Characterizing multiple molecular States in single-molecule multiparameter fluorescence detection by probability distribution analysis

Probability distribution analysis (PDA) [M. Antonik et al., J. Phys. Chem. B 2006, 110, 6970] allows one to quantitatively analyze single-molecule (SM) data obtained in Forster resonance energy transfer (FRET) or fluorescence polarization experiments. By taking explicitly background and shot noise contributions into account, PDA accurately predicts the shape of one-dimensional histograms of various parameters, such as FRET efficiency or fluorescence anisotropy. In order to describe complex experimental SM-FRET or polarization data obtained for systems consisting of multiple non-interconverting fluorescent states, several extensions to the PDA theory are presented. Effects of brightness variations and multiple-molecule events are considered independently of the detection volume parameters by using only the overall experimental signal intensity distribution. The extended PDA theory can now be applied to analyze any mixture, by using any a priori model or a model-free deconvolution approach based on the maximum entropy method (MEM). The accuracy of the analysis and the number of free parameters are limited only by data quality. Correction of the PDA model function for the presence of multiple-molecule events allows one to measure at high SM concentrations to avoid artifacts due to a very long measurement time. Tools such as MEM and combined mean donor fluorescence lifetime analysis have been developed to distinguish whether extra broadening of PDA histograms could be attributed to structural heterogeneities or dye artifacts. In this way, an ultimate resolution in FRET experiments in the range of a few Angstrom is achieved which allows for molecular Angstrom optics distinguishing between a set of fixed distances and a distribution of distances. The extended theory is verified by analyzing simulations and experimental data.     

The effect of Brownian motion of fluorescent probes on measuring nanoscale distances by Förster resonance energy transfer

F?rster resonance energy transfer (FRET) is a powerful optical technique to determine intra-molecular distances. However, the dye rotational motion and the linker flexibility complicate the relationship between the measured energy transfer efficiency and the distance between the anchoring points of the dyes. In this study, we present a simple model that describes the linker and dye dynamics as diffusion on a sphere. Single-pair energy transfer was treated in the weak excitation limit, photon statistics and scaffold flexibility were ignored, and different time-averaging regimes were considered. Despite the approximations, our model provides new insights for experimental designs and results interpretation in single-molecule FRET. Monte Carlo simulations produced distributions of the inter-dye distance, the dipole orientation factor, κ(2), and the transfer efficiency, E, which were in perfect agreement with independently derived theoretical functions. Contrary to common perceptions, our data show that longer linkers will actually restrict the motion of dye dipoles and hence worsen the isotropic 2∕3 approximation of κ(2). It is also found that the thermal motions of the dye-linker system cause fast and large efficiency fluctuations, as shown by the simulated FRET time-trajectories binned on a microsecond time scale. A fundamental resolution limit of single-molecule FRET measurements emerges around 1-10 μs, which should be considered for the interpretation of data recorded on such fast time scales.     

Single-molecule FRET with diffusion and conformational dynamics

Under relatively mild conditions, we show how one can extract information about conformational dynamics from F?rster resonance energy transfer (FRET) experiments on diffusing molecules without modeling diffusion. Starting from a rigorous theory that does treat diffusion, we first examine when the single-molecule FRET efficiency distribution can be decomposed into the measured distribution of the total number of photons and the efficiency distribution of an immobilized molecule in the absence of shot noise. If the conformation does not change during the time the molecule spends in the laser spot, this is possible when (I) the efficiency is independent of the location in the laser spot and (II) the total number of photons does not depend on conformation. This decomposition is approximate when the conformation changes during the diffusion time. However, it does provide a simple framework for analyzing data. This is illustrated for a two-state system where the FRET efficiency distribution can be found analytically for all values of the interconversion rates. If the arrival time of each donor and acceptor photon can be monitored, we introduce an alternative procedure that allows one to rigorously extract the rates of conformational changes when the above two conditions hold. In this case, the pattern of colors in the photon trajectory depends solely on conformational dynamics. This can be exploited in the framework of statistical inference because the likelihood function, which must be optimized with respect to the model rate parameters, depends only on how the conformation changes during the interval between photons with specified colors.     

Fluorescence resonance energy transfer between a quantum dot donor and a dye acceptor attached to DNA

We show that direct coupling of a dye-labelled DNA (acceptor) to a quantum dot (QD) donor significantly reduces the donor-acceptor distance and improves the FRET efficiency: a highly efficient FRET (approximately 88%) at a low acceptor-to-donor ratio of 2 has been achieved at the single-molecule level.     

