Soft magnetic tweezers: a proof of principle

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 Nanoparticles as a Tool for Remote DNA Manipulations at a Single-Molecule Level

Remote control of cells and single molecules by magnetic nanoparticles in nonheating external magnetic fields is a perspective approach for many applications such as cancer treatment and enzyme activity regulation. However, the possibility and mechanisms of direct effects of small individual magnetic nanoparticles on such processes in magneto-mechanical experiments still remain unclear. In this work, we have shown remote-controlled mechanical dissociation of short DNA duplexes (18-60 bp) under the influence of nonheating low-frequency alternating magnetic fields using individual 11 nm magnetic nanoparticles. The developed technique allows (1) simultaneous manipulation of millions of individual DNA molecules and (2) evaluation of energies of intermolecular interactions in short DNA duplexes or in other molecules. Finally, we have shown that DNA duplexes dissociation is mediated by mechanical stress and produced by the movement of magnetic nanoparticles in magnetic fields, but not by local overheating. The presented technique opens a new avenue for high-precision manipulation of DNA and generation of biosensors for quantification of energies of intermolecular interaction.

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.

Particle Manipulation with External Field; From Recent Advancement to Perspectives

Physical forces, such as dielectric, magnetic, electric, optical, and acoustic force, provide useful principles for the manipulation of particles, which are impossible or difficult with other approaches. Microparticles, including polymer particles, liquid droplets, and biological cells, can be trapped at a particular position and are also transported to arbitrary locations in an appropriate external physical field. Since the force can be externally controlled by the field strength, we can evaluate physicochemical properties of particles from the shift of the particle location. Most of the manipulation studies are conducted for particles of sub-micrometer or larger dimensions, because the force exerted on nanomaterials or molecules is so weak that their direct manipulation is generally difficult. However, the behavior, interactions, and reactions of such small substances can be indirectly evaluated by observing microparticles, on which the targets are tethered, in a physical field. We review the recent advancements in the manipulation of particles using a physical force and discuss its potentials, advantages, and limitations from fundamental and practical perspectives.

Development of Magnetic Torque Stimulation (MTS) Utilizing Rotating Uniform Magnetic Field for Mechanical Activation of Cardiac Cells

Regulation of cell signaling through physical stimulation is an emerging topic in biomedicine. Background: While recent advances in biophysical technologies show capabilities for spatiotemporal stimulation, interfacing those tools with biological systems for intact signal transfer and noncontact stimulation remains challenging. Here, we describe the use of a magnetic torque stimulation (MTS) system combined with engineered magnetic particles to apply forces on the surface of individual cells. MTS utilizes an externally rotating magnetic field to induce a spin on magnetic particles and generate torsional force to stimulate mechanotransduction pathways in two types of human heart cells—cardiomyocytes and cardiac fibroblasts. Methods: The MTS system operates in a noncontact mode with two magnets separated (60 mm) from each other and generates a torque of up to 15 pN µm across the entire area of a 35-mm cell culture dish. The MTS system can mechanically stimulate both types of human heart cells, inducing maturation and hypertrophy. Results: Our findings show that application of the MTS system under hypoxic conditions induces not only nuclear localization of mechanoresponsive YAP proteins in human heart cells but also overexpression of hypertrophy markers, including β-myosin heavy chain (βMHC), cardiotrophin-1 (CT-1), microRNA-21 (miR-21), and transforming growth factor beta-1 (TGFβ-1). Conclusions: These results have important implications for the applicability of the MTS system to diverse in vitro studies that require remote and noninvasive mechanical regulation.

A benchmark data set for the mechanical properties of double-stranded DNA and RNA under torsional constraint

Nucleic acids are central to the storage and transmission of genetic information and play essential roles in many cellular processes. Quantitative understanding and modeling of their functions and properties requires quantitative experimental characterization. We use magnetic tweezers (MT) to apply precisely calibrated stretching forces and linking number changes to DNA and RNA molecules tethered between a surface and superparamagnetic beads. Magnetic torque tweezers (MTT) allow to control the linking number of double-stranded DNA or RNA tethers, while directly measuring molecular torque by monitoring changes in the equilibrium rotation angle upon over- or underwinding of the helical molecules. Here, we provide a comprehensive data set of double-stranded DNA and RNA under controlled stretching as a function of the linking number. We present data for extension and torque as a function of linking number in equilibrium. We report data for the critical torque of buckling and of the torsional stiffness of DNA and RNA as a function of applied force. Finally, we provide dynamic data for the hopping behavior at the DNA buckling point.

