Angular Trapping Research Articles

Optical manipulation of ratio-designable Janus microspheres

Angular optical trapping based on Janus microspheres has been proven to be a novel method to achieve controllable rotation. In contrast to natural birefringent crystals, Janus microspheres are chemically synthesized of two compositions with different refractive indices. Thus, their structures can be artificially regulated, which brings excellent potential for fine and multi-degree-of-freedom manipulation in the optical field. However, it is a considerable challenge to model the interaction of heterogeneous particles with the optical field, and there has also been no experimental study on the optical manipulation of microspheres with such designable refractive index distributions. How the specific structure affects the kinematic properties of Janus microspheres remains unknown. Here, we report systematic research on the optical trapping and rotating of various ratio-designable Janus microspheres. We employ an efficient T-matrix method to rapidly calculate the optical force and torque on Janus microspheres to obtain their trapped postures and rotational characteristics in the optical field. We have developed a robust microfluidic-based scheme to prepare Janus microspheres. Our experimental results demonstrate that within a specific ratio range, the rotation radii of microspheres vary linearly and the orientations of microsphere are always aligned with the light polarization direction. This is of great importance in guiding the design of Janus microspheres. And their orientations flip at a particular ratio, all consistent with the simulations. Our work provides a reliable theoretical analysis and experimental strategy for studying the interaction of heterogeneous particles with the optical field and further expands the diverse manipulation capabilities of optical tweezers.

Angular trapping of a linear-cavity mirror with an optical torsional spring

Optomechanical systems have attracted intensive attention in various physical experiments. With an optomechanical system, the displacement of or the force acting on a mechanical oscillator can be precisely measured by utilizing optical interferometry. As a mechanical oscillator, a suspended mirror is often used in over a milligram scale optomechanical systems. However, the tiny suspended mirror in a linear cavity can be unstable in its yaw rotational degree of freedom due to optical radiation pressure. This instability curbs the optical power that the cavity can accumulate in it and imposes a limitation on the sensitivity. Here, we show that the optical radiation pressure can be used to trap the rotational motion of the suspended mirror without additional active feedback control when the $g$ factors of the cavity are negative and one mirror is much heavier than the other one. Furthermore, we demonstrate experimentally the validity of the trapping. We measured the rotational stiffness of a suspended tiny mirror with various intracavity power. The result indicates that the radiation pressure of the laser beam inside the cavity actually works as a positive restoring torque. Moreover, we discuss the feasibility of observing quantum radiation pressure fluctuation with our experimental setup as an application of our trapping configuration.

Angular Optical Trapping to Directly Measure DNA Torsional Mechanics.

Angular optical trapping (AOT) is a powerful technique that permits direct angular manipulation of a trapped particle with simultaneous measurement of torque and rotation, while also retaining the capabilities of position and force detection. This technique provides unique approaches to investigate the torsional properties of nucleic acids and DNA-protein complexes, as well as impacts of torsional stress on fundamental biological processes, such as transcription and replication. Here we describe the principle, construction, and calibration of the AOT in detail and provide a guide to the performance of single-molecule torque measurements on DNA molecules. We include the constant-force method and, notably, a new constant-extension method that enables measurement of the twist persistence length of both extended DNA, under an extremely low force, and plectonemic DNA. This chapter can assist in the implementation and application of this technique for general researchers in the single-molecule field.

Numerical study on the angular light trapping of the energy yield of organic solar cells with an optical cavity

A limiting factor in organic solar cells (OSCs) is the incomplete absorption in the thin absorber layer. One concept to enhance absorption is to apply an optical cavity design. In this study, the performance of an OSC with cavity is evaluated. By means of a comprehensive energy yield (EY) model, the improvement is demonstrated by applying realistic sky irradiance, covering a wide range of incidence angles. The relative enhancement in EY for different locations is found to be 11-14% compared to the reference device with an indium tin oxide front electrode. The study highlights the improved angular light absorption as well as the angular robustness of an OSC with cavity.

Angular Trapping of Spherical Janus Particles

AbstractDeveloping angular trapping methods, which enable optical tweezers to rotate a micronsized bead, is of great importance for studies of biomacromolecules in a wide range of torque‐generation processes. Here a novel controlled angular trapping method based on model composite Janus particles is reported, which consist of two hemispheres made of polystyrene and poly(methyl methacrylate). Through computational and experimental studies, the feasibility to control the rotation of a Janus particle in a linearly polarized laser trap is demonstrated. The results show that the Janus particle aligned its two hemispheres interface parallel to the laser propagation direction and polarization direction. The rotational state of the particle can be directly visualized by using a camera. The rotation of the Janus particle in the laser trap can be fully controlled in real time by controlling the laser polarization direction. The newly developed angular trapping technique has the great advantage of easy implementation and real‐time controllability. Considering the easy chemical preparation of Janus particles and implementation of the angular trapping, this novel method has the potential of becoming a general angular trapping method. It is anticipated that this new method will significantly broaden the availability of angular trapping in the biophysics community.

