Skewed Brownian Fluctuations in Single-Molecule Magnetic Tweezers

Measurements in magnetic tweezers rely upon precise determination of the position of a magnetic microsphere. Fluctuations in the position due to Brownian motion allows calculation of the applied force, enabling deduction of the force-extension response function for a single DNA molecule that is attached to the microsphere. The standard approach relies upon using the mean of position fluctuations, which is valid when the microsphere axial position fluctuations obey a normal distribution. However, here we demonstrate that nearby surfaces and the non-linear elasticity of DNA can skew the distribution. Through experiment and simulations, we show that such a skewing leads to inaccurate position measurements which significantly affect the extracted DNA extension and mechanical properties, leading to up to two-fold errors in measured DNA persistence length. We develop a simple, robust and easily implemented method to correct for such mismeasurements.     

Step length measurement--theory and simulation for tethered bead constant-force single molecule assay

Linear molecular motors translocate along polymeric tracks using discrete steps. The step length is usually measured using constant-force single molecule experiments in which the polymer is tethered to a force-clamped microsphere. During the enzymatic cycle the motor shortens the tether contour length. Experimental conditions influence the achievable step length resolution, and ideally experiments should be conducted with high clamp-force using slow motors linked to small beads via stiff short tethers. We focus on the limitations that the polymer-track flexibility, the thermal motion of the microsphere, and the motor kinetics pose for step-length measurement in a typical optical tweezers experiment. An expression for the signal/noise ratio in a constant-force, worm-like chain tethered particle, single-molecule experiment is developed. The signal/noise ratio is related to the Fourier transform of the pairwise distance distribution, commonly used to determine step length from a time-series. Monte Carlo simulations verify the proposed theory for experimental parameter values typically encountered with molecular motors (polymerases and helicases) translocating along single- or double-stranded nucleic acids. The predictions are consistent with recent experimental results for double-stranded DNA tethers. Our results map favorable experimental conditions for observing single motor steps on various substrates but indicate that principal resolution limits are set by thermal fluctuations.     

Quantitative study of polymer conformation and dynamics by single-particle tracking

We present a new method for analyzing the dynamics of conformational fluctuations of individual flexible polymer molecules. In single-particle tracking (SPT), one end of the polymer molecule is tethered to an immobile substratum. A microsphere attached to the other end serves as an optical marker. The conformational fluctuations of the polymer molecule can be measured by optical microscopy via the motion of the microsphere. The bead-and-spring theory for polymer dynamics is further developed to account for the microsphere, and together the measurement and the theory yield quantitative information about molecular conformations and dynamics under nonperturbing conditions. Applying the method to measurements carried out on DNA molecules provides information complementary to recent studies of single DNA molecules under extensional force. Combining high precision measurements with the theoretical analysis presented here creates a powerful tool for studying conformational dynamics of biological and synthetic macromolecules at the single-molecule level.     

Probing DNA conformational changes with high temporal resolution by tethered particle motion

The tethered particle motion (TPM) technique informs about conformational changes of DNA molecules, e.g. upon looping or interaction with proteins, by tracking the Brownian motion of a particle probe tethered to a surface by a single DNA molecule and detecting changes of its amplitude of movement. We discuss in this context the time resolution of TPM, which strongly depends on the particle-DNA complex relaxation time, i.e. the characteristic time it takes to explore its configuration space by diffusion. By comparing theory, simulations and experiments, we propose a calibration of TPM at the dynamical level: we analyze how the relaxation time grows with both DNA contour length (from 401 to 2080 base pairs) and particle radius (from 20 to 150 nm). Notably we demonstrate that, for a particle of radius 20 nm or less, the hydrodynamic friction induced by the particle and the surface does not significantly slow down the DNA. This enables us to determine the optimal time resolution of TPM in distinct experimental contexts which can be as short as 20 ms.     

DNA looping kinetics analyzed using diffusive hidden Markov model

Tethered particle experiments use light microscopy to measure the position of a micrometer-sized bead tethered to a microscope slide via an approximately micrometer-length polymer, to infer the behavior of the invisible polymer. Currently, this method is used to measure rate constants of DNA loop formation and breakdown mediated by repressor protein that binds to the DNA. We report a new technique for measuring these rates using a modified hidden Markov analysis that directly incorporates the diffusive motion of the bead, which is an inherent complication of tethered particle motion because it occurs on a timescale between the sampling frequency and the looping time. We compare looping lifetimes found with our method, which are consistent over a range of sampling frequencies, to those obtained via the traditional threshold-crossing analysis, which vary depending on how the raw data are filtered in the time domain. Our method does not involve such filtering, and so can detect short-lived looping events and sudden changes in looping behavior.     