Rotating magnetic particles for lab-on-chip applications - a comprehensive review

Magnetic particles are widely used in lab-on-chip and biosensing applications, because they have a high surface-to-volume ratio, they can be actuated with magnetic fields and many biofunctionalization options are available. The most well-known actuation method is to apply a magnetic field gradient which generates a translational force on the particles and allows separation of the particles from a suspension. A more recently developed magnetic actuation method is to exert torque on magnetic particles by a rotating magnetic field. Rotational actuation can be achieved with a field that is uniform in space and it allows for a precise control of torque, orientation, and angular velocity of magnetic particles in lab-on-chip devices. A wide range of studies have been performed with rotating MPs, demonstrating fluid mixing, concentration determination of biological molecules in solution, and characterization of structure and function of biomolecules at the single-molecule level. In this paper we give a comprehensive review of the historical development of MP rotation studies, including configurations for field generation, physical model descriptions, and biological applications. We conclude by sketching the scientific and technological developments that can be expected in the future in the field of rotating magnetic particles for lab-on-chip applications.

Biomechanical Characterization at the Cell Scale: Present and Prospects

The rapidly growing field of mechanobiology demands for robust and reproducible characterization of cell mechanical properties. Recent achievements in understanding the mechanical regulation of cell fate largely rely on technological platforms capable of probing the mechanical response of living cells and their physico–chemical interaction with the microenvironment. Besides the established family of atomic force microscopy (AFM) based methods, other approaches include optical, magnetic, and acoustic tweezers, as well as sensing substrates that take advantage of biomaterials chemistry and microfabrication techniques. In this review, we introduce the available methods with an emphasis on the most recent advances, and we discuss the challenges associated with their implementation.

Force-Mediating Magnetic Nanoparticles to Engineer Neuronal Cell Function

Cellular processes like membrane deformation, cell migration, and transport of organelles are sensitive to mechanical forces. Technically, these cellular processes can be manipulated through operating forces at a spatial precision in the range of nanometers up to a few micrometers through chaperoning force-mediating nanoparticles in electrical, magnetic, or optical field gradients. But which force-mediating tool is more suitable to manipulate cell migration, and which, to manipulate cell signaling? We review here the differences in forces sensation to control and engineer cellular processes inside and outside the cell, with a special focus on neuronal cells. In addition, we discuss technical details and limitations of different force-mediating approaches and highlight recent advancements of nanomagnetics in cell organization, communication, signaling, and intracellular trafficking. Finally, we give suggestions about how force-mediating nanoparticles can be used to our advantage in next-generation neurotherapeutic devices.

Quantifying the Precision of Single-Molecule Torque and Twist Measurements Using Allan Variance

Single-molecule manipulation techniques have provided unprecedented insights into the structure, function, interactions, and mechanical properties of biological macromolecules. Recently, the single-molecule toolbox has been expanded by techniques that enable measurements of rotation and torque, such as the optical torque wrench (OTW) and several different implementations of magnetic (torque) tweezers. Although systematic analyses of the position and force precision of single-molecule techniques have attracted considerable attention, their angle and torque precision have been treated in much less detail. Here, we propose Allan deviation as a tool to systematically quantitate angle and torque precision in single-molecule measurements. We apply the Allan variance method to experimental data from our implementations of (electro)magnetic torque tweezers and an OTW and find that both approaches can achieve a torque precision better than 1 pN · nm. The OTW, capable of measuring torque on (sub)millisecond timescales, provides the best torque precision for measurement times ≲10 s, after which drift becomes a limiting factor. For longer measurement times, magnetic torque tweezers with their superior stability provide the best torque precision. Use of the Allan deviation enables critical assessments of the torque precision as a function of measurement time across different measurement modalities and provides a tool to optimize measurement protocols for a given instrument and application.

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.

