Revealing time bunching effect in single-molecule enzyme conformational dynamics

In this perspective, we focus our discussion on how the single-molecule spectroscopy and statistical analysis are able to reveal enzyme hidden properties, taking the study of T4 lysozyme as an example. Protein conformational fluctuations and dynamics play a crucial role in biomolecular functions, such as in enzymatic reactions. Single-molecule spectroscopy is a powerful approach to analyze protein conformational dynamics under physiological conditions, providing dynamic perspectives on a molecular-level understanding of protein structure-function mechanisms. Using single-molecule fluorescence spectroscopy, we have probed T4 lysozyme conformational motions under the hydrolysis reaction of a polysaccharide of E. coli B cell walls by monitoring the fluorescence resonant energy transfer (FRET) between a donor-acceptor probe pair tethered to T4 lysozyme domains involving open-close hinge-bending motions. Based on the single-molecule spectroscopic results, molecular dynamics simulation, a random walk model analysis, and a novel 2D statistical correlation analysis, we have revealed a time bunching effect in protein conformational motion dynamics that is critical to enzymatic functions. Bunching effect implies that conformational motion times tend to bunch in a finite and narrow time window. We show that convoluted multiple Poisson rate processes give rise to the bunching effect in the enzymatic reaction dynamics. Evidently, the bunching effect is likely common in protein conformational dynamics involving in conformation-gated protein functions. In this perspective, we will also discuss a new approach of 2D regional correlation analysis capable of analyzing fluctuation dynamics of complex multiple correlated and anti-correlated fluctuations under a non-correlated noise background. Using this new method, we are able to map out any defined segments along the fluctuation trajectories and determine whether they are correlated, anti-correlated, or non-correlated; after which, a cross correlation analysis can be applied for each specific segment to obtain a detailed fluctuation dynamics analysis.     

Single-molecule Förster resonance energy transfer reveals an innate fidelity checkpoint in DNA polymerase I

Enzymatic reactions typically involve complex dynamics during substrate binding, conformational rearrangement, chemistry, and product release. The noncovalent steps provide kinetic checkpoints that contribute to the overall specificity of enzymatic reactions. DNA polymerases perform DNA replication with outstanding fidelity by actively rejecting noncognate nucleotide substrates early in the reaction pathway. Substrates are delivered to the active site by a flexible fingers subdomain of the enzyme, as it converts from an open to a closed conformation. The conformational dynamics of the fingers subdomain might also play a role in nucleotide selection, although the precise role is currently unknown. Using single-molecule F?rster resonance energy transfer, we observed individual Escherichia coli DNA polymerase I (Klenow fragment) molecules performing substrate selection. We discovered that the fingers subdomain actually samples through three distinct conformations--open, closed, and a previously unrecognized intermediate conformation. We measured the overall dissociation rate of the polymerase-DNA complex and the distribution among the various conformational states in the absence and presence of nucleotide substrates, which were either correct or incorrect. Correct substrates promote rapid progression of the polymerase to the catalytically competent closed conformation, whereas incorrect nucleotides block the enzyme in the intermediate conformation and induce rapid dissociation from DNA. Remarkably, incorrect nucleotide substrates also promote partitioning of DNA to the spatially separated 3'-5' exonuclease domain, providing an additional mechanism to prevent misincorporation at the polymerase active site. These results reveal the existence of an early innate fidelity checkpoint, rejecting incorrect nucleotide substrates before the enzyme encloses the nascent base pair.     

Exploring protein structure and dynamics under denaturing conditions by single-molecule FRET analysis

Proteins are highly complex biopolymers, exhibiting a substantial degree of structural variability in their properly folded, native state. In the presence of denaturants, this heterogeneity is greatly enhanced, and fluctuations take place among vast numbers of folded and unfolded conformations via many different pathways. To better understand protein folding it is necessary to explore the structural and energetic properties of the folded and unfolded polypeptide chain, as well as the trajectories along which the chain navigates through its multi-dimensional conformational energy landscape. In recent years, single-molecule fluorescence spectroscopy has been established as a powerful tool in this research area, as it allows one to monitor the structure and dynamics of individual polypeptide chains in real time with atomic scale resolution using F?rster resonance energy transfer (FRET). Consequently, time trajectories of folding transitions can be directly observed, including transient intermediates that may exist along these pathways. Here we illustrate the power of single-molecule fluorescence with our recent work on the structure and dynamics of the small enzyme RNase H in the presence of the chemical denaturant guanidinium chloride (GdmCl). For FRET analysis, a pair of fluorescent dyes was attached to the enzyme at specific locations. In order to observe conformational changes of individual protein molecules for up to several hundred seconds, the proteins were immobilized on nanostructured, polymer coated glass surfaces specially developed to have negligible interactions with folded and unfolded proteins. The single-molecule FRET analysis gave insight into structural changes of the unfolded polypeptide chain in response to varying the denaturant concentration, and the time traces revealed stepwise transitions in the FRET levels, reflecting conformational dynamics. Barriers in the free energy landscape of RNase H were estimated from the kinetics of the transitions.     

