An optical apparatus for rotation and trapping

Optical torque calculations and measurements for DNA torsional studies

The angular optical trap (AOT) is a powerful instrument for measuring the torsional and rotational properties of a biological molecule. Thus far, AOT studies of DNA torsional mechanics have been carried out using a high numerical aperture oil-immersion objective, which permits strong trapping but inevitably introduces spherical aberrations due to the glass-aqueous interface. However, the impact of these aberrations on torque measurements is not fully understood experimentally, partly due to a lack of theoretical guidance. Here, we present a numerical platform based on the finite element method to calculate forces and torques on a trapped quartz cylinder. We have also developed a new experimental method to accurately determine the shift in the trapping position due to the spherical aberrations by using a DNA molecule as a distance ruler. We found that the calculated and measured focal shift ratios are in good agreement. We further determined how the angular trap stiffness depends on the trap height and the cylinder displacement from the trap center and found full agreement between predictions and measurements. As a further verification of the methodology, we showed that DNA torsional properties, which are intrinsic to DNA, could be determined robustly under different trap heights and cylinder displacements. Thus, this work has laid both a theoretical and experimental framework that can be readily extended to investigate the trapping forces and torques exerted on particles with arbitrary shapes and optical properties.

Optical Torque Calculations and Measurements for DNA Torsional Studies

The angular optical trap (AOT) is a powerful instrument for measuring the torsional and rotational properties of a biological molecule. Thus far, AOT studies of DNA torsional mechanics have been carried out using a high numerical aperture oil-immersion objective, which permits strong trapping, but inevitably introduces spherical aberrations due to the glass-aqueous interface. However, the impact of these aberrations on torque measurements is not fully understood experimentally, partly due to a lack of theoretical guidance. Here, we present a numerical platform based on the finite element method to calculate forces and torques on a trapped quartz cylinder. We have also developed a new experimental method to accurately determine the shift in the trapping position due to the spherical aberrations by using a DNA molecule as a distance ruler. We found that the calculated and measured focal shift ratios are in good agreement. We further determined how the angular trap stiffness depends on the trap height and the cylinder displacement from the trap center and found full agreement between predictions and measurements. As further verification of the methodology, we showed that DNA torsional properties, which are intrinsic to DNA, could be determined robustly under different trap heights and cylinder displacements. Thus, this work has laid both a theoretical and experimental framework that can be readily extended to investigate the trapping forces and torques exerted on particles with arbitrary shapes and optical properties.

SIGNIFICANCE

We developed a simulation platform based on the finite element method for force and torque calculation for particles in an angular optical trap (AOT), with considerations of tightly focused Gaussian beam, spherical aberrations, and optically anisotropic particles. Experimental measurements of focal shift ratio, force, and torque under multiple conditions were in good agreement with predictions from the simulations. We also demonstrated that intrinsic DNA torsional properties can be robustly measured under different AOT measurement conditions, strongly validating our simulations and calibrations. Our platform can facilitate trapping particle design for single-molecule assays using the AOT.

Optical Tweezers to Study Viruses

A virus is a complex molecular machine that propagates by channeling its genetic information from cell to cell. Unlike macroscopic engines, it operates in a nanoscopic world under continuous thermal agitation. Viruses have developed efficient passive and active strategies to pack and release nucleic acids. Some aspects of the dynamic behavior of viruses and their substrates can be studied using structural and biochemical techniques. By the turn of the millennium, physical techniques have been applied to dynamic studies of viruses in which their intrinsic mechanical activity can be measured directly. Optical tweezers are a technology that can be used to measure the force, torque, and strain produced by molecular motors, as a function of time and at the single-molecule level. Thanks to this technique, some bacteriophages are now known to be powerful nanomachines; they exert force in the piconewton range and their motors work in a highly coordinated fashion for packaging the viral nucleic acid genome. Nucleic acids, whose elasticity and condensation behavior are inherently coupled to the viral packaging mechanisms, virion assembly, and virion-cell interactions are also amenable to examination with optical tweezers. In this chapter, we provide a comprehensive analysis of this laser-based tool, its combination with imaging methods, and its application to the study of viruses and viral molecules.

