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

Direct observation of base-pair stepping by RNA polymerase

During transcription, RNA polymerase (RNAP) moves processively along a DNA template, creating a complementary RNA. Here we present the development of an ultra-stable optical trapping system with ångström-level resolution, which we used to monitor transcriptional elongation by single molecules of Escherichia coli RNAP. Records showed discrete steps averaging 3.7 +/- 0.6 A, a distance equivalent to the mean rise per base found in B-DNA. By combining our results with quantitative gel analysis, we conclude that RNAP advances along DNA by a single base pair per nucleotide addition to the nascent RNA. We also determined the force-velocity relationship for transcription at both saturating and sub-saturating nucleotide concentrations; fits to these data returned a characteristic distance parameter equivalent to one base pair. Global fits were inconsistent with a model for movement incorporating a power stroke tightly coupled to pyrophosphate release, but consistent with a brownian ratchet model incorporating a secondary NTP binding site.

Passive all-optical force clamp for high-resolution laser trapping

Optical traps are useful for studying the effects of forces on single molecules. Feedback-based force clamps are often used to maintain a constant load, but the response time of the feedback limits bandwidth and can introduce instability. We developed a novel force clamp that operates without feedback, taking advantage of the anharmonic region of the trapping potential where the differential stiffness vanishes. We demonstrate the utility of such a force clamp by measuring the unfolding of DNA hairpins and the effect of trap stiffness on opening distance and transition rates.

Single-Molecule Michaelis−Menten Equations

This paper summarizes our present theoretical understanding of single-molecule kinetics associated with the Michaelis-Menten mechanism of enzymatic reactions. Single-molecule enzymatic turnover experiments typically measure the probability density f(t) of the stochastic waiting time t for individual turnovers. While f(t) can be reconciled with ensemble kinetics, it contains more information than the ensemble data; in particular, it provides crucial information on dynamic disorder, the apparent fluctuation of the catalytic rates due to the interconversion among the enzyme's conformers with different catalytic rate constants. In the presence of dynamic disorder, f(t) exhibits a highly stretched multiexponential decay at high substrate concentrations and a monoexponential decay at low substrate concentrations. We derive a single-molecule Michaelis-Menten equation for the reciprocal of the first moment of f(t), 1/<t>, which shows a hyperbolic dependence on the substrate concentration [S], similar to the ensemble enzymatic velocity. We prove that this single-molecule Michaelis-Menten equation holds under many conditions, in particular when the intercoversion rates among different enzyme conformers are slower than the catalytic rate. However, unlike the conventional interpretation, the apparent catalytic rate constant and the apparent Michaelis constant in this single-molecule Michaelis-Menten equation are complicated functions of the catalytic rate constants of individual conformers. We also suggest that the randomness parameter r, defined as <(t - <t>)2> / t2, can serve as an indicator for dynamic disorder in the catalytic step of the enzymatic reaction, as it becomes larger than unity at high substrate concentrations in the presence of dynamic disorder.

Multipoint correlation functions for continuous-time random walk models of anomalous diffusion

Recursive relations are developed for computing the multipoint correlation functions of a particle undergoing a biased continuous-time random walk (CTRW) in an external potential. Two- and three-point correlation functions are calculated for waiting-time distributions with an anomalous power-law profile t(-alpha-1), 0 < alpha < 1, on intermediate time scales with a crossover to an exponential long time decay. Comparison of the CTRW with the Brownian harmonic oscillator model (Gaussian process) illustrates how higher-order correlation functions may be used to distinguish between dynamical models that have the same two-point correlation function.

Kinetics of the Initial Steps of G Protein-Coupled Receptor-Mediated Cellular Signaling Revealed by Single-Molecule Imaging

We report on an in vivo single-molecule study of the signaling kinetics of G protein-coupled receptors (GPCR) performed using the neurokinin 1 receptor (NK1R) as a representative member. The NK1R signaling cascade is triggered by the specific binding of a fluorescently labeled agonist, substance P (SP). The diffusion of single receptor-ligand complexes in plasma membrane of living HEK 293 cells is imaged using fast single-molecule wide-field fluorescence microscopy at 100 ms time resolution. Diffusion trajectories are obtained which show intra- and intertrace heterogeneity in the diffusion mode. To investigate universal patterns in the diffusion trajectories we take the ligand-binding event as the common starting point. This synchronization allows us to observe changes in the character of the ligand-receptor-complex diffusion. Specifically, we find that the diffusion of ligand-receptor complexes is slowed down significantly and becomes more constrained as a function of time during the first 1000 ms. The decelerated and more constrained diffusion is attributed to an increasing interaction of the GPCR with cellular structures after the ligand-receptor complex is formed.

