules profoundly depend on their mutual three-dimensional orientation. Recently, we demonstrated a technique that allows for orientation determination of single dipole emitters using a polarization-resolved distribution of fluorescence into several detection channels. As the method is based on the detection of single photons, it additionally allows for performing fluorescence correlation spectroscopy (FCS) as well as dynamical anisotropy measurements thereby providing access to fast orientational dynamics down to the nanosecond time scale. The 3D orientation is particularly interesting in non-isotropic environments such as lipid membranes, which are of great importance in biology. We used giant unilamellar vesicles (GUVs) labeled with fluorescent dyes down to a single molecule concentration as a model system for both, assessing the robustness of the orientation determination at different timescales and quantifying the associated errors. The vesicles provide a well-defined spherical surface, such that the use of fluorescent lipid dyes (DiO) allows to establish a a wide range of dipole orientations experimentally. To complement our experimental data, we performed Monte Carlo simulations of the rotational dynamics of dipoles incorporated into lipid membranes. Our study offers a comprehensive view on the dye orientation behavior in a lipid membrane with high spatiotemporal resolution representing a six-dimensional fluorescence detection approach.

Excited-state annihilation reduces power dependence of single-molecule FRET experiments.

Single-molecule Förster resonance energy transfer (FRET) experiments are an important method for probing biomolecular structure and dynamics. The results from such experiments appear to be surprisingly independent of the excitation power used, in contradiction to the simple photophysical mechanism usually invoked for FRET. Here we show that excited-state annihilation processes are an essential cause of this behavior. Singlet-singlet annihilation (SSA) is a mechanism of fluorescence quenching induced by Förster-type energy transfer between two fluorophores while they are both in their first excited singlet states (S1S1), which is usually neglected in the interpretation of FRET experiments. However, this approximation is only justified in the limit of low excitation rates. We demonstrate that SSA is evident in fluorescence correlation measurements for the commonly used FRET pair Alexa 488/Alexa 594, with a rate comparable to the rate of energy transfer between the donor excited state and the acceptor ground state (S1S0) that is exploited in FRET experiments. Transient absorption spectroscopy shows that SSA occurs exclusively via energy transfer from Alexa 488 to Alexa 594. Excitation-power dependent microsecond correlation experiments support the conclusion based on previously reported absorption spectra of triplet states that singlet-triplet annihilation (STA) analogously mediates energy transfer if the acceptor is in the triplet state. The results indicate that both SSA and STA have a pronounced effect on the overall FRET process and reduce the power dependence of the observed FRET efficiencies. The existence of annihilation processes thus seems to be essential for using FRET as a reliable spectroscopic ruler at the high excitation rates commonly employed in single-molecule spectroscopy.

The spectroscopic ruler revisited at 77 K.

We report on single-molecule FRET measurements on the classical molecular ruler polyproline immersed in amorphous ice at 77 K. Confocal scanning microscopy allows for observation of the fluorescence of the dyes Alexa Fluor 488 as the donor and Alexa Fluor 594 as the acceptor in the FRET experiment. The dipole orientations are fixed in amorphous ice leading to a broad distribution of transfer efficiencies. The measured transfer efficiency distributions are mainly in accordance with simulated distributions, with a significant deviation at low transfer efficiencies, which are absent in the experimental distribution, in stark contrast to the theory.

Intrinsic motions along an enzymatic reaction trajectory.

The mechanisms by which enzymes achieve extraordinary rate acceleration and specificity have long been of key interest in biochemistry. It is generally recognized that substrate binding coupled to conformational changes of the substrate-enzyme complex aligns the reactive groups in an optimal environment for efficient chemistry. Although chemical mechanisms have been elucidated for many enzymes, the question of how enzymes achieve the catalytically competent state has only recently become approachable by experiment and computation. Here we show crystallographic evidence for conformational substates along the trajectory towards the catalytically competent 'closed' state in the ligand-free form of the enzyme adenylate kinase. Molecular dynamics simulations indicate that these partially closed conformations are sampled in nanoseconds, whereas nuclear magnetic resonance and single-molecule fluorescence resonance energy transfer reveal rare sampling of a fully closed conformation occurring on the microsecond-to-millisecond timescale. Thus, the larger-scale motions in substrate-free adenylate kinase are not random, but preferentially follow the pathways that create the configuration capable of proficient chemistry. Such preferred directionality, encoded in the fold, may contribute to catalysis in many enzymes.

Exonucleolytic degradation of high-density labeled DNA studied by fluorescence correlation spectroscopy.