Single-molecule techniques in biophysics: a review of the progress in methods and applications

Single-molecule biophysics has transformed our understanding of biology, but also of the physics of life. More exotic than simple soft matter, biomatter lives far from thermal equilibrium, covering multiple lengths from the nanoscale of single molecules to up to several orders of magnitude higher in cells, tissues and organisms. Biomolecules are often characterized by underlying instability: multiple metastable free energy states exist, separated by levels of just a few multiples of the thermal energy scale k _B T, where k _B is the Boltzmann constant and T absolute temperature, implying complex inter-conversion kinetics in the relatively hot, wet environment of active biological matter. A key benefit of single-molecule biophysics techniques is their ability to probe heterogeneity of free energy states across a molecular population, too challenging in general for conventional ensemble average approaches. Parallel developments in experimental and computational techniques have catalysed the birth of multiplexed, correlative techniques to tackle previously intractable biological questions. Experimentally, progress has been driven by improvements in sensitivity and speed of detectors, and the stability and efficiency of light sources, probes and microfluidics. We discuss the motivation and requirements for these recent experiments, including the underpinning mathematics. These methods are broadly divided into tools which detect molecules and those which manipulate them. For the former we discuss the progress of super-resolution microscopy, transformative for addressing many longstanding questions in the life sciences, and for the latter we include progress in 'force spectroscopy' techniques that mechanically perturb molecules. We also consider in silico progress of single-molecule computational physics, and how simulation and experimentation may be drawn together to give a more complete understanding. Increasingly, combinatorial techniques are now used, including correlative atomic force microscopy and fluorescence imaging, to probe questions closer to native physiological behaviour. We identify the trade-offs, limitations and applications of these techniques, and discuss exciting new directions.

Measuring Single-Molecule Twist and Torque in Multiplexed Magnetic Tweezers

Magnetic tweezers permit application of precisely calibrated stretching forces to nucleic acid molecules tethered between a surface and superparamagnetic beads. In addition, magnetic tweezers can control the tethers' twist. Here, we focus on recent extensions of the technique that expand the capabilities of conventional magnetic tweezers by enabling direct measurements of single-molecule torque and twist. Magnetic torque tweezers (MTT) still control the DNA or RNA tether's twist, but directly measure molecular torque by monitoring changes in the equilibrium rotation angle upon overwinding and underwinding of the tether. In freely orbiting magnetic tweezers (FOMT), one end of the tether is allowed to rotate freely, while still applying stretching forces and monitoring rotation angle. Both MTT and FOMT have provided unique insights into the mechanical properties, structural transitions, and interactions of DNA and RNA. Here, we provide step-by-step protocols to carry out FOMT and MTT measurements. In particular, we focus on multiplexed measurements, i.e., measurements that record data for multiple nucleic acid tethers at the same time, to improve statistics and to facilitate the observation of rare events.

Probing the salt dependence of the torsional stiffness of DNA by multiplexed magnetic torque tweezers

The mechanical properties of DNA fundamentally constrain and enable the storage and transmission of genetic information and its use in DNA nanotechnology. Many properties of DNA depend on the ionic environment due to its highly charged backbone. In particular, both theoretical analyses and direct single-molecule experiments have shown its bending stiffness to depend on salt concentration. In contrast, the salt-dependence of the twist stiffness of DNA is much less explored. Here, we employ optimized multiplexed magnetic torque tweezers to study the torsional stiffness of DNA under varying salt conditions as a function of stretching force. At low forces (<3 pN), the effective torsional stiffness is ∼10% smaller for high salt conditions (500 mM NaCl or 10 mM MgCl₂) compared to lower salt concentrations (20 mM NaCl and 100 mM NaCl). These differences, however, can be accounted for by taking into account the known salt dependence of the bending stiffness. In addition, the measured high-force (6.5 pN) torsional stiffness values of C = 103 ± 4 nm are identical, within experimental errors, for all tested salt concentration, suggesting that the intrinsic torsional stiffness of DNA does not depend on salt.

Applying torque to the Escherichia coli flagellar motor using magnetic tweezers

The bacterial flagellar motor of Escherichia coli is a nanoscale rotary engine essential for bacterial propulsion. Studies on the power output of single motors rely on the measurement of motor torque and rotation under external load. Here, we investigate the use of magnetic tweezers, which in principle allow the application and active control of a calibrated load torque, to study single flagellar motors in Escherichia coli. We manipulate the external load on the motor by adjusting the magnetic field experienced by a magnetic bead linked to the motor, and we probe the motor’s response. A simple model describes the average motor speed over the entire range of applied fields. We extract the motor torque at stall and find it to be similar to the motor torque at drag-limited speed. In addition, use of the magnetic tweezers allows us to force motor rotation in both forward and backward directions. We monitor the motor’s performance before and after periods of forced rotation and observe no destructive effects on the motor. Our experiments show how magnetic tweezers can provide active and fast control of the external load while also exposing remaining challenges in calibration. Through their non-invasive character and straightforward parallelization, magnetic tweezers provide an attractive platform to study nanoscale rotary motors at the single-motor level.