Statistical kinetics of macromolecular dynamics

Fluctuations in biochemical processes can provide insights into the underlying kinetics beyond what can be gleaned from studies of average rates alone. Historically, analysis of fluctuating transmembrane currents supplied information about ion channel conductance states and lifetimes before single-channel recording techniques emerged. More recently, fluctuation analysis has helped to define mechanochemical pathways and coupling ratios for the motor protein kinesin as well as to probe the contributions of static and dynamic disorder to the kinetics of single enzymes. As growing numbers of assays are developed for enzymatic or folding behaviors of single macromolecules, the range of applications for fluctuation analysis increases. To evaluate specific biochemical models against experimental data, one needs to predict analytically the distribution of times required for completion of each reaction pathway. Unfortunately, using traditional methods, such calculations can be challenging for pathways of even modest complexity. Here, we derive an exact expression for the distribution of completion times for an arbitrary pathway with a finite number of states, using a recursive method to solve algebraically for the appropriate moment-generating function. To facilitate comparisons with experiments on processive motor proteins, we develop a theoretical formalism for the randomness parameter, a dimensionless measure of the variance in motor output. We derive the randomness for motors that take steps of variable sizes or that move on heterogeneous substrates, and then discuss possible applications to enzymes such as RNA polymerase, which transcribes varying DNA sequences, and to myosin V and cytoplasmic dynein, which may advance by variable increments.

Single-molecule fluorescence detection in microfluidic channels—the Holy Grail in μTAS?

Both single-molecule detection (SMD) methods and miniaturization technologies have developed very rapidly over the last ten years. By merging these two techniques, it may be possible to achieve the optimal requirements for the analysis and manipulation of samples on a single molecule scale. While miniaturized structures and channels provide the interface required to handle small particles and molecules, SMD permits the discovery, localization, counting and identification of compounds. Widespread applications, across various bioscience/analytical science fields, such as DNA-analysis, cytometry and drug screening, are envisaged. In this review, the unique benefits of single fluorescent molecule detection in microfluidic channels are presented. Recent and possible future applications are discussed.

Measurement of the surface concentration for bioassay kinetics in microchannels

We present a simple and versatile method, based on fluorescence microscopy, to reliably measure the concentration of advected molecules in the vicinity of surfaces in microchannels. This tool is relevant to many microfluidic applications such as immunoassays and single-molecule experiments, where one probes the kinetics of a reaction between an immobilized target and a reactant carried by the bulk flow. The characterization of the surface concentration highlights the dominant role of transverse diffusion, which generates an apparent diffusivity at the surface 3-4 orders of magnitude greater than molecular diffusion alone, even close to the point of injection. We directly measure the effects of the longitudinal position along the channel and of the flow rate on the concentration front and develop a simple analytical model that compares well with the data. Finally, we propose a method to properly account for concentration fronts in single-molecule measurements and use it to directly access the kinetics parameters of protamine-induced condensation of DNA.

Dynamics of molecular motors with finite processivity on heterogeneous tracks

The dynamics of molecular motors which occasionally detach from a heterogeneous track like DNA or RNA is considered. Motivated by recent single-molecule experiments, we study a simple model for a motor moving along a disordered track using chemical energy while an external force opposes its motion. The motors also have finite processivity, i.e., they can leave the track with a position-dependent rate. We show that the response of the system to disorder in the hopping-off rate depends on the value of the external force. For most values of the external force, strong disorder causes the motors which survive for long times on the track to be localized at preferred positions. However, near the stall force, localization occurs for any amount of disorder. To obtain these results, we study the complex eigenvalue spectrum of the time evolution operator. Existence of localized states near the top of the band implies a stretched exponential contribution to the decay of the survival probability. A similar spectral analysis also provides a very efficient method for studying the dynamics of motors with infinite processivity.

Using Single-Molecule Fluorescence Spectroscopy to Study Electron Transfer

Techniques in single-molecule fluorescence spectroscopy now allow sophisticated studies of photophysical processes in single molecules. As interest grows in the possibilities of molecular electronics, researchers have begun to turn these techniques to the study of electron transfer. Electron-transfer reactions have now been detected and measured at the single-molecule level in a variety of systems and on a variety of timescales by adapting techniques from previous single-molecule fluorescence studies.

Exonuclease I hydrolyzes DNA with a distribution of rates

We report heterogeneity in the time necessary for Exonuclease I to hydrolyze identical DNA fragments. A real-time fluorescence method measured the time required by molecules of Exonuclease I to hydrolyze single-stranded DNA that was synthesized to have two fluorescently labeled nucleotides. One fluorescently labeled nucleotide was located near the 3' end of the DNA and the other near the 5' end. Heterogeneity in the hydrolysis rate of the exonuclease population was inferred from the distribution of times necessary to cleave these DNA fragments. In particular, we found simple first-order kinetics, using a single hydrolysis rate, did not result in a good fit to the data. Better fits to the data were obtained if one assumed a distribution of hydrolysis rates for the exonuclease population. Under our experimental conditions, this broad distribution of rates was centered near 100 nt/s.

