Torque spectroscopy for the study of rotary motion in biological systems

Single-molecule force spectroscopy of toehold-mediated strand displacement

Toehold-mediated strand displacement (TMSD) is extensively utilized in dynamic DNA nanotechnology and for a wide range of DNA or RNA-based reaction circuits. Investigation of TMSD kinetics typically relies on bulk fluorescence measurements providing effective, bulk-averaged reaction rates. Information on individual molecules or even base pairs is scarce. In this work, we explore the dynamics of strand displacement processes at the single-molecule level using single-molecule force spectroscopy with a microfluidics-enhanced optical trap supported by state-of-the-art coarse-grained simulations. By applying force, we can trigger and observe TMSD in real-time with microsecond and nanometer resolution. We find TMSD proceeds very rapidly under load with single step times of 1 µs. Tuning invasion efficiency by introducing mismatches allows studying thousands of forward/backward invasion events on a single molecule and analyze the kinetics of the invasion process. Extrapolation to zero force reveals single step times for DNA invading DNA four times faster than for RNA invading RNA. We also study the kinetics of DNA invading RNA, a process that in the absence of force would rarely occur. Our results reveal the importance of sequence effects for the TMSD process and have relevance for a wide range of applications in nucleic acid nanotechnology and synthetic biology.

Epigenetic Histone Modifications H3K36me3 and H4K5/8/12/16ac Induce Open Polynucleosome Conformations via Different Mechanisms

Nucleosomes are the basic compaction unit of chromatin and nucleosome structure and their higher-order assemblies regulate genome accessibility. Many post-translational modifications alter nucleosome dynamics, nucleosome-nucleosome interactions, and ultimately chromatin structure and gene expression. Here, we investigate the role of two post-translational modifications associated with actively transcribed regions, H3K36me3 and H4K5/8/12/16ac, in the contexts of tri-nucleosome arrays that provide a tractable model system for quantitative single-molecule analysis, while enabling us to probe nucleosome-nucleosome interactions. Direct visualization by AFM imaging reveals that H3K36me3 and H4K5/8/12/16ac nucleosomes adopt significantly more open and loose conformations than unmodified nucleosomes. Similarly, magnetic tweezers force spectroscopy shows a reduction in DNA outer turn wrapping and nucleosome-nucleosome interactions for the modified nucleosomes. The results suggest that for H3K36me3 the increased breathing and outer DNA turn unwrapping seen in mononucleosomes propagates to more open conformations in nucleosome arrays. In contrast, the even more open structures of H4K5/8/12/16ac nucleosome arrays do not appear to derive from the dynamics of the constituent mononucleosomes, but are driven by reduced nucleosome-nucleosome interactions, suggesting that stacking interactions can overrule DNA breathing of individual nucleosomes. We anticipate that our methodology will be broadly applicable to reveal the influence of other post-translational modifications and to observe the activity of nucleosome remodelers.

Supercoiling-dependent DNA binding: quantitative modeling and applications to bulk and single-molecule experiments

DNA stores our genetic information and is ubiquitous in applications, where it interacts with binding partners ranging from small molecules to large macromolecular complexes. Binding is modulated by mechanical strains in the molecule and can change local DNA structure. Frequently, DNA occurs in closed topological forms where topology and supercoiling add a global constraint to the interplay of binding-induced deformations and strain-modulated binding. Here, we present a quantitative model with a straight-forward numerical implementation of how the global constraints introduced by DNA topology modulate binding. We focus on fluorescent intercalators, which unwind DNA and enable direct quantification via fluorescence detection. Our model correctly describes bulk experiments using plasmids with different starting topologies, different intercalators, and over a broad range of intercalator and DNA concentrations. We demonstrate and quantitatively model supercoiling-dependent binding in a single-molecule assay, where we directly observe the different intercalator densities going from supercoiled to nicked DNA. The single-molecule assay provides direct access to binding kinetics and DNA supercoil dynamics. Our model has broad implications for the detection and quantification of DNA, including the use of psoralen for UV-induced DNA crosslinking to quantify torsional tension in vivo, and for the modulation of DNA binding in cellular contexts.

