Single-molecule kinetics of lambda exonuclease reveal base dependence and dynamic disorder

Dynamics of DNA replication loops reveal temporal control of lagging-strand synthesis

In all organisms, the protein machinery responsible for the replication of DNA, the replisome, is faced with a directionality problem. The antiparallel nature of duplex DNA permits the leading-strand polymerase to advance in a continuous fashion, but forces the lagging-strand polymerase to synthesize in the opposite direction. By extending RNA primers, the lagging-strand polymerase restarts at short intervals and produces Okazaki fragments. At least in prokaryotic systems, this directionality problem is solved by the formation of a loop in the lagging strand of the replication fork to reorient the lagging-strand DNA polymerase so that it advances in parallel with the leading-strand polymerase. The replication loop grows and shrinks during each cycle of Okazaki fragment synthesis. Here we use single-molecule techniques to visualize, in real time, the formation and release of replication loops by individual replisomes of bacteriophage T7 supporting coordinated DNA replication. Analysis of the distributions of loop sizes and lag times between loops reveals that initiation of primer synthesis and the completion of an Okazaki fragment each serve as a trigger for loop release. The presence of two triggers may represent a fail-safe mechanism ensuring the timely reset of the replisome after the synthesis of every Okazaki fragment.

Structure and dynamics of single DNA molecules manipulated by magnetic tweezers and or flow

Here we describe the use of magnetic tweezers and or microfluidics to manipulate single DNA molecules. We describe experiment which employ magnetic tweezers coupled to an inverted microscope as well as the use of a magnetic tweezers setup with an upright microscope. Using a chamber prepared via soft lithography, we also describe a microfluidic device for the manipulation of individual DNA molecules. Finally, we present some past successful examples of using these approaches to elucidate unique information about protein-nucleic acid interactions.

The interrelationship of helicase and nuclease domains during DNA translocation by the molecular motor EcoR124I

The type I restriction–modification enzyme EcoR124I comprises three subunits with the stoichiometry HsdR₂/HsdM₂/HsdS₁. The HsdR subunits are archetypical examples of the fusion between nuclease and helicase domains into a single polypeptide, a linkage that is found in a great many other DNA processing enzymes. To explore the interrelationship between these physically linked domains, we examined the DNA translocation properties of EcoR124I complexes in which the HsdR subunits had been mutated in the RecB-like nuclease motif II or III. We found that nuclease mutations can have multiple effects on DNA translocation despite being distinct from the helicase domain. In addition to reductions in DNA cleavage activity, we also observed decreased translocation and ATPase rates, different enzyme populations with different characteristic translocation rates, a tendency to stall during initiation and altered HsdR turnover dynamics. The significance of these observations to our understanding of domain interactions in molecular machines is discussed.

See me, feel me: methods to concurrently visualize and manipulate single DNA molecules and associated proteins

Direct visualization of DNA and proteins allows researchers to investigate DNA–protein interactions with great detail. Much progress has been made in this area as a result of increasingly sensitive single-molecule fluorescence techniques. At the same time, methods that control the conformation of DNA molecules have been improving constantly. The combination of both techniques has appealed to researchers ever since single-molecule measurements have become possible and indeed first implementations of such combined approaches have proven useful in the study of several DNA-binding proteins in real time. Here, we describe the technical state-of-the-art of various integrated manipulation-and-visualization methods. We first discuss methods that allow only little control over the DNA conformation, such as DNA combing. We then describe DNA flow-stretching approaches that allow more control, and end with the full control on position and extension obtained by manipulating DNA with optical tweezers. The advantages and limitations of the various techniques are discussed, as well as several examples of applications to biophysical or biochemical questions. We conclude with an outlook describing potential future technical developments in combining fluorescence microscopy with DNA micromanipulation technology.

Laminar flow cells for single-molecule studies of DNA-protein interactions

Microfluidic flow cells are used in single-molecule experiments, enabling measurements to be made with high spatial and temporal resolution. We discuss the fundamental processes affecting flow cell operation and describe the flow cells in use at present for studying the interaction of optically trapped or mechanically isolated, single DNA molecules with proteins. To assist the experimentalist in flow cell selection, we review the construction techniques and materials used to fabricate both single- and multiple-channel flow cells and the advantages of each design for different experiments.

Do-it-yourself guide: how to use the modern single-molecule toolkit

Single-molecule microscopy has evolved into the ultimate-sensitivity toolkit to study systems from small molecules to living cells, with the prospect of revolutionizing the modern biosciences. Here we survey the current state of the art in single-molecule tools including fluorescence spectroscopy, tethered particle microscopy, optical and magnetic tweezers, and atomic force microscopy. We also provide guidelines for choosing the right approach from the available single-molecule toolkit for applications as diverse as structural biology, enzymology, nanotechnology and systems biology.