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.

DNA supercoiling during transcription

The twin-supercoiled-domain model describes how transcription can drive DNA supercoiling, and how DNA supercoiling, in turn plays an important role in regulating gene transcription. In vivo and in vitro experiments have disclosed many details of the complex interactions in this relationship, and recently new insights have been gained with the help of genome-wide DNA supercoiling mapping techniques and single molecule methods. This review summarizes the general mechanisms of the interplay between DNA supercoiling and transcription, considers the biological implications, and focuses on recent important discoveries and technical advances in this field. We highlight the significant impact of DNA supercoiling in transcription, but also more broadly in all processes operating on DNA.

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.

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.

Force Spectroscopy in Studying Infection

Biophysical force spectroscopy tools-for example, optical tweezers, magnetic tweezers, atomic force microscopy-have been used to study elastic, mechanical, conformational and dynamic properties of single biological specimens from single proteins to whole cells to reveal information not accessible by ensemble average methods such as X-ray crystallography, mass spectroscopy, gel electrophoresis and so on. Here, we review the application of these tools on a range of infection-related questions from antibody-inhibited protein processivity to virus-cell adhesion. In each case, we focus on how the instrumental design tailored to the biological system in question translates into the functionality suitable for that particular study. The unique insights that force spectroscopy has gained to complement knowledge learned through population averaging techniques in interrogating biomolecular details prove to be instrumental in therapeutic innovations such as those in structure-based drug design.

Biological magnetometry: torque on superparamagnetic beads in magnetic fields

Superparamagnetic beads are widely used in biochemistry and single-molecule biophysics, but the nature of the anisotropy that enables the application of torques remains controversial. To quantitatively investigate the torques experienced by superparamagnetic particles, we use a biological motor to rotate beads in a magnetic field and demonstrate that the underlying potential is π periodic. In addition, we tether a bead to a single DNA molecule and show that the angular trap stiffness increases nonlinearly with magnetic field strength. Our results indicate that the superparamagnetic beads' anisotropy derives from a nonuniform intrabead distribution of superparamagnetic nanoparticles.

Single-molecule portrait of DNA and RNA double helices

The composition and geometry of the genetic information carriers were described as double-stranded right helices sixty years ago. The flexibility of their sugar-phosphate backbones and the chemistry of their nucleotide subunits, which give rise to the RNA and DNA polymers, were soon reported to generate two main structural duplex states with biological relevance: the so-called A and B forms. Double-stranded (ds) RNA adopts the former whereas dsDNA is stable in the latter. The presence of flexural and torsional stresses in combination with environmental conditions in the cell or in the event of specific sequences in the genome can, however, stabilize other conformations. Single-molecule manipulation, besides affording the investigation of the elastic response of these polymers, can test the stability of their structural states and transition models. This approach is uniquely suited to understanding the basic features of protein binding molecules, the dynamics of molecular motors and to shedding more light on the biological relevance of the information blocks of life. Here, we provide a comprehensive single-molecule analysis of DNA and RNA double helices in the context of their structural polymorphism to set a rigorous interpretation of their material response both inside and outside the cell. From early knowledge of static structures to current dynamic investigations, we review their phase transitions and mechanochemical behaviour and harness this fundamental knowledge not only through biological sciences, but also for Nanotechnology and Nanomedicine.

Quantifying bacterial adhesion on antifouling polymer brushes via single-cell force spectroscopy

The adhesion forces between a single bacterial cell and different polymer brushes were measured directly with an atomic force microscope and correlated with their resistance to fouling.