Temperature-cycle single-molecule FRET microscopy on polyprolines

Accessing the microsecond dynamics of a single fluorescent molecule in real time is difficult because molecular fluorescence rates usually limit the time resolution to milliseconds. We propose to apply single-molecule temperature-cycle microscopy to probe molecular dynamics at microsecond timescales. Here, we follow donor and acceptor signals of single FRET-labeled polyprolines in glycerol to investigate their conformational dynamics. We observe a steady-state FRET efficiency distribution which differs from theoretical distributions for isotropically orientated fluorescent labels. This may indicate that the orientation of fluorescent labels in glycerol is not isotropic and may reflect the influence of the dye linkers. With proper temperature-cycle parameters, we observed large FRET changes in long series of cycles of the same molecule. We attribute the main conformational changes to reorientations of the fluorescent labels with respect to the oligopeptide chain, which take place in less than a few microseconds at the highest temperature of the cycle (250 K). We were able to follow the FRET efficiency of a particular construct for more than 2000 cycles. This trajectory displays switching between two conformations, which give rise to maxima in the FRET efficiency histogram. Our experiments open the possibility to study biomolecular dynamics at a time scale of a few microseconds at the single-molecule level.     

Single-molecule quantum-dot fluorescence resonance energy transfer.

Colloidal semiconductor quantum dots are promising for single-molecule biological imaging due to their outstanding brightness and photostability. As a proof of concept for single-molecule fluorescence resonance energy transfer (FRET) applications, we measured FRET between a single quantum dot and a single organic fluorophore Cy5. DNA Holliday junction dynamics measured with the quantum dot/Cy5 pair are identical to those obtained with the conventional Cy3/Cy5 pair, that is, conformational changes of individual molecules can be observed by using the quantum dot as the donor.     

A distribution-based method to resolve single-molecule Förster resonance energy transfer observations

We introduce a new approach to analyze single-molecule Fo?rster resonance energy transfer (FRET) data. The method recognizes that FRET efficiencies assumed by traditional ensemble methods are unobservable for single molecules. We propose instead a method to predict distributions of FRET parameters obtained directly from the data. Distributions of FRET rates, given the data, are precisely defined using Bayesian methods and increase the information derived from the data. Benchmark comparisons find that the response time of the new method outperforms traditional methods of averaging. Our approach makes no assumption about the number or distribution of underlying FRET states. The new method also yields information about joint parameter distributions going beyond the standard framework of FRET analysis. For example, the running distribution of FRET means contains more information than any conceivable single measure of FRET efficiency. The method is tested against simulated data and then applied to a pilot-study sample of calmodulin molecules immobilized in lipid vesicles, revealing evidence for multiple dynamical states.     

Novel "lipid-flow chip" configuration to determine donor-to-acceptor ratio-dependent fluorescence resonance energy transfer efficiency

We report on the determination of fluorescence resonance energy transfer (FRET) efficiency, which is dependent on the donor-to-acceptor (D-A) ratio, by using a new type of microchannel device called a "lipid-flow chip". The chip comprises two supported lipid bilayers (SLBs) that self-spread from either side of 10 microm wide straight lines and carry molecules embedded in them. We first show that the diffusion process that occurs when the two SLBs collide with each other in the channel and form a unified SLB can be expressed by a one-dimensional diffusion equation. Next we describe a method for determining the FRET efficiency between NBD (donor) and Texas Red (acceptor) from observations using the lipid-flow chip by employing a one-dimensional diffusion model. The advantages of our method are that all the D-A ratios are achieved in one chip, and a large number of data are recorded in one chip. The FRET efficiency varies depending on the D-A ratio under conditions whereby the concentration of the sum of the donors and acceptors is constant. The F?rster radius is also estimated from our results using a known model describing two-dimensional FRET systems, which yields a radius consistent with the previously reported value for NBD and Texas Red.     