Single-molecule mechanical identification and sequencing

High-throughput, low-cost DNA sequencing has emerged as one of the challenges of the postgenomic era. Here we present the proof of concept for a single-molecule platform that allows DNA identification and sequencing. In contrast to most present methods, our scheme is not based on the detection of the fluorescent nucleotides but on DNA hairpin length. By pulling on magnetic beads tethered by a DNA hairpin to the surface, the molecule can be unzipped. In this open state it can hybridize with complementary oligonucleotides, which transiently block the hairpin rezipping when the pulling force is reduced. By measuring from the surface to the bead of a blocked hairpin, one can determine the position of the hybrid along the molecule with nearly single-base precision. Our approach can be used to identify a DNA fragment of known sequence in a mix of various fragments and to sequence an unknown DNA fragment by hybridization or ligation.     

Detecting protein analytes that modulate transmembrane movement of a polymer chain within a single protein pore

Here we describe a new type of biosensor element for detecting proteins in solution at nanomolar concentrations. We tethered a 3.4 kDa polyethylene glycol chain at a defined site within the lumen of the transmembrane protein pore formed by staphylococcal alpha-hemolysin. The free end of the polymer was covalently attached to a biotin molecule. On incorporation of the modified pore into a lipid bilayer, the biotinyl group moves from one side of the membrane to the other, and is detected by reversible capture with a mutant streptavidin. The capture events are observed as changes in ionic current passing through single pores in planar bilayers. Accordingly, the modified pore allows detection of a protein analyte at the single-molecule level, facilitating both quantification and identification through a distinctive current signature. The approach has higher time resolution compared with other kinetic measurements, such as those obtained by surface plasmon resonance.     

Single-particle tracking for DNA tether length monitoring

We describe a simple single-particle tracking approach for monitoring the length of DNA molecules in tethered particle motion experiments. In this method, the trajectory of a submicroscopic bead tethered by a DNA molecule to a glass surface is determined by videomicroscopy coupled to image analysis. The amplitude of motion of the bead is measured by the standard deviation of the distribution of successive positions of the bead in a given time interval. We were able to describe theoretically the variation of the equilibrium value of the amplitude of the bead motion with the DNA tether length for the entire applicable DNA length range (up to ~3500 bp). The sensitivity of the approach was illustrated by the evidence obtained for conformational changes introduced into a Holliday junction by the binding of the Escherichia coli RuvA protein. An advantage of this method is that the trajectory of the tethered bead, rather than its averaged motion, is measured, allowing analysis of the conformational dynamics of DNA chains at the single-molecule level.     

Diffusion-controlled reactions on spherical surfaces. Application to bacteriophage tail fiber attachment.

We have explored the kinetic implications of a model that may account for the acceleration of tail fiber (F) attachment to baseplates (B) by whiskers (W) on bacteriophage T4. The model assumes that a W-F complex is formed initially, and that the tethered fiber then undergoes rotational diffusion until a B-F encounter takes place. In the absence of whiskers, B-F complexes must form unassisted. Formation of a W-F intermediate will accelerate F attachment to B if (a) the bimolecular rate constant for W-F complex formation is larger than that for direct B-F interaction and (b) subsequent rotational diffusion of the tip of F to B is not much slower than the dissociation of W-F. Condition a was investigated by applying a recent theory of orientational effects on translational diffusion-controlled reactions. This theory suggests that substantial rate enhancement is expected if the reaction half-angle theta 0 is larger for W-F than for B-F complex formation. Condition b was investigated by calculating the mean and the variance of the time required for the diffusion of a molecule (the proximal tip of the fiber) on a spherical surface (whose radius is the distance from the tip to the whisker tethering point) into a circular sink (the baseplate site). The mean time is on the order of the inverse rotational diffusion coefficient, DR, of the fiber, but is sensitive to theta 0. Both conditions are satisfied for plausible choices of parameters. The solution to the diffusion equation we have obtained should have application to other physical situations, such as the rate of quenching of a fluorophore as it diffuses on the surface of a spherical membrane into proximity with a quencher.     