Transcription Factor Regulation of RNA Polymerase's Torque Generation Capacity

During transcription, RNA polymerase (RNAP) supercoils DNA as it translocates. The resulting torsional stress in DNA can accumulate and, in the absence of regulatory mechanisms, becomes a barrier to RNAP elongation, causing RNAP stalling, backtracking, and transcriptional arrest. Here we investigate whether and how a transcription factor may regulate both torque-induced Escherichia coli RNAP stalling and the torque generation capacity of RNAP. Using a unique real-time angular optical trapping assay, we found that RNAP working against a resisting torque was highly prone to extensive backtracking. We then investigated transcription in the presence of GreB, a transcription factor known to rescue RNAP from the backtracked state. We found that GreB greatly suppressed RNAP backtracking and remarkably increased the torque that RNAP was able to generate by 65%, from 11.2 pN⋅nm to 18.5 pN·nm. Variance analysis of the real-time positional trajectories of RNAP after a stall revealed the kinetic parameters of backtracking and GreB rescue. These results demonstrate that backtracking is the primary mechanism by which torsional stress limits transcription and that the transcription factor GreB effectively enhances the torsional capacity of RNAP. These findings suggest a broader role for transcription factors in regulating RNAP functionality and elongation.

Transcription factor regulation of RNA polymerase’s torque generation capacity

During transcription, RNA polymerase (RNAP) supercoils DNA as it translocates. The resulting torsional stress in DNA can accumulate and, in the absence of regulatory mechanisms, becomes a barrier to RNAP elongation, causing RNAP stalling, backtracking, and transcriptional arrest. Here we investigate whether and how a transcription factor may regulate both torque-induced Escherichia coli RNAP stalling and the torque generation capacity of RNAP. Using a unique real-time angular optical trapping assay, we found that RNAP working against a resisting torque was highly prone to extensive backtracking. We then investigated transcription in the presence of GreB, a transcription factor known to rescue RNAP from the backtracked state. We found that GreB greatly suppressed RNAP backtracking and remarkably increased the torque that RNAP was able to generate by 65%, from 11.2 pN⋅nm to 18.5 pN·nm. Variance analysis of the real-time positional trajectories of RNAP after a stall revealed the kinetic parameters of backtracking and GreB rescue. These results demonstrate that backtracking is the primary mechanism by which torsional stress limits transcription and that the transcription factor GreB effectively enhances the torsional capacity of RNAP. These findings suggest a broader role for transcription factors in regulating RNAP functionality and elongation.

Ultrasensitive rotating photonic probes for complex biological systems

We use rotational photonic tweezers to access local viscoelastic properties of complex fluids over a wide frequency range. This is done by monitoring both passive rotational Brownian motion and also actively driven transient rotation between two angular trapping states of a birefringent microsphere. These enable measurement of high- and low-frequency properties, respectively. Complex fluids arise frequently in microscopic biological systems, typically with length scales at the cellular level. Thus, high spatial resolution as provided by rotational photonic tweezers is important. We measure the properties of tear film on a contact lens and demonstrate variations in these properties between two subjects over time. We also show excellent agreement between our theoretical model and experimental results. We believe that this is the first time that active microrheology using rotating tweezers has been used for biologically relevant questions. Our method demonstrates potential for future applications to determine the spatial-temporal properties of biologically relevant and complex fluids that are only available in very small volumes.

Trapping of Highly Birefringent Rutile Nanocylinders in the Optical Torque Wrench

The optical torque wrench (OTW) is a powerful technique to measure the torsional properties of different biomolecules, including DNA, DNA- processing protein complexes and rotary motors. To date, quartz has proven to be a convenient birefringent material out of which to synthesize the micron-sized particles essential for this technique. However, the relatively low birefringence of quartz, which limits the maximal torque that can be applied in OTW, hampers the study of certain biological systems. A more attractive material is rutile, which has a thirty-fold higher birefringence. To date, however, the application of rutile in the trapping has been restricted due to its high refractive index, which results in low trapping efficiency. Here, we have employed finite element method calculations to determine the optimal dimensions of sub-micron-sized rutile cylinders for tight stable optical trapping. Using these calculations as a guideline, we have designed and devel- oped a nanofabrication protocol that allows us to produce rutile cylinders with the desired sizes at high yield. We have characterized the fabricated cylinders in the OTW setup and quantified both their linear and angular trapping proper- ties. In addition, we demonstrate full translational and rotational control of these functionalized cylinders tethered to individual DNA molecules for use in single-molecule applications.

