Bunching effect in single-molecule T4 lysozyme nonequilibrium conformational dynamics under enzymatic reactions

Main role of fractal-like nature of conformational space in subdiffusion in proteins

Protein dynamics involves a myriad of mechanical movements happening at different time and space scales, which make it highly complex. One of the less understood features of protein dynamics is subdiffusivity, defined as sublinear dependence between displacement and time. Here, we use all-atoms molecular dynamics (MD) simulations to directly interrogate an already well-established theory and demonstrate that subdiffusivity arises from the fractal nature of the network of metastable conformations over which the dynamics, thought of as a diffusion process, takes place.

Superscalability of the random batch Ewald method

Coulomb interaction, following an inverse-square force-law, quantifies the amount of force between two stationary and electrically charged particles. The long-range nature of Coulomb interactions poses a major challenge to molecular dynamics simulations, which are major tools for problems at the nano-/micro-scale. Various algorithms are developed to calculate the pairwise Coulomb interactions to a linear scale, but poor scalability limits the size of simulated systems. Here, we use an efficient molecular dynamics algorithm with the random batch Ewald method on all-atom systems where the complete Fourier components in the Coulomb interaction are replaced by randomly selected mini-batches. By simulating the N-body systems up to 10⁸ particles using 10 000 central processing unit cores, we show that this algorithm furnishes O(N) complexity, almost perfect scalability, and an order of magnitude faster computational speed when compared to the existing state-of-the-art algorithms. Further examinations of our algorithm on distinct systems, including pure water, a micro-phase separated electrolyte, and a protein solution, demonstrate that the spatiotemporal information on all time and length scales investigated and thermodynamic quantities derived from our algorithm are in perfect agreement with those obtained from the existing algorithms. Therefore, our algorithm provides a promising solution on scalability of computing the Coulomb interaction. It is particularly useful and cost-effective to simulate ultra-large systems, which is either impossible or very costly to conduct using existing algorithms, and thus will be beneficial to a broad range of problems at nano-/micro-scales.

FRET-based dynamic structural biology: Challenges, perspectives and an appeal for open-science practices

Single-molecule FRET (smFRET) has become a mainstream technique for studying biomolecular structural dynamics. The rapid and wide adoption of smFRET experiments by an ever-increasing number of groups has generated significant progress in sample preparation, measurement procedures, data analysis, algorithms and documentation. Several labs that employ smFRET approaches have joined forces to inform the smFRET community about streamlining how to perform experiments and analyze results for obtaining quantitative information on biomolecular structure and dynamics. The recent efforts include blind tests to assess the accuracy and the precision of smFRET experiments among different labs using various procedures. These multi-lab studies have led to the development of smFRET procedures and documentation, which are important when submitting entries into the archiving system for integrative structure models, PDB-Dev. This position paper describes the current 'state of the art' from different perspectives, points to unresolved methodological issues for quantitative structural studies, provides a set of 'soft recommendations' about which an emerging consensus exists, and lists openly available resources for newcomers and seasoned practitioners. To make further progress, we strongly encourage 'open science' practices.

Enzyme Kinetics in Femtoliter Arrays

Over the last decade, femtoliter arrays have been used as a simple and robust way to encapsulate and monitor the kinetics of single enzyme molecules. Encapsulating individual enzyme molecules within a femtoliter-sized reaction chamber does not require immobilization of the enzyme molecules or fluorescent tagging of the enzyme molecules, which offers the unique advantage of observing unmodified single enzyme molecules free in solution. Several fascinating details about enzyme kinetics have been revealed using these femtoliter arrays, which were unattainable from traditional ensemble experiments. Here, we discuss various considerations to take into account when developing single-molecule enzyme assays in femtoliter arrays and the advantages and disadvantages of various protocols.

