A high-speed magnetic tweezer beyond 10,000 frames per second

Robust, high-yield, rapid fabrication of DNA constructs for Magnetic Tweezers

Single-molecule techniques are highly sensitive tools that can reveal reaction intermediates often obscured in experiments involving large ensembles of molecules. Therefore, they provide unprecedented information on the mechanisms that control biomolecular reactions. Currently, one of the most significant single-molecule assays is Magnetic Tweezers (MT), which probes enzymatic reactions at high spatio-temporal resolutions on tens, if not hundreds, of molecules simultaneously. For high-resolution MT experiments, a short double-stranded DNA molecule (less than 2000 base pairs) is typically attached between a micron-sized superparamagnetic bead and a surface. The fabrication of such a substrate is key for successful single-molecule assays, and several papers have discussed the possibility of improving the fabrication of short DNA constructs. However, reported yields are usually low and require additional time-consuming purification steps (e.g., gel purification). In this paper, we propose the use of a Golden Gate Assembly assay that allows for the production of DNA constructs within minutes (starting from PCR products). We discuss how relevant parameters may affect the yield and offer single-molecule experimentalists a simple yet robust approach to fabricate DNA constructs.

Magnetic tweezers principles and promises

Magnetic tweezers have become popular with the outbreak of single molecule micromanipulation: catching a single molecule of DNA, RNA or a single protein and applying mechanical constrains using micron-size magnetic beads and magnets turn out to be easy. Various factors have made this possible: the fact that manufacturers have been preparing these beads to catch various biological entities-the ease of use provided by magnets which apply a force or a torque at a distance thus inside a flow cell-some chance: since the forces so generated are in the right range to stretch a single molecule. This is a little less true for torque. Finally, one feature which also appears very important is the simplicity of their calibration using Brownian motion. Here we start by describing magnetic tweezers used routinely in our laboratory where we have tried to develop a device as simple as possible so that the experimentalist can really focus on the biological aspect of the biomolecules that he/she is interested in. We discuss the implications of the various components and their important features. Next, we summarize what is easy to achieve and what is less easy. Then we refer to contributions by other groups who have brought valuable insights to improve magnetic tweezers.

Magnetic tweezers in cell mechanics

The chapter provides an overview of the applications of magnetic tweezers in living cells. It discusses the advantages and disadvantages of magnetic tweezers technology with a focus on individual magnetic tweezers configurations, such as electromagnetic tweezers. Solutions to the disadvantages identified are also outlined. The specific role of magnetic tweezers in the field of mechanobiology, such as mechanosensitivity, mechano-allostery and mechanotransduction are also emphasized. The specific usage of magnetic tweezers in mechanically probing cells via specific cell surface receptors, such as mechanosensitive channels is discussed and why mechanical probing has revealed the opening and closing of the channels. Finally, the future direction of magnetic tweezers is presented.

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.

Chromatinization Modulates Topoisomerase II Processivity

Type IIA topoisomerases are essential DNA processing enzymes that must robustly and reliably relax DNA torsional stress in vivo. While cellular processes constantly create different degrees of torsional stress, how this stress feeds back to control type IIA topoisomerase function remains obscure. Using a suite of single-molecule approaches, we examined the torsional impact on supercoiling relaxation of both naked DNA and chromatin by eukaryotic topoisomerase II (topo II). We observed that topo II was at least ~ 50-fold more processive on plectonemic DNA than previously estimated, capable of relaxing > 6000 turns. We further discovered that topo II could relax supercoiled DNA prior to plectoneme formation, but with a ~100-fold reduction in processivity; strikingly, the relaxation rate in this regime decreased with diminishing torsion in a manner consistent with the capture of transient DNA loops by topo II. Chromatinization preserved the high processivity of the enzyme under high torsional stress. Interestingly, topo II was still highly processive (~ 1000 turns) even under low torsional stress, consistent with the predisposition of chromatin to readily form DNA crossings. This work establishes that chromatin is a major stimulant of topo II function, capable of enhancing function even under low torsional stress.

Insights into the Dynamics and Helicase Activity of RecD2 of Deinococcus radiodurans during DNA Repair: A Single-Molecule Perspective

While the double helix is the most stable conformation of DNA inside cells, its transient unwinding and subsequent partial separation of the two complementary strands yields an intermediate single-stranded DNA (ssDNA). The ssDNA is involved in all major DNA transactions such as replication, transcription, recombination, and repair. The process of DNA unwinding and translocation is shouldered by helicases that transduce the chemical energy derived from nucleotide triphosphate (NTP) hydrolysis to mechanical energy and utilize it to destabilize hydrogen bonds between complementary base pairs. Consequently, a comprehensive understanding of the molecular mechanisms of these enzymes is essential. In the last few decades, a combination of single-molecule techniques (force-based manipulation and visualization) have been employed to study helicase action. These approaches have allowed researchers to study the single helicase-DNA complex in real-time and the free energy landscape of their interaction together with the detection of conformational intermediates and molecular heterogeneity during the course of helicase action. Furthermore, the unique ability of these techniques to resolve helicase motion at nanometer and millisecond spatial and temporal resolutions, respectively, provided surprising insights into their mechanism of action. This perspective outlines the contribution of single-molecule methods in deciphering molecular details of helicase activities. It also exemplifies how each technique was or can be used to study the helicase action of RecD2 in recombination DNA repair.