High-yield ligation-free assembly of DNA constructs with nucleosome positioning sequence repeats for single-molecule manipulation assays

Force and torque spectroscopy have provided unprecedented insights into the mechanical properties, conformational transitions, and dynamics of DNA and DNA-protein complexes, notably nucleosomes. Reliable single-molecule manipulation measurements require, however, specific and stable attachment chemistries to tether the molecules of interest. Here, we present a functionalization strategy for DNA that enables high-yield production of constructs for torsionally constrained and very stable attachment. The method is based on two subsequent PCRs: first ∼380 bp long DNA strands are generated that contain multiple labels, which are used as "megaprimers" in a second PCR to generate ∼kbp long double-stranded DNA constructs with multiple labels at the respective ends. To achieve high-force stability, we use dibenzocyclooctyne-based click chemistry for covalent attachment to the surface and biotin-streptavidin coupling to the bead. The resulting tethers are torsionally constrained and extremely stable under load, with an average lifetime of 70 ± 3 h at 45 pN. The high yield of the approach enables nucleosome reconstitution by salt dialysis on the functionalized DNA, and we demonstrate proof-of-concept measurements on nucleosome assembly statistics and inner turn unwrapping under force. We anticipate that our approach will facilitate a range of studies of DNA interactions and nucleoprotein complexes under forces and torques.

DNA fluctuations reveal the size and dynamics of topological domains

DNA supercoiling is a key regulatory mechanism that orchestrates DNA readout, recombination, and genome maintenance. DNA-binding proteins often mediate these processes by bringing two distant DNA sites together, thereby inducing (transient) topological domains. In order to understand the dynamics and molecular architecture of protein-induced topological domains in DNA, quantitative and time-resolved approaches are required. Here, we present a methodology to determine the size and dynamics of topological domains in supercoiled DNA in real time and at the single-molecule level. Our approach is based on quantifying the extension fluctuations-in addition to the mean extension-of supercoiled DNA in magnetic tweezers (MT). Using a combination of high-speed MT experiments, Monte Carlo simulations, and analytical theory, we map out the dependence of DNA extension fluctuations as a function of supercoiling density and external force. We find that in the plectonemic regime, the extension variance increases linearly with increasing supercoiling density and show how this enables us to determine the formation and size of topological domains. In addition, we demonstrate how the transient (partial) dissociation of DNA-bridging proteins results in the dynamic sampling of different topological states, which allows us to deduce the torsional stiffness of the plectonemic state and the kinetics of protein-plectoneme interactions. We expect our results to further the understanding and optimization of magnetic tweezer measurements and to enable quantification of the dynamics and reaction pathways of DNA processing enzymes in the context of physiologically relevant forces and supercoiling densities.

Recent Progress on Optical Micro/Nanomanipulations: Structured Forces, Structured Particles, and Synergetic Applications

Optical manipulation has achieved great success in the fields of biology, micro/nano robotics and physical sciences in the past few decades. To date, the optical manipulation is still witnessing substantial progress powered by the growing accessibility of the complex light field, advanced nanofabrication and developed understandings of light-matter interactions. In this perspective, we highlight recent advancements of optical micro/nanomanipulations in cutting-edge applications, which can be fostered by structured optical forces enabled with diverse auxiliary multiphysical field/forces and structured particles. We conclude with our vision of ongoing and futuristic directions, including heat-avoided and heat-utilized manipulation, nonlinearity-mediated trapping and manipulation, metasurface/two-dimensional material based optical manipulation, as well as interface-based optical manipulation.

Twisting DNA by salt

The structure and properties of DNA depend on the environment, in particular the ion atmosphere. Here, we investigate how DNA twist -one of the central properties of DNA- changes with concentration and identity of the surrounding ions. To resolve how cations influence the twist, we combine single-molecule magnetic tweezer experiments and extensive all-atom molecular dynamics simulations. Two interconnected trends are observed for monovalent alkali and divalent alkaline earth cations. First, DNA twist increases monotonously with increasing concentration for all ions investigated. Second, for a given salt concentration, DNA twist strongly depends on cation identity. At 100 mM concentration, DNA twist increases as Na+ < K+ < Rb+ < Ba2+ < Li+ ≈ Cs+ < Sr2+ < Mg2+ < Ca2+. Our molecular dynamics simulations reveal that preferential binding of the cations to the DNA backbone or the nucleobases has opposing effects on DNA twist and provides the microscopic explanation of the observed ion specificity. However, the simulations also reveal shortcomings of existing force field parameters for Cs+ and Sr2+. The comprehensive view gained from our combined approach provides a foundation for understanding and predicting cation-induced structural changes both in nature and in DNA nanotechnology.