Bounds and algorithms for fast exact searches of chemical fingerprints in linear and sublinear time

Chemical fingerprints are used to represent chemical molecules by recording the presence or absence, or by counting the number of occurrences, of particular features or substructures, such as labeled paths in the 2D graph of bonds, of the corresponding molecule. These fingerprint vectors are used to search large databases of small molecules, currently containing millions of entries, using various similarity measures, such as the Tanimoto or Tversky's measures and their variants. Here, we derive simple bounds on these similarity measures and show how these bounds can be used to considerably reduce the subset of molecules that need to be searched. We consider both the case of single-molecule and multiple-molecule queries, as well as queries based on fixed similarity thresholds or aimed at retrieving the top K hits. We study the speedup as a function of query size and distribution, fingerprint length, similarity threshold, and database size |D| and derive analytical formulas that are in excellent agreement with empirical values. The theoretical considerations and experiments show that this approach can provide linear speedups of one or more orders of magnitude in the case of searches with a fixed threshold, and achieve sublinear speedups in the range of O(|D|0.6) for the top K hits in current large databases. This pruning approach yields subsecond search times across the 5 million compounds in the ChemDB database, without any loss of accuracy.     

Probability distribution analysis of single-molecule fluorescence anisotropy and resonance energy transfer

Analysis of anisotropy in single-molecule fluorescence experiments using the probability distribution analysis (PDA) method is presented. The theory of anisotropy-PDA is an extension of the PDA theory recently developed for the analysis of F?rster resonance energy transfer (FRET) signals [Antonik, M.; et al. J. Phys. Chem. B 2006, 110, 6970]. The PDA method predicts the shape of anisotropy histograms for any given expected ensemble anisotropy, signal intensity distribution, and background. Further improvements of the PDA theory allow one to work with very low photon numbers, i.e., starting from the level of background signal. Analysis of experimental and simulated data shows that PDA has the major advantage to unambiguously distinguish between shot noise broadening and broadening caused by heterogeneities in the sample. Fitting of experimental histograms yields anisotropy values of individual species, which can be directly compared with those measured in ensemble experiments. Excellent agreement between the ensemble data and the results of PDA demonstrates a good absolute accuracy of the PDA method. The precision in determination of mean values depends mainly on the total number of photons, whereas the ability of PDA to detect the presence of heterogeneities strongly depends on the time window length. In its present form PDA can be also applied to computed fluorescence parameters such as FRET efficiency and scatter-corrected fluorescence anisotropy. Extension of the PDA theory to low photon numbers makes it possible to apply PDA to dynamic systems, for which high time resolution is required. In this way PDA is developed as a sensitive tool to detect biomolecular heterogeneities in space and time.     

Photobleaching pathways in single-molecule FRET experiments

To acquire accurate structural and dynamical information on complex biomolecular machines using single-molecule fluorescence resonance energy transfer (sm-FRET), a large flux of donor and acceptor photons is needed. To achieve such fluxes, one may use higher laser excitation intensity; however, this induces increased rates of photobleaching. Anti-oxidant additives have been extensively used for reducing acceptor's photobleaching. Here we focus on deciphering the initial step along the photobleaching pathway. Utilizing an array of recently developed single-molecule and ensemble spectroscopies and doubly labeled Acyl-CoA binding protein and double-stranded DNA as model systems, we study these photobleaching pathways, which place fundamental limitations on sm-FRET experiments. We find that: (i) acceptor photobleaching scales with FRET efficiency, (ii) acceptor photobleaching is enhanced under picosecond-pulsed (vs continuous-wave) excitation, and (iii) acceptor photobleaching scales with the intensity of only the short wavelength (donor) excitation laser. We infer from these findings that the main pathway for acceptor's photobleaching is through absorption of a short wavelength photon from the acceptor's first excited singlet state and that donor's photobleaching is usually not a concern. We conclude by suggesting the use of short pulses for donor excitation, among other possible remedies, for reducing acceptor's photobleaching in sm-FRET measurements.     

Energy Relay from an Unconventional Yellow Dye to CdS/CdSe Quantum Dots for Enhanced Solar Cell Performance

A new design for a quasi‐solid‐state Forster resonance energy transfer (FRET) enabled solar cell with unattached Lucifer yellow (LY) dye molecules as donors and CdS/CdSe quantum dots (QDs) tethered to titania (TiO₂) as acceptors is presented. The Forster radius is experimentally determined to be 5.29 nm. Sequential energy transfer from the LY dye to the QDs and electron transfer from the QDs to TiO₂ is followed by fluorescence quenching and electron lifetime studies. Cells with a donor–acceptor architecture (TiO₂/CdS/CdSe/ZnS‐LY/S^2?‐multi‐walled carbon nanotubes) show a maximum incident photon‐to‐current conversion efficiency of 53 % at 530 nm. This is the highest efficiency among Ru‐dye free FRET‐enabled quantum dot solar cells (QDSCs), and is much higher than the donor or acceptor‐only cells. The FRET‐enhanced solar cell performance over the majority of the visible spectrum paves the way to harnessing the untapped potential of the LY dye as an energy relay fluorophore for the entire gamut of dye sensitized, organic, or hybrid solar cells.     