Etoposide promotes DNA loop trapping and barrier formation by topoisomerase II

Etoposide is a broadly employed chemotherapeutic and eukaryotic topoisomerase II poison that stabilizes cleaved DNA intermediates to promote DNA breakage and cytotoxicity. How etoposide perturbs topoisomerase dynamics is not known. Here we investigated the action of etoposide on yeast topoisomerase II, human topoisomerase IIα and human topoisomerase IIβ using several sensitive single-molecule detection methods. Unexpectedly, we found that etoposide induces topoisomerase to trap DNA loops, compacting DNA and restructuring DNA topology. Loop trapping occurs after ATP hydrolysis but before strand ejection from the enzyme. Although etoposide decreases the innate stability of topoisomerase dimers, it increases the ability of the enzyme to act as a stable roadblock. Interestingly, the three topoisomerases show similar etoposide-mediated resistance to dimer separation and sliding along DNA but different abilities to compact DNA and chirally relax DNA supercoils. These data provide unique mechanistic insights into the functional consequences of etoposide on topoisomerase II dynamics.

How sticky? How Tight? How Hot? Imaging probes for fluid viscosity, membrane tension and temperature measurements at the cellular level

We review the progress made in imaging probes for three important physical parameters: viscosity, membrane tension, and temperature, all of which play important roles in many cellular processes. Recent evidences showed that cell migration speed can be modulated by extracellular fluid viscosity; membrane tension contributes to the regulation of cell motility, exo-/endo-cytosis, and cell spread area; and temperature affects neural activity and adipocyte differentiation. We discuss the techniques implementing imaging-based probes to measure viscosity, membrane tension, and temperature at subcellular resolution dynamically. The merits and shortcomings of each technique are examined, and the future applications of the recently developed techniques are also explored.

A compact rotary magnetic tweezers device for dynamic material analysis

Here we present a new, compact magnetic tweezers design that enables precise application of a wide range of dynamic forces to soft materials without the need to raise or lower the magnet height above the sample. This is achieved through the controlled rotation of the permanent magnet array with respect to the fixed symmetry axis defined by a custom-built iron yoke. These design improvements increase the portability of the device and can be implemented within existing microscope setups without the need for extensive modification of the sample holders or light path. This device is particularly well-suited to active microrheology measurements using either creep analysis, in which a step force is applied to a micron-sized magnetic particle that is embedded in a complex fluid, or oscillatory microrheology, in which the particle is driven with a periodic waveform of controlled amplitude and frequency. In both cases, the motions of the particle are measured and analyzed to determine the local dynamic mechanical properties of the material.

High-resolution Single-molecule Magnetic Tweezers

Single-molecule magnetic tweezers deliver magnetic force and torque to single target molecules, permitting the study of dynamic changes in biomolecular structures and their interactions. Because the magnetic tweezer setups can generate magnetic fields that vary slowly over tens of millimeters-far larger than the nanometer scale of the single molecule events being observed-this technique can maintain essentially constant force levels during biochemical experiments while generating a biologically meaningful force on the order of 1-100 pN. When using bead-tether constructs to pull on single molecules, smaller magnetic beads and shorter submicrometer tethers improve dynamic response times and measurement precision. In addition, employing high-speed cameras, stronger light sources, and a graphics programming unit permits true high-resolution single-molecule magnetic tweezers that can track nanometer changes in target molecules on a millisecond or even submillisecond time scale. The unique force-clamping capacity of the magnetic tweezer technique provides a way to conduct measurements under near-equilibrium conditions and directly map the energy landscapes underlying various molecular phenomena. High-resolution single-molecule magnetic tweezers can thus be used to monitor crucial conformational changes in single-protein molecules, including those involved in mechanotransduction and protein folding. Expected final online publication date for the Annual Review of Biochemistry, Volume 91 is June 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Nano-Precision Tweezers for Mechanosensitive Proteins and Beyond

Mechanical forces play pivotal roles in regulating cell shape, function, and fate. Key players that govern the mechanobiological interplay are the mechanosensitive proteins found on cell membranes and in cytoskeleton. Their unique nanomechanics can be interrogated using single-molecule tweezers, which can apply controlled forces to the proteins and simultaneously measure the ensuing structural changes. Breakthroughs in high-resolution tweezers have enabled the routine monitoring of nanometer-scale, millisecond dynamics as a function of force. Undoubtedly, the advancement of structural biology will be further fueled by integrating static atomic-resolution structures and their dynamic changes and interactions observed with the force application techniques. In this minireview, we will introduce the general principles of single-molecule tweezers and their recent applications to the studies of force-bearing proteins, including the synaptic proteins that need to be categorized as mechanosensitive in a broad sense. We anticipate that the impact of nano-precision approaches in mechanobiology research will continue to grow in the future.

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.

Modification to axial tracking for mobile magnetic microspheres

Three-dimensional particle tracking is a routine experimental procedure for various biophysical applications including magnetic tweezers. A common method for tracking the axial position of particles involves the analysis of diffraction rings whose pattern depends sensitively on the axial position of the bead relative to the focal plane. To infer the axial position, the observed rings are compared with reference images of a bead at known axial positions. Often the precision or accuracy of these algorithms is measured on immobilized beads over a limited axial range, while many experiments are performed using freely mobile beads. This inconsistency raises the possibility of incorrect estimates of experimental uncertainty. By manipulating magnetic beads in a bidirectional magnetic tweezer setup, we evaluated the error associated with tracking mobile magnetic beads and found that the error of tracking a moving magnetic bead increases by almost an order of magnitude compared to the error of tracking a stationary bead. We found that this additional error can be ameliorated by excluding the center-most region of the diffraction ring pattern from tracking analysis. Evaluation of the limitations of a tracking algorithm is essential for understanding the error associated with a measurement. These findings promise to bring increased resolution to three-dimensional bead tracking of magnetic microspheres.