Conformational dynamics of the isoalloxazine in substrate-free p-hydroxybenzoate hydroxylase: single-molecule studies

p-Hydroxybenzoate hydroxylase (PHBH) is a homodimeric enzyme in which each subunit noncovalently binds one molecule of FAD in the active site. PHBH is a model system for how flavoenzymes regulate reactions with oxygen. We report single-molecule fluorescence studies of PHBH in the absence of substrate that provide data consistent with the hypothesis that a critical step in substrate binding is the movement of the isoalloxazine between an "in" conformation and a more exposed or "open" conformation. The isoalloxazine is observed to move between these conformations in the absence of substrate. Studies with the Y222A mutant form of PHBH suggest that the exposed conformation is fluorescent while the in-conformation is quenched. Finally, we note that many of the single-molecule-fluorescence trajectories reveal a conformational heterogeneity, with populations of the enzyme characterized by either fast or slow switching between the in- and open-conformations. Our data also allow us to hypothesize a model in which one flavin in the dimer inhibits the motion of the other.     

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.     

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.     

Catalytic itinerary in 1,3-1,4-β-glucanase unraveled by QM/MM metadynamics. Charge is not yet fully developed at the oxocarbenium ion-like transition state

Retaining glycoside hydrolases (GHs), key enzymes in the metabolism of polysaccharides and glycoconjugates and common biocatalysts used in chemoenzymatic oligosaccharide synthesis, operate via a double-displacement mechanism with the formation of a glycosyl-enzyme intermediate. However, the degree of oxocarbenium ion character of the reaction transition state and the precise conformational itinerary of the substrate during the reaction, pivotal in the design of efficient inhibitors, remain elusive for many GHs. By means of QM/MM metadynamics, we unravel the catalytic itinerary of 1,3-1,4-β-glucanase, one of the most active GHs, belonging to family 16. We show that, in the Michaelis complex, the enzyme environment restricts the conformational motion of the substrate to stabilize a (1,4)B/(1)S(3) conformation of the saccharide ring at the -1 subsite, confirming that this distortion preactivates the substrate for catalysis. The metadynamics simulation of the enzymatic reaction captures the complete conformational itinerary of the substrate during the glycosylation reaction ((1,4)B/(1)S(3) -(4)E/(4)H(3) - (4)C(1)) and shows that the transition state is not the point of maximum charge development at the anomeric carbon. The overall catalytic mechanism is of dissociative type, and proton transfer to the glycosidic oxygen is a late event, clarifying previous kinetic studies of this enzyme.     

Analytical solution of non-linear enzyme reaction equations arising in mathematical chemistry

The boundary value problem in basic enzyme reactions is formulated and approximate expressions for substrate and substrate-enzyme complex are presented. He’s Homotopy Perturbation method is used to give approximate and analytical solutions of non-linear reaction equations containing a non-linear term related to enzymatic reaction. The pertinent analytical solutions for the substrate, enzyme- substrate complex and free enzyme are discussed in terms of dimensionless parameters σ, ρ and e{\varepsilon} . The obtained concentration results are compared with the numerical solution acquired using Matlab program. They are found to be in satisfactory agreement.     

2D regional correlation analysis of single-molecule time trajectories

We report a new approach of 2D regional correlation analysis capable of analyzing fluctuation dynamics of complex multiple correlated and anticorrelated fluctuations under a noncorrelated noise background. Using this new method, by changing and scanning the start time and end time along a pair of fluctuation trajectories, we are able to map out any defined segments along the fluctuation trajectories and determine whether they are correlated, anticorrelated, or noncorrelated; after which, a cross-correlation analysis can be applied for each specific segment to obtain a detailed fluctuation dynamics analysis. We specifically discuss an application of this approach to analyze single-molecule fluorescence resonance energy transfer (FRET) fluctuation dynamics where the fluctuations are often complex, although this approach can be useful for analyzing other types of fluctuation dynamics of various physical variables as well.     

