Concentration effects in "single-molecule" spectroscopy

Impact of Molecule Concentration, Diffusion Rates and Surface Passivation on Single-Molecule Fluorescence Studies in Solution

For single-molecule studies in solution, very small concentrations of dye-labelled molecules are employed in order to achieve single-molecule sensitivity. In typical studies with confocal microscopes, often concentrations in the pico-molar regime are required. For various applications that make use of single-molecule Förster resonance energy transfer (smFRET) or two-color coincidence detection (TCCD), the molecule concentration must be set explicitly to targeted values and furthermore needs to be stable over a period of several hours. As a consequence, specific demands must be imposed on the surface passivation of the cover slides during the measurements. The aim of having only one molecule in the detection volume at the time is not only affected by the absolute molecule concentration, but also by the rate of diffusion. Therefore, we discuss approaches to control and to measure absolute molecule concentrations. Furthermore, we introduce an approach to calculate the probability of chance coincidence events and demonstrate that measurements with challenging smFRET samples require a strict limit of maximal sample concentrations in order to produce meaningful results.

FRETBursts: An Open Source Toolkit for Analysis of Freely-Diffusing Single-Molecule FRET

Single-molecule Förster Resonance Energy Transfer (smFRET) allows probing intermolecular interactions and conformational changes in biomacromolecules, and represents an invaluable tool for studying cellular processes at the molecular scale. smFRET experiments can detect the distance between two fluorescent labels (donor and acceptor) in the 3-10 nm range. In the commonly employed confocal geometry, molecules are free to diffuse in solution. When a molecule traverses the excitation volume, it emits a burst of photons, which can be detected by single-photon avalanche diode (SPAD) detectors. The intensities of donor and acceptor fluorescence can then be related to the distance between the two fluorophores. While recent years have seen a growing number of contributions proposing improvements or new techniques in smFRET data analysis, rarely have those publications been accompanied by software implementation. In particular, despite the widespread application of smFRET, no complete software package for smFRET burst analysis is freely available to date. In this paper, we introduce FRETBursts, an open source software for analysis of freely-diffusing smFRET data. FRETBursts allows executing all the fundamental steps of smFRET bursts analysis using state-of-the-art as well as novel techniques, while providing an open, robust and well-documented implementation. Therefore, FRETBursts represents an ideal platform for comparison and development of new methods in burst analysis. We employ modern software engineering principles in order to minimize bugs and facilitate long-term maintainability. Furthermore, we place a strong focus on reproducibility by relying on Jupyter notebooks for FRETBursts execution. Notebooks are executable documents capturing all the steps of the analysis (including data files, input parameters, and results) and can be easily shared to replicate complete smFRET analyzes. Notebooks allow beginners to execute complex workflows and advanced users to customize the analysis for their own needs. By bundling analysis description, code and results in a single document, FRETBursts allows to seamless share analysis workflows and results, encourages reproducibility and facilitates collaboration among researchers in the single-molecule community.

Testing Landscape Theory for Biomolecular Processes with Single Molecule Fluorescence Spectroscopy

Although Kramers' theory for diffusive barrier crossing on a 1D free energy profile plays a central role in landscape theory for complex biomolecular processes, it has not yet been rigorously tested by experiment. Here we test this 1D diffusion scenario with single molecule fluorescence measurements of DNA hairpin folding. We find an upper bound of 2.5  μs for the average transition path time, consistent with the predictions by theory with parameters determined from optical tweezer measurements.

Inter-dye distance distributions studied by a combination of single-molecule FRET-filtered lifetime measurements and a weighted accessible volume (wAV) algorithm

Förster resonance energy transfer (FRET) is an important tool for studying the structural and dynamical properties of biomolecules. The fact that both the internal dynamics of the biomolecule and the movements of the biomolecule-attached dyes can occur on similar timescales of nanoseconds is an inherent problem in FRET studies. By performing single-molecule FRET-filtered lifetime measurements, we are able to characterize the amplitude of the motions of fluorescent probes attached to double-stranded DNA standards by means of flexible linkers. With respect to previously proposed experimental approaches, we improved the precision and the accuracy of the inter-dye distance distribution parameters by filtering out the donor-only population with pulsed interleaved excitation. A coarse-grained model is employed to reproduce the experimentally determined inter-dye distance distributions. This approach can easily be extended to intrinsically flexible proteins allowing, under certain conditions, to decouple the macromolecule amplitude of motions from the contribution of the dye linkers.