Electrochemical detection of low-copy number salivary RNA based on specific signal amplification with a hairpin probe

We developed a technique for electrochemical detection of salivary mRNA employing a hairpin probe (HP). Steric hindrance (SH) suppresses unspecific signal and generates a signal-on amplification process for target detection. The stem-loop configuration brings the reporter end of the probe into close proximity with the surface and makes it unavailable for binding with the mediator. Target binding opens the hairpin structure of the probe, and the mediator can then bind to the accessible reporter. Horseradish peroxidase is utilized to generate electrochemical signal. This signal-on process is characterized by a low basal signal, a strong positive readout and a large dynamic range. The SH is controlled via hairpin design and electrical field. By applying electric field control to HPs, the limit of detection of RNA is about 0.4 fM, which is 10 000-fold more sensitive than conventional linear probes. Endogenous Interleukin-8 mRNA is detected with the HP, and good correlation with the quantitative PCR technique is obtained. The resultant process allows a simple setup and by reducing the number of steps it is suited for the point-of-care detection of specific nucleic acid sequences from complex body fluids such as saliva.

The importance of surfaces in single-molecule bioscience

The last ten years have witnessed an explosion of new techniques that can be used to probe the dynamic behavior of individual biological molecules, leading to discoveries that would not have been possible with more traditional biochemical methods. A common feature among these single-molecule approaches is the need for the biological molecules to be anchored to a solid support surface. This must be done under conditions that minimize nonspecific adsorption without compromising the biological integrity of the sample. In this review we highlight why surface attachments are a critical aspect of many single-molecule studies and we discuss current methods for anchoring biomolecules. Finally, we provide a detailed description of a new method developed by our laboratory for anchoring and organizing hundreds of individual DNA molecules on a surface, allowing "high-throughput" studies of protein-DNA interactions at the single-molecule level.

Distinct and long-lived activity states of single enzyme molecules

Individual enzyme molecules have been observed to possess discrete and different turnover rates due to the presence of long-lived activity states. These stable activity states are thought to result from different molecular conformations or post-translational modifications. The distributions in kinetic activity observed in previous studies were obtained from small numbers of single enzyme molecules. Due to this limitation, it has not been possible to fully characterize the different kinetic and equilibrium binding parameters of single enzyme molecules. In this paper, we analyze hundreds of single beta-galactosidase molecules simultaneously; using a high-density array of 50,000 fL-reaction chambers, we confirm the presence of long-lived kinetic states within a population of enzyme molecules. Our analysis has isolated the source of kinetic variability to kcat. The results explain the kinetic variability within enzyme molecule populations and offer a deeper understanding of the unique properties of single enzyme molecules. Gaining a more fundamental understanding of how individual enzyme molecules work within a population should provide insight into how they affect downstream biochemical processes. If the results reported here can be generalized to other enzymes, then the stochastic nature of individual enzyme molecule kinetics should have a substantial impact on the overall metabolic activity within a cell.

Single-molecule studies of fork dynamics in Escherichia coli DNA replication

We present single-molecule studies of the Escherichia coli replication machinery. We visualize individual E. coli DNA polymerase III (Pol III) holoenzymes engaging in primer extension and leading-strand synthesis. When coupled to the replicative helicase DnaB, Pol III mediates leading-strand synthesis with a processivity of 10.5 kilobases (kb), eight-fold higher than that by Pol III alone. Addition of the primase DnaG causes a three-fold reduction in the processivity of leading-strand synthesis, an effect dependent upon the DnaB-DnaG protein-protein interaction rather than primase activity. A single-molecule analysis of the replication kinetics with varying DnaG concentrations indicates that a cooperative binding of two or three DnaG monomers to DnaB halts synthesis. Modulation of DnaB helicase activity through the interaction with DnaG suggests a mechanism that prevents leading-strand synthesis from outpacing lagging-strand synthesis during slow primer synthesis on the lagging strand.

Two-dimensional reaction free energy surfaces of catalytic reaction: effects of protein conformational dynamics on enzyme catalysis

We introduce a two-dimensional (2D) multisurface reaction free energy description of the catalytic cycle that explicitly connects the recently observed multi-time-scale conformational dynamics as well as dispersed enzymatic kinetics to the classical Michaelis-Menten equation. A slow conformational motion on a collective enzyme coordinate Q facilitates the catalytic reaction along the intrinsic reaction coordinate X, providing a dynamic realization of Pauling's well-known idea of transition-state stabilization. The catalytic cycle is modeled as transitions between multiple displaced harmonic wells in the XQ space representing different states of the cycle, which is constructed according to the free energy driving force of the cycle. Subsequent to substrate association with the enzyme, the enzyme-substrate complex under strain exhibits a nonequilibrium relaxation toward a new conformation that lowers the activation energy of the reaction, as first proposed by Haldane. The chemical reaction in X is thus enslaved to the down hill slow motion on the Q surface. One consequence of the present theory is that, in spite of the existence of dispersive kinetics, the Michaelis-Menten expression of the catalysis rate remains valid under certain conditions, as observed in recent single-molecule experiments. This dynamic theory builds the relationship between the protein conformational dynamics and the enzymatic reaction kinetics and offers a unified description of enzyme fluctuation-assisted catalysis.