Fabrication and Surface Functionalization of Highly Birefringent Rutile Particles for Trapping in an Optical Torque Wrench

The optical torque wrench (OTW) allows the direct application and measure- ment of torque on biomolecules, such as DNA or DNA-protein complexes, or rotary motors like the F0F1-ATP-synthase or the bacterial flagellar motor. The applicable torque of the OTW is a function of the size and birefringence of the particle. Quartz has proven a convenient material, but its quite low birefringence limits full investigation of torque-speed relationships of diverse biological systems. In contrast, rutile exhibits a much higher birefringence - exceeding that of quartz by a factor of 30 - but its utilization has been infrequent because of the difficulties in optical trapping and fabrication. To enhance the applicability of the OTW, we have improved both the design and fabrication of cylindrical rutile particles. We have employed finite element method calculations to determine the optimal dimension of stably trappable rutile cylinders. To obtain rutile cylinders with the optimal dimensions, we developed a protocol for full control of size and sidewall angle. In our fabrica- tion protocol, a chromium etch mask provides increased resistance to dry etching and allows the fabrication of structures with both high aspect ratio and anisotropy. Also, the sidewall angle of cylinders can be readily tuned by adjusting a single process parameter, namely the oxygen flow rate during dry etching. The fabricated cylinders were characterized in the OTW setup to reveal their linear and angular trapping properties. The fabrication process is compatible with common chemical functionalization procedures and permits covalent biomolecule attachment. To enhance biomolecule coverage, we used ethanolamine and poly(ethylene glycol) as biomolecular crosslinkers to obtain homogenous and dense coatings. Our recent results, in which we use functionalized, trapped rutile cylinders to study single biomolecules and motor proteins, will be presented.

Molecular branch of a small highly elongated Fermi gas with an impurity: Full three-dimensional versus effective one-dimensional description

We consider an impurity immersed in a small Fermi gas under highly elongated harmonic confinement. The impurity interacts with the atoms of the Fermi gas through an isotropic short-range potential with three-dimensional free-space $s$-wave scattering length ${a}_{3\text{D}}$. We investigate the energies of the molecular branch, i.e., the energies of the state that corresponds to a gas consisting of a weakly bound diatomic molecule and ``unpaired'' atoms, as a function of the $s$-wave scattering length ${a}_{3\text{D}}$ and the ratio $\ensuremath{\eta}$ between the angular trapping frequencies in the tight and weak confinement directions. The energies obtained from our three-dimensional description that accounts for the dynamics in the weak and tight confinement directions are compared with those obtained within an effective one-dimensional framework, which accounts for the dynamics in the tight confinement direction via a renormalized one-dimensional coupling constant. Our theoretical results are related to recent experimental measurements.

Torque modulates nucleosome stability and facilitates H2A/H2B dimer loss

The nucleosome, the fundamental packing unit of chromatin, has a distinct chirality: 147 bp of DNA are wrapped around the core histones in a left-handed, negative superhelix. It has been suggested that this chirality has functional significance, particularly in the context of the cellular processes that generate DNA supercoiling, such as transcription and replication. However, the impact of torsion on nucleosome structure and stability is largely unknown. Here we perform a detailed investigation of single nucleosome behavior on the high affinity 601 positioning sequence under tension and torque using the angular optical trapping technique. We find that torque has only a moderate effect on nucleosome unwrapping. In contrast, we observe a dramatic loss of H2A/H2B dimers upon nucleosome disruption under positive torque, while (H3/H4)2 tetramers are efficiently retained irrespective of torsion. These data indicate that torque could regulate histone exchange during transcription and replication.

Biomolecular Processes under Torque

Due to the double helical nature of DNA, motor proteins that translocate along DNA may have to rotate around the DNA helical axis. For example, during transcription, the translocation of RNA polymerase along the double helical DNA will generate torque that introduces (+) supercoils in front and (-) supercoils behind. Torque introduced by motor proteins is an essential regulatory factor in biology; however direct measurements of torque have proven to be challenging. To meet this challenge, we have developed an angular optical trapping (AOT) instrument that permits direct and simultaneous measurements of force and torque. I will discuss our recent efforts in using the AOT to directly measure the torques involved in biomolecular processes.

Natural and unnatural parity states of small trapped equal-mass two-component Fermi gases at unitarity and fourth-order virial coefficient

Equal-mass two-component Fermi gases under spherically symmetric external harmonic confinement with large $s$-wave scattering length are considered. Using the stochastic variational approach, we determine the lowest 286 and 164 relative eigenenergies of the $(2,2)$ and $(3,1)$ systems at unitarity as a function of the range ${r}_{0}$ of the underlying two-body potential and extrapolate to the ${r}_{0}\ensuremath{\rightarrow}0$ limit. Our calculations include all states with vanishing and finite angular momentum $L$ (and natural and unnatural parity $\ensuremath{\Pi}$) with relative energy up to 10.5 $\ensuremath{\hbar}\ensuremath{\Omega}$, where $\ensuremath{\Omega}$ denotes the