Solution structure of the ESCRT-I and -II supercomplex: implications for membrane budding and scission

The ESCRT-I and ESCRT-II supercomplex induces membrane buds that invaginate into the lumen of endosomes, a process central to the lysosomal degradation of ubiquitinated membrane proteins. The solution conformation of the membrane-budding ESCRT-I-II supercomplex from yeast was refined against small-angle X-ray scattering (SAXS), single-molecule Förster resonance energy transfer (smFRET), and double electron-electron resonance (DEER) spectra. These refinements yielded an ensemble of 18 ESCRT-I-II supercomplex structures that range from compact to highly extended. The crescent shapes of the ESCRT-I-II supercomplex structures provide the basis for a detailed mechanistic model, in which ESCRT-I-II stabilizes membrane buds and coordinates cargo sorting by lining the pore of the nascent bud necks. The hybrid refinement used here is general and should be applicable to other dynamic multiprotein assmeblies.

Disentangling subpopulations in single-molecule FRET and ALEX experiments with photon distribution analysis

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.

Single-molecule tracking of carbohydrate-binding modules on cellulose using fluorescence microscopy

Single-molecule fluorescence detection is an invaluable technique for the study of molecular behavior in biological systems, both in vitro and in vivo. In this chapter, we focus on detailed protocols that utilize Total Internal Reflection Fluorescence Microscopy (TIRF-M) to visualize single molecules of carbohydrate-binding module (CBM) labeled with green fluorescent protein (GFP). The content describes step-by-step sample preparation and data acquisition, processing, and analysis. These methods can also be further used to study interactions between domains of cellulase molecules and between cellulases and cellulose.

Fluorescence molecule counting for single-molecule studies in crowded environment of living cells without and with broken ergodicity

We present a new approach to distinguish between non-ergodic and ergodic behavior. Performing ensemble averaging in a subpopulation of individual molecules leads to a mean value that can be similar to the mean value obtained in an ergodic system. The averaging is carried out by minimizing the variation between the sum of the temporal averaged mean square deviation of the simulated data with respect to the logarithmic scaling behavior of the subpopulation. For this reason, we first introduce a kind of Continuous Time Random Walks (CTRW), which we call Limited Continuous Time Random Walks (LCTRW) on fractal support. The random waiting time distributions are sampled at points which fulfill the condition N < 1, where N is the Poisson probability of finding a single molecule in the femtoliter-sized observation volume ΔV at the single-molecule level. Given a subpopulation of different single molecules of the same kind, the ratio T/ T_m between the measurement time T and the meaningful time T_m, which is the time for observing just one and the same single molecule, is the experimentally accessible quantity that allows to compare different molecule numbers in the subpopulation. In addition, the mean square displacement traveled by the molecule during the time t is determined by an upper limit of the geometric dimension of the living cell or its nucleus.

Detection of structural dynamics by FRET: a photon distribution and fluorescence lifetime analysis of systems with multiple states

Two complementary methods in confocal single-molecule fluorescence spectroscopy are presented to analyze conformational dynamics by Forster resonance energy transfer (FRET) measurements considering simulated and experimental data. First, an extension of photon distribution analysis (PDA) is applied to characterize conformational exchange between two or more states via global analysis of the shape of FRET peaks for different time bins. PDA accurately predicts the shape of FRET efficiency histograms in the presence of FRET fluctuations, taking into account shot noise and background contributions. Dynamic-PDA quantitatively recovers FRET efficiencies of the interconverting states and relaxation times of dynamics on the time scale of the diffusion time t(d) (typically milliseconds), with a dynamic range of the method of about +/-1 order of magnitude with respect to t(d). Correction procedures are proposed to consider the factors limiting the accuracy of dynamic-PDA, such as brightness variations, shortening of the observation time due to diffusion, and a contribution of multimolecular events. Second, an analysis procedure for multiparameter fluorescence detection is presented, where intensity-derived FRET efficiency is correlated with the fluorescence lifetime of the donor quenched by FRET. If a maximum likelihood estimator is applied to compute a mean fluorescence lifetime of mixed states, one obtains a fluorescence weighted mean lifetime. Thus a mixed state is detected by a characteristic shift of the fluorescence lifetime, which becomes longer than that expected for a single species with the same intensity-derived FRET efficiency. Analysis tools for direct visual inspection of two-dimensional diagrams of FRET efficiency versus donor lifetime are presented for the cases of static and dynamic FRET. Finally these new techniques are compared with fluorescence correlation spectroscopy.