Flexible, charged biopolymers in monovalent and mixed-valence salt: Regimes of anomalous electrostatic stiffening and of salt insensitivity

The conformations of biological polyelectrolytes (PEs), such as polysaccharides, proteins, and nucleic acids, affect how they behave and interact with other biomolecules. Relative to neutral polymers, PEs in solution are more locally rigid due to intrachain electrostatic repulsion, the magnitude of which depends on the concentration of added salt. This is typically quantified using the Odijk-Skolnick-Fixman (OSF) electrostatic-stiffening model, in which salt-dependent Debye-Hückel (DH) screening modulates intrachain repulsion. However, the applicability of this approach to flexible PEs has long been questioned. To investigate this, we use high-precision single-molecule elasticity measurements to infer the scaling with salt of the local stiffness of three flexible biopolymers (hyaluronic acid, single-stranded RNA, and single-stranded DNA) in both monovalent and mixed-valence salt solutions. In monovalent salt, we collapse the data across all three polymers by accounting for charge spacing, and find a common power-law scaling of the electrostatic persistence length with ionic strength with an exponent of 0.66±0.02. This result rules out simple OSF pictures of electrostatic stiffening. It is roughly compatible with a modified OSF picture developed by Netz and Orland; alternatively, we posit the exponent can be explained if the relevant electrostatic screening length is the interion spacing rather than the DH length. In mixed salt solutions, we find a regime where adding monovalent salt, in the presence of multivalent salt, does not affect PE stiffness. Using coarse-grained simulations, and a three-state model of condensed, chain-proximate, and bulk ions, we attribute this regime to a "jacket" of ions surrounding the PE that regulates the chain's effective charge density as ionic strength varies. The size of this jacket in simulations is again consistent with a screening length controlled by interion spacing rather than the DH length. Taken together, our results describe a unified picture of the electrostatic stiffness of polyelectrolytes in the mixed-valence salt conditions of direct relevance to cellular and intercellular biological systems.

Parallel, linear, and subnanometric 3D tracking of microparticles with Stereo Darkfield Interferometry

While crucial for force spectroscopists and microbiologists, three-dimensional (3D) particle tracking suffers from either poor precision, complex calibration, or the need of expensive hardware, preventing its massive adoption. We introduce a new technique, based on a simple piece of cardboard inserted in the objective focal plane, that enables simple 3D tracking of dilute microparticles while offering subnanometer frame-to-frame precision in all directions. Its linearity alleviates calibration procedures, while the interferometric pattern enhances precision. We illustrate its utility in single-molecule force spectroscopy and single-algae motility analysis. As with any technique based on back focal plane engineering, it may be directly embedded in a commercial objective, providing a means to convert any preexisting optical setup in a 3D tracking system. Thanks to its precision, its simplicity, and its versatility, we envision that the technique has the potential to enhance the spreading of high-precision and high-throughput 3D tracking.

Transition Path Dynamics of a Dielectric Particle in a Bistable Optical Trap

Many processes in chemistry, physics, and biology involve rare events in which the system escapes from a metastable state by surmounting an activation barrier. Examples range from chemical reactions, protein folding, and nucleation events to the catastrophic failure of bridges. A challenge in understanding the underlying mechanisms is that the most interesting information is contained within the rare transition paths, the exceedingly short periods when the barrier is crossed. To establish a model process that enables access to all relevant timescales, although highly disparate, we probe the dynamics of single dielectric particles in a bistable optical trap in solution. Precise localization by high-speed tracking enables us to resolve the transition paths and relate them to the detailed properties of the 3D potential within which the particle diffuses. By varying the barrier height and shape, the experiments provide a stringent benchmark of current theories of transition path dynamics.

Synergistic Coordination of Chromatin Torsional Mechanics and Topoisomerase Activity

DNA replication in eukaryotes generates DNA supercoiling, which may intertwine (braid) daughter chromatin fibers to form precatenanes, posing topological challenges during chromosome segregation. The mechanisms that limit precatenane formation remain unclear. By making direct torque measurements, we demonstrate that the intrinsic mechanical properties of chromatin play a fundamental role in dictating precatenane formation and regulating chromatin topology. Whereas a single chromatin fiber is torsionally soft, a braided fiber is torsionally stiff, indicating that supercoiling on chromatin substrates is preferentially directed in front of the fork during replication. We further show that topoisomerase II relaxation displays a strong preference for a single chromatin fiber over a braided fiber. These results suggest a synergistic coordination-the mechanical properties of chromatin inherently suppress precatenane formation during replication elongation by driving DNA supercoiling ahead of the fork, where supercoiling is more efficiently removed by topoisomerase II. VIDEO ABSTRACT.