The exonucleolytic degradation of high-density labeled DNA by exonuclease III was monitored using two-color fluorescence correlation spectroscopy (FCS). One strand of the double stranded template DNA was labeled on either one or two base types and additionally at one end via a 5' Cy5 tagged primer. Exonucleolytic degradation was followed via the diffusion time, the brightness of the remaining DNA as well as the concentration of released labeled bases. We found a hydrolyzation rate of about 11 to 17 nucleotides per minute per enzyme (nt/min/enzyme) for high-density labeled DNA, which is by a factor of about 4 slower than for unlabeled DNA. The exonucleolytic degradation of a 488 base pair long double stranded DNA resulted in a short double stranded DNA segment of 112 ± 40 base pairs (bp) length with two single-stranded tails.

Efficient simultaneous fluorescence orientation, spectrum, and lifetime detection for single molecule dynamics.

We report on the simultaneous detection of the fluorescence lifetime, spectrum, and three-dimensional dipole orientation determination of single perylene diimide molecules deposited on a silica surface as a model system for studying fluorophore internal and orientational dynamics. We employ a multi-parameter detection scheme to demonstrate how jumps in the orientation of the molecule can be disentangled from spectral jumps, both leading to changes of the detected total fluorescence intensity. The fluorescence lifetime determined simultaneously from the same photons is also sensitive to the orientation of the dipole with respect to the interface between media with different refractive indices. The correlated changes of the lifetime and orientation we observe are in good agreement with theory.

Spectral diffusion of single molecules in a hierarchical energy landscape.

Spectral diffusion as a result of both the transitions between different molecular conformers and the ''molecular softness'' of quasi-free perylene diimides on a SiO(2) surface is investigated by means of single-molecule spectroscopy, which reveals the time dependence of both the fluorescence spectra and the three-dimensional orientation. Spectral wavelengths of all single emitters cover a wide energy range of about 0.27 eV, which is due to different types of conformers with large differences in optical transition energy. Time-dependent spectral trajectories of single emitters within this wavelength manifold are evaluated with a model transcribed from the analysis of spatial diffusion. Spectral diffusion processes are closely correlated with fluorescence emission and excitation power. The overall analysis of spectral diffusion reveals, similar to proteins, a hierarchy of energy barriers in a broad energy landscape.

Photoblinking and photobleaching of rylene diimide dyes.

We investigate photoblinking and photobleaching of perylene diimide (PDI) and its higher homologue terrylene diimide (TDI). Single molecule fluorescence trajectories of the dye molecules embedded in PMMA under ambient conditions exhibit "on"-"off" blinking in the time range from ms to s. Due to the limited statistics of individual trajectories we construct ensemble distributions of "on" and "off" times which follow power laws with similar power law coefficients (m(on) ≈ 1.18, m(off) ≈ 1.31). The blinking is attributed to reversible formation of radical cations which are presumably created by electron transfer from higher excited triplet states T(n) of the molecules to acceptor levels in the PMMA host. This view is corroborated by the properties of TDI, which blinks at an excitation wavelength of 520 nm but does not at lower energy excitation (647 nm). In line with this observation, T(1)-T(n) absorption data of TDI (and PDI) indicate that above a certain illumination wavelength population of higher excited triplet states T(n) does not occur, preventing blinking. It is furthermore argued that the long-lived dark ("off") states, i.e. the radical cations, are precursors for the photobleaching process of the dye molecules. Consequently, the photobleaching quantum yield Y(bl) for TDI is very small at an excitation wavelength of 647 nm (Y(bl) = 2 × 10(-10)) but increases by two orders of magnitude at 520 nm (Y(bl) = 2 × 10(-8)), which lies in the range observed for PDI investigated with an excitation wavelength of 488 nm. Additional studies of a PDI-TDI donor-acceptor dyad give further insights into the blinking and bleaching processes. Important findings include the observation of power law blinking of TDI and PDI (after bleaching of TDI) with similar coefficients as found for the isolated chromophores. Furthermore, in the dyad the photostability of TDI decreases due to efficient population of the states T(n) by singlet-triplet annihilation, while that of PDI (after bleaching of TDI) is the same as for the isolated dye. These findings support the conclusions drawn for the isolated chromophores, in particular the involvement of the triplet manifold in the blinking (and bleaching) behavior.

Three-dimensional orientation determination of the emission dipoles of single molecules: the shot-noise limit.