A force calibration standard for magnetic tweezers

To study the behavior of biological macromolecules and enzymatic reactions under force, advances in single-molecule force spectroscopy have proven instrumental. Magnetic tweezers form one of the most powerful of these techniques, due to their overall simplicity, non-invasive character, potential for high throughput measurements, and large force range. Drawbacks of magnetic tweezers, however, are that accurate determination of the applied forces can be challenging for short biomolecules at high forces and very time-consuming for long tethers at low forces below ∼1 piconewton. Here, we address these drawbacks by presenting a calibration standard for magnetic tweezers consisting of measured forces for four magnet configurations. Each such configuration is calibrated for two commonly employed commercially available magnetic microspheres. We calculate forces in both time and spectral domains by analyzing bead fluctuations. The resulting calibration curves, validated through the use of different algorithms that yield close agreement in their determination of the applied forces, span a range from 100 piconewtons down to tens of femtonewtons. These generalized force calibrations will serve as a convenient resource for magnetic tweezers users and diminish variations between different experimental configurations or laboratories.

Magnetic steering control of multi-cellular bio-hybrid microswimmers

Bio-hybrid devices, which integrate biological cells with synthetic components, have opened a new path in miniaturized systems with the potential to provide actuation and control for systems down to a few microns in size. Here, we address the challenge of remotely controlling bio-hybrid microswimmers propelled by multiple bacterial cells. These devices have been proposed as a viable method for targeted drug delivery but have also been shown to exhibit stochastic motion. We demonstrate a method of remote magnetic control that significantly reduces the stochasticity of the motion, enabling steering control. The demonstrated microswimmers consist of multiple Serratia marcescens (S. marcescens) bacteria attached to a 6 μm-diameter superparamagnetic bead. We characterize their motion and define the parameters governing their controllability. We show that the microswimmers can be controlled along two-dimensional (2-D) trajectories using weak magnetic fields (≤10 mT) and can achieve 2-D swimming speeds up to 7.3 μm s(-1). This magnetic steering approach can be integrated with sensory-based steering in future work, enabling new control strategies for bio-hybrid microsystems.

Blind predictions of DNA and RNA tweezers experiments with force and torque

Single-molecule tweezers measurements of double-stranded nucleic acids (dsDNA and dsRNA) provide unprecedented opportunities to dissect how these fundamental molecules respond to forces and torques analogous to those applied by topoisomerases, viral capsids, and other biological partners. However, tweezers data are still most commonly interpreted post facto in the framework of simple analytical models. Testing falsifiable predictions of state-of-the-art nucleic acid models would be more illuminating but has not been performed. Here we describe a blind challenge in which numerical predictions of nucleic acid mechanical properties were compared to experimental data obtained recently for dsRNA under applied force and torque. The predictions were enabled by the HelixMC package, first presented in this paper. HelixMC advances crystallography-derived base-pair level models (BPLMs) to simulate kilobase-length dsDNAs and dsRNAs under external forces and torques, including their global linking numbers. These calculations recovered the experimental bending persistence length of dsRNA within the error of the simulations and accurately predicted that dsRNA's “spring-like” conformation would give a two-fold decrease of stretch modulus relative to dsDNA. Further blind predictions of helix torsional properties, however, exposed inaccuracies in current BPLM theory, including three-fold discrepancies in torsional persistence length at the high force limit and the incorrect sign of dsRNA link-extension (twist-stretch) coupling. Beyond these experiments, HelixMC predicted that ‘nucleosome-excluding’ poly(A)/poly(T) is at least two-fold stiffer than random-sequence dsDNA in bending, stretching, and torsional behaviors; Z-DNA to be at least three-fold stiffer than random-sequence dsDNA, with a near-zero link-extension coupling; and non-negligible effects from base pair step correlations. We propose that experimentally testing these predictions should be powerful next steps for understanding the flexibility of dsDNA and dsRNA in sequence contexts and under mechanical stresses relevant to their biology.

DNA and RNA are fundamental molecules in the central dogma of molecular biology. Many biological behaviors of double-stranded DNA and RNA – including transcription/translation by proteins and packaging into compact structures – depend on their ability to flex and twist. Single-molecule tweezers now provide accurate mechanical measurements of DNA and RNA helices under force and torque but have not been used to rigorously falsify and thereby advance computational models. Here we present the first such blind challenge, involving recent dsRNA tweezers data that were kept hidden from modelers and a new HelixMC toolkit that resolves challenges in simulating long double helices from base-pair level models. The predictions gave excellent agreement with bending and stretching measurements of dsRNA but failed to recover twisting properties, pinpointing a critical area of future investigation. HelixMC also predicted that poly(A)/poly(T) and Z-DNA–biologically important variants whose elastic responses have not been studied with tweezers–will have distinct mechanical properties. These results open a route to iteratively falsifying and refining computational models of long nucleic acid helices, as is necessary for attaining a predictive understanding of their biological behaviors.

