Theory of photon statistics in single-molecule Förster resonance energy transfer

We present the theory for the distribution of the number of donor and acceptor photons detected in a time bin and the corresponding energy-transfer efficiency distribution obtained from single-molecule Forster resonance energy-transfer measurements. Photon counts from both immobilized and freely diffusing molecules are considered. Our starting point is the joint distribution for the donor and acceptor photons for a system described by an arbitrary kinetic scheme. This is simplified by exploiting the time scale separation between fast fluorescent transitions and slow processes which include conformational dynamics, intersystem conversion to a dark state, and translational diffusion in and out of the laser spot. The fast fluorescent transitions result in a Poisson distribution of the number of photons which is then averaged over slow fluctuations of the local transfer efficiency and the total number of photons. The contribution of various processes to the distribution and the variance of the energy-transfer efficiency are analyzed.     

Quantifying heterogeneity and conformational dynamics from single molecule FRET of diffusing molecules: recurrence analysis of single particles (RASP)

Single molecule F?rster resonance energy transfer (FRET) experiments are a versatile method for investigating the conformational distributions and dynamics of biological macromolecules. In a common type of experiment, the fluorescence bursts from individual molecules freely diffusing in solution are detected as they pass through the observation volume of a confocal microscope. Correlation analysis of the fluorescence bursts shows that under typical experimental conditions, for time scales up to several tens of milliseconds, the probability for a molecule to return to the confocal volume is greater than the probability of a new molecule being detected. Here we present RASP (recurrence analysis of single particles), a method that is based on this recurrence behavior and allows us to significantly extend the information that can be extracted from single molecule FRET experiments. The number and peak shapes of subpopulations within the sample can be identified essentially in a model-free way by constructing recurrence FRET efficiency histograms. These are obtained by first selecting photon bursts from a small transfer efficiency range (initial bursts), and then building the FRET efficiency histogram only from bursts detected within a short time (the recurrence interval) after the initial bursts. Systematic variation of the recurrence interval allows the kinetics of interconversion between subpopulations to be determined on time scales from ~50 μs up to ~100 ms from equilibrium measurements. We demonstrate the applicability of the method on measurements of several peptides and proteins with different degrees of conformational heterogeneity and folding dynamics. The concepts presented here can be extended to other observables available from single molecule fluorescence experiments.     

Loading Dynamics of a Sliding DNA Clamp

Sliding DNA clamps are loaded at a ss/dsDNA junction by a clamp loader that depends on ATP binding for clamp opening. Sequential ATP hydrolysis results in closure of the clamp so that it completely encircles and diffuses on dsDNA. We followed events during loading of an E. coli β clamp in real time by using single‐molecule FRET (smFRET). Three successive FRET states were retained for 0.3 s, 0.7 s, and 9 min: Hydrolysis of the first ATP molecule by the γ clamp loader resulted in closure of the clamp in 0.3 s, and after 0.7 s in the closed conformation, the clamp was released to diffuse on the dsDNA for at least 9 min. An additional single‐molecule polarization study revealed that the interfacial domain of the clamp rotated in plane by approximately 8° during clamp closure. The single‐molecule polarization and FRET studies thus revealed the real‐time dynamics of the ATP‐hydrolysis‐dependent 3D conformational change of the β clamp during loading at a ss/dsDNA junction.     

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.     

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.     

Fluorescence lifetime based distance measurement illustrates conformation changes of PYL10-CL2 upon ABA binding in solution state

The fluorescence lifetime based FRET distance measurements using sitespecific incorporated unnatural amino acid HC and Alexa488 as FRET pair revealed the different conformations of PYL10-CL2 upon ABA binding.     

Energy distributions in multiple photon absorption experiments

Photofragmentation experiments on molecules and clusters often involve multiple photon absorption. The distributions of the absorbed number of photons are frequently approximated by Poisson distributions. For realistic laser beam profiles, this approximation fails seriously due to the spatial variation of the mean number of absorbed photons across the laser beam. We calculate the distribution of absorbed energy for various laser and molecular-beam parameters. For a Gaussian laser beam, the spatially averaged distributions have a power-law behavior for low energy with a cutoff at an energy which is proportional to fluence. The power varies between -1 for an almost parallel laser beam and -5/2 for a divergent beam (on the scale of the molecular beam). We show that the experimental abundance spectra of fullerenes and small carbon clusters can be used to reconstruct the distribution of internal energy in the excited C60 molecule prior to fragmentation and find good agreement with the calculated curves.     