Multiplexed Nanometric 3D Tracking of Microbeads Using an FFT-Phasor Algorithm

Many single-molecule biophysical techniques rely on nanometric tracking of microbeads to obtain quantitative information about the mechanical properties of biomolecules such as chromatin fibers. Their three-dimensional (3D) position can be resolved by holographic analysis of the diffraction pattern in wide-field imaging. Fitting this diffraction pattern to Lorenz-Mie scattering theory yields the bead's position with nanometer accuracy in three dimensions but is computationally expensive. Real-time multiplexed bead tracking therefore requires a more efficient tracking method, such as comparison with previously measured diffraction patterns, known as look-up tables. Here, we introduce an alternative 3D phasor algorithm that provides robust bead tracking with nanometric localization accuracy in a z range of over 10 μm under nonoptimal imaging conditions. The algorithm is based on a two-dimensional cross correlation using fast Fourier transforms with computer-generated reference images, yielding a processing rate of up to 10,000 regions of interest per second. We implemented the technique in magnetic tweezers and tracked the 3D position of over 100 beads in real time on a generic CPU. The accuracy of 3D phasor tracking was extensively tested and compared to a look-up table approach using Lorenz-Mie simulations, avoiding experimental uncertainties. Its easy implementation, efficiency, and robustness can improve multiplexed biophysical bead-tracking applications, especially when high throughput is required and image artifacts are difficult to avoid.

High spatiotemporal resolution data from a custom magnetic tweezers instrument

Gene expression is achieved by enzymes as RNA polymerases that translocate along nucleic acids with steps as small as a single base pair, i.e., 0.34 nm for DNA. Deciphering the complex biochemical pathway that describes the activity of such enzymes requires an exquisite spatiotemporal resolution. Magnetic tweezers are a powerful single molecule force spectroscopy technique that uses a camera-based detection to enable the simultaneous observation of hundreds of nucleic acid tethered magnetic beads at a constant force with subnanometer resolution [1,2]. High spatiotemporal resolution magnetic tweezers have recently been reported [3–5]. We present data acquired using a bespoke magnetic tweezers instrument that is able to perform either in high throughput or at high resolution. The data reports on the best achievable resolution for surface-attached polystyrene beads and DNA tethered magnetic beads, and highlights the influence of mechanical stability for such assay. We also present data where we are able to detect 0.3 nm steps along the z-axis using DNA tethered magnetic beads. Because the data presented here are in agreement with the best resolution obtained with magnetic tweezers, they provide a useful benchmark comparison for setup adjustment and optimization.

Polyelectrolyte Conformation Controlled by a Trivalent-Rich Ion Jacket

The configuration of charged polymers is heavily dependent on interactions with surrounding salt ions, typically manifesting as a sensitivity to the bulk ionic strength. Here, we use single-molecule mechanical measurements to show that a charged polysaccharide, hyaluronic acid, shows a surprising regime of insensitivity to ionic strength in the presence of trivalent ions. Using simulations and theory, we propose that this is caused by the formation of a "jacket" of ions, tightly associated with the polymer, whose charge (and thus effect on configuration) is robust against changes in solution composition.

Model-free 3D localization with precision estimates for brightfield-imaged particles

Volumetric imaging and 3D particle tracking are becoming increasingly common and have a variety of microscopy applications including in situ fluorescent imaging, in-vitro single-molecule characterization, and analysis of colloidal systems. While recent interest has generated discussion of optimal schemes for localizing diffraction-limited fluorescent puncta, there have been relatively few published routines for tracking particles imaged with bright-field illumination. To address this, we outline a simple, look-up-table based 3D tracking strategy, which can be adapted to most commercially available wide-field microscopes, and present two image processing algorithms that together yield high-precision localization and return estimates of statistical accuracy. Under bright-field illumination, a particle's depth can be determined based on the size and shape of its diffractive pattern due to Mie scattering. Contrary to typical "super-resolution" fluorescence tracking routines, which typically fit a diffraction-limited spot to a model point-spread-function, the lateral (XY) tracking routine relies on symmetry to locate a particle without prior knowledge of the form of the particle. At low noise levels (signal:noise > 1000), the symmetry routine estimates particle positions with accuracy better than 0.01 pixel. Depth localization is accomplished by matching images of particles to those in a pre-recorded look-up-table. The routine presented here optimally interpolates between LUT entries with better than 0.05 step accuracy. Both routines are tolerant of high levels of image noise, yielding sub-pixel/step accuracy with signal-to-noise ratios as small as 1, and, by design, return confidence intervals indicating the expected accuracy of each calculated position. The included implementations operate extremely quickly and are amenable to real-time analysis at frame rates exceeding several hundred frames per second.

Multiplexed protein force spectroscopy reveals equilibrium protein folding dynamics and the low-force response of von Willebrand factor

Single-molecule force spectroscopy has provided unprecedented insights into protein folding, force regulation, and function. So far, the field has relied primarily on atomic force microscope and optical tweezers assays that, while powerful, are limited in force resolution, throughput, and require feedback for constant force measurements. Here, we present a modular approach based on magnetic tweezers (MT) for highly multiplexed protein force spectroscopy. Our approach uses elastin-like polypeptide linkers for the specific attachment of proteins, requiring only short peptide tags on the protein of interest. The assay extends protein force spectroscopy into the low force (<1 pN) regime and enables parallel and ultra-stable measurements at constant forces. We present unfolding and refolding data for the small, single-domain protein ddFLN4, commonly used as a molecular fingerprint in force spectroscopy, and for the large, multidomain dimeric protein von Willebrand factor (VWF) that is critically involved in primary hemostasis. For both proteins, our measurements reveal exponential force dependencies of unfolding and refolding rates. We directly resolve the stabilization of the VWF A2 domain by Ca²⁺ and discover transitions in the VWF C domain stem at low forces that likely constitute the first steps of VWF's mechano-activation. Probing the force-dependent lifetime of biotin-streptavidin bonds, we find that monovalent streptavidin constructs with specific attachment geometry are significantly more force stable than commercial, multivalent streptavidin. We expect our modular approach to enable multiplexed force-spectroscopy measurements for a wide range of proteins, in particular in the physiologically relevant low-force regime.