Torque correlation length and stochastic twist dynamics of DNA

We introduce a short correlation length for torque in twisting-stiff biomolecules, which is necessary for the physical property that torque fluctuations be finite in amplitude. We develop a nonequilibrium theory of dynamics of DNA twisting which predicts two crossover time scales for temporal torque correlations in single-molecule experiments. Bending fluctuations can be included, and at linear order we find that they do not affect the twist dynamics. However, twist fluctuations affect bending, and we predict the spatial inhomogeneity of twist, torque, and buckling arising in nonequilibrium "rotor-bead" experiments.

Gold rotor bead tracking for high-speed measurements of DNA twist, torque and extension

Simultaneous measurements of DNA twist and extension have been used to measure physical properties of the double helix and to characterize structural dynamics and mechanochemistry in nucleoprotein complexes. However, the spatiotemporal resolution of twist measurements has been limited by the use of angular probes with large rotational drags, preventing the detection of short-lived intermediates or small angular steps. Here we introduce AuRBT, demonstrating a >100X improvement in time resolution over previous techniques. AuRBT employs gold nanoparticles as bright low-drag rotational and extensional probes, relying on instrumentation that combines magnetic tweezers with objective-side evanescent darkfield microscopy. In an initial application to molecular motor mechanism, we have examined the high-speed structural dynamics of DNA gyrase, revealing an unanticipated transient intermediate. AuRBT also enables direct measurements of DNA torque with >50X shorter integration times than previous techniques; here we demonstrate high-resolution torque spectroscopy by mapping the conformational landscape of a Z-forming DNA sequence.

In silico single-molecule manipulation of DNA with rigid body dynamics

We develop a new powerful method to reproduce in silico single-molecule manipulation experiments. We demonstrate that flexible polymers such as DNA can be simulated using rigid body dynamics thanks to an original implementation of Langevin dynamics in an open source library called Open Dynamics Engine. We moreover implement a global thermostat which accelerates the simulation sampling by two orders of magnitude. We reproduce force-extension as well as rotation-extension curves of reference experimental studies. Finally, we extend the model to simulations where the control parameter is no longer the torsional strain but instead the torque, and predict the expected behavior for this case which is particularly challenging theoretically and experimentally.

Video game techniques are designed to simulate rigid body dynamics of macroscopic bodies, e.g. characters or vehicles, in a realistic manner. However they are not able to deal with temperature effects, hence they are not able to deal with molecules. In order to extend these powerful techniques to molecular modeling, we implement here Langevin Dynamics in an open source library called Open Dynamics Engine. Moreover we add a “global thermostat” to this Langevin Dynamics, which accelerates the simulation sampling by two orders of magnitude. With these radically new simulation techniques, we prove that we can accurately reproduce single-molecule manipulation experiments in silico, in particular force-extension as well as rotation-extension curves of reference experimental studies. The method developed here represents an unparalleled tool for the study of more complex single molecule manipulation experiments, notably when DNA interacts with proteins. Furthermore the simulation technique that we propose here has all the functionalities required to tackle the nuclear organization of chromosomes at every length scale, from DNA to whole nuclei.

Torque measurement at the single-molecule level

Methods for exerting and measuring forces on single molecules have revolutionized the study of the physics of biology. However, it is often the case that biological processes involve rotation or torque generation, and these parameters have been more difficult to access experimentally. Recent advances in the single-molecule field have led to the development of techniques that add the capability of torque measurement. By combining force, displacement, torque, and rotational data, a more comprehensive description of the mechanics of a biomolecule can be achieved. In this review, we highlight a number of biological processes for which torque plays a key mechanical role. We describe the various techniques that have been developed to directly probe the torque experienced by a single molecule, and detail a variety of measurements made to date using these new technologies. We conclude by discussing a number of open questions and propose systems of study that would be well suited for analysis with torsional measurement techniques.