Multiple-state reactions between the epidermal growth factor receptor and Grb2 as observed by using single-molecule analysis

Phosphorylation of the cytoplasmic tyrosine residues of the epidermal growth factor receptor (EGFR) upon binding of EGF induces recognition of various intracellular signaling molecules, including Grb2. Here, the reaction kinetics between EGFR and Grb2 was analyzed by visualizing single molecules of Grb2 conjugated to the fluorophore Cy3 (Cy3-Grb2). The plasma membrane fraction was purified from human epithelial carcinoma A431 cells after stimulation with EGF and attached to coverslips. Unitary events of association and dissociation of Cy3-Grb2 on the EGFR in the membrane fraction were observed at different concentrations of Grb2 (0.1-100 nM). The dissociation kinetics could be explained by using a multiple-exponential function with a major (>90%) dissociation rate of 8 s(-1) and a few minor components, suggesting the presence of multiple bound states. In contrast, the association kinetics could be described by a stretched exponential function, suggesting the presence of multiple reaction channels from many unbound substates. Transitions between the unbound substates were also suggested. Unexpectedly, the rate of association was not proportional to the Grb2 concentration: an increase in Cy3-Grb2 concentration by a factor of 10 induced an increase in the reaction frequency approximately by a factor of three. This effect can compensate for fluctuation of the signal transduction from EGFR to Grb2 caused by variations in the expression level of Grb2 in living cells.

Single phage T4 DNA packaging motors exhibit large force generation, high velocity, and dynamic variability

Terminase enzyme complexes, which facilitate ATP-driven DNA packaging in phages and in many eukaryotic viruses, constitute a wide and potentially diverse family of molecular motors about which little dynamic or mechanistic information is available. Here we report optical tweezers measurements of single DNA molecule packaging dynamics in phage T4, a large, tailed Escherichia coli virus that is an important model system in molecular biology. We show that a complex is formed between the empty prohead and the large terminase protein (gp17) that can capture and begin packaging a target DNA molecule within a few seconds, thus demonstrating a distinct viral assembly pathway. The motor generates forces >60 pN, similar to those measured with phage phi29, suggesting that high force generation is a common property of viral DNA packaging motors. However, the DNA translocation rate for T4 was strikingly higher than that for phi29, averaging approximately 700 bp/s and ranging up to approximately 2,000 bp/s, consistent with packaging by phage T4 of an enormous, 171-kb genome in <10 min during viral infection and implying high ATP turnover rates of >300 s(-1). The motor velocity decreased with applied load but averaged 320 bp/s at 45 pN, indicating very high power generation. Interestingly, the motor also exhibited large dynamic changes in velocity, suggesting that it can assume multiple active conformational states gearing different translocation rates. This capability, in addition to the reversible pausing and slipping capabilities that were observed, may allow phage T4 to coordinate DNA packaging with other ongoing processes, including viral DNA transcription, recombination, and repair.

Experimental test of connector rotation during DNA packaging into bacteriophage phi29 capsids

The bacteriophage ϕ29 generates large forces to compact its double-stranded DNA genome into a protein capsid by means of a portal motor complex. Several mechanical models for the generation of these high forces by the motor complex predict coupling of DNA translocation to rotation of the head-tail connector dodecamer. Putative connector rotation is investigated here by combining the methods of single-molecule force spectroscopy with polarization-sensitive single-molecule fluorescence. In our experiment, we observe motor function in several packaging complexes in parallel using video microscopy of bead position in a magnetic trap. At the same time, we follow the orientation of single fluorophores attached to the portal motor connector. From our data, we can exclude connector rotation with greater than 99% probability and therefore answer a long-standing mechanistic question.

The life cycles of many viruses include a self-assembly stage in which a powerful molecular motor packs the DNA genome into the virus's preformed shell (the capsid). Biochemical and biophysical studies have identified essential components of the packaging machinery and measured various characteristics of the packaging process, while crystallography and electron microscopy have provided snapshots of viral structure before and after packaging. In bacteriophage ϕ29 assembly, the DNA passes into the shell through a channel formed by a structure called the connector. Structurally motivated models over the past 30 years have coupled DNA movement to rotation of the connector relative to the capsid. We describe a direct test of the connector rotation hypothesis, combining magnetic single-molecule manipulation techniques and single-molecule fluorescence spectroscopy. In our experiments, we use a single-dye molecule attached specifically to the connector as a reporter for its orientation and simultaneously observe the translocation of a magnetic bead attached to the DNA that is being packaged. From our data, we can exclude connector rotation with greater than 99% probability and therefore answer a long-standing mechanistic question.

dsDNA compaction into bacteriophage capsids is observed in packaging complexes. Unlike in previous models, this compaction is found not to be driven by a rotating motor complex.