Probing ground-state single-electron self-exchange across a molecule-metal interface

We have probed single-molecule redox reaction dynamics of hemin (chloride) adsorbed on Ag nanoparticle surfaces by single-molecule surface-enhanced Raman spectroscopy (SMSERS) combined with spectroelectrochemistry. Redox reaction at the molecule/Ag interface is identified and probed by the prominent fluctuations of the Raman frequency of a specific vibrational mode, ν(4), which is a typical marker of the redox state of the iron center in a hemin molecule. On the basis of the autocorrelation and cross-correlation analysis of the single-molecule Raman spectral trajectories and the control measurements of single-molecule spectroelectochemistry and electrochemical STM, we suggest that the single-molecule redox reaction dynamics at the hemin-Ag interface is primarily driven by thermal fluctuations. The spontaneous fluctuation dynamics of the single-molecule redox reaction is measured under no external electric potential across the molecule-metal interfaces, which provides a novel and unique approach to characterize the interfacial electron transfer at the molecule-metal interfaces. Our demonstrated approaches are powerful for obtaining molecular coupling and dynamics involved in interfacial electron transfer processes. The new information obtained is critical for a further understanding, design, and manipulation of the charge transfer processes at the molecule-metal interface or metal-molecule-metal junctions, which are fundamental elements in single-molecule electronics, catalysis, and solar energy conversion.     

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.     

Protein-induced excited-state dynamics of protochlorophyllide

The light-driven NADPH:protochlorophyllide oxidoreductase (POR) is a key enzyme of chlorophyll biosynthesis in angiosperms. POR's unique requirement for light to become catalytically active makes the enzyme an attractive model to study the dynamics of enzymatic reactions in real time. Here, we use picosecond time-resolved fluorescence and femtosecond pump-probe spectroscopy to examine the influence of the protein environment on the excited-state dynamics of the substrate, protochlorophyllide (PChlide), in the enzyme/substrate (PChlide/POR) and pseudoternary complex including the nucleotide cofactor NADP(+) (PChlide/NADP(+)/ POR). In comparison with the excited-state processes of unbound PChlide, the lifetime of the thermally equilibrated S(1) excited state is lengthened from 3.4 to 4.4 and 5.4 ns in the PChlide/POR and PChlide/NADP(+)/POR complex, whereas the nonradiative rates are decreased by ～30 and 40%, respectively. This effect is most likely due to the reduced probability of nonradiative decay into the triplet excited state, thus keeping the risk of photosensitized side reactions in the enzyme low. Further, the initial reaction path involves the formation of an intramolecular charge-transfer state (S(ICT)) as an intermediate product. From a strong blue shift in the excited-state absorption, it is concluded that the S(ICT) state is stabilized by local interactions with specific protein sites in the catalytic pocket. The possible relevance of this result for the catalytic reaction in the enzyme POR is discussed.     

Mathematical modelling of enzyme kinetics reaction mechanisms and analytical solutions of non-linear reaction equations

The boundary value problem in basic enzyme reactions is formulated and approximate expressions for substrate and product concentrations are presented. He’s variational iteration method is used to give approximate and analytical solutions of non-linear reaction equations containing a non-linear term related to enzymatic reaction. The relevant analytical solutions for the substrate, enzyme, substrate-enzyme and product concentration profiles are discussed in terms of dimensionless reaction diffusion parameters K, λ and e{\varepsilon}.     

When does the Michaelis-Menten equation hold for fluctuating enzymes?

Enzymes are dynamic entities: both their conformation and catalytic activity fluctuate over time. When such fluctuations are relatively fast, it is not surprising that the classical Michaelis-Menten (MM) relationship between the steady-state enzymatic velocity and the substrate concentration still holds. However, recent single-molecule experiments have shown that this is the case even for an enzyme whose catalytic activity fluctuates on the 10(-4)-10 s range. The purpose of this paper is to examine various scenarios in which slowly fluctuating enzymes would still obey the MM relationship. Specifically, we consider (1) the quasi-static condition (e.g., the conformational fluctuation of the enzyme-substrate complex is much slower than binding, catalysis, and the conformational fluctuations of the free enzyme), (2) the quasi-equilibrium condition (when the substrate dissociation is much faster than catalysis, irrespective of the time scales or amplitudes of conformational fluctuations), and (3) the conformational-equilibrium condition (when the dissociation and catalytic rates depend on the conformational coordinate in the same way). For each of these scenarios, the physical meaning of the apparent Michaelis constant and catalytic rate constant is provided. Finally, as an example, the theoretical analysis of a recent single-molecule enzyme assay is considered in light of the perspectives presented in this paper.     