Submicrometer elasticity of double-stranded DNA revealed by precision force-extension measurements with magnetic tweezers

Submicrometer elasticity of double-stranded DNA (dsDNA) governs nanoscale bending of DNA segments and their interactions with proteins. Single-molecule force spectroscopy, including magnetic tweezers (MTs), is an important tool for studying DNA mechanics. However, its application to short DNAs under 1 μm is limited. We developed an MT-based method for precise force-extension measurements in the 100-nm regime that enables in situ correction of the error in DNA extension measurement, and normalizes the force variability across beads by exploiting DNA hairpins. The method reduces the lower limit of tractable dsDNA length down to 198 base pairs (bp) (67 nm), an order-of-magnitude improvement compared to conventional tweezing experiments. Applying this method and the finite worm-like chain model we observed an essentially constant persistence length across the chain lengths studied (198 bp to 10 kbp), which steeply depended on GC content and methylation. This finding suggests a potential sequence-dependent mechanism for short-DNA elasticity.

Single-molecule approach for studying RNAP II transcription initiation using magnetic tweezers

The initiation of transcription underlies the ability of cells to modulate genome expression as a function of both internal and external signals and the core process of initiation has features that are shared across all domains of life. Specifically, initiation can be sub-divided into promoter recognition, promoter opening, and promoter escape. However, the molecular players and mechanisms used are significantly different in Eukaryotes and Bacteria. In particular, bacterial initiation requires only the formation of RNA polymerase (RNAP) holoenzyme and proceeds as a series of spontaneous conformational changes while eukaryotic initiation requires the formation of the 31-subunit pre-initiation complex (PIC) and often requires ATP hydrolysis by the Ssl2/XPB subunit of the general transcription factor TFIIH. Our mechanistic view of this process in Eukaryotes has recently been improved through a combination of structural and single-molecule approaches which are providing a detailed picture of the structural dynamics that lead to the production of an elongation competent RNAP II and thus, an RNA transcript. Here we provide the methodological details of our single-molecule magnetic tweezers studies of transcription initiation using purified factors from Saccharomyces cerevisiae.

High-Performance Image-Based Measurements of Biological Forces and Interactions in a Dual Optical Trap

Optical traps enable the nanoscale manipulation of individual biomolecules while measuring molecular forces and lengths. This ability relies on the sensitive detection of optically trapped particles, typically accomplished using laser-based interferometric methods. Recently, image-based particle tracking techniques have garnered increased interest as a potential alternative to laser-based detection; however, successful integration of image-based methods into optical trapping instruments for biophysical applications and force measurements has remained elusive. Here, we develop a camera-based detection platform that enables accurate and precise measurements of biological forces and interactions in a dual optical trap. In demonstration, we stretch and unzip DNA molecules while measuring the relative distances of trapped particles from their trapping centers with sub-nanometer accuracy and precision. We then use the DNA unzipping technique to localize bound proteins with sub-base-pair precision, revealing how thermal DNA "breathing" fluctuations allow an unzipping fork to detect and respond to the presence of a protein bound downstream. This work advances the capabilities of image tracking in optical traps, providing a state-of-the-art detection method that is accessible, highly flexible, and broadly compatible with diverse experimental substrates and other nanometric techniques.

Real-time parallel 3D multiple particle tracking with single molecule centrifugal force microscopy

Real-time tracking of multiple particles is key for quantitative analysis of dynamic biophysical processes and materials science via time-lapse microscopy image data, especially for single molecule biophysical techniques, such as magnetic tweezers and centrifugal force microscopy. However, real-time multiple particle tracking with high resolution is limited by the current imaging processes or tracking algorithms. Here, we demonstrate 1 nm resolution in three dimensions in real-time with a graphics-processing unit (GPU) based on a compute unified device architecture (CUDA) parallel computing framework instead of only a central processing unit (CPU). We also explore the trade-offs between processing speed and size of the utilized regions of interest and a maximum speedup of 137 is achieved with the GPU compared with the CPU. Moreover, we utilize this method with our recently self-built centrifugal force microscope (CFM) in experiments that track multiple DNA-tethered particles. Our approach paves the way for high-throughput single molecule techniques with high resolution and efficiency. LAY DESCRIPTION: Particles are widely used as probes in life sciences through their motions. In single molecule techniques such as optical tweezers and magnetic tweezers, microbeads are used to study intermolecular or intramolecular interactions via beads tracking. Also tracking multiple beads' motions could study cell-cell or cell-ECM interactions in traction force microscopy. Therefore, particle tracking is of key important during these researches. However, parallel 3D multiple particle tracking in real-time with high resolution is a challenge either due to the algorithm or the program. Here, we combine the performance of CPU and CUDA-based GPU to make a hybrid implementation for particle tracking. In this way, a speedup of 137 is obtained compared the program before only with CPU without loss of accuracy. Moreover, we improve and build a new centrifugal force microscope for multiple single molecule force spectroscopy research in parallel. Then we employed our program into centrifugal force microscope for DNA stretching study. Our results not only demonstrate the application of this program in single molecule techniques, also indicate the capability of multiple single molecule study with centrifugal force microscopy.