Studying individual events in biology

Studying the properties of individual events and molecules offers a host of advantages over taking only macroscopic measurements of populations. Here we review such advantages, as well as some pitfalls, focusing on examples from biological imaging. Examples include single proteins, their interactions in cells, organelles, and their interactions both with each other and with parts of the cell. Additionally, we discuss constraints that limit the study of single events, along with the criteria that must be fulfilled to determine whether single molecules or events are being detected.

Elasticity of short DNA molecules: theory and experiment for contour lengths of 0.6-7 microm

The wormlike chain (WLC) model currently provides the best description of double-stranded DNA elasticity for micron-sized molecules. This theory requires two intrinsic material parameters-the contour length L and the persistence length p. We measured and then analyzed the elasticity of double-stranded DNA as a function of L (632 nm-7.03 microm) using the classic solution to the WLC model. When the elasticity data were analyzed using this solution, the resulting fitted value for the persistence length p(wlc) depended on L; even for moderately long DNA molecules (L = 1300 nm), this apparent persistence length was 10% smaller than its limiting value for long DNA. Because p is a material parameter, and cannot depend on length, we sought a new solution to the WLC model, which we call the "finite wormlike chain (FWLC)," to account for effects not considered in the classic solution. Specifically we accounted for the finite chain length, the chain-end boundary conditions, and the bead rotational fluctuations inherent in optical trapping assays where beads are used to apply the force. After incorporating these corrections, we used our FWLC solution to generate force-extension curves, and then fit those curves with the classic WLC solution, as done in the standard experimental analysis. These results qualitatively reproduced the apparent dependence of p(wlc) on L seen in experimental data when analyzed with the classic WLC solution. Directly fitting experimental data to the FWLC solution reduces the apparent dependence of p(fwlc) on L by a factor of 3. Thus, the FWLC solution provides a significantly improved theoretical framework in which to analyze single-molecule experiments over a broad range of experimentally accessible DNA lengths, including both short (a few hundred nanometers in contour length) and very long (microns in contour length) molecules.

NS3 helicase actively separates RNA strands and senses sequence barriers ahead of the opening fork

RNA helicases regulate virtually all RNA-dependent cellular processes. Although much is known about helicase structures, very little is known about how they deal with barriers in RNA and the factors that affect their processivity. The hepatitis C virus encodes NS3, an RNA helicase that is essential for viral RNA replication. We have used optical tweezers to determine at the single-molecule level how the local stability of the RNA substrate affects the enzyme rate of strand separation, whether separation occurs by an active or a passive mechanism, and whether processivity is affected. We show that sequence barriers in RNA modulate NS3 activity. NS3 processivity depends on barriers ahead of the opening fork. Our results rule out a model where NS3 passively waits for the thermal fraying of double-stranded RNA. Instead, we find that NS3 destabilizes the duplex before separating the strands. Failure to do so before a strong barrier leads to helicase dissociation and limits the processivity of the enzyme.

Information theoretical approach to single-molecule experimental design and interpretation

We use Shannon's definition of information to develop a theory to predict a photon-counting-based single-molecule experiment's ability to measure the desired property. We treat three phenomena that are commonly measured on single molecules: spectral fluctuations of a solvatochromic dye; assignment of the azimuthal dipole angle; determination of a distance by fluorescence resonant energy transfer using Förster's theory. We consider the effect of background and other "imperfections" on the measurement through the decrease in information.

Single-molecule and ensemble fluorescence assays for a functionally important conformational change in T7 DNA polymerase

We report fluorescence assays for a functionally important conformational change in bacteriophage T7 DNA polymerase (T7 pol) that use the environmental sensitivity of a Cy3 dye attached to a DNA substrate. An increase in fluorescence intensity of Cy3 is observed at the single-molecule level, reflecting a conformational change within the T7 pol ternary complex upon binding of a dNTP substrate. This fluorescence change is believed to reflect the closing of the T7 pol fingers domain, which is crucial for polymerase function. The rate of the conformational change induced by a complementary dNTP substrate was determined by both conventional stopped-flow and high-time-resolution continuous-flow fluorescence measurements at the ensemble-averaged level. The rate of this conformational change is much faster than that of DNA synthesis but is significantly reduced for noncomplementary dNTPs, as revealed by single-molecule measurements. The high level of selectivity of incoming dNTPs pertinent to this conformational change is a major contributor to replicative fidelity.