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.     

Assay Development and Identification of the First Plasmodium falciparum 7,8-dihydro-6-hydroxymethylpterin-pyrophosphokinase Inhibitors

In the fight towards eradication of malaria, identifying compounds active against new drug targets constitutes a key approach. Plasmodium falciparum 7,8-dihydro-6-hydroxymethylpterin-pyrophosphokinase (PfHPPK) has been advanced as a promising target, as being part of the parasite essential folate biosynthesis pathway while having no orthologue in the human genome. However, no drug discovery efforts have been reported on this enzyme. In this study, we conducted a three-step screening of our in-house antifolate library against PfHPPK using a newly designed PfHPPK-GFP protein construct. Combining virtual screening, differential scanning fluorimetry and enzymatic assay, we identified 14 compounds active against PfHPPK. Compounds’ binding modes were investigated by molecular docking, suggesting competitive binding with the HMDP substrate. Cytotoxicity and in vitro ADME properties of hit compounds were also assessed, showing good metabolic stability and low toxicity. The most active compounds displayed low micromolar IC₅₀ against drug-resistant parasites. The reported hit compounds constitute a good starting point for inhibitor development against PfHPPK, as an alternative approach to tackle the malaria parasite.     

Enzymatic effects on reactant and transition states. The case of chalcone isomerase

Chalcone isomerase catalyzes the transformation of chalcone to naringerin as a part of flavonoid biosynthetic pathways. The global reaction takes place through a conformational change of the substrate followed by chemical reaction, being thus an excellent example to analyze current theories about enzyme catalysis. We here present a detailed theoretical study of the enzymatic action on the conformational pre-equilibria and on the chemical steps for two different substrates of this enzyme. Free-energy profiles are obtained in terms of potentials of mean force using hybrid quantum mechanics/molecular mechanics potentials. The role of the enzyme becomes clear when compared to the counterpart equilibria and reactions in aqueous solution. The enzyme does not only favor the chemical reaction lowering the corresponding activation free energy but also displaces the conformational equilibria of the substrates toward the reactive form. These results, which can be rationalized in terms of the electrostatic interactions established in the active site between the substrate and the environment, agree with a more general picture of enzyme catalysis. According to this, an active site designed to accommodate the transition state of the reaction would also have consequences on the reactant state, stabilizing those forms which are geometrically and/or electronically closer to the transition structure.     

Structure-dependent photophysics studied in single molecules of polythiophene derivatives.

We report on the photophysical characterization at the single-molecule level of a graft copolymer consisting of a polythiophene backbone and long polystyrene branches. The presence of the branches prevents the polymer chain from forming a collapsed conformational state. The photophysical properties of the resulting solution-like conformation are studied by measuring single-molecule photobleaching dynamics, emission polarization anisotropy and emission spectra. The results are compared with those obtained on the same polythiophene derivative without the branches. It is found that the presence of the branches is a decisive factor in determining the photophysical properties of the polymers on the single-molecule level.     

A theoretical analysis of rate constants and kinetic isotope effects corresponding to different reactant valleys in lactate dehydrogenase

In some enzymatic systems large conformational changes are coupled to the chemical step, in such a way that dispersion of rate constants can be observed in single-molecule experiments, each corresponding to the reaction from a different reactant valley. Under this perspective here we present a computational study of pyruvate to lactate transformation catalyzed by lactate dehydrogenase. The reaction consists of a hydride transfer and a proton transfer that seem to take place concertedly. The degree of asynchronicity and the energy barrier depend on the particular starting reactant valley. In order to estimate rate constants we used a free energy perturbation technique adapted to follow the intrinsic reaction coordinate for several possible reaction paths. Tunneling effects are also obtained with a slightly modified version of the ensemble-averaged variational transition state theory with multidimensional tunneling contributions. According to our results the closure of the active site by means of a flexible loop can lead to the formation of different reactant complexes displaying different features in the disposition of some key residues (such as Arg109), interactions with the substrate and number of water molecules in the active site. The chemical step of the reaction takes place with a different reaction rate from each of these complexes. Finally, primary kinetic isotope effects for replacement of the transferring hydrogen of the cofactor with a deuteride are in good agreement with experimental observations, thus validating our methodology.