Fast initiation of chemical reactions with laser-induced breakdown of a nanoscale partition

This letter describes a new strategy for initiating a chemical reaction that is based on the laser-induced breakdown of a nanoscopic barrier, which physically separates the reactants in space. Because the breakdown of the barrier is fast ( approximately 0.3 micros) and owing to the nanometer dimension of the barrier, the reactants can be brought together and the reaction can be initiated rapidly. The time scale most suited for this method (from microseconds to tens of milliseconds) bridges nicely between the faster time scales that are accessible mostly with laser-based triggering experiments and the slower time scales that are studied most frequently with flow-based devices.

Dynamics of ATP-binding cassette contribute to allosteric control, nucleotide binding and energy transduction in ABC transporters

ATP-binding cassette (ABC) transporters move solutes across membranes and are associated with important diseases, including cystic fibrosis and multi-drug resistance. These molecular machines are energized by their charateristic ABC modules, molecular engines fuelled by ATP hydrolysis. A solution NMR study of a model ABC, Methanococcus jannaschii protein MJ1267, reveals that ADP-Mg binding alters the flexibilities of key ABC motifs and induces allosteric changes in conformational dynamics in the LivG insert, over 30A away from the ATPase active site. (15)N spin relaxation data support a "selected-fit" model for nucleotide binding. Transitions between rigidity and flexibility in key motifs during the ATP hydrolysis cycle may be crucial to mechanochemical energy transduction in ABC transporters. The restriction of correlated protein motions is likely a central mechanism for allosteric communications. Comparison between dynamics data from NMR and X-ray crystallography reveals their overall consistency and complementarity.

Single molecule acid-base kinetics and thermodynamics

We report a method in which temperature dependent single-molecule fluorescence measurements are used to study the kinetics and thermodynamics of the acid-base interaction in films of photoresist polymer. We use the two distinct fluorescent prototropic forms of Coumarin 6 (C6-->C6+) to indicate the state of the acid-base system. Data are analyzed using a statistical model of the intensity probability distributions, yielding temperature dependent proton exchange rates, which is confirmed through agreement with a simple two-state Monte Carlo model. The temperature dependent rates are used to calculate the activation enthalpy for proton exchange.

The 'right' size in nanobiotechnology

The biological and physical sciences share a common interest in small structures (the definition of 'small' depends on the application, but can range from 1 nm to 1 mm). A vigorous trade across the borders of these areas of science is developing around new materials and tools (largely from the physical sciences) and new phenomena (largely from the biological sciences). The physical sciences offer tools for synthesis and fabrication of devices for measuring the characteristics of cells and sub-cellular components, and of materials useful in cell and molecular biology; biology offers a window into the most sophisticated collection of functional nanostructures that exists.

Specificity of the Endonuclease Activity of the Baculovirus Alkaline Nuclease for Single-stranded DNA

The Autographa californica multiple nucleocapsid nucleopolyhedrovirus (AcMNPV) alkaline nuclease (AN) likely participates in the maturation of virus genomes and in DNA recombination. AcMNPV AN was expressed in a recombinant baculovirus as a His -tagged fusion and obtained in pure form (*AN) or as a (6)complex with the baculoviral single-stranded DNA-binding protein LEF-3 (*AN/L3). Both AN preparations possessed potent 5' --> 3'-exonuclease and weak endonuclease activities. Mutant *AN(S146A)/L3 with a change from serine to alanine at position 146 in a conservative motif was impaired in both activities. This proved that the endonuclease is an intrinsic activity of baculovirus AN. The AN endonuclease showed specificity for single-stranded DNA and converted supercoiled plasmid DNA (replicative form I, RFI) into the open circular form (RFII) by a single strand break. Plasmid DNA relaxed with topoisomerase I was resistant to *AN/L3 indicating that the partially single-stranded regions in negatively supercoiled molecules served as targets for the endonuclease. Unwinding the supercoiled DNA with ethidium bromide also made DNA resistant to AN/L3. In reactions with nicked circular DNA (RFII), AN and AN/L3 hydrolyzed exonucleolytically the broken strand or cut endonucleolytically the intact strand at the position opposite the nick (gap). When LEF-3 was added to the assay, the balance between the exonucleolytic and endonucleolytic modes of hydrolysis shifted in favor of the exonuclease. The data suggest that the AN endonuclease may digest the intermediates in replication and recombination at positions of structural irregularities in DNA duplexes, whereas LEF-3 may further regulate processing of the intermediates by AN via the endonuclease and exonuclease pathways.

Protein Conformational Dynamics Probed by Single-Molecule Electron Transfer

Electron transfer is used as a probe for angstrom-scale structural changes in single protein molecules. In a flavin reductase, the fluorescence of flavin is quenched by a nearby tyrosine residue by means of photo-induced electron transfer. By probing the fluorescence lifetime of the single flavin on a photon-by-photon basis, we were able to observe the variation of flavin-tyrosine distance over time. We could then determine the potential of mean force between the flavin and the tyrosine, and a correlation analysis revealed conformational fluctuation at multiple time scales spanning from hundreds of microseconds to seconds. This phenomenon suggests the existence of multiple interconverting conformers related to the fluctuating catalytic reactivity.