Theory of the statistics of kinetic transitions with application to single-molecule enzyme catalysis

Single-molecule spectroscopy can monitor transitions between two microscopic states when these transitions are associated with the emission of photons. A general formalism is developed for obtaining the statistics of such transitions from a microscopic model when the dynamics is described by master or rate equations or their continuum analog, multidimensional reaction-diffusion equations. The focus is on the distribution of the number of transitions during a fixed observation time, the distribution of times between transitions, and the corresponding correlation functions. It is shown how these quantities are related to each other and how they can be explicitly calculated in a straightforward way for both immobile and diffusing molecules. Our formalism reduces to renewal theory when the monitored transitions either go to or originate from a single state. The influence of dynamics slow compared with the time between monitored transitions is treated in a simple way, and the probability distributions are expressed in terms of Mandel-type formulas. The formalism is illustrated by a detailed analysis of the statistics of catalytic turnovers of enzymes. When the rates of conformational changes are slower than the catalytic rates which are in turn slower than the binding relaxation rate, (1) the mean number of turnovers is shown to have the classical Michaelis-Menten form, (2) the correlation function of the number of turnovers is a direct measure of the time scale of catalytic rate fluctuations, and (3) the distribution of the time between consecutive turnovers is determined by the steady-state distribution.

Stretching and immobilization of DNA for studies of protein–DNA interactions at the single-molecule level

Single-molecule studies of the interactions of DNA and proteins are important in a variety of biological or biotechnology processes ranging from the protein’s search for its DNA target site, DNA replication, transcription, or repair, and genome sequencing. A critical requirement for single-molecule studies is the stretching and immobilization of otherwise randomly coiled DNA molecules. Several methods for doing so have been developed over the last two decades, including the use of forces derived from light, magnetic and electric fields, and hydrodynamic flow. Here we review the immobilization and stretching mechanisms for several of these techniques along with examples of single-molecule DNA–protein interaction assays that can be performed with each of them.

Multiplexed single-molecule assay for enzymatic activity on flow-stretched DNA

We report a single-molecule assay for nucleic-acid enzymes on flow-stretched DNA templates. To facilitate the detection of slow or intermittent enzymatic activities, we developed the assay with 15-nm spatial resolution at a frame rate of 1 Hz and approximately 10 nm mechanical stability over the timescale of hours. With multiplexed data collection, we applied the assay to phi29 DNA polymerase, HIV-1 reverse transcriptase, lambda exonuclease and Escherichia coli RNA polymerase.

Honey, I shrunk the DNA: DNA length as a probe for nucleic-acid enzyme activity

The replication, recombination, and repair of DNA are processes essential for the maintenance of genomic information and require the activity of numerous enzymes that catalyze the polymerization or digestion of DNA. This review will discuss how differences in elastic properties between single- and double-stranded DNA can be used as a probe to study the dynamics of these enzymes at the single-molecule level.

Inferring DNA sequences from mechanical unzipping data: the large-bandwidth case

The complementary strands of DNA molecules can be separated when stretched apart by a force; the unzipping signal is correlated to the base content of the sequence but is affected by thermal and instrumental noise. We consider here the ideal case where opening events are known to a very good time resolution (very large bandwidth), and study how the sequence can be reconstructed from the unzipping data. Our approach relies on the use of statistical Bayesian inference and of Viterbi decoding algorithm. Performances are studied numerically on Monte Carlo generated data, and analytically. We show how multiple unzippings of the same molecule may be exploited to improve the quality of the prediction, and calculate analytically the number of required unzippings as a function of the bandwidth, the sequence content, and the elasticity parameters of the unzipped strands.

Single-molecule studies of complex systems: the replisome

A complete, system-level understanding of biological processes requires comprehensive information on the kinetics and thermodynamics of the underlying biochemical reactions. A wide variety of structural, biochemical, and molecular biological techniques have led to a quantitative understanding of the molecular properties and mechanisms essential to the processes of life. Yet, the ensemble averaging inherent to these techniques limits us in understanding the dynamic behavior of the molecular participants. Recent advances in imaging and molecular manipulation techniques have made it possible to observe the activity of individual enzymes and record "molecular movies" that provide insight into their dynamics and reaction mechanisms. An important future goal is extending the applicability of single-molecule techniques to the study of larger, more complex multi-protein systems. In this review, the DNA replication machinery will be used as an example to illustrate recent progress in the development of various single-molecule techniques and its contribution to our understanding of the orchestration of multiple enzymatic processes in large biomolecular systems.

Processive enzyme mimic: Kinetics and thermodynamics of the threading and sliding process

The kinetics and thermodynamics of the threading and dethreading process of polymers through the cavity of a synthetic toroidal host is investigated by studying its complexation with a series of end-functionalized polymers of different lengths containing an end group that is selectively recognized by the host. The system is designed in such a way that complexation is only observed if the host has traveled all of the way across the complete polymer. Detailed kinetic investigations using fluorescence spectroscopy have revealed that the barrier for this process is length dependent and most likely related to the stretching of the polymer. Moreover, the results indicate that our previously reported processive enzyme mimic most likely operates by randomly sliding along its macromolecular substrate.

