Skewed brownian fluctuations in single-molecule magnetic tweezers

An Introduction to Magnetic Tweezers

Magnetic tweezers are a single-molecule force and torque spectroscopy technique that enable the mechanical interrogation in vitro of biomolecules, such as nucleic acids and proteins. They use a magnetic field originating from either permanent magnets or electromagnets to attract a magnetic particle, thus stretching the tethering biomolecule. They nicely complement other force spectroscopy techniques such as optical tweezers and atomic force microscopy (AFM) as they operate as a very stable force clamp, enabling long-duration experiments over a very broad range of forces spanning from 10 fN to 1 nN, with 1-10 milliseconds time and sub-nanometer spatial resolution. Their simplicity, robustness, and versatility have made magnetic tweezers a key technique within the field of single-molecule biophysics, being broadly applied to study the mechanical properties of, e.g., nucleic acids, genome processing molecular motors, protein folding, and nucleoprotein filaments. Furthermore, magnetic tweezers allow for high-throughput single-molecule measurements by tracking hundreds of biomolecules simultaneously both in real-time and at high spatiotemporal resolution. Magnetic tweezers naturally combine with surface-based fluorescence spectroscopy techniques, such as total internal reflection fluorescence microscopy, enabling correlative fluorescence and force/torque spectroscopy on biomolecules. This chapter presents an introduction to magnetic tweezers including a description of the hardware, the theory behind force calibration, its spatiotemporal resolution, combining it with other techniques, and a (non-exhaustive) overview of biological applications.

Modeling multiple duplex DNA attachments in a force-extension experiment

Optical tweezers-based DNA stretching often relies on tethering a single end-activated DNA molecule between optically manipulated end-binding beads. Measurement success can depend on DNA concentration. At lower DNA concentrations tethering is less common, and many trials may be required to observe a single-molecule stretch. At higher DNA concentrations tethering is more common; however, the resulting force-extensions observed are more complex and may vary from measurement to measurement. Typically these more complex results are attributed to the formation of multiple tethers between the beads; however, to date there does not appear to have been a critical examination of this hypothesis or the potential usefulness of such data. Here we examine stretches at a higher DNA concentration and use analysis and simulation to show how the more complex force-extensions observed can be understood in terms of multiple DNA attachments.

Magnetic tweezers: development and use in single-molecule research

The use of magnetic tweezers for single-molecule micromanipulation has evolved rapidly since its introduction approximately 30 years ago. Magnetic tweezers have provided important insights into the dynamic activity of DNA-processing enzymes, as well as detailed, high-resolution information on the mechanical properties of DNA. These successes have been enabled by major advancements in the hardware and software components of these devices. These developments now allow for a much richer mechanistic understanding of the functions and mechanisms of DNA-binding enzymes. In this review, the authors briefly discuss the fundamental principles of magnetic tweezers and describe the advancements that have made it a superlative tool for investigating, at the single-molecule level, DNA and its interactions with DNA-binding proteins.

Correction-free force calibration for magnetic tweezers experiments

Magnetic tweezers are a powerful technique to perform high-throughput and high-resolution force spectroscopy experiments at the single-molecule level. The camera-based detection of magnetic tweezers enables the observation of hundreds of magnetic beads in parallel, and therefore the characterization of the mechanochemical behavior of hundreds of nucleic acids and enzymes. However, magnetic tweezers experiments require an accurate force calibration to extract quantitative data, which is limited to low forces if the deleterious effect of the finite camera open shutter time (τ_sh) is not corrected. Here, we provide a simple method to perform correction-free force calibration for high-throughput magnetic tweezers at low image acquisition frequency (f_ac). By significantly reducing τ_sh to at least 4-fold the characteristic times of the tethered magnetic bead, we accurately evaluated the variance of the magnetic bead position along the axis parallel to the magnetic field, estimating the force with a relative error of ~10% (standard deviation), being only limited by the bead-to-bead difference. We calibrated several magnets - magnetic beads configurations, covering a force range from ~50 fN to ~60 pN. In addition, for the presented configurations, we provide a table with the mathematical expressions that describe the force as a function of the magnets position.