Another way to view the chain conformation broadening of the line-width distribution measured in dynamic light scattering

In dynamic laser light scattering (LLS), for a given polydisperse sample, a line-width distribution G(Γ) or the translational diffusion coefficient distribution G(D) can be obtained from the measured time correlation function. For rigid colloid particles, G(Γ) can be directly related to the hydrodynamic size distribution. However, for flexible polymer chains, G(Γ) depends not only on the chain length distribution, but also on the relaxation of the chain conformation; that is, even for a monodisperse polymer sample there still exists a chain conformation distribution. If the time scale of the chain conformation relaxation is comparable to that of the translational diffusion, such as in the case of a very long polymer chain, the conformation relaxation might lead to an additional broadening in G (Γ). This "conformation broadening" has been directly observed for the first time by comparing two G(Γ) s obtained from a poly(N-isopropyl-acrylamide) solution at～25℃ and～32℃ at which the solution is ther     

Yotta-photonic excitation spectroscopy of salicylidene-m-bromo-aniline

The observation of triplet-triplet absorption and emission spectra of salicylidene-m-bromo-aniline in solution, is complicated by the possible colored isomer formation during the optical pumping for yotta-photonic excitation at room temperature. The short-lived (singlet-singlet) and long-lived (triplet-triplet) absorption spectra were recorded phographically by microsecond flash and nano-second laser flash photolysis techniques. Salicylidene-m-bromo-aniline complexes were purified by repeated recrystallization until further recrystallization produced no further changes for X-ray diffraction pattern and optical absorption, emission properties. For yotta-photon excitation system, light could be faster than usual, because of heat and to many photonic collisions in the cavity, slowed down by the molecule, and stopped or frozen in a molecular orbital for a short time from nano-second to atto-second. The physical properties of the absorbed photons, in a very high photon flux density (i.e. in a photon field) are different in photonic character, and the emitted photons by the excited states behaves differently in photon field, no splitting occurs for the absorbed or emitted lines like in electrical or magnetic fields.     

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.     

A robust force field based method for calculating conformational energies of charged drug-like molecules

The binding affinity of a drug-like molecule depends among other things on the availability of the bioactive conformation. If the bioactive conformation has a significantly higher energy than the global minimum energy conformation, then the molecule is unlikely to bind to its target. Determination of the global minimum energy conformation and calculation of conformational penalties of binding is a prerequisite for prediction of reliable binding affinities. Here, we present a simple and computationally efficient procedure to estimate the global energy minimum for a wide variety of structurally diverse molecules, including polar and charged compounds. Identifying global energy minimum conformations of such compounds with force field methods is problematic due to the exaggeration of intramolecular electrostatic interactions. We demonstrate that the global energy minimum conformations of zwitterionic compounds generated by conformational analysis with modified electrostatics are good approximations of the conformational distributions predicted by experimental data and with molecular dynamics performed in explicit solvent. Finally the method is used to calculate conformational penalties for zwitterionic GluA2 agonists and to filter false positives from a docking study.     

Nonfluorescent quenchers to correlate single-molecule conformational and compositional dynamics

Single-molecule F?rster resonance energy transfer (smFRET) is a powerful method for studying the conformational dynamics of a biomolecule in real-time. However, studying how interacting ligands correlate with and regulate the conformational dynamics of the biomolecule is extremely challenging because of the availability of a limited number of fluorescent dyes with both high quantum yield and minimal spectral overlap. Here we report the use of a nonfluorescent quencher (Black Hole Quencher, BHQ) as an acceptor for smFRET. Using a Cy3/BHQ pair, we can accurately follow conformational changes of the ribosome during elongation in real time. We demonstrate the application of single-color FRET to correlate the conformational dynamics of the ribosome with the compositional dynamics of tRNA. We use the normal Cy5 FRET acceptor to observe arrival of a fluorescently labeled tRNA with a concomitant transition of the ribosome from the locked to the unlocked conformation. Our results illustrate the potential of nonfluorescent quenchers in single-molecule correlation studies.     

Conformational elasticity theory of chain molecules

This paper develops a conformational elasticity theory of chain molecules, which is based on three key points: (i) the molecular model is the rotational isomeric state (RIS) model; (ii) the conformational distribution function of a chain molecule is described by a function of two variables, the end-to-end distance of a chain conformation and the energy of the conformation; (iii) the rule of changes in the chain conformational states during deformation is that a number of chain conformations would vanish. The ideal deformation behavior calculated by the theory shows that the change in chain conformations is physically able to make the upward curvature of the stress-strain curve at the large-scale deformation of natural rubber. With the theory, different deformation behaviors between polymers with different chemical structures can be described, the energy term of the stress in the deformations can be predicted, and for natural rubber the fraction of the energy term is around 13%, coinciding with the experi     

Isolated monohydrates of a model peptide chain: effect of a first water molecule on the secondary structure of a capped phenylalanine