Nucleotide specificity versus complex heterogeneity in exonuclease activity measurements

A recent publication reported on measurements of Exonuclease I activity using a real-time fluorescence method that measures the time required by molecules of Exonuclease I to hydrolyze single-stranded DNA that was synthesized to have two fluorescently labeled nucleotides. The observed fluorescence-intensity curves were interpreted as a sign of strong heterogeneity of the activity of Exonuclease I. Here, I propose a different model, which assumes that Exonuclease I activity is nucleotide-dependent, and that a fluorescent label bound to a nucleotide significantly slows its cleavage rate. The presented model fits the observed data equally well, but can be used to make specific predictions upon observable sequence dependence of measured fluorescence-intensity curves.

Direct evaluation of a kinetic model for RecA-mediated DNA-strand exchange: the importance of nucleic acid dynamics and entropy during homologous genetic recombination

The Escherichia coli RecA protein is the prototype of a class of proteins that play central roles in genomic repair and recombination in all organisms. The unresolved mechanistic strategy by which RecA aligns a single strand of DNA with a duplex DNA and mediates a DNA strand switch is central to understanding homologous recombination. We explored the mechanism of RecA-mediated DNA-strand exchange using oligonucleotide substrates with the intrinsic fluorophore 6-methylisoxanthopterin. Pre-steady-state spectrofluorometric analysis elucidated the earliest transient intermediates formed during recombination and delineated the mechanistic strategy by which RecA facilitates this process. The structural features of the first detectable intermediate and the energetic characteristics of its formation were consistent with interactions between a few bases of the single-stranded DNA and the minor groove of a locally melted or stretched duplex DNA. Further analysis revealed RecA to be an unusual enzyme in that entropic rather than enthalpic contributions dominate its catalytic function, and no unambiguously active role for the protein was detected in the earliest molecular events of recombination. The data best support the conclusion that the mechanistic strategy of RecA likely relies on intrinsic DNA dynamics.

On stochastic models of dynamic disorder

In this paper we investigate some general aspects of stochastic models of dynamic disorder. First, we reexamine the Zwanzig model for the kinetics of escape through a fluctuating hole. We show that this model is trivially connected to the canonical model of the broadening of the zero-phonon line (ZPL) in crystals. This provides a new perspective of the Wang-Wolynes expression for the rate of escape from a geometric bottleneck with non-Markovian Gaussian fluctuations. Motivated by recent single-molecule experiments, we examine more general examples of fluctuation processes from the perspective of cumulant expansions. Finally, we discuss recent single-molecule experiments probing enzyme turnover performed by Xie and co-workers.

Single molecule Michaelis-Menten equation beyond quasistatic disorder

The classic Michaelis-Menten equation describes the catalytic activities for ensembles of enzyme molecules very well. But recent single-molecule experiments showed that the waiting time distribution and other properties of single enzyme molecules were not consistent with the prediction based on the ensemble viewpoint. They have contributed to the slow conformational changes of a single enzyme in the catalytic processes. In this work, we study the general dynamics of single enzymes in the presence of dynamic disorder. We find that, within the time separation regimes, i.e., the slow reaction and nondiffusion limits, the Michaelis-Menten equation holds exactly. In particular, by employing the decoupling approximation we demonstrate analytically that the classic Michaelis-Menten equation is still an excellent approximation in the presence of general dynamic disorder.

Epifluorescence, confocal and total internal reflection microscopy for single-molecule experiments: a quantitative comparison

Epifluorescence, confocal and total internal reflection microscopy are the most widely used techniques for optical single-molecule experiments. Employing these methods, we recorded the emission intensity of the same single molecule as a function of the excitation rate under otherwise identical experimental conditions. Evaluation of these data provides a quantitative comparison of the signal-to-background ratios that can be achieved for the three microscopic techniques.

Complex chemical kinetics in single enzyme molecules: Kramers’s model with fractional Gaussian noise

A model of barrier crossing dynamics governed by fractional Gaussian noise and the generalized Langevin equation is used to study the reaction kinetics of single enzymes subject to conformational fluctuations. The direct application of Kramers's flux-over-population method to this model yields analytic expressions for the time-dependent transmission coefficient and the distribution of waiting times for barrier crossing. These expressions are found to reproduce the observed trends in recent simulations and experiments.

Subunit Exchange of MjHsp16.5 Studied by Single-Molecule Imaging and Fluorescence Resonance Energy Transfer

MjHsp16.5 was separately labeled by fluorescent dye Cy3 and Cy5.5. The dissociation event of a single 24-mer MjHsp16.5 molecule was captured by single-molecule imaging (SMI). Temperature-regulated subunit exchange was revealed by the real-time fluorescence resonance energy transfer (FRET). The combination of single-molecular statistics and kinetic parameters from FRET experiments leads to the conclusion that below 75 degrees C the rate-determining step of the subunit exchange was the dissociation of the dye-labeled 24-mer in which the dimer was intact, whereas above 75 degrees C, smaller units emerged in the exchange and the rate-determining step had the character of a bimolecular reaction.