Magnetic bio-hybrid micro actuators

Over the past two decades, there has been a growing body of work on wireless devices that can operate on the length scales of biological cells and even smaller. A class of these devices receiving increasing attention are referred to as bio-hybrid actuators: tools that integrate biological cells or subcellular parts with synthetic or inorganic components. These devices are commonly controlled through magnetic manipulation as magnetic fields and gradients can be generated with a high level of control. Recent work has demonstrated that magnetic bio-hybrid actuators can address common challenges in small scale fabrication, control, and localization. Additionally, it is becoming apparent that these magnetically driven bio-hybrid devices can display high efficiency and, in many cases, have the potential for self-repair and even self-replication. Combining these properties with magnetically driven forces and torques, which can be transmitted over significant distances, can be highly controlled, and are biologically safe, gives magnetic bio-hybrid actuators significant advantages over other classes of small scale actuators. In this review, we describe the theory and mechanisms required for magnetic actuation, classify bio-hybrid actuators by their diverse organic components, and discuss their current limitations. Insights into the future of coupling cells and cell-derived components with magnetic materials to fabricate multi-functional actuators are also provided.

Spin-Orbit Angular-Momentum Transfer from a Nanogap Surface Plasmon to a Trapped Nanodiamond

The ability to control the motion of single nanoparticles or molecules is currently one of the major scientific and technological challenges. Despite tremendous progress in the field of plasmonic nanotweezers, controlled nanoscale manipulation of nanoparticles trapped by a plasmonic nanogap antenna has not been reported yet. Here, we demonstrate the controlled orbital rotation of a single fluorescent nanodiamond trapped by a gold trimer nanoantenna irradiated by a rotating linearly polarized light or circularly polarized light. Remarkably, the rotation direction is opposite to the light's polarization rotation. We numerically show that this inversion comes from sequential excitation of individual nanotriangles in the reverse order when the linear polarization is rotated, whereas using a circular polarization, light-nanoparticle angular momentum transfer occurs via the generation of a Poynting vector vortex of reversed handedness. This work provides a new path for the control of light-matter angular momentum transfer using plasmonic nanogap antennas.

A molecular view of DNA flexibility

DNA dynamics can only be understood by taking into account its complex mechanical behavior at different length scales. At the micrometer level, the mechanical properties of single DNA molecules have been well-characterized by polymer models and are commonly quantified by a persistence length of 50 nm (~150 bp). However, at the base pair level (~3.4 Å), the dynamics of DNA involves complex molecular mechanisms that are still being deciphered. Here, we review recent single-molecule experiments and molecular dynamics simulations that are providing novel insights into DNA mechanics from such a molecular perspective. We first discuss recent findings on sequence-dependent DNA mechanical properties, including sequences that resist mechanical stress and sequences that can accommodate strong deformations. We then comment on the intricate effects of cytosine methylation and DNA mismatches on DNA mechanics. Finally, we review recently reported differences in the mechanical properties of DNA and double-stranded RNA, the other double-helical carrier of genetic information. A thorough examination of the recent single-molecule literature permits establishing a set of general 'rules' that reasonably explain the mechanics of nucleic acids at the base pair level. These simple rules offer an improved description of certain biological systems and might serve as valuable guidelines for future design of DNA and RNA nanostructures.

Non-contact long-range magnetic stimulation of mechanosensitive ion channels in freely moving animals

Among physical stimulation modalities, magnetism has clear advantages, such as deep penetration and untethered interventions in biological subjects. However, some of the working principles and effectiveness of existing magnetic neurostimulation approaches have been challenged, leaving questions to be answered. Here we introduce m-Torquer, a magnetic toolkit that mimics magnetoreception in nature. It comprises a nanoscale magnetic torque actuator and a circular magnet array, which deliver piconewton-scale forces to cells over a working range of ~70 cm. With m-Torquer, stimulation of neurons expressing bona fide mechanosensitive ion channel Piezo1 enables consistent and reproducible neuromodulation in freely moving mice. With its long working distance and cellular targeting capability, m-Torquer provides versatility in its use, which can range from single cells to in vivo systems, with the potential application in large animals such as primates.