Optical tweezers in single-molecule biophysics

Optical tweezers have become the method of choice in single-molecule manipulation studies. In this Primer, we first review the physical principles of optical tweezers and the characteristics that make them a powerful tool to investigate single molecules. We then introduce the modifications of the method to extend the measurement of forces and displacements to torques and angles, and to develop optical tweezers with single-molecule fluorescence detection capabilities. We discuss force and torque calibration of these instruments, their various modes of operation and most common experimental geometries. We describe the type of data obtained in each experimental design and their analyses. This description is followed by a survey of applications of these methods to the studies of protein-nucleic acid interactions, protein/RNA folding and molecular motors. We also discuss data reproducibility, the factors that lead to the data variability among different laboratories and the need to develop field standards. We cover the current limitations of the methods and possible ways to optimize instrument operation, data extraction and analysis, before suggesting likely areas of future growth.

Dual-fiber microfluidic chip for multimodal manipulation of single cells

On-chip single-cell manipulation is imperative in cell biology and it is desirable for a microfluidic chip to have multimodal manipulation capability. Here, we embedded two counter-propagating optical fibers into the microfluidic chip and configured their relative position in space to produce different misalignments. By doing so, we demonstrated multimodal manipulation of single cells, including capture, stretching, translation, orbital revolution, and spin rotation. The rotational manipulation can be in-plane or out-of-plane, providing flexibility and capability to observe the cells from different angles. Based on out-of-plane rotation, we performed a 3D reconstruction of cell morphology and extracted its five geometric parameters as biophysical features. We envision that this type of microfluidic chip configured with dual optical fibers can be helpful in manipulating cells as the upstream process of single-cell analysis.

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.

High sensitivity, levitated microsphere apparatus for short-distance force measurements

A high sensitivity force sensor based on dielectric microspheres in vacuum, optically trapped by a single, upward-propagating laser beam, is described. Off-axis parabolic mirrors are used both to focus the 1064 nm trapping beam and to recollimate it to provide information on the horizontal position of the microsphere. The vertical degree of freedom is readout by forming an interferometer between the light retroreflected by the microsphere and a reference beam, hence eliminating the need for auxiliary beams. The focus of the trapping beam has a 1/E² radius of 3.2 µm and small non-Gaussian tails, suitable for bringing devices close to the trapped microsphere without disturbing the optical field. Electrodes surrounding the trapping region provide excellent control of the electric field, which can be used to drive the translational degrees of freedom of a charged microsphere and the rotational degrees of freedom of a neutral microsphere, coupling to its electric dipole moment. With this control, the charge state can be determined with single electron precision, the mass of individual microspheres can be measured, and empirical calibrations of the force sensitivity can be made for each microsphere. A force noise of <1 × 10^-17 N/Hz, which is comparable to previous reports, is measured on all three degrees of freedom for 4.7 µm diameter, 84 pg silica microspheres. Various devices have been brought within 1.6 µm of the surface of a trapped microsphere. Metrology in the trapping region is provided by two custom-designed microscopes providing views in the horizontal and one of the vertical planes. The apparatus opens the way to performing high sensitivity three-dimensional force measurements at a short distance.

High-Resolution Photonic Force Microscopy Based on Sharp Nanofabricated Tips

Although near-field imaging techniques reach sub-nanometer resolution on rigid samples, it remains extremely challenging to image soft interfaces, such as biological membranes, due to the deformations induced by the probe. In photonic force microscopy, optical tweezers are used to manipulate and measure the scanning probe, allowing imaging of soft materials without force-induced artifacts. However, the size of the optically trapped probe still limits the maximum resolution. Here, we show a novel and simple nanofabrication protocol to massively produce optically trappable quartz particles which mimic the sharp tips of atomic force microscopy. Imaging rigid nanostructures with our tips, we resolve features smaller than 80 nm. Scanning the membrane of living malaria-infected red blood cells reveals, with no visible artifacts, submicron features termed knobs, related to the parasite activity. The use of nanoengineered particles in photonic force microscopy opens the way to imaging soft samples at high resolution.

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.

Fluorescence Anisotropy Reloaded-Emerging Polarization Microscopy Methods for Assessing Chromophores' Organization and Excitation Energy Transfer in Single Molecules, Particles, Films, and Beyond

Fluorescence polarization is widely used to assess the orientation/rotation of molecules, and the excitation energy transfer between closely located chromophores. Emerging since the 1990s, single molecule fluorescence spectroscopy and imaging stimulate the application of light polarization for studying molecular organization and energy transfer beyond ensemble averaging. Here, traditional fluorescence polarization and linear dichroism methods used for bulk samples are compared with techniques specially developed for, or inspired by, single molecule fluorescence spectroscopy. Techniques for assessing energy transfer in anisotropic samples, where the traditional fluorescence anisotropy framework is not readily applicable, are discussed in depth. It is shown that the concept of a polarization portrait and the single funnel approximation can lay the foundation for alternative energy transfer metrics. Examples ranging from fundamental studies of photoactive materials (conjugated polymers, light-harvesting aggregates, and perovskite semiconductors) to Förster resonant energy transfer (FRET)-based biomedical imaging are presented. Furthermore, novel uses of light polarization for super-resolution optical imaging are mentioned as well as strategies for avoiding artifacts in polarization microscopy.