A comparison of the fluorescence dynamics of single molecules of a green fluorescent protein: one- versus two-photon excitation.

We report on the dynamics of fluorescence from individual molecules of a mutant of the wild-type green fluorescent protein (GFP) from Aequorea victoria, super folder GFP (SFGFP). SFGFP is a novel and robust variant designed for in vivo high-throughput screening of protein expression levels. It shows increased thermal stability and is able to retain its fluorescence when fused to poorly folding proteins. We use a recently developed single-molecule technique which combines fluorescence-fluctuation spectroscopy and time-correlated single photon counting in order to characterize the photophysical properties of SFGFP under one- (OPE) and two- (TPE) photon excitation conditions. We use Rhodamine 110 as a model chromophore to validate the methodology and to explain the single-molecule results of SFGFP. Under OPE, single SFGFP molecules undergo fluorescence flickering on the time scale of micros and tens of micros due to triplet formation and ground-state protonation-deprotonation, respectively, as demonstrated by excitation intensity- and pH-dependent experiments. OPE single-molecule fluorescence lifetimes indicate heterogeneity in the population of SFGFP, indicating the presence of the deprotonated I and B forms of the SFGFP chromophore. TPE of single SFGFP molecules results in the photoconversion of the chromophore. TPE of single SFGFP molecules show fluorescence flickering on the time scale of micros due to triplet formation. A flicker connected with protonation-deprotonation of the SFGFP chromophore is detected only at low pH. Our results show that SFGFP is a promising fusion reporter for intracellular applications using OPE and TPE microscopy.     

Quantitative single-molecule conformational distributions: a case study with poly-(L-proline)

Precise measurement of the potential of mean force is necessary for a fundamental understanding of the dynamics and chemical reactivity of a biological macromolecule. The unique advantage provided by the recently developed constant-information approach to analyzing time-dependent single-molecule fluorescence measurements was used with maximum entropy deconvolution to create a procedure for the accurate determination of molecular conformational distributions, and analytical expressions for the errors in these distributions were derived. This new method was applied to a derivatized poly(L-proline) series, P(n)CG3K(biotin) (n = 8, 12, 15, 18, and 24), using a modular, server-based single-molecule spectrometer that is capable of registering photon arrival times with a continuous-wave excitation source. To account for potential influence from the microscopic environment, factors that were calibrated and corrected molecule by molecule include background, cross-talk, and detection efficiency. For each single poly(L-proline) molecule, sharply peaked F?rster type resonance energy transfer (FRET) efficiency and distance distributions were recovered, indicating a static end-to-end distance on the time scale of measurement. The experimental distances were compared with models of varying rigidity. The results suggest that the 23 angstroms persistence length wormlike chain model derived from experiments with high molecular weight poly(L-proline) is applicable to short chains as well.     

Single-molecule studies on DNA and RNA.

DNA and RNA are the most individual molecules known. Therefore, single-molecule experiments with these nucleic acids are particularly useful. This review reports on recent experiments with single DNA and RNA molecules. First, techniques for their preparation and handling are summarised including the use of AFM nanotips and optical or magnetic tweezers. As important detection techniques, conventional and near-field microscopy as well as fluorescence resonance energy transfer (FRET) and fluorescence correlation spectroscopy (FCS) are touched on briefly. The use of single-molecule techniques currently includes force measurements in stretched nucleic acids and in their complexes with binding partners, particularly proteins, and the analysis of DNA by restriction mapping, fragment sizing and single-molecule hybridisation. Also, the reactions of RNA polymerases and enzymes involved in DNA replication and repair are dealt with in some detail, followed by a discussion of the transport of individual nucleic acid molecules during the readout and use of genetic information and during the infection of cells by viruses. The final sections show how the enormous addressability in nucleic acid molecules can be exploited to construct a single-molecule field-effect transistor and a walking single-molecule robot, and how individual DNA molecules can be used to assemble a single-molecule DNA computer.     