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.

A Horizontal Magnetic Tweezers and Its Use for Studying Single DNA Molecules

We report the development of a magnetic tweezers that can be used to micromanipulate single DNA molecules by applying picoNewton (pN)-scale forces in the horizontal plane. The resulting force–extension data from our experiments show high-resolution detection of changes in the DNA tether’s extension: ~0.5 pN in the force and <10 nm change in extension. We calibrate our instrument using multiple orthogonal techniques including the well-characterized DNA overstretching transition. We also quantify the repeatability of force and extension measurements, and present data on the behavior of the overstretching transition under varying salt conditions. The design and experimental protocols are described in detail, which should enable straightforward reproduction of the tweezers.

Combined Magnetic Tweezers and Micro-mirror Total Internal Reflection Fluorescence Microscope for Single-Molecule Manipulation and Visualization

Magnetic tweezers is a versatile yet simple single-molecule manipulation technique that has been used to study a broad range of nucleic acids and nucleic acid-based molecular motors. In this chapter, we combine micro-mirror-based total internal reflection microscopy with a magnetic tweezers instrument, permitting simultaneous single-molecule visualization and mechanical manipulation. We provide a simple method to calibrate the evanescent wave penetration depth via supercoiling of DNA with a fluorescent nanodiamond-labeled magnetic bead and a complementary method employing a surface-immobilized fluorescent nanodiamond.

Probing Chromatin Structure with Magnetic Tweezers

Magnetic tweezers form a unique tool to study the topology and mechanical properties of chromatin fibers. Chromatin is a complex of DNA and proteins that folds the DNA in such a way that meter-long stretches of DNA fit into the micron-sized cell nucleus. Moreover, it regulates accessibility of the genome to the cellular replication, transcription, and repair machinery. However, the structure and mechanisms that govern chromatin folding remain poorly understood, despite recent spectacular improvements in high-resolution imaging techniques. Single-molecule force spectroscopy techniques can directly measure both the extension of individual chromatin fragments with nanometer accuracy and the forces involved in the (un)folding of single chromatin fibers. Here, we report detailed methods that allow one to successfully prepare in vitro reconstituted chromatin fibers for use in magnetic tweezers-based force spectroscopy. The higher-order structure of different chromatin fibers can be inferred from fitting a statistical mechanics model to the force-extension data. These methods for quantifying chromatin folding can be extended to study many other processes involving chromatin, such as the epigenetic regulation of transcription.

A multiplexed magnetic tweezer with precision particle tracking and bi-directional force control

Background

In the past two decades, methods have been developed to measure the mechanical properties of single biomolecules. One of these methods, Magnetic tweezers, is amenable to aquisition of data on many single molecules simultaneously, but to take full advantage of this "multiplexing" ability, it is necessary to simultaneously incorprorate many capabilities that ahve been only demonstrated separately.

Methods

Our custom built magnetic tweezer combines high multiplexing, precision bead tracking, and bi-directional force control into a flexible and stable platform for examining single molecule behavior. This was accomplished using electromagnets, which provide high temporal control of force while achieving force levels similar to permanent magnets via large paramagnetic beads.

Results

Here we describe the instrument and its ability to apply 2–260 pN of force on up to 120 beads simultaneously, with a maximum spatial precision of 12 nm using a variety of bead sizes and experimental techniques. We also demonstrate a novel method for increasing the precision of force estimations on heterogeneous paramagnetic beads using a combination of density separation and bi-directional force correlation which reduces the coefficient of variation of force from 27% to 6%. We then use the instrument to examine the force dependence of uncoiling and recoiling velocity of type 1 fimbriae from Eschericia coli (E. coli) bacteria, and see similar results to previous studies.

Conclusion

This platform provides a simple, effective, and flexible method for efficiently gathering single molecule force spectroscopy measurements.

A mechanistic study of helicases with magnetic traps

Helicases are a broad family of enzymes that separate nucleic acid double strand structures (DNA/DNA, DNA/RNA, or RNA/RNA) and thus are essential to DNA replication and the maintenance of nucleic acid integrity. We review the picture that has emerged from single molecule studies of the mechanisms of DNA and RNA helicases and their interactions with other proteins. Many features have been uncovered by these studies that were obscured by bulk studies, such as DNA strands switching, mechanical (rather than biochemical) coupling between helicases and polymerases, helicase-induced re-hybridization and stalled fork rescue.

Tweezing of Magnetic and Non-Magnetic Objects with Magnetic Fields

Although strong magnetic fields cannot be conveniently "focused" like light, modern microfabrication techniques enable preparation of microstructures with which the field gradients - and resulting magnetic forces - can be localized to very small dimensions. This ability provides the foundation for magnetic tweezers which in their classical variant can address magnetic targets. More recently, the so-called negative magnetophoretic tweezers have also been developed which enable trapping and manipulations of completely nonmagnetic particles provided that they are suspended in a high-magnetic-susceptibility liquid. These two modes of magnetic tweezing are complimentary techniques tailorable for different types of applications. This Progress Report provides the theoretical basis for both modalities and illustrates their specific uses ranging from the manipulation of colloids in 2D and 3D, to trapping of living cells, control of cell function, experiments with single molecules, and more.