Spin to orbital light momentum conversion visualized by particle trajectory

In a tightly focused beam of light having both spin and orbital angular momentum, the beam exhibits the spin-orbit interaction phenomenon. We demonstrate here that this interaction gives rise to series of subtle, but observable, effects on the dynamics of a dielectric microsphere trapped in such a beam. In our setup, we control the strength of spin-orbit interaction with the width, polarization and vorticity of the beam and record how these parameters influence radius and orbiting frequency of the same single orbiting particle pushed by the laser beam. Using Richard and Wolf model of the non-paraxial beam focusing, we found a very good agreement between the experimental results and the theoretical model based on calculation of the optical forces using the generalized Lorenz-Mie theory extended to a non-paraxial vortex beam. Especially the radius of the particle orbit seems to be a promising parameter characterizing the spin to orbital momentum conversion independently on the trapping beam power.

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.

Single-Molecule Angular Optical Trapping for Studying Transcription Under Torsion

Optical tweezers are flexible and powerful single-molecule tools that have been extensively utilized in biophysical studies. With their ability to stretch and twist DNA, and measure its force and torque simultaneously, they provide excellent opportunities to gain novel insights into the function of protein motors and protein-DNA interactions. Recently, a novel DNA supercoiling assay using an angular optical tweezers (AOT) has been developed to investigate torque generation during transcription. Here, we provide a detailed and practical guide to performing this technique. Using bacterial RNA polymerase (RNAP) as an example, we present protocols for constructing and calibrating an AOT instrument, preparing DNA templates, and acquiring and analyzing real-time data for transcription under DNA supercoiling. While these protocols were initially developed with E. coli RNAP, they can be readily adapted to study other DNA-based motor proteins.

Interfacing 3D magnetic twisting cytometry with confocal fluorescence microscopy to image force responses in living cells

Cells and tissues can undergo a variety of biological and structural changes in response to mechanical forces. Only a few existing techniques are available for quantification of structural changes at high resolution in response to forces applied along different directions. 3D-magnetic twisting cytometry (3D-MTC) is a technique for applying local mechanical stresses to living cells. Here we describe a protocol for interfacing 3D-MTC with confocal fluorescence microscopy. In 3D-MTC, ferromagnetic beads are bound to the cell surface via surface receptors, followed by their magnetization in any desired direction. A magnetic twisting field in a different direction is then applied to generate rotational shear stresses in any desired direction. This protocol describes how to combine magnetic-field-induced mechanical stimulation with confocal fluorescence microscopy and provides an optional extension for super-resolution imaging using stimulated emission depletion (STED) nanoscopy. This technology allows for rapid real-time acquisition of a living cell's mechanical responses to forces via specific receptors and for quantifying structural and biochemical changes in the same cell using confocal fluorescence microscopy or STED. The integrated 3D-MTC-microscopy platform takes ∼20 d to construct, and the experimental procedures require ∼4 d when carried out by a life sciences graduate student.

Custom-Made Microspheres for Optical Tweezers

Due to their high position and force sensitivity and the ability to remotely apply forces and torques, optical tweezers are widely used in diverse fields, such as biology, material science, and physics. Often, small dielectric particles are trapped and used as probes, which for experimental convenience are mostly spherical and composed of silica or polystyrene. The optical properties of these materials together with the microsphere size determine the trapping efficiency, and the position and force resolution. However, using only a single, homogeneous, isotropic, and unstructured material limits the range of trapping properties and thereby the applications of optical tweezers. Here, we show how custom-made microspheres composed of coated high-refractive-index materials-titania and nanodiamonds-and birefringent, liquid crystals extend the range and combination of desired trapping properties. These custom-made microspheres either enable the generation of high forces, a high force or time resolution, or the applications of torques. Custom-made probes expand the range of possible experiments and approaches broadening the scope and applicability of optical tweezers.

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.

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.

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.