Versatile Multilayer Metamaterial Nanoparticles with Tailored Optical Constants for Force and Torque Transduction

The ability to apply force and torque directly to micro- and nanoscale particles in optical traps has a wide range of applications. While full control of both force and torque in three dimensions has been realized using top-down fabrication of rod-shaped particles composed of birefringent crystalline materials, widespread usage of such particles is limited as the optical constants of the predominant birefringent materials (quartz SiO2 and rutile TiO2) preclude coverage of the full application space of optical trapping. Here, we show that multilayer metamaterial nanoparticles provide access to a wide range of optical constants that can be specifically tuned for each application. Selecting the material pair Nb2O5/SiO2 from the library of amorphous dielectrics as our metamaterial, we show that its refractive index and birefringence can be designed by adapting the ratio of layer thicknesses. Using a robust top-down fabrication process, we show that uniformly sized, free-floating Nb2O5/SiO2 particles with high birefringence at moderate refractive index are obtained at high yield. Using an optical torque wrench, we show that these particles function as joint force and torque transducers while maintaining excellent stability in aqueous solutions and can be controllably optimized for particular physical characteristics such as maximal torque transfer or rapid response time. We expect that such customizable birefringent metamaterial nanoparticles whose properties surpass those of conventional crystalline particles will provide a means to unleash the full potential of optical trapping applications.

Designed anchoring geometries determine lifetimes of biotin-streptavidin bonds under constant load and enable ultra-stable coupling

The small molecule biotin and the homotetrameric protein streptavidin (SA) form a stable and robust complex that plays a pivotal role in many biotechnological and medical applications. In particular, the SA-biotin linkage is frequently used in single-molecule force spectroscopy (SMFS) experiments. Recent data suggest that SA-biotin bonds show strong directional dependence and a broad range of multi-exponential lifetimes under load. Here, we investigate engineered SA variants with different valencies and a unique tethering point under constant forces using a magnetic tweezers assay. We observed orders-of-magnitude differences in the lifetimes under force, which we attribute to the distinct force-loading geometries in the different SA variants. Lifetimes showed exponential dependencies on force, with extrapolated lifetimes at zero force that are similar for the different SA variants and agree with parameters determined from constant-speed dynamic SMFS experiments. We identified an especially long-lived tethering geometry that will facilitate ultra-stable SMFS experiments.

Force Spectroscopy on Single Molecules of Life

Biomolecules such as nucleic acids and proteins constitute the cells and its organelles that form the crucial components in all living organisms. They are associated with a variety of cellular processes during which they undergo conformational orientations. The structural rearrangements resulting from protein-protein, protein-DNA, and protein-drug interactions vary in spatial and temporal length scales. Force is one of the important key factors which regulate these interactions. The magnitude of the force can vary from sub-piconewtons to several thousands of piconewtons. Single-molecule force spectroscopy acts as a powerful tool which is capable of investigating mechanical stability and conformational rearrangements arising in biomolecules due to the above interactions. Real-time observation of conformational dynamics including access to rare or transient states and the estimation of mean dwell times using these tools aids in the kinetic analysis of these interactions. In this review, we highlight the capabilities of common force spectroscopy techniques such as optical tweezers, magnetic tweezers, and atomic force microscopy with case studies on emerging applications.

Dynamics of the Buckling Transition in Double-Stranded DNA and RNA

DNA under torsional strain undergoes a buckling transition that is the fundamental step in plectoneme nucleation and supercoil dynamics, which are critical for the processing of genomic information. Despite its importance, quantitative models of the buckling transition, in particular to also explain the surprising two-orders-of-magnitude difference between the buckling times for RNA and DNA revealed by single-molecule tweezers experiments, are currently lacking. Additionally, little is known about the configurations of the DNA during the buckling transition because they are not directly observable experimentally. Here, we use a discrete worm-like chain model and Brownian dynamics to simulate the DNA/RNA buckling transition. Our simulations are in good agreement with experimentally determined parameters of the buckling transition. The simulations show that the buckling time strongly and exponentially depends on the bending stiffness, which accounts for more than half the measured difference between DNA and RNA. Analyzing the microscopic conformations of the chain revealed by our simulations, we find clear evidence for a solenoid-shaped transition state and a curl intermediate. The curl intermediate features a single loop and becomes increasingly populated at low forces. Taken together, the simulations suggest that the worm-like chain model can account semiquantitatively for the buckling dynamics of both DNA and RNA.

The Dissociation Rate of Acetylacetonate Ligands Governs the Size of Ferrimagnetic Zinc Ferrite Nanocubes

Magnetic nanoparticles are critical to a broad range of applications from medical diagnostics and therapeutics to biotechnological processes and single-molecule manipulation. To advance these applications, facile and robust routes to synthesize highly magnetic nanoparticles over a wide size range are needed. Here, we demonstrate that changing the degassing temperature of thermal decomposition of metal acetylacetonate precursors from 90 to 25 °C tunes the size of ferrimagnetic Zn_xFe_3-xO₄ nanocubes from 25 to 100 nm, respectively. We show that degassing at 90 °C nearly entirely removes acetylacetone ligands from the reaction, which results in an early formation of monomers and a reaction-controlled growth following LaMer's model toward small nanocubes. In contrast, degassing at 25 °C only partially dissociates acetylacetone ligands from the metal center and triggers a delayed formation of monomers, which leads to intermediate assembled structures made of tiny irregular crystallites and an eventual formation of large nanocubes via a diffusion-controlled growth mechanism. Using complementary techniques, we determine the substitution fraction x of Zn²⁺ to be in the range of 0.35-0.37. Our method reduces the complexity of the thermal decomposition method by narrowing the synthesis parameter space to a single physical parameter and enables fabrication of highly magnetic and uniform zinc ferrite nanocubes over a broad size range. The resulting particles are promising for a range of applications from magnetic fluid hyperthermia to actuation of macromolecules.

Supercoiling DNA optically

Torsional stress plays a vital role in many genomic transactions, including replication and transcription, and often results in underwound (negatively supercoiled) DNA. Here, we present a single-molecule method, termed Optical DNA Supercoiling (ODS), that advances our ability to study negatively supercoiled DNA. Since ODS is based on dual-trap optical tweezers, it is compatible with a wide range of functionalities that are difficult to combine with traditional methods of DNA twist control. This includes the ability to image supercoiled DNA with fluorescence microscopy and move the supercoiled substrate rapidly between different buffer/protein solutions. We demonstrate that ODS yields unique and important insights into both the biomechanical properties of negatively supercoiled DNA and the dynamics of DNA–protein interactions on underwound DNA.

Cellular DNA is regularly subject to torsional stress during genomic processes, such as transcription and replication, resulting in a range of supercoiled DNA structures. For this reason, methods to prepare and study supercoiled DNA at the single-molecule level are widely used, including magnetic, angular-optical, micropipette, and magneto-optical tweezers. However, it is currently challenging to combine DNA supercoiling control with spatial manipulation and fluorescence microscopy. This limits the ability to study complex and dynamic interactions of supercoiled DNA. Here we present a single-molecule assay that can rapidly and controllably generate negatively supercoiled DNA using a standard dual-trap optical tweezers instrument. This method, termed Optical DNA Supercoiling (ODS), uniquely combines the ability to study supercoiled DNA using force spectroscopy, fluorescence imaging of the whole DNA, and rapid buffer exchange. The technique can be used to generate a wide range of supercoiled states, with between <5 and 70% lower helical twist than nonsupercoiled DNA. Highlighting the versatility of ODS, we reveal previously unobserved effects of ionic strength and sequence on the structural state of underwound DNA. Next, we demonstrate that ODS can be used to directly visualize and quantify protein dynamics on supercoiled DNA. We show that the diffusion of the mitochondrial transcription factor TFAM can be significantly hindered by local regions of underwound DNA. This finding suggests a mechanism by which supercoiling could regulate mitochondrial transcription in vivo. Taken together, we propose that ODS represents a powerful method to study both the biophysical properties and biological interactions of negatively supercoiled DNA.

Rotation tracking of genome-processing enzymes using DNA origami rotors

Many genome-processing reactions, such as transcription, replication and repair, generate DNA rotation. Methods that directly measure DNA rotation, including rotor bead tracking^1–3, angular optical trap⁴, and magnetic tweezers⁵ have helped unravel the action mechanisms of a range of genome-processing enzymes, such as RNA polymerase (RNAP)⁶, gyrase², viral DNA packaging motor⁷, and DNA recombination enzymes⁸. However, despite the potential of rotation measurements to transform our understanding of genome-processing reactions, measuring DNA rotation remains a difficult task. The time resolution of existing methods is insufficient to track rotation induced by many enzymes under physiological conditions, and the measurement throughput is typically low. Here we introduce Origami-Rotor-Based Imaging and Tracking (ORBIT), a method that uses fluorescently labeled DNA origami rotors to track DNA rotation at the single-molecule level with millisecond time resolution. We used ORBIT to track DNA rotation resulted from unwinding by RecBCD, a helicase involved in DNA repair⁹, and transcription by RNAP. We characterized a series of events during RecBCD-induced DNA unwinding, including initiation, processive translocation, pausing and backtracking, and revealed an initiation mechanism that involves reversible, ATP-independent DNA unwinding and engagement of the RecB motor. During transcription by RNAP, we directly observed rotational steps corresponding to single-base-pair unwinding. We envision ORBIT will enable studies of a wide range of protein-DNA interactions.

A Tour de Force on the Double Helix: Exploiting DNA Mechanics To Study DNA-Based Molecular Machines

DNA is both a fundamental building block of life and a fascinating natural polymer. The advent of single-molecule manipulation tools made it possible to exert controlled force on individual DNA molecules and measure their mechanical response. Such investigations elucidated the elastic properties of DNA and revealed its distinctive structural configurations across force regimes. In the meantime, a detailed understanding of DNA mechanics laid the groundwork for single-molecule studies of DNA-binding proteins and DNA-processing enzymes that bend, stretch, and twist DNA. These studies shed new light on the metabolism and transactions of nucleic acids, which constitute a major part of the cell's operating system. Furthermore, the marriage of single-molecule fluorescence visualization and force manipulation has enabled researchers to directly correlate the applied tension to changes in the DNA structure and the behavior of DNA-templated complexes. Overall, experimental exploitation of DNA mechanics has been and will continue to be a unique and powerful strategy for understanding how molecular machineries recognize and modify the physical state of DNA to accomplish their biological functions.

Single-Crystal Rutile TiO2 Nanocylinders are Highly Effective Transducers of Optical Force and Torque

Optical trapping of (sub)micron-sized particles is broadly employed in nanoscience and engineering. The materials commonly employed for these particles, however, have physical properties that limit the transfer of linear or angular momentum (or both). This reduces the magnitude of forces and torques, and the spatiotemporal resolution, achievable in linear and angular traps. Here, we overcome these limitations through the use of single-crystal rutile TiO₂, which has an exceptionally large optical birefringence, a high index of refraction, good chemical stability, and is amenable to geometric control at the nanoscale. We show that rutile TiO₂ nanocylinders form powerful joint force and torque transducers in aqueous environments by using only moderate laser powers to apply nN·nm torques at kHz rotational frequencies to tightly trapped particles. In doing so, we demonstrate how rutile TiO₂ nanocylinders outperform other materials and offer unprecedented opportunities to expand the control of optical force and torque at the nanoscale.

Single-molecule polarization microscopy of DNA intercalators sheds light on the structure of S-DNA

DNA structural transitions facilitate genomic processes, mediate drug-DNA interactions, and inform the development of emerging DNA-based biotechnology such as programmable materials and DNA origami. While some features of DNA conformational changes are well characterized, fundamental information such as the orientations of the DNA base pairs is unknown. Here, we use concurrent fluorescence polarization imaging and DNA manipulation experiments to probe the structure of S-DNA, an elusive, elongated conformation that can be accessed by mechanical overstretching. To this end, we directly quantify the orientations and rotational dynamics of fluorescent DNA-intercalated dyes. At extensions beyond the DNA overstretching transition, intercalators adopt a tilted (θ ~ 54°) orientation relative to the DNA axis, distinct from the nearly perpendicular orientation (θ ~ 90°) normally assumed at lower extensions. These results provide the first experimental evidence that S-DNA has substantially inclined base pairs relative to those of the standard (Watson-Crick) B-DNA conformation.

The temperature dependence of the helical twist of DNA

DNA is the carrier of all cellular genetic information and increasingly used in nanotechnology. Quantitative understanding and optimization of its functions requires precise experimental characterization and accurate modeling of DNA properties. A defining feature of DNA is its helicity. DNA unwinds with increasing temperature, even for temperatures well below the melting temperature. However, accurate quantitation of DNA unwinding under external forces and a microscopic understanding of the corresponding structural changes are currently lacking. Here we combine single-molecule magnetic tweezers measurements with atomistic molecular dynamics and coarse-grained simulations to obtain a comprehensive view of the temperature dependence of DNA twist. Experimentally, we find that DNA twist changes by ΔTw(T) = (-11.0 ± 1.2)°/(°C·kbp), independent of applied force, in the range of forces where torque-induced melting is negligible. Our atomistic simulations predict ΔTw(T) = (-11.1 ± 0.3)°/(°C·kbp), in quantitative agreement with experiments, and suggest that the untwisting of DNA with temperature is predominantly due to changes in DNA structure for defined backbone substates, while the effects of changes in substate populations are minor. Coarse-grained simulations using the oxDNA framework yield a value of ΔTw(T) = (-6.4 ± 0.2)°/(°C·kbp) in semi-quantitative agreement with experiments.

Rotation of a floating hydrophobic disk: influence of line tension

The rotation of a sub-millimeter size disk over a water bath is reported. The origin of the rotation arises from the transfer of angular momentum from a plane wave diffracted by an asymmetrical picture printed on the disk. Because of its hydrophobic character, the viscous friction contribution to the rotational motion of the object floating on the air/liquid interface is weak. From the driving optical torque and the steady-state rotation, we measure the contribution of the line tension in the femto-Newton range.

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.

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.

Kinesin rotates unidirectionally and generates torque while walking on microtubules

Cytoskeletal motors drive many essential cellular processes. For example, kinesin-1 transports cargo in a step-wise manner along microtubules. To resolve rotations during stepping, we used optical tweezers combined with an optical microprotractor and torsion balance using highly birefringent microspheres to directly and simultaneously measure the translocation, rotation, force, and torque generated by individual kinesin-1 motors. While, at low adenosine 5'-triphosphate (ATP) concentrations, motors did not generate torque, we found that motors translocating along microtubules at saturating ATP concentrations rotated unidirectionally, producing significant torque on the probes. Accounting for the rotational work makes kinesin a highly efficient machine. These results imply that the motor's gait follows a rotary hand-over-hand mechanism. Our method is generally applicable to study rotational and linear motion of molecular machines, and our findings have implications for kinesin-driven cellular processes.

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.

Optical Torque Wrench Design and Calibration

Expanding the capabilities of optical traps with angular control of the trapped particle has numerous potential applications in all fields where standard linear optical tweezers are employed. Here we describe in detail the construction, alignment, and calibration of the Optical Torque Wrench, a mode of function that can be added to linear optical tweezers to simultaneously apply and measure both force and torque on birefringent microscopic cylindrical particles. The interaction between the linear polarization of the laser and the birefringent cylinder creates an angular trap for the particle orientation, described by a periodic potential. As a consequence of the experimental control of the tilt of the periodic potential, the dynamical excitability of the system can be observed. Angular optical tweezers remain less widespread than their linear counterpart. We hope this technical guide can foster their development and new applications.

The dynamic interplay between DNA topoisomerases and DNA topology

Topological properties of DNA influence its structure and biochemical interactions. Within the cell, DNA topology is constantly in flux. Transcription and other essential processes, including DNA replication and repair, not only alter the topology of the genome but also introduce additional complications associated with DNA knotting and catenation. These topological perturbations are counteracted by the action of topoisomerases, a specialized class of highly conserved and essential enzymes that actively regulate the topological state of the genome. This dynamic interplay among DNA topology, DNA processing enzymes, and DNA topoisomerases is a pervasive factor that influences DNA metabolism in vivo. Building on the extensive structural and biochemical characterization over the past four decades that has established the fundamental mechanistic basis of topoisomerase activity, scientists have begun to explore the unique roles played by DNA topology in modulating and influencing the activity of topoisomerases. In this review we survey established and emerging DNA topology-dependent protein-DNA interactions with a focus on in vitro measurements of the dynamic interplay between DNA topology and topoisomerase activity.

Rotational friction of dipolar colloids measured by driven torsional oscillations

Despite its prominent role in the dynamics of soft materials, rotational friction remains a quantity that is difficult to determine for many micron-sized objects. Here, we demonstrate how the Stokes coefficient of rotational friction can be obtained from the driven torsional oscillations of single particles in a highly viscous environment. The idea is that the oscillation amplitude of a dipolar particle under combined static and oscillating fields provides a measure for the Stokes friction. From numerical studies we derive a semi-empirical analytic expression for the amplitude of the oscillation, which cannot be calculated analytically from the equation of motion. We additionally demonstrate that this expression can be used to experimentally determine the rotational friction coefficient of single particles. Here, we record the amplitudes of a field-driven dipolar Janus microsphere with optical microscopy. The presented method distinguishes itself in its experimental and conceptual simplicity. The magnetic torque leaves the local environment unchanged, which contrasts with other approaches where, for example, additional mechanical (frictional) or thermal contributions have to be regarded.

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.

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.

The Dynamic Interplay Between DNA Topoisomerases and DNA Topology

Topological properties of DNA influence its structure and biochemical interactions. Within the cell DNA topology is constantly in flux. Transcription and other essential processes including DNA replication and repair, alter the topology of the genome, while introducing additional complications associated with DNA knotting and catenation. These topological perturbations are counteracted by the action of topoisomerases, a specialized class of highly conserved and essential enzymes that actively regulate the topological state of the genome. This dynamic interplay among DNA topology, DNA processing enzymes, and DNA topoisomerases, is a pervasive factor that influences DNA metabolism in vivo. Building on the extensive structural and biochemical characterization over the past four decades that established the fundamental mechanistic basis of topoisomerase activity, the unique roles played by DNA topology in modulating and influencing the activity of topoisomerases have begun to be explored. In this review we survey established and emerging DNA topology dependent protein-DNA interactions with a focus on in vitro measurements of the dynamic interplay between DNA topology and topoisomerase activity.

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.

Tunable top-down fabrication and functional surface coating of single-crystal titanium dioxide nanostructures and nanoparticles

Titanium dioxide (TiO2) is a key component of diverse optical and electronic applications that exploit its exceptional material properties. In particular, the use of TiO2 in its single-crystalline phase can offer substantial advantages over its amorphous and polycrystalline phases for existing and yet-to-be-developed applications. However, the implementation of single-crystal TiO2 has been hampered by challenges in its fabrication and subsequent surface functionalization. Here, we introduce a novel top-down approach that allows for batch fabrication of uniform high-aspect-ratio single-crystal TiO2 nanostructures with targeted sidewall profiles. We complement our fabrication approach with a functionalization strategy that achieves dense, uniform, and area-selective coating with a variety of biomolecules. This allows us to fabricate single-crystal rutile TiO2 nanocylinders tethered with individual DNA molecules for use as force- and torque-transducers in an optical torque wrench. These developments provide the means for increased exploitation of the superior material properties of single-crystal TiO2 at the nanoscale.

Energy utilization in fluctuating biological energy converters

We have argued previously [Szoke et al., FEBS Lett. 553, 18-20 (2003); Curr. Chem. Biol. 1, 53-57 (2007)] that energy utilization and evolution are emergent properties based on a small number of established laws of physics and chemistry. The relevant laws constitute a framework for biology on a level intermediate between quantum chemistry and cell biology. There are legitimate questions whether these concepts are valid at the mesoscopic level. Such systems fluctuate appreciably, so it is not clear what their efficiency is. Advances in fluctuation theorems allow the description of such systems on a molecular level. We attempt to clarify this topic and bridge the biochemical and physical descriptions of mesoscopic systems.

Rotation of millimeter-sized objects using ordinary light

The ability to optically rotate bodies offers new degrees of control of micro-objects with applications in various domains, including microelectromechanical systems (MEMS), biomanipulations, or optofluidics. Here we demonstrate the optically-induced rotation of simple asymmetric two-dimensional objects using plane waves originating either from ordinary laser sources or from black body radiation. The objects are floating on an air/water interface. We observe a steady-state rotation depending on the light intensity and on the asymmetry of the object. We interpret this rotation in terms of light diffraction by the edges of the object. Such systems could be easily implemented in optofluidic devices to induce liquid flow without the need for special light sources.

Magneto-electrical orientation of lipid-coated graphitic micro-particles in solution

We demonstrate, for the first time, confinement of the orientation of graphitic micro-flakes to a well-defined plane in solution by applying two perpendicular fields: a vertical static magnetic field and a horizontal time-varying electric field.

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.