Stretching short sequences of DNA with constant force axial optical tweezers

Single-molecule techniques for stretching DNA of contour lengths less than a kilobase are fraught with experimental difficulties. However, many interesting biological events such as histone binding and protein-mediated looping of DNA, occur on this length scale. In recent years, the mechanical properties of DNA have been shown to play a significant role in fundamental cellular processes like the packaging of DNA into compact nucleosomes and chromatin fibers. Clearly, it is then important to understand the mechanical properties of short stretches of DNA. In this paper, we provide a practical guide to a single-molecule optical tweezing technique that we have developed to study the mechanical behavior of DNA with contour lengths as short as a few hundred basepairs. The major hurdle in stretching short segments of DNA is that conventional optical tweezers are generally designed to apply force in a direction lateral to the stage (see Fig. 1). In this geometry, the angle between the bead and the coverslip, to which the DNA is tethered, becomes very steep for submicron length DNA. The axial position must now be accounted for, which can be a challenge, and, since the extension drags the microsphere closer to the coverslip, steric effects are enhanced. Furthermore, as a result of the asymmetry of the microspheres, lateral extensions will generate varying levels of torque due to rotation of the microsphere within the optical trap since the direction of the reactive force changes during the extension. Alternate methods for stretching submicron DNA run up against their own unique hurdles. For instance, a dual-beam optical trap is limited to stretching DNA of around a wavelength, at which point interference effects between the two traps and from light scattering between the microspheres begin to pose a significant problem. Replacing one of the traps with a micropipette would most likely suffer from similar challenges. While one could directly use the axial potential to stretch the DNA, an active feedback scheme would be needed to apply a constant force and the bandwidth of this will be quite limited, especially at low forces. We circumvent these fundamental problems by directly pulling the DNA away from the coverslip by using a constant force axial optical tweezers. This is achieved by trapping the bead in a linear region of the optical potential, where the optical force is constant-the strength of which can be tuned by adjusting the laser power. Trapping within the linear region also serves as an all optical force-clamp on the DNA that extends for nearly 350 nm in the axial direction. We simultaneously compensate for thermal and mechanical drift by finely adjusting the position of the stage so that a reference microsphere stuck to the coverslip remains at the same position and focus, allowing for a virtually limitless observation period.     

Exonuclease Degradation of DNA Studied by Fluorescence Correlation Spectroscopy

Abstract

Here we developed an accurate method for kinetic analysis of enzymatic degradation processes of double and/or single-stranded DNA/oligonucleotides using fluorescent reporter dyes. 217-bp DNA fragments were produced by polymerase chain reaction and cleaved by the 3′ to 5′ exonuclease activity of T7-DNA polymerase. The analysis of the products was performed by Fluorescence Correlation Spectroscopy measuring autocorrelation amplitudes and diffusion times. We give proof of (i) complete enzymatic degradation, (ii) retardation of complete enzymatic degradation by internally labelled Rhodamine-4-nucleotides and Cy5-nucleotides, respectively. Data evaluation by global analysis indicated first-order reaction kinetics with full-length DNA and free fluorescent nucleotides in the time window of measurements used.     

High-throughput single-molecule analysis of DNA-protein interactions by tethered particle motion

Tethered particle motion (TPM) monitors the variations in the effective length of a single DNA molecule by tracking the Brownian motion of a bead tethered to a support by the DNA molecule. Providing information about DNA conformations in real time, this technique enables a refined characterization of DNA-protein interactions. To increase the output of this powerful but time-consuming single-molecule assay, we have developed a biochip for the simultaneous acquisition of data from more than 500 single DNA molecules. The controlled positioning of individual DNA molecules is achieved by self-assembly on nanoscale arrays fabricated through a standard microcontact printing method. We demonstrate the capacity of our biochip to study biological processes by applying our method to explore the enzymatic activity of the T7 bacteriophage exonuclease. Our single molecule observations shed new light on its behaviour that had only been examined in bulk assays previously and, more specifically, on its processivity.     

Orientation of DNA on a surface from simulation

DNA orientation near surfaces determines many properties related to hybridization efficiency. We performed a 40-ns molecular dynamics simulation to study the structure and orientation of a 12-base-pair DNA duplex tethered to a neutral, epoxide-coated silica surface. Starting with a canonical B-form tethered in an up-right position, normal to the surface, the DNA tilted to over 55 degrees and back. The time scale was a few nanoseconds for tilting events. The linker between the DNA and the surface went from standing upright to tilted, and finally collapsed on the surface. Although the DNA conformation fluctuated, it remained closed to B-form for the entire 40 ns. Calculations of helical parameters of the DNA show that the tethered end of the DNA changed its conformation noticeably when attracted to the surface.     