Magnetic tweezers measurements of the nanomechanical stability of DNA against denaturation at various conditions of pH and ionic strength

The opening of DNA double strands is extremely relevant to several biological functions, such as replication and transcription or binding of specific proteins. Such opening phenomenon is particularly sensitive to the aqueous solvent conditions in which the DNA molecule is dispersed, as it can be observed by considering the classical dependence of DNA melting temperature on pH and salt concentration. In the present work, we report a single-molecule study of the stability of DNA against denaturation when subjected to changes in solvent. We investigated the appearance of DNA instability under specific external applied force and imposed twist values, which was revealed by an increase in the temporal fluctuations in the DNA extension. These fluctuations occur in the presence of a continuous interval of equilibrium states, ranging from a plectonemic state to a state characterized by denaturation bubbles. In particular, we observe the fluctuations only around a characteristic force value. Moreover, this characteristic force is demonstrated to be notably sensitive to variations in the pH and ionic strength. Finally, an extension of a theoretical model of plectoneme formation is used to estimate the average denaturation energy, which is found to be linearly correlated to the melting temperature of the DNA double strands.

Electromagnetic torque tweezers: a versatile approach for measurement of single-molecule twist and torque

The well-established single-molecule force-spectroscopy techniques have recently been complemented by methods that can measure torque and twist directly, notably magnetic torque tweezers and the optical torque wrench. A limitation of the current torque measurement schemes is the intrinsic coupling between the force and torque degrees of freedom. Here we present electromagnetic torque tweezers (eMTT) that combine permanent and electromagnets to enable independent control of the force and torsional trap stiffness for sensitive measurements of single molecule torque and twist. Using the eMTT, we demonstrate sensitive torque measurements on tethered DNA molecules from simple tracking of the beads' (x,y)-position, obviating the need for any angular tracking algorithms or markers. Employing the eMTT for high-resolution torque measurements, we experimentally confirm the theoretically predicted torque overshoot at the DNA buckling transition in high salt conditions. We envision that the flexibility and control afforded by the eMTT will enable a range of new torque and twist measurement schemes from single-molecules to living cells.

Multifunctional magnetic rotator for micro and nanorheological studies

We report on the development of a multifunctional magnetic rotator that has been built and used during the last five years by two groups from Clemson and Drexel Universities studying the rheological properties of microdroplets. This magnetic rotator allows one to generate rotating magnetic fields in a broad frequency band, from hertz to tens kilohertz. We illustrate its flexibility and robustness by conducting the rheological studies of simple and polymeric fluids at the nano and microscale. First we reproduce a temperature-dependent viscosity of a synthetic oil used as a viscosity standard. Magnetic rotational spectroscopy with suspended nickel nanorods was used in these studies. As a second example, we converted the magnetic rotator into a pump with precise controlled flow modulation. Using multiwalled carbon nanotubes, we were able to estimate the shear modulus of sickle hemoglobin polymer. We believe that this multifunctional magnetic system will be useful not only for micro and nanorheological studies, but it will find much broader applications requiring remote controlled manipulation of micro and nanoobjects.

Recent developments in single-molecule DNA mechanics

Over the past two decades, measurements on individual stretched and twisted DNA molecules have helped define the basic elastic properties of the double helix and enabled real-time functional assays of DNA-associated molecular machines. Recently, new magnetic tweezers approaches for simultaneously measuring freely fluctuating twist and extension have begun to shed light on the structural dynamics of large nucleoprotein complexes. Related technical advances have facilitated direct measurements of DNA torque, contributing to a better understanding of abrupt structural transitions in mechanically stressed DNA. The new measurements have also been exploited in studies that hint at a developing synergistic relationship between single-molecule manipulation and structural DNA nanotechnology.

Torque measurements reveal sequence-specific cooperative transitions in supercoiled DNA

B-DNA becomes unstable under superhelical stress and is able to adopt a wide range of alternative conformations including strand-separated DNA and Z-DNA. Localized sequence-dependent structural transitions are important for the regulation of biological processes such as DNA replication and transcription. To directly probe the effect of sequence on structural transitions driven by torque, we have measured the torsional response of a panel of DNA sequences using single molecule assays that employ nanosphere rotational probes to achieve high torque resolution. The responses of Z-forming d(pGpC)(n) sequences match our predictions based on a theoretical treatment of cooperative transitions in helical polymers. "Bubble" templates containing 50-100 bp mismatch regions show cooperative structural transitions similar to B-DNA, although less torque is required to disrupt strand-strand interactions. Our mechanical measurements, including direct characterization of the torsional rigidity of strand-separated DNA, establish a framework for quantitative predictions of the complex torsional response of arbitrary sequences in their biological context.