Anomalous behavior in length distributions of 3D random Brownian walks and measured photon count rates within observation volumes of single-molecule trajectories in fluorescence fluctuation microscopy

Based on classical mean-field approximation using the diffusion equation for ergodic normal motion of single 24-nm and 100-nm nanospheres, we simulated and measured molecule number counting in fluorescence fluctuation microscopy. The 3D-measurement set included a single molecule, or an ensemble average of single molecules, an observation volume DeltaV and a local environment, e.g. aqueous solution. For the molecule number N << 1 per DeltaV, there was only one molecule at a time inside DeltaV or no molecule. The mean rate k of re-entries defined by k = N/tau(dif) was independent of the geometry of DeltaV but depended on the size of DeltaV and the diffusive properties tau(dif). The length distribution l of single-molecule trajectories inside DeltaV and the measured photon count rates I obeyed power laws with anomalous exponent kappa =-1.32 approximately -4/3.

Extracting rate coefficients from single-molecule photon trajectories and FRET efficiency histograms for a fast-folding protein

Recently developed statistical methods by Gopich and Szabo were used to extract folding and unfolding rate coefficients from single-molecule Förster resonance energy transfer (FRET) data for proteins with kinetics too fast to measure waiting time distributions. Two types of experiments and two different analyses were performed. In one experiment bursts of photons were collected from donor and acceptor fluorophores attached to a 73-residue protein, α(3)D, freely diffusing through the illuminated volume of a confocal microscope system. In the second, the protein was immobilized by linkage to a surface, and photons were collected until one of the fluorophores bleached. Folding and unfolding rate coefficients and mean FRET efficiencies for the folded and unfolded subpopulations were obtained from a photon by photon analysis of the trajectories using a maximum likelihood method. The ability of the method to describe the data in terms of a two-state model was checked by recoloring the photon trajectories with the extracted parameters and comparing the calculated FRET efficiency histograms with the measured histograms. The sum of the rate coefficients for the two-state model agreed to within 30% with the relaxation rate obtained from the decay of the donor-acceptor cross-correlation function, confirming the high accuracy of the method. Interestingly, apparently reliable rate coefficients could be extracted using the maximum likelihood method, even at low (<10%) population of the minor component where the cross-correlation function was too noisy to obtain any useful information. The rate coefficients and mean FRET efficiencies were also obtained in an approximate procedure by simply fitting the FRET efficiency histograms, calculated by binning the donor and acceptor photons, with a sum of three-Gaussian functions. The kinetics are exposed in these histograms by the growth of a FRET efficiency peak at values intermediate between the folded and unfolded peaks as the bin size increases, a phenomenon with similarities to NMR exchange broadening. When comparable populations of folded and unfolded molecules are present, this method yields rate coefficients in very good agreement with those obtained with the maximum likelihood method. As a first step toward characterizing transition paths, the Viterbi algorithm was used to locate the most probable transition points in the photon trajectories.

Decoding the pattern of photon colors in single-molecule FRET

Conformational dynamics of a single molecule can be studied using Forster resonance energy transfer (FRET) by recording a sequence of photons emitted by a donor and an acceptor dye attached to the molecule. We describe a simple and robust method to estimate the rates of transitions between different conformational states and the FRET efficiencies associated with these states. For a photon trajectory with measured interphoton times, the pattern of colors is decoded by maximizing the appropriate likelihood function. This approach can be used to analyze bursts of photons from diffusing molecules as well as photon trajectories generated by immobilized molecules. The procedure is illustrated using simulated photon trajectories corresponding to two-state and three-state molecules. The method works even when the photon colors appear to be scrambled because of high background noise, the photophysical properties of the conformers are similar, or the conformational and photon count rates are comparable. The consistency of the model with the data can be checked by recoloring the photon trajectories and comparing the predicted and observed FRET efficiency histograms.