ENDO-Pore: high-throughput linked-end mapping of single DNA cleavage events using nanopore sequencing

Mapping the precise position of DNA cleavage events plays a key role in determining the mechanism and function of endonucleases. ENDO-Pore is a high-throughput nanopore-based method that allows the time resolved mapping single molecule DNA cleavage events in vitro. Following linearisation of a circular DNA substrate by the endonuclease, a resistance cassette is ligated recording the position of the cleavage event. A library of single cleavage events is constructed and subjected to rolling circle amplification to generate concatemers. These are sequenced and used to produce accurate consensus sequences. To identify the cleavage site(s), we developed CSI (Cleavage Site Investigator). CSI recognizes the ends of the cassette ligated into the cleaved substrate and triangulates the position of the dsDNA break. We firstly benchmarked ENDO-Pore using Type II restriction endonucleases. Secondly, we analysed the effect of crRNA length on the cleavage pattern of CRISPR Cas12a. Finally, we mapped the time-resolved DNA cleavage by the Type ISP restriction endonuclease LlaGI that introduces random double-strand breaks into its DNA substrates.     

Enhanced Tethered-Particle Motion Analysis Reveals Viscous Effects

Tethered-particle motion experiments do not require expensive or technically complex hardware, and increasing numbers of researchers are adopting this methodology to investigate the topological effects of agents that act on the tethering polymer or the characteristics of the polymer itself. These investigations depend on accurate measurement and interpretation of changes in the effective length of the tethering polymer (often DNA). However, the bead size, tether length, and buffer affect the confined diffusion of the bead in this experimental system. To evaluate the effects of these factors, improved measurements to calibrate the two-dimensional range of motion (excursion) versus DNA length were carried out. Microspheres of 160 or 240 nm in radius were tethered by DNA molecules ranging from 225 to 3477 basepairs in length in aqueous buffers containing 100 mM potassium glutamate and 8 mM MgCl₂ or 10 mM Tris-HCl and 200 mM KCl, with or without 0.5% Tween added to the buffer, and the motion was recorded. Different buffers altered the excursion of beads on identical DNA tethers. Buffer with only 10 mM NaCl and >5 mM magnesium greatly reduced excursion. Glycerol added to increase viscosity slowed confined diffusion of the tethered beads but did not change excursion. The confined-diffusion coefficients for all tethered beads were smaller than those expected for freely diffusing beads and decreased for shorter tethers. Tethered-particle motion is a sensitive framework for diffusion experiments in which small beads on long leashes most closely resemble freely diffusing, untethered beads.     

Low- and high-resolution mapping of DNA damage at specific sites

Measurement of DNA damage and repair at the nucleotide level in intact cells has provided compelling evidence for the molecular details of these events as they occur in intact organisms. Furthermore, these measurements give the most accurate picture of the rates of repair in different structural domains of DNA in chromatin. In this report, we describe two methods currently used in our laboratories to map DNA lesions at (or near) nucleotide resolution in yeast cells. The low-resolution method couples damage-specific strand breaks in DNA with indirect end-labeling to measure DNA lesions over a span of 1.5 to 2 kb of DNA sequence. The resolution of this method is limited by the resolution of DNA length measurements on alkaline agarose gels (about +/-20 bp on average). The high-resolution method uses streptavidin magnetic beads and special biotinylated oligonucleotides to facilitate end-labeling of DNA fragments specifically cleaved at damage sites. The latter method maps DNA damage sites at nucleotide resolution over a shorter distance (<500 bp), and is constrained to the length of DNA resolvable on DNA sequencing gels. These methods are used in tandem for answering questions regarding DNA damage and repair in different chromatin domains and states of gene expression.     

Application of single molecule technology to rapidly map long DNA and study the conformation of stretched DNA

Herein we describe the first application of direct linear analysis (DLA) to the mapping of a bacterial artificial chromosome (BAC), specifically the 185.1 kb-long BAC 12M9. DLA is a single molecule mapping technology, based on microfluidic elongation and interrogation of individual DNA molecules, sequence-specifically tagged with bisPNAs. A DNA map with S/N ratio sufficiently high to detect all major binding sites was obtained using only 200 molecule traces. A new method was developed to extract an oriented map from an averaged map that included a mixture of head-first and tail-first DNA traces. In addition, we applied DLA to study the conformation and tagging of highly stretched DNA. Optimal conditions for promoting sequence-specific binding of bisPNA to an 8 bp target site were elucidated using DLA, which proved superior to electromobility shift assays. DLA was highly reproducible with a hybridized tag position localized with an accuracy of ±0.7 µm or ±2.1 kb demonstrating its utility for rapid mapping of large DNA at the single molecule level. Within this accuracy, DNA molecules, stretched to at least 85% of their contour length, were stretched uniformly, so that the map expressed in relative coordinates, was the same regardless of the molecule extension.