Direct mechanical measurements reveal the material properties of three-dimensional DNA origami

The application of three-dimensional DNA origami objects as rigid mechanical mediators or force sensing elements requires detailed knowledge about their complex mechanical properties. Using magnetic tweezers, we directly measure the bending and torsional rigidities of four- and six-helix bundles assembled by this technique. Compared to duplex DNA, we find the bending rigidities to be greatly increased while the torsional rigidities are only moderately augmented. We present a mechanical model explicitly including the crossovers between the individual helices in the origami structure that reproduces the experimentally observed behavior. Our results provide an important basis for the future application of 3D DNA origami in nanomechanics.

A method to track rotational motion for use in single-molecule biophysics

The double helical nature of DNA links many cellular processes such as DNA replication, transcription, and repair to rotational motion and the accumulation of torsional strain. Magnetic tweezers (MTs) are a single-molecule technique that enables the application of precisely calibrated stretching forces to nucleic acid tethers and to control their rotational motion. However, conventional magnetic tweezers do not directly monitor rotation or measure torque. Here, we describe a method to directly measure rotational motion of particles in MT. The method relies on attaching small, non-magnetic beads to the magnetic beads to act as fiducial markers for rotational tracking. CCD images of the beads are analyzed with a tracking algorithm specifically designed to minimize crosstalk between translational and rotational motion: first, the in-plane center position of the magnetic bead is determined with a kernel-based tracker, while subsequently the height and rotation angle of the bead are determined via correlation-based algorithms. Evaluation of the tracking algorithm using both simulated images and recorded images of surface-immobilized beads demonstrates a rotational resolution of 0.1°, while maintaining a translational resolution of 1-2 nm. Example traces of the rotational fluctuations exhibited by DNA-tethered beads confined in magnetic potentials of varying stiffness demonstrate the robustness of the method and the potential for simultaneous tracking of multiple beads. Our rotation tracking algorithm enables the extension of MTs to magnetic torque tweezers (MTT) to directly measure the torque in single molecules. In addition, we envision uses of the algorithm in a range of biophysical measurements, including further extensions of MT, tethered particle motion, and optical trapping measurements.

Freely orbiting magnetic tweezers to directly monitor changes in the twist of nucleic acids

The double-stranded nature of DNA links its replication, transcription and repair to rotational motion and torsional strain. Magnetic tweezers (MT) are a powerful single-molecule technique to apply both forces and torques to individual DNA or RNA molecules. However, conventional MT do not track rotational motion directly and constrain the free rotation of the nucleic acid tether. Here we present freely orbiting MT (FOMT) that allow the measurement of equilibrium fluctuations and changes in the twist of tethered nucleic acid molecules. Using a precisely aligned vertically oriented magnetic field, FOMT enable tracking of the rotation angle from straight forward (x,y)-position tracking and permits the application of calibrated stretching forces, without biasing the tether's free rotation. We utilize FOMT to measure the force-dependent torsional stiffness of DNA from equilibrium rotational fluctuations and to follow the assembly of recombination protein A filaments on DNA.

Rotational motion and torsional strain affects DNA replication, transcription and repair. Lipfert et al. have developed a new technique that uses freely orbiting magnetic tweezers to measure equilibrium fluctuations and determine the twist of tethered nucleic acid molecules.

A novel constant-force scanning probe incorporating mechanical-magnetic coupled structures

A one-dimensional scanning probe with constant measuring force is designed and fabricated by utilizing the negative stiffness of the magnetic coupled structure, which mainly consists of the magnetic structure, the parallel guidance mechanism, and the pre-stressed spring. Based on the theory of material mechanics and the equivalent surface current model for computing the magnetic force, the analytical model of the scanning probe subjected to multi-forces is established, and the nonlinear relationship between the measuring force and the probe displacement is obtained. The practicability of introducing magnetic coupled structure in the constant-force probe is validated by the consistency of the results in numerical simulation and experiments.