The formation of monohydrates of capped phenylalanine model peptides, CH(3)-CO-Phe-NH(2) and CH(3)-CO-Phe-NH-CH(3), in a supersonic expansion has been investigated using laser spectroscopy and quantum chemistry methods. Conformational distributions of the monohydrates have been revealed by IR/UV double-resonance spectroscopy and their structures assigned by comparison with DFT-D calculations. A careful analysis of the final hydrate distribution together with a detailed theoretical investigation of the potential energy surface of the monohydrates demonstrates that solvation occurs from the conformational distribution of the isolated peptide monomers. The distribution of the monohydrates appears to be strongly dependent on both the initial monomer conformation (extended or folded backbone) and the solvation site initially occupied by the water molecule. The solvation processes taking place during the cooling can be categorized as follows: (a) solvation without significant structural changes of the peptide, (b) solvation inducing significant distortions of the backbone but retaining the secondary structure, and (c) solvation triggering backbone isomerizations, leading to a modification of the peptide secondary structure. It is observed that solvation by a single water molecule can fold a β-strand into a γ-turn structure (type c) or induce a significant opening of a γ-turn characterized by an elongated C(7) hydrogen bond (type b). These structural changes can be considered as a first step toward the polyproline II condensed-phase structure, illustrating the role played by the very first water molecule in the solvation process.     

Probing single-molecule enzyme active-site conformational state intermittent coherence

The relationship between protein conformational dynamics and enzymatic reactions has been a fundamental focus in modern enzymology. Using single-molecule fluorescence resonance energy transfer (FRET) with a combined statistical data analysis approach, we have identified the intermittently appearing coherence of the enzymatic conformational state from the recorded single-molecule intensity-time trajectories of enzyme 6-hydroxymethyl-7,8-dihydropterin pyrophosphokinase (HPPK) in catalytic reaction. The coherent conformational state dynamics suggests that the enzymatic catalysis involves a multistep conformational motion along the coordinates of substrate-enzyme complex formation and product releasing, presenting as an extreme dynamic behavior intrinsically related to the time bunching effect that we have reported previously. The coherence frequency, identified by statistical results of the correlation function analysis from single-molecule FRET trajectories, increases with the increasing substrate concentrations. The intermittent coherence in conformational state changes at the enzymatic reaction active site is likely to be common and exist in other conformation regulated enzymatic reactions. Our results of HPPK interaction with substrate support a multiple-conformational state model, being consistent with a complementary conformation selection and induced-fit enzymatic loop-gated conformational change mechanism in substrate-enzyme active complex formation.     

Structures of photo-produced transient species

An overview of recent advances in the experimental measurements, theoretical interpretations, and practical applications of bond length and bond angle changes that occur after a molecule absorbs one or more photons is presented. “Gentle” changes are those in which the chemical bonds remain intact, but the lengths and angles increase or decrease. The bond length and bond angle changes that occur when a molecule absorbs a photon are measured by using a combination of electronic (emission and absorption) spectroscopy, resonance Raman spectroscopy, and the time-dependent theory of spectroscopy. “Catastrophic” changes are those in which multiple bonds are broken, leading to extensive photofragmentation. Luminescence spectroscopy is used to identify the transient fragments of metal-containing compounds that are precursors for laser assisted chemical vapor deposition.     

Conformational Dynamics of apo‐GlnBP Revealed by Experimental and Computational Analysis

The glutamine binding protein (GlnBP) binds l ‐glutamine and cooperates with its cognate transporters during glutamine uptake. Crystal structure analysis has revealed an open and a closed conformation for apo‐ and holo‐GlnBP, respectively. However, the detailed conformational dynamics have remained unclear. Herein, we combined NMR spectroscopy, MD simulations, and single‐molecule FRET techniques to decipher the conformational dynamics of apo‐GlnBP. The NMR residual dipolar couplings of apo‐GlnBP were in good agreement with a MD‐derived structure ensemble consisting of four metastable states. The open and closed conformations are the two major states. This four‐state model was further validated by smFRET experiments and suggests the conformational selection mechanism in ligand recognition of GlnBP.     

Accurate single molecule FRET efficiency determination for surface immobilized DNA using maximum likelihood calculated lifetimes

Single molecule fluorescent lifetime trajectories of surface immobilized double-stranded DNA coupled with a tetramethylrhodmaine and Cy5 FRET pair were directly measured using time-tagged single-photon counting and scanning confocal microscopy. A modified maximum likelihood estimator (MLE) was developed to compensate for localized background fluorescence and instrument response. With this algorithm, we were able to robustly extract fluorescent lifetimes from their respective decays with as few as 20 photons. Fluorescent lifetimes extracted using an MLE were found to be highly dependent on background fluorescence. We show that appropriate factors are required to extract true lifetime trajectories from single fluorophores.