Simulated data sets for single molecule kinetics: some limitations and complications of data analysis

When the fluorescence intensity of a chromophore attached to or bound in an enzyme relates to a specific reactive step in the enzymatic reaction, a single molecule fluorescence study of the process reveals a time sequence in the fluorescence emission that can be analyzed to derive kinetic and mechanistic information. Reports of various experimental results and corresponding theoretical studies have provided a basis for interpreting these data and understanding the methodology. We have found it useful to parallel experiments with Monte Carlo simulations of potential models hypothesized to describe the reaction kinetics. The simulations can be adapted to include experimental limitations, such as limited data sets, and complexities such as dynamic disorder, where reaction rates appear to change over time. By using models that are known a priori, the simulations reveal some of the challenges of interpreting finite single-molecule data sets by employing various statistical signatures that have been identified.

A base-excision DNA-repair protein finds intrahelical lesion bases by fast sliding in contact with DNA

A central mystery in the function of site-specific DNA-binding proteins is the detailed mechanism for rapid location and binding of target sites in DNA. Human oxoguanine DNA glycosylase 1 (hOgg1), for example, must search out rare 8-oxoguanine lesions to prevent transversion mutations arising from oxidative stress. Here we report high-speed imaging of single hOgg1 enzyme molecules diffusing along DNA stretched by shear flow. Salt-concentration-dependent measurements reveal that such diffusion occurs as hOgg1 slides in persistent contact with DNA. At near-physiologic pH and salt concentration, hOgg1 has a subsecond DNA-binding time and slides with a diffusion constant as high as 5 x 10(6) bp(2)/s. Such a value approaches the theoretical upper limit for one-dimensional diffusion and indicates an activation barrier for sliding of only 0.5 kcal/mol (1 kcal = 4.2 kJ). This nearly barrierless Brownian sliding indicates that DNA glycosylases locate lesion bases by a massively redundant search in which the enzyme selectively binds 8-oxoguanine under kinetic control.

Inference of DNA sequences from mechanical unzipping: an ideal-case study

The performances of Bayesian inference to predict the sequence of DNA molecules from fixed-force unzipping experiments are investigated. We show that the probability of misprediction decreases exponentially with the amount of collected data. The decay rate is calculated as a function of biochemical parameters (binding free energies), the sequence content, the applied force, the elastic properties of a DNA single strand, and time resolution.

Cooperativity in the motor activities of the ATP-fueled molecular motors

Kinesin, myosin and F1-ATPase are multi-domain molecular motors with multiple catalytic subunits. The motor mechanochemics are achieved via the conversion of ATP hydrolysis energy into forces and motions. We find that the catalysis of these molecular motors do not follow the simple Michaelis-Menten mechanism. The motor activities, such as the hydrolysis or processive rates, of kinesin, myosin and F1-ATPase have a complex ATP-dependent cooperativity. To understand this complexity in kinetics and mechanochemics, we develop a conformation correlation theory of cooperativity for the ATP-fueled motor proteins. The quantitative analysis and simulations indicate that cooperativity is induced by the conformational coupling of binding states of different subunits and prevails in the motor activities.

Volume-exclusion effects in tethered-particle experiments: bead size matters

We give a theoretical analysis of bead motion in tethered-particle experiments, a single-molecule technique that has been used to explore the dynamics of a variety of macromolecules of biological interest. Our analysis reveals that the proximity of the tethered bead to a nearby surface gives rise to a volume-exclusion effect, resulting in an entropic stretching-force on the molecule that changes its statistical properties. In addition, volume exclusion brings about intriguing scaling relations between key observables (statistical moments of the bead) and parameters such as bead size and contour length of the molecule. We present analytic and numerical results for these effects in both flexible and semiflexible tethers. Finally, our results give a precise, experimentally testable prediction for the probability distribution of the bead center measured from the polymer attachment point.

Real-time enzyme dynamics illustrated with fluorescence spectroscopy of p-hydroxybenzoate hydroxylase

We have used the flavoenzyme p-hydroxybenzoate hydroxylase (PHBH) to illustrate that a strongly fluorescent donor label can communicate with the flavin via single-pair Förster resonance energy transfer (spFRET). The accessible Cys-116 of PHBH was labeled with two different fluorescent maleimides with full preservation of enzymatic activity. One of these labels shows overlap between its fluorescence spectrum and the absorption spectrum of the FAD prosthetic group in the oxidized state, while the other fluorescent probe does not have this spectral overlap. The spectral overlap strongly diminished when the flavin becomes reduced during catalysis. The donor fluorescence properties can then be used as a sensitive antenna for the flavin redox state. Time-resolved fluorescence experiments on ensembles of labeled PHBH molecules were carried out in the absence and presence of enzymatic turnover. Distinct changes in fluorescence decays of spFRET-active PHBH can be observed when the enzyme is performing catalysis using both substrates p-hydroxybenzoate and NADPH. Single-molecule fluorescence correlation spectroscopy on spFRET-active PHBH showed the presence of a relaxation process (relaxation time of 23 micros) that is related to catalysis. In addition, in both labeled PHBH preparations the number of enzyme molecules reversibly increased during enzymatic turnover indicating that the dimer-monomer equilibrium is affected.