Single-Molecule Magnetic Tweezer Analysis of Topoisomerases

Magnetic tweezers (MT) provide a powerful single-molecule approach to study the mechanism of topoisomerases, giving the experimenter the ability to change and read out DNA topology in real time. By using diverse DNA substrates, one can study different aspects of topoisomerase function and arrive at a better mechanistic understanding of these fascinating enzymes. Here we describe methods for the creation of three different DNA substrates used in MT experiments with topoisomerases: double-stranded DNA (dsDNA) tethers, "braided" (intertwined or catenated) DNA tether pairs, and dsDNA tethers with single-stranded DNA (ssDNA) regions. Additionally, we discuss how to build flow cells for bright-field MT microscopy, as well as how to noncovalently attach anti-digoxigenin to the coverslip surface for tethering digoxigenin-labeled DNAs. Finally, we describe procedures for the identification of a suitable DNA substrate for MT study and data collection.

An orthogonal single-molecule experiment reveals multiple-attempt dynamics of type IA topoisomerases

Topoisomerases are enzymes involved in maintaining the topological state of cellular DNA. Despite many structural, biophysical, and biochemical studies, their dynamic characteristics remain poorly understood. Recent single molecule experiments revealed that an important feature of the type IA topoisomerase mechanism is the presence of pauses between relaxation events. However, these experiments cannot determine whether the protein remains DNA bound during the pauses or the relationship between domain movements in the protein and topological changes in the DNA. By combining two orthogonal single molecule techniques, we observed that topoisomerase IA is constantly changing conformation and attempting to modify the topology of DNA, but only succeeds in a fraction of the attempts. Thus, its mechanism can be described as a series of DNA strand passage attempts that culminate in a successful relaxation event.

High Spatiotemporal-Resolution Magnetic Tweezers: Calibration and Applications for DNA Dynamics

The observation of biological processes at the molecular scale in real time requires high spatial and temporal resolution. Magnetic tweezers are straightforward to implement, free of radiation or photodamage, and provide ample multiplexing capability, but their spatiotemporal resolution has lagged behind that of other single-molecule manipulation techniques, notably optical tweezers and AFM. Here, we present, to our knowledge, a new high-resolution magnetic tweezers apparatus. We systematically characterize the achievable spatiotemporal resolution for both incoherent and coherent light sources, different types and sizes of beads, and different types and lengths of tethered molecules. Using a bright coherent laser source for illumination and tracking at 6 kHz, we resolve 3 Å steps with a 1 s period for surface-melted beads and 5 Å steps with a 0.5 s period for double-stranded-dsDNA-tethered beads, in good agreement with a model of stochastic bead motion in the magnetic tweezers. We demonstrate how this instrument can be used to monitor the opening and closing of a DNA hairpin on millisecond timescales in real time, together with attendant changes in the hairpin dynamics upon the addition of deoxythymidine triphosphate. Our approach opens up the possibility of observing biological events at submillisecond timescales with subnanometer resolution using camera-based detection.

Effects of non-Gaussian Brownian motion on direct force optical tweezers measurements of the electrostatic forces between pairs of colloidal particles

Measurements of the electrostatic force with separation between a fixed and an optically trapped colloidal particle are examined with experiment, simulation and analytical calculation. Non-Gaussian Brownian motion is observed in the position of the optically trapped particle when particles are close and traps weak. As a consequence of this motion, a simple least squares parameterization of direct force measurements, in which force is inferred from the displacement of an optically trapped particle as separation is gradually decreased, contains forces generated by the rectification of thermal fluctuations in addition to those originating directly from the electrostatic interaction between the particles. Thus, when particles are close and traps weak, simply fitting the measured direct force measurement to DLVO theory extracts parameters with modified meanings when compared to the original formulation. In such cases, however, physically meaningful DLVO parameters can be recovered by comparing the measured non-Gaussian statistics to those predicted by solutions to Smoluchowski's equation for diffusion in a potential.