Fluorescence fluctuation of an antigen-antibody complex: circular dichroism, FCS and smFRET of enhanced GFP and its antibody

The structure and dynamics of an antigen-antibody complex are monitored by circular dichroism (CD) spectroscopy, fluorescence correlation spectroscopy (FCS) and single molecule FRET (smFRET). In this work, the antigen is enhanced GFP (EGFP) and the antibody is anti-EGFP VHH-His6. From FCS measurements, the hydrodynamic radius (rH) of EGFP and its antibody (VHH-His6) is found to be 24 ± 2 Å and 18 ± 2 Å, respectively. For the antigen-antibody complex (EGFP:anti-EGFP VHH-His6), rH is 41 ± 3 Å. CD spectra indicate that the addition of guanidium hydrochloride (GdnHCl) causes unfolding of the antigen, its antibody and their complex, and a consequent increase in size is observed from FCS data. smFRET between EGFP (donor, D) and Alexa 594 (acceptor, A) bound to anti-EGFP VHH-His6 reveals a time dependent fluctuation in donor-acceptor distances. This suggests that the structure of the antigen-antibody complex is dynamic in nature and is not rigid.

Observing lysozyme's closing and opening motions by high-resolution single-molecule enzymology

Single-molecule techniques can monitor the kinetics of transitions between enzyme open and closed conformations, but such methods usually lack the resolution to observe the underlying transition pathway or intermediate conformational dynamics. We have used a 1 MHz bandwidth carbon nanotube transistor to electronically monitor single molecules of the enzyme T4 lysozyme as it processes substrate. An experimental resolution of 2 μs allowed the direct recording of lysozyme's opening and closing transitions. Unexpectedly, both motions required 37 μs, on average. The distribution of transition durations was also independent of the enzyme's state: either catalytic or nonproductive. The observation of smooth, continuous transitions suggests a concerted mechanism for glycoside hydrolysis with lysozyme's two domains closing upon the polysaccharide substrate in its active site. We distinguish these smooth motions from a nonconcerted mechanism, observed in approximately 10% of lysozyme openings and closings, in which the enzyme pauses for an additional 40-140 μs in an intermediate, partially closed conformation. During intermediate forming events, the number of rate-limiting steps observed increases to four, consistent with four steps required in the stepwise, arrow-pushing mechanism. The formation of such intermediate conformations was again independent of the enzyme's state. Taken together, the results suggest lysozyme operates as a Brownian motor. In this model, the enzyme traces a single pathway for closing and the reverse pathway for enzyme opening, regardless of its instantaneous catalytic productivity. The observed symmetry in enzyme opening and closing thus suggests that substrate translocation occurs while the enzyme is closed.

Direct observation of the growth and shrinkage of microtubules by single molecule Förster resonance energy transfer

Single molecule Förster resonance energy transfer (FRET) has been applied to monitor the growth and the shrinkage of the dynamic microtubules.

Probing protein multidimensional conformational fluctuations by single-molecule multiparameter photon stamping spectroscopy

Conformational motions of proteins are highly dynamic and intrinsically complex. To capture the temporal and spatial complexity of conformational motions and further to understand their roles in protein functions, an attempt is made to probe multidimensional conformational dynamics of proteins besides the typical one-dimensional FRET coordinate or the projected conformational motions on the one-dimensional FRET coordinate. T4 lysozyme hinge-bending motions between two domains along α-helix have been probed by single-molecule FRET. Nevertheless, the domain motions of T4 lysozyme are rather complex involving multiple coupled nuclear coordinates and most likely contain motions besides hinge-bending. It is highly likely that the multiple dimensional protein conformational motions beyond the typical enzymatic hinged-bending motions have profound impact on overall enzymatic functions. In this report, we have developed a single-molecule multiparameter photon stamping spectroscopy integrating fluorescence anisotropy, FRET, and fluorescence lifetime. This spectroscopic approach enables simultaneous observations of both FRET-related site-to-site conformational dynamics and molecular rotational (or orientational) motions of individual Cy3-Cy5 labeled T4 lysozyme molecules. We have further observed wide-distributed rotational flexibility along orientation coordinates by recording fluorescence anisotropy and simultaneously identified multiple intermediate conformational states along FRET coordinate by monitoring time-dependent donor lifetime, presenting a whole picture of multidimensional conformational dynamics in the process of T4 lysozyme open-close hinge-bending enzymatic turnover motions under enzymatic reaction conditions. By analyzing the autocorrelation functions of both lifetime and anisotropy trajectories, we have also observed the dynamic and static inhomogeneity of T4 lysozyme multidimensional conformational fluctuation dynamics, providing a fundamental understanding of the enzymatic reaction turnover dynamics associated with overall enzyme as well as the specific active-site conformational fluctuations that are not identifiable and resolvable in the conventional ensemble-averaged experiment.