Intramolecular directional förster resonance energy transfer at the single-molecule level in a dendritic system

We report on the directional F?rster resonance energy transfer (FRET) process taking place in single molecules of a first (T1P4) and a second (T2P8) generation of a perylenemonoimide (P)-terrylenediimide (T)-based dendrimer in which the chromophores are separated by rigid polyphenylene arms. At low excitation powers, single-molecule detection and spectroscopy of T1P4 and T2P8 dendrimers point to a highly efficient directional FRET from P donors to the central T acceptor, optical excitation at 488 nm resulting in exclusively acceptor emission in the beginning of the detected fluorescence intensity. Donor emission is seen only upon the bleaching of the acceptor. High-resolution time-resolved single-molecule fluorescence data measured with a microchannel plate photomultiplier reveal, for T2P8, a broad range of FRET rates as a result of a broad range of distances and orientations experienced by the donor-acceptor dendrimers when immobilized in a polymer matrix. Single-molecule data from T2P8 on 488 nm excitation are indicative for the presence, after terrylenediimide bleaching, of a P-P excited dimer characterized by a broad emission spectrum peaking around 600 nm and by fluctuating fluorescence decay times. At high excitation powers, single T1P4 and T2P8 molecules display simultaneous emission from both donor and acceptor chromophores. The effect, called "exciton blockade", occurs due to the presence of multiple excitations in a single molecule.     

Multicolor single-molecule spectroscopy with alternating laser excitation for the investigation of interactions and dynamics

We have developed confocal multicolor single-molecule spectroscopy with optimized detection sensitivity on three spectrally distinct channels for the study of biomolecular interactions and FRET between more than two molecules. Using programmable acousto-optical devices as beamsplitter and excitation filter, we overcome some of the limitations of conventional multichroic beamsplitters and implement rapid alternation between three laser lines. This enables to visualize the synthesis of DNA three-way junctions on a single-molecule basis and to resolve seven stoichiometric subpopulations as well as to quantify FRET in the presence of competing energy transfer pathways. Furthermore, the ability to study correlated molecular movements by monitoring several distances within a biomolecular complex simultaneously is demonstrated.     

Multilayer Microcapsules for FRET Analysis and Two‐Photon‐Activated Photodynamic Therapy

Microcapsules obtained by layer‐by‐layer assembly provide a good platform for biological analysis owing to their component diversity, multiple binding sites, and controllable wall thickness. Herein, different assembly species were obtained from two‐photon dyes and traditional photosensitizers, and further assembled into microcapsules. Fluorescence resonance energy transfer (FRET) was shown to occur between the two‐photon dyes and photosensitizers. Confocal laser scanning microscopy (CLSM) with one‐ and two‐photon lasers, fluorescence lifetime imaging microscopy (FLIM), and time‐resolved fluorescence spectroscopy were used to analyze the FRET effects in the microcapsules. The FRET efficiency could easily be controlled through changing the assembly sequence. Furthermore, the capsules are phototoxic upon one‐ or two‐photon excitation. These materials are thus expected to be applicable in two‐photon‐activated photodynamic therapy for deep‐tissue treatment.     

Unfolded protein and peptide dynamics investigated with single-molecule FRET and correlation spectroscopy from picoseconds to seconds

Single-molecule fluorescence spectroscopy and correlation methods are finding increasing applications in the investigation of biomolecular dynamics, especially together with F?rster resonance energy transfer (FRET). Here, we use the combination of start-stop experiments and classical fluorescence correlation spectroscopy (FCS) to obtain complete intensity auto- and cross-correlation functions from picoseconds to seconds for investigating the dynamics of unfolded proteins and peptides. In combination with distance information from single-molecule transfer efficiency histograms, we can analyze the data in terms of a diffusive process on a potential of mean force to obtain intramolecular diffusion coefficients. This allows us to extend our previous analysis of the time scales of chain dynamics into the low nanosecond range for peptides and into the microsecond range for a small cold shock protein (Csp). Dynamics in short unstructured peptides can be detected down to a time scale of about 10 ns, placing a lower limit on the time scales accessible with correlation methods and currently used dye pairs. We find no evidence for microsecond fluctuations in unfolded Csp, suggesting that its global chain dynamics occur predominantly in the tens of nanosecond range. We further investigate the position dependence of these dynamics by placing donor and acceptor dyes at different positions within the chain and find a decrease in the intramolecular diffusion coefficient by a factor of 3 upon moving one of the dyes toward the center of the polypeptide. Obtaining dynamic information on a wide range of time scales from single-molecule photon statistics will be of increasing importance for the study of unfolded proteins and for biomolecules in general.