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.

Magnetic tweezers force calibration for molecules that exhibit conformational switching

High spatial and temporal resolution magnetic tweezers experiments allow for the direct calibration of pulling forces applied to short biomolecules. In one class of experiments, a force is applied to a structured RNA or protein to induce an unfolding transition; when the force is maintained at particular values, the molecule can exhibit conformational switching between the folded and unfolded states or between intermediate states. Here, we analyze the degree to which common force calibration approaches, involving the fitting of model functions to the Allan variance or power spectral density of the bead trajectory, are biased by this conformational switching. We find significant effects in two limits: that of large molecular extension changes between the two states, in which alternative fitting functions must be used, and that of very fast switching kinetics, in which the force calibration cannot be recovered due to the slow diffusion time of the magnetic bead. We use simulations and high-resolution RNA hairpin data to show that most biophysical experiments do not occur in either of these limits.

Electromagnetic tweezers with independent force and torque control

Magnetic tweezers are powerful tools to manipulate and study the mechanical properties of biological molecules and living cells. In this paper we present a novel, bona fide electromagnetic tweezer (EMT) setup that allows independent control of the force and torque applied via micrometer-sized magnetic beads to a molecule under study. We implemented this EMT by combining a single solenoid that generates force (f-EMT) with a set of four solenoids arranged into a symmetric quadrupole to generate torque (τ-EMT). To demonstrate the capability of the tweezers, we attached optically asymmetric Janus beads to single, tethered DNA molecules. We show that tension in the piconewton force range can be applied to single DNA molecules and the molecule can simultaneously be twisted with torques in the piconewton-nanometer range. Furthermore, the EMT allows the two components to be independently controlled. At various force levels applied to the Janus bead, the trap torsional stiffness can be continuously changed simply by varying the current magnitude applied to the τ-EMT. The flexible and independent control of force and torque by the EMT makes it an ideal tool for a range of measurements where tensional and torsional properties need to be studied simultaneously on a molecular or cellular level.

Probing the mechanical properties, conformational changes, and interactions of nucleic acids with magnetic tweezers

Nucleic acids are central to the storage and transmission of genetic information. Mechanical properties, along with their sequence, both enable and fundamentally constrain the biological functions of DNA and RNA. For small deformations from the equilibrium conformations, nucleic acids are well described by an isotropic elastic rod model. However, external forces and torsional strains can induce conformational changes, giving rise to a complex force-torque phase diagram. This review focuses on magnetic tweezers as a powerful tool to precisely determine both the elastic parameters and conformational transitions of nucleic acids under external forces and torques at the single-molecule level. We review several variations of magnetic tweezers, in particular conventional magnetic tweezers, freely orbiting magnetic tweezers and magnetic torque tweezers, and discuss their characteristic capabilities. We then describe the elastic rod model for DNA and RNA and discuss conformational changes induced by mechanical stress. The focus lies on the responses to torque and twist, which are crucial in the mechanics and interactions of nucleic acids and can directly be measured using magnetic tweezers. We conclude by highlighting several recent studies of nucleic acid-protein and nucleic acid-small-molecule interactions as further applications of magnetic tweezers and give an outlook of some exciting developments to come.

Extending the range for force calibration in magnetic tweezers

Magnetic tweezers are a wide-spread tool used to study the mechanics and the function of a large variety of biomolecules and biomolecular machines. This tool uses a magnetic particle and a strong magnetic field gradient to apply defined forces to the molecule of interest. Forces are typically quantified by analyzing the lateral fluctuations of the biomolecule-tethered particle in the direction perpendicular to the applied force. Since the magnetic field pins the anisotropy axis of the particle, the lateral fluctuations follow the geometry of a pendulum with a short pendulum length along and a long pendulum length perpendicular to the field lines. Typically, the short pendulum geometry is used for force calibration by power-spectral-density (PSD) analysis, because the movement of the bead in this direction can be approximated by a simple translational motion. Here, we provide a detailed analysis of the fluctuations according to the long pendulum geometry and show that for this direction, both the translational and the rotational motions of the particle have to be considered. We provide analytical formulas for the PSD of this coupled system that agree well with PSDs obtained in experiments and simulations and that finally allow a faithful quantification of the magnetic force for the long pendulum geometry. We furthermore demonstrate that this methodology allows the calibration of much larger forces than the short pendulum geometry in a tether-length-dependent manner. In addition, the accuracy of determination of the absolute force is improved. Our force calibration based on the long pendulum geometry will facilitate high-resolution magnetic-tweezers experiments that rely on short molecules and large forces, as well as highly parallelized measurements that use low frame rates.

Simple horizontal magnetic tweezers for micromanipulation of single DNA molecules and DNA-protein complexes

We report the development of a simple-to-implement magnetic force transducer that can apply a wide range of piconewton (pN) scale forces on single DNA molecules and DNA-protein complexes in the horizontal plane. The resulting low-noise force-extension data enable very high-resolution detection of changes in the DNA tether's extension: ~0.05 pN in force and <10 nm change in extension. We have also verified that we can manipulate DNA in near equilibrium conditions through the wide range of forces by ramping the force from low to high and back again, and observing minimal hysteresis in the molecule's force response. Using a calibration technique based on Stokes' drag law, we have confirmed our force measurements from DNA force-extension experiments obtained using the fluctuation-dissipation theorem applied to transverse fluctuations of the magnetic microsphere. We present data on the force-distance characteristics of a DNA molecule complexed with histones. The results illustrate how the tweezers can be used to study DNA binding proteins at the single molecule level.