Elucidating the relationship between substrate and inhibitor binding to the active sites of tetrameric β-galactosidase

The stochastic binding and release of two different inhibitors from a tetrameric enzyme is described at the single molecule level.

Single molecule recordings of lysozyme activity

Single molecule bioelectronic circuits provide an opportunity to study chemical kinetics and kinetic variability with bond-by-bond resolution. To demonstrate this approach, we examined the catalytic activity of T4 lysozyme processing peptidoglycan substrates. Monitoring a single lysozyme molecule through changes in a circuit's conductance helped elucidate unexplored and previously invisible aspects of lysozyme's catalytic mechanism and demonstrated lysozyme to be a processive enzyme governed by 9 independent time constants. The variation of each time constant with pH or substrate crosslinking provided different insights into catalytic activity and dynamic disorder. Overall, ten lysozyme variants were synthesized and tested in single molecule circuits to dissect the transduction of chemical activity into electronic signals. Measurements show that a single amino acid with the appropriate properties is sufficient for good signal generation, proving that the single molecule circuit technique can be easily extended to other proteins.

Electronic measurements of single-molecule processing by DNA polymerase I (Klenow fragment)

Bioconjugating single molecules of the Klenow fragment of DNA polymerase I into electronic nanocircuits allowed electrical recordings of enzymatic function and dynamic variability with the resolution of individual nucleotide incorporation events. Continuous recordings of DNA polymerase processing multiple homopolymeric DNA templates extended over 600 s and through >10,000 bond-forming events. An enzymatic processivity of 42 nucleotides for a template of the same length was directly observed. Statistical analysis determined key kinetic parameters for the enzyme's open and closed conformations. Consistent with these nanocircuit-based observations, the enzyme's closed complex forms a phosphodiester bond in a highly efficient process >99.8% of the time, with a mean duration of only 0.3 ms for all four dNTPs. The rate-limiting step for catalysis occurs during the enzyme's open state, but with a nearly 2-fold longer duration for dATP or dTTP incorporation than for dCTP or dGTP into complementary, homopolymeric DNA templates. Taken together, the results provide a wealth of new information complementing prior work on the mechanism and dynamics of DNA polymerase I.

Dissecting single-molecule signal transduction in carbon nanotube circuits with protein engineering

Single-molecule experimental methods have provided new insights into biomolecular function, dynamic disorder, and transient states that are all invisible to conventional measurements. A novel, nonfluorescent single-molecule technique involves attaching single molecules to single-walled carbon nanotube field-effective transistors (SWNT FETs). These ultrasensitive electronic devices provide long-duration, label-free monitoring of biomolecules and their dynamic motions. However, generalization of the SWNT FET technique first requires design rules that can predict the success and applicability of these devices. Here, we report on the transduction mechanism linking enzymatic processivity to electrical signal generation by a SWNT FET. The interaction between SWNT FETs and the enzyme lysozyme was systematically dissected using eight different lysozyme variants synthesized by protein engineering. The data prove that effective signal generation can be accomplished using a single charged amino acid, when appropriately located, providing a foundation to widely apply SWNT FET sensitivity to other biomolecular systems.