The power of three-dimensional orientation detection of single emitting dipoles using a sophisticated scheme with three detectors in a confocal microscope is quantitatively explored by means of Monte Carlo simulations. We show that several hundreds of photons are sufficient for a reliable orientation determination. In typical single-molecule experiments, time resolutions in the submillisecond range for orientation trajectories become accessible. Experimental data on fluorescent latex beads and single perylene monoimide molecules show that a properly aligned setup can perfectly reproduce the simulated data. The simulations and experimental data highlight the potential of our method and give practical guidelines for its application.

Cooperativity of Spin Crossover Complexes: Combining Periodic Density Functional Calculations and Monte Carlo Simulation.

The total enthalpies of the 16 different spin configurations that can be realized in the unit cell of the archetype spin crossover complex [Fe(phen)2(NCS)2] (phen = 1,2-phenanthroline) were calculated, applying periodic density functional theory combined with the Hubbard model and the Grimme-D2 dispersion correction (DFT+U+D2). The obtained enthalpy differences between the individual spin configurations were used to determine spin couplings of an Ising-like model, and subsequent Monte Carlo simulations for this model allowed the estimation of the phenomenological interaction parameter Γ of the Slichter-Drickamer model, which is commonly used to describe the cooperativity of the spin transition. The calculation procedure described here-which led to an estimate of about 3 kJ·mol-1 for Γ, in good agreement with experiment-may be used to predict from first principles how modifications of spin crossover complexes can change the character of the spin transition from gradual to abrupt and vice versa.

Coulomb forces control the density of the collapsed unfolded state of barstar.

Although it has been recently shown that unfolded polypeptide chains undergo a collapse on transfer from denaturing to native conditions, the forces determining the dynamics and the size of the collapsed form have not yet been understood. Here, we use single-molecule fluorescence resonance energy transfer experiments on the small protein barstar to characterize the unfolded chain in guanidinium chloride (GdmCl) and urea. The unfolded protein collapses on decreasing the concentration of denaturants. Below the critical concentration of 3.5 M denaturant, the collapse in GdmCl leads to a more dense state than in urea. Since it is known that GdmCl suppresses electrostatic interactions, we infer that Coulomb forces are the dominant forces acting in the unfolded barstar under native conditions. This hypothesis is clearly buttressed by the finding of a compaction of the unfolded barstar by addition of KCl at low urea concentrations.

Recurrence and photon statistics in fluorescence fluctuation spectroscopy.

We report on fluorescence fluctuations of nanoparticles diffusing through a laser focus. Subject to an intensity threshold the fluorescence signal is transformed into time traces of on and off periods. The distribution functions of the experimental on and off times follow power laws t -alpha over several orders of magnitude with exponents alpha approximately 1.5-2. At long times the distribution functions cross over to exponential decays. For the interpretation of the experimental data a diffusion-reaction equation is proposed which covers both, the diffusion controlled recurrence and the photon statistics as the relevant processes.

Photon antibunching and collective effects in the fluorescence of single bichromophoric molecules.

The fluorescence of individual pairs of perylenemonoimide chromophores coupled via a short rigid linker is investigated. Photon antibunching is reported, indicating collective effects in the fluorescence, which are further substantiated by the observation of collective triplet off times and triplet lifetime shortening. The experimental findings are analyzed in terms of singlet-singlet and singlet-triplet annihilation based on Förster type energy transfer. The results reported here demonstrate that the statistical properties of the emission light of isolated single quantum systems can serve as a hallmark of intermolecular interactions.

Three-dimensional orientational colocalization of individual donor--acceptor pairs.

We report on the determination of the three-dimensional orientation of the donor and acceptor transition dipoles in individual fluorescence resonance energy transfer (FRET) pairs by means of scanning optical microscopy with annular illumination. Knowledge of the mutual orientation of the donor and acceptor dipole is mandatory for reliable distance determination based on FRET efficiency measurements. In our model system perylenediimide as the donor and terryelenediimide as the acceptor are coupled via a stiff p-terphenyl linker. The absorption dipoles of the donor and acceptor are selectively addressed by the 488 nm and 647 line of an Ar/Kr mixed gas laser, respectively. A clear deviation from collinearity is observed with a distribution of misalignment angles peaked around 22 degrees.

Coherent electronic coupling versus localization in individual molecular dimers.

We have investigated electronic excitation transfer in individual molecular dimers by time and spectrally resolved confocal fluorescence microscopy. The single molecule measurements allow for directly probing the distribution of the electronic coupling strengths due to static disorder in the polymer host. We find dimers where the excitation is delocalized (superradiant emission) while for others emission originates from a localized state. Transitions between delocalized and localized states as observed for a given dimer are attributed to structural fluctuations of the guest-host system.