Controlling nanoflake motion using stiffness gradients on hexagonal boron nitride

Molecular dynamics simulations are performed to investigate the possibility of generating motion from stiffness gradients with no external energy source.

Untangling reaction pathways through modern approaches to high-throughput single-molecule force-spectroscopy experiments

Single-molecule experiments provide a unique means for real-time observation of the activity of individual biomolecular machines. Through such techniques, insights into the mechanics of for example, polymerases, helicases, and packaging motors have been gleaned. Here we describe the recent advances in single-molecule force spectroscopy instrumentation that have facilitated high-throughput acquisition at high spatiotemporal resolution. The large datasets attained by such methods can capture rare but important events, and contain information regarding stochastic behaviors covering many orders of magnitude in time. We further discuss analysis of such data sets, and with a special focus on the pause states described in the general literature on RNA polymerase pausing we compare and contrast the signatures of different reaction pathways.

Ultrastable measurement platform: sub-nm drift over hours in 3D at room temperature

Advanced optical traps can probe single molecules with Ångstrom-scale precision, but drift limits the utility of these instruments. To achieve Å-scale stability, a differential measurement scheme between a pair of laser foci was introduced that substantially exceeds the inherent mechanical stability of various types of microscopes at room temperature. By using lock-in detection to measure both lasers with a single quadrant photodiode, we enhanced the differential stability of this optical reference frame and thereby stabilized an optical-trapping microscope to 0.2 Å laterally over 100 s based on the Allan deviation. In three dimensions, we achieved stabilities of 1 Å over 1,000 s and 1 nm over 15 h. This stability was complemented by high measurement bandwidth (100 kHz). Overall, our compact back-scattered detection enables an ultrastable measurement platform compatible with optical traps, atomic force microscopy, and optical microscopy, including super-resolution techniques.

Camera-based three-dimensional real-time particle tracking at kHz rates and Ångström accuracy

Optical and magnetic tweezers are widely employed to probe the mechanics and activity of individual biomolecular complexes. They rely on micrometer-sized particles to detect molecular conformational changes from the particle position. Real-time particle tracking with Ångström accuracy has so far been only achieved using laser detection through photodiodes. Here we demonstrate that camera-based imaging can provide a similar performance for all three dimensions. Particle imaging at kHz rates is combined with real-time data processing being accelerated by a graphics processing unit. For particles that are fixed in the sample cell we can detect 3 Å sized steps that are introduced by cell translations at rates of 10 Hz, while for DNA-tethered particles 5 Å steps at 1 Hz can be resolved. Moreover, 20 particles can be tracked in parallel with comparable accuracy. Our approach provides a simple and robust way for high-resolution tweezers experiments using multiple particles at a time.

An optimized software framework for real-time, high-throughput tracking of spherical beads

Numerous biophysical techniques such as magnetic tweezers, flow stretching assays, or tethered particle motion assays rely on the tracking of spherical beads to obtain quantitative information about the individual biomolecules to which these beads are bound. The determination of these beads' coordinates from video-based images typically forms an essential component of these techniques. Recent advances in camera technology permit the simultaneous imaging of many beads, greatly increasing the information that can be captured in a single experiment. However, computational aspects such as frame capture rates or tracking algorithms often limit the rapid determination of such beads' coordinates. Here, we present a scalable and open source software framework to accelerate bead localization calculations based on the CUDA parallel computing framework. Within this framework, we implement the Quadrant Interpolation algorithm in order to accurately and simultaneously track hundreds of beads in real time using consumer hardware. In doing so, we show that the scatter derived from the bead tracking algorithms remains close to the theoretical optimum defined by the Cramer-Rao Lower Bound. We also explore the trade-offs between processing speed, size of the region-of-interests utilized, and tracking bias, highlighting in passing a bias in tracking along the optical axis that has previously gone unreported. To demonstrate the practical application of this software, we demonstrate how its implementation on magnetic tweezers can accurately track (with ∼1 nm standard deviation) 228 DNA-tethered beads at 58 Hz. These advances will facilitate the development and use of high-throughput single-molecule approaches.

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.

Efficient illumination for microsecond tracking microscopy

The possibility to observe microsecond dynamics at the sub-micron scale, opened by recent technological advances in fast camera sensors, will affect many biophysical studies based on particle tracking in optical microscopy. A main limiting factor for further development of fast video microscopy remains the illumination of the sample, which must deliver sufficient light to the camera to allow microsecond exposure times. Here we systematically compare the main illumination systems employed in holographic tracking microscopy, and we show that a superluminescent diode and a modulated laser diode perform the best in terms of image quality and acquisition speed, respectively. In particular, we show that the simple and inexpensive laser illumination enables less than s camera exposure time at high magnification on a large field of view without coherence image artifacts, together with a good hologram quality that allows nm-tracking of microscopic beads to be performed. This comparison of sources can guide in choosing the most efficient illumination system with respect to the specific application.