Direct observation of T4 lysozyme hinge-bending motion by fluorescence correlation spectroscopy

Bacteriophage T4 Lysozyme (T4L) catalyzes the hydrolysis of the peptidoglycan layer of the bacterial cell wall late in the infection cycle. It has long been postulated that equilibrium dynamics enable substrate access to the active site located at the interface between the N- and C-terminal domains. Crystal structures of WT-T4L and point mutants captured a range of conformations that differ by the hinge-bending angle between the two domains. Evidence of equilibrium between open and closed conformations in solution was gleaned from distance measurements between the two domains but the nature of the equilibrium and the timescale of the underlying motion have not been investigated. Here, we used fluorescence fluctuation spectroscopy to directly detect T4L equilibrium conformational fluctuations in solution. For this purpose, Tetramethylrhodamine probes were introduced at pairs of cysteines in regions of the molecule that undergo relative displacement upon transition from open to closed conformations. Correlation analysis of Tetramethylrhodamine intensity fluctuations reveals hinge-bending motion that changes the relative distance and orientation of the N- and C-terminal domains with ≅ 15 μs relaxation time. That this motion involves interconversion between open and closed conformations was further confirmed by the dampening of its amplitude upon covalent substrate trapping. In contrast to the prevalent two-state model of T4L equilibrium, molecular brightness and number of particles obtained from cumulant analysis suggest that T4L populates multiple intermediate states, consistent with the wide range of hinge-bending angles trapped in the crystal structure of T4L mutants.

Single-molecule lysozyme dynamics monitored by an electronic circuit

Tethering a single lysozyme molecule to a carbon nanotube field-effect transistor produced a stable, high-bandwidth transducer for protein motion. Electronic monitoring during 10-minute periods extended well beyond the limitations of fluorescence techniques to uncover dynamic disorder within a single molecule and establish lysozyme as a processive enzyme. On average, 100 chemical bonds are processively hydrolyzed, at 15-hertz rates, before lysozyme returns to its nonproductive, 330-hertz hinge motion. Statistical analysis differentiated single-step hinge closure from enzyme opening, which requires two steps. Seven independent time scales governing lysozyme's activity were observed. The pH dependence of lysozyme activity arises not from changes to its processive kinetics but rather from increasing time spent in either nonproductive rapid motions or an inactive, closed conformation.

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.

Binding of organic dyes with human serum albumin: a single-molecule study

Kinetics of binding of dyes at different sites of human serum albumin (HSA) has been studied by single-molecule spectroscopy. The protein was immobilized on a glass surface. To probe different binding sites (hydrophobic and hydrophilic) two dyes, coumarin 153 (C153, neutral) and rhodamine 6G (R6G, cationic) were chosen. For both the dyes, a major (ca. 96-98%) and minor (ca. 3%) binding site were detected. Rate constants of association and dissociation were simultaneously determined from directly measuring fluctuations in fluorescence intensity (τ(off) and τ(on)) and from this the equilibrium (binding) constants were calculated. Fluorescence lifetimes at individual sites were obtained from burst-integrated lifetime analysis. Distributions of lifetime histograms for both the probes (C153 and R6G) exhibit two maxima, which indicates the presence of two binding domains in the protein. Unfolding of the protein has been studied by adding guanidinium hydrochloride (GdnHCl) to the solution. It is observed that addition of GdnHCl affects the dissociation and association kinetics and hence, binding equilibrium of the association of C153. However, the effect of binding of R6G is not affected much. It is proposed that GdnHCl affects the hydrophobic binding sites more than the hydrophilic site.

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.

Improved resolution of complex single-molecule FRET systems via wavelet shrinkage

The resolution of complex interactions found in single-molecule fluorescence resonance energy transfer (smFRET) experiments is hindered by noise. Wavelet shrinkage is proven to reduce noise, but traditional methods introduce artifacts when acting on discontinuous signals, such as those acquired in smFRET experiments. Modifications to the basic method that are specific to smFRET are developed and tested on simulated systems. Use of the Haar wavelet basis produces the most optimally denoised estimates. We also assess various thresholding methods, develop a time-localized noise estimator, and implement a translation-invariant wavelet transformation to reduce artifacts associated with discontinuities and inadequate distinction of noise. The time-local estimator enhances noise reduction by 5-20%, and translation-invariant transformation nearly eliminates the aforementioned artifacts. Kinetic parameters extracted from denoised estimates are accurate to within 5% of the simulated values. Overall, the improved resolution results in the complete and accurate characterization of both simple and complex smFRET systems.