DNA primase acts as a molecular brake in DNA replication

A hallmark feature of DNA replication is the coordination between the continuous polymerization of nucleotides on the leading strand and the discontinuous synthesis of DNA on the lagging strand. This synchronization requires a precisely timed series of enzymatic steps that control the synthesis of an RNA primer, the recycling of the lagging-strand DNA polymerase, and the production of an Okazaki fragment. Primases synthesize RNA primers at a rate that is orders of magnitude lower than the rate of DNA synthesis by the DNA polymerases at the fork. Furthermore, the recycling of the lagging-strand DNA polymerase from a finished Okazaki fragment to a new primer is inherently slower than the rate of nucleotide polymerization. Different models have been put forward to explain how these slow enzymatic steps can take place at the lagging strand without losing coordination with the continuous and fast leading-strand synthesis. Nonetheless, a clear picture remains elusive. Here we use single-molecule techniques to study the kinetics of a multiprotein replication complex from bacteriophage T7 and to characterize the effect of primase activity on fork progression. We observe the synthesis of primers on the lagging strand to cause transient pausing of the highly processive leading-strand synthesis. In the presence of both leading- and lagging-strand synthesis, we observe the formation and release of a replication loop on the lagging strand. Before loop formation, the primase acts as a molecular brake and transiently halts progression of the replication fork. This observation suggests a mechanism that prevents leading-strand synthesis from outpacing lagging-strand synthesis during the slow enzymatic steps on the lagging strand.

Kramers model with a power-law friction kernel: dispersed kinetics and dynamic disorder of biochemical reactions

Kramers' model for the rate of chemical reaction is generalized to explain the phenomena of dispersed kinetics and dynamic disorder in biochemical reactions, by incorporating the newly observed power-law friction kernel into the generalized Langevin equation for a one-dimensional reaction ordinate. This new model accounts for time scale overlap between conformational and chemical dynamics, and quantitatively describes the multi-exponential kinetics and memory effects of fluctuating rate constants, which have been revealed by recent single-molecule experiments.

Ever-fluctuating single enzyme molecules: Michaelis-Menten equation revisited

Enzymes are biological catalysts vital to life processes and have attracted century-long investigation. The classic Michaelis-Menten mechanism provides a highly satisfactory description of catalytic activities for large ensembles of enzyme molecules. Here we tested the Michaelis-Menten equation at the single-molecule level. We monitored long time traces of enzymatic turnovers for individual beta-galactosidase molecules by detecting one fluorescent product at a time. A molecular memory phenomenon arises at high substrate concentrations, characterized by clusters of turnover events separated by periods of low activity. Such memory lasts for decades of timescales ranging from milliseconds to seconds owing to the presence of interconverting conformers with broadly distributed lifetimes. We proved that the Michaelis-Menten equation still holds even for a fluctuating single enzyme, but bears a different microscopic interpretation.

Fluctuating enzymes: lessons from single-molecule studies

Recent single-molecule enzymology measurements with improved statistics have demonstrated that a single enzyme molecule exhibits large temporal fluctuations of the turnover rate constant at a broad range of time scales (from 1 ms to 100 s). The rate constant fluctuations, termed as dynamic disorder, are associated with fluctuations of the protein conformations observed on the same time scales. We discuss the unique information extractable from these experiments and the reconciliation of these observations with ensemble-averaged Michaelis-Menten equation. A theoretical model based on the generalized Langevin equation (GLE) treatment of Kramers' barrier crossing problem for chemical reactions accounts naturally for the observation of dynamic disorder and highly dispersed kinetics.

Sequence heterogeneity and the dynamics of molecular motors

The effect of sequence heterogeneity on the dynamics of molecular motors is reviewed and analysed using a set of recently introduced lattice models. First, we review results for the influence of heterogeneous tracks such as a single strand of DNA or RNA on the dynamics of the motors. We stress how the predicted behaviour might be observed experimentally in anomalous drift and diffusion of motors over a wide range of parameters near the stall force and discuss the extreme limit of strongly biased motors with one-way hopping. We then consider the dynamics in an environment containing a variety of different fuels which supply chemical energy for the motor motion, either on a heterogeneous or on a periodic track. The results for motion along a periodic track are relevant to kinesin motors in a solution with a mixture of different nucleotide triphosphate fuel sources.