Non-spherical gold nanoparticles trapped in optical tweezers: shape matters

We present the results of a theoretical analysis focused on three-dimensional optical trapping of non-spherical gold nanoparticles using a tightly focused laser beam (i.e. optical tweezers). We investigate how the wavelength of the trapping beam enhances trapping stiffness and determines the stable orientation of nonspherical nanoparticles in the optical trap which reveals the optimal trapping wavelength. We consider nanoparticles with diameters being between 20 nm and 254 nm illuminated by a highly focused laser beam at wavelength 1064 nm and compare our results based on the coupled-dipole method with published theoretical and experimental data. We demonstrate that by considering the non-spherical morphology of the nanoparticle we can explain the experimentally observed three-dimensional trapping of plasmonic nanoparticles with size higher than 170 nm. These results will contribute to a better understanding of the trapping and alignment of real metal nanoparticles in optical tweezers and their applications as optically controllable nanosources of heat or probes of weak forces and torques.

Complex rotational dynamics of multiple spheroidal particles in a circularly polarized, dual beam trap

We examine the rotational dynamics of spheroidal particles in an optical trap comprising counter-propagating Gaussian beams of opposing helicity. Isolated spheroids undergo continuous rotation with frequencies determined by their size and aspect ratio, whilst pairs of spheroids display phase locking behaviour. The introduction of additional particles leads to yet more complex behaviour. Experimental results are supported by numerical calculations.

Polarization-controlled TIRFM with focal drift and spatial field intensity correction

Total internal reflection fluorescence microscopy (TIRFM) is becoming an increasingly common methodology to narrow the illumination excitation thickness to study cellular process such as exocytosis, endocytosis, and membrane dynamics. It is also frequently used as a method to improve signal/noise in other techniques such as in vitro single-molecule imaging, stochastic optical reconstruction microscopy/photoactivated localization microscopy imaging, and fluorescence resonance energy transfer imaging. The unique illumination geometry of TIRFM also enables a distinct method to create an excitation field for selectively exciting fluorophores that are aligned either parallel or perpendicular to the optical axis. This selectivity has been used to study orientation of cell membranes and cellular proteins. Unfortunately, the coherent nature of laser light, the typical excitation source in TIRFM, often creates spatial interference fringes across the illuminated area. These fringes are particularly problematic when imaging large cellular areas or when accurate quantification is necessary. Methods have been developed to minimize these fringes by modulating the TIRFM field during a frame capture period; however, these approaches eliminate the possibility to simultaneously excite with a specific polarization. A new, to our knowledge, technique is presented, which compensates for spatial fringes while simultaneously permitting rapid image acquisition of both parallel and perpendicular excitation directions in ~25 ms. In addition, a back reflection detection scheme was developed that enables quick and accurate alignment of the excitation laser. The detector also facilitates focus drift compensation, a common problem in TIRFM due to the narrow excitation depth, particularly when imaging over long time courses or when using a perfusion flow chamber. The capabilities of this instrument were demonstrated by imaging membrane orientation using DiO on live cells and on lipid bilayers that were supported on a glass slide (supported lipid bilayer). The use of the approach to biological problems was illustrated by examining the temporal and spatial dynamics of exocytic vesicles.

AC electric field induced dipole-based on-chip 3D cell rotation

The precise rotation of suspended cells is one of the many fundamental manipulations used in a wide range of biotechnological applications such as cell injection and enucleation in nuclear transfer (NT) cloning. Noticeably scarce among the existing rotation techniques is the three-dimensional (3D) rotation of cells on a single chip. Here we present an alternating current (ac) induced electric field-based biochip platform, which has an open-top sub-mm square chamber enclosed by four sidewall electrodes and two bottom electrodes, to achieve rotation about the two axes, thus 3D cell rotation. By applying an ac potential to the four sidewall electrodes, an in-plane (yaw) rotating electric field is generated and in-plane rotation is achieved. Similarly, by applying an ac potential to two opposite sidewall electrodes and the two bottom electrodes, an out-of-plane (pitch) rotating electric field is generated and rolling rotation is achieved. As a prompt proof-of-concept, bottom electrodes were constructed with transparent indium tin oxide (ITO) using the standard lift-off process and the sidewall electrodes were constructed using a low-cost micro-milling process and then assembled to form the chip. Through experiments, we demonstrate rotation of bovine oocytes of ~120 μm diameter about two axes, with the capability of controlling the rotation direction and the rate for each axis through control of the ac potential amplitude, frequency, and phase shift, and cell medium conductivity. The maximum observed rotation rate reached nearly 140° s⁻¹, while a consistent rotation rate reached up to 40° s⁻¹. Rotation rate spectra for zona pellucida-intact and zona pellucida-free oocytes were further compared and found to have no effective difference. This simple, transparent, cheap-to-manufacture, and open-top platform allows additional functional modules to be integrated to become a more powerful cell manipulation system.

Rotation, oscillation and hydrodynamic synchronization of optically trapped oblate spheroidal microparticles

While the behavior of optically trapped dielectric spherical particles has been extensively studied, the behavior of non-spherical particles remains mainly unexplored. In this work we focus on the dynamics of oblate spheroidal particles trapped in a tightly focused elliptically-polarized vortex beam. In our experiments we used polystyrene spheroids of aspect ratio of major to minor axes equal to 2.55 and of a volume equal to a sphere of diameter 1.7μm. We demonstrate that such particles can be trapped in three dimensions, with the minor axis oriented perpendicular to both the beam polarization (linear) and the beam propagation, can spin in a circularly polarized beam and an optical vortex beam around the axis parallel with the beam propagation. We also observed that these particles can exhibit a periodic motion in the plane transversal to the beam propagation. We measured that the transfer of the orbital angular momentum from the vortex beam to the spheroid gives rise to torques one order of magnitude stronger comparing to the circularly polarized Gaussian beam. We employed a phase-only spatial light modulator to generate several vortex beam traps with one spheroid in each of them. Due to independent setting of beams parameters we controlled spheroids frequency and sense of rotation and observed hydrodynamic phase and frequency locking of rotating spheroids. These optically driven spheroids offer a simple alternative approach to the former techniques based on birefringent, absorbing or chiral microrotors.

Fabrication of birefringent nanocylinders for single-molecule force and torque measurement

Optically anisotropic subwavelength scale dielectric particles have been shown to enable studies of the mechanical properties of bio-molecules via optical trapping and manipulation. However, techniques emphasized to date for fabrication of such particles generally suffer from limited uniformity and control over particle dimensions, or low throughput and high cost. Here, an approach for rapid, low-cost, fabrication of large quantities of birefringent quartz nanocylinders with dimensions optimized for optical torque wrench experiments is described. For a typical process, 10(8) or more quartz cylinders with diameters of 500 nm and heights of 800 nm, with uniformity of ±5% in each dimension, can be fabricated over ∼10 cm(2) areas, for binding to a single bio-molecule, and harvested for use in optical trapping experiments. Use of these structures to measure extensional and torsional dynamics of single DNA molecules is demonstrated with measured forces and torques shown to be in very good agreement with previously reported results.

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.

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.

A minimal optical trapping and imaging microscopy system

We report the construction and testing of a simple and versatile optical trapping apparatus, suitable for visualizing individual microtubules (∼25 nm in diameter) and performing single-molecule studies, using a minimal set of components. This design is based on a conventional, inverted microscope, operating under plain bright field illumination. A single laser beam enables standard optical trapping and the measurement of molecular displacements and forces, whereas digital image processing affords real-time sample visualization with reduced noise and enhanced contrast. We have tested our trapping and imaging instrument by measuring the persistence length of individual double-stranded DNA molecules, and by following the stepping of single kinesin motor proteins along clearly imaged microtubules. The approach presented here provides a straightforward alternative for studies of biomaterials and individual biomolecules.

Optical tweezers to study viruses

A virus is a complex molecular machine that propagates by channeling its genetic information from cell to cell. Unlike macroscopic engines, it operates in a nanoscopic world under continuous thermal agitation. Viruses have developed efficient passive and active strategies to pack and release nucleic acids. Some aspects of the dynamic behavior of viruses and their substrates can be studied using structural and biochemical techniques. Recently, physical techniques have been applied to dynamic studies of viruses in which their intrinsic mechanical activity can be measured directly. Optical tweezers are a technology that can be used to measure the force, torque and strain produced by molecular motors, as a function of time and at the single-molecule level. Thanks to this technique, some bacteriophages are now known to be powerful nanomachines; they exert force in the piconewton range and their motors work in a highly coordinated fashion for packaging the viral nucleic acid genome. Nucleic acids, whose elasticity and condensation behavior are inherently coupled to the viral packaging mechanisms, are also amenable to examination with optical tweezers. In this chapter, we provide a comprehensive analysis of this laser-based tool, its combination with imaging methods and its application to the study of viruses and viral molecules.

Single-molecule studies of RNAPII elongation

Elongation, the transcriptional phase in which RNA polymerase (RNAP) moves processively along a DNA template, occurs via a fundamental enzymatic mechanism that is thought to be universally conserved among multi-subunit polymerases in all kingdoms of life. Beyond this basic mechanism, a multitude of processes are integrated into transcript elongation, among them fidelity control, gene regulatory interactions involving elongation factors, RNA splicing or processing factors, and regulatory mechanisms associated with chromatin structure. Many kinetic and molecular details of the mechanism of the nucleotide addition cycle and its regulation, however, remain elusive and generate continued interest and even controversy. Recently, single-molecule approaches have emerged as powerful tools for the study of transcription in eukaryotic organisms. Here, we review recent progress and discuss some of the unresolved questions and ongoing debates, while anticipating future developments in the field. This article is part of a Special Issue entitled: RNA Polymerase II Transcript Elongation.

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.

Calibration of the optical torque wrench

The optical torque wrench is a laser trapping technique that expands the capability of standard optical tweezers to torque manipulation and measurement, using the laser linear polarization to orient tailored microscopic birefringent particles. The ability to measure torque of the order of kBT (∼4 pN nm) is especially important in the study of biophysical systems at the molecular and cellular level. Quantitative torque measurements rely on an accurate calibration of the instrument. Here we describe and implement a set of calibration approaches for the optical torque wrench, including methods that have direct analogs in linear optical tweezers as well as introducing others that are specifically developed for the angular variables. We compare the different methods, analyze their differences, and make recommendations regarding their implementations.

Application of the discrete dipole approximation to optical trapping calculations of inhomogeneous and anisotropic particles

The accuracy of the discrete dipole approximation (DDA) for computing forces and torques in optical trapping experiments is discussed in the context of dielectric spheres and a range of low symmetry particles, including particles with geometric anisotropy (spheroids), optical anisotropy (birefringent spheres) and structural inhomogeneity (core-shell spheres). DDA calculations are compared with the results of exact T-matrix theory. In each case excellent agreement is found between the two methods for predictions of optical forces, torques, trap stiffnesses and trapping positions. Since the DDA lends itself to calculations on particles of arbitrary shape, the study is augmented by considering more general systems which have received recent experimental interest. In particular, optical forces and torques on low symmetry letter-shaped colloidal particles, birefringent quartz cylinders and biphasic Janus particles are computed and the trapping behaviour of the particles is discussed. Very good agreement is found with the available experimental data. The efficiency of the DDA algorithm and methods of accelerating the calculations are also discussed.

Soft magnetic tweezers: a proof of principle

We present here the principle of soft magnetic tweezers which improve the traditional magnetic tweezers allowing the simultaneous application and measurement of an arbitrary torque to a deoxyribonucleic acid (DNA) molecule. They take advantage of a nonlinear coupling regime that appears when a fast rotating magnetic field is applied to a superparamagnetic bead immersed in a viscous fluid. In this work, we present the development of the technique and we compare it with other techniques capable of measuring the torque applied to the DNA molecule. In this proof of principle, we use standard electromagnets to achieve our experiments. Despite technical difficulties related to the present implementation of these electromagnets, the agreement of measurements with previous experiments is remarkable. Finally, we propose a simple way to modify the experimental design of electromagnets that should bring the performances of the device to a competitive level.

Electron beam fabrication of birefringent microcylinders

Numerous biological and biotechnological applications rely on the use of micrometer- and nanometer-scale particles, benefiting tremendously from quantitative control of their physical and chemical properties. Here, we describe the use of electron beam lithography for the design, fabrication, and functionalization of micrometer-scale birefringent quartz cylinders for use in sensing and detection. We demonstrate excellent control of the cylinders' geometry, fabricating cylinders with heights of 0.5-2 μm and diameters of 200-500 nm with high precision while maintaining control of their side-wall angle. The flexible fabrication allows cylinders to be selectively shaped into conical structures or to include centered protrusions for the selective attachment of biomolecules. The latter is facilitated by straightforward functionalization targeted either to a cylinder's face or to the centered protrusion alone. The fabricated quartz cylinders are characterized in an optical torque wrench, permitting correlation of their geometrical properties to measured torques. Lastly, we tether individual DNA molecules to the functionalized cylinders and demonstrate the translational and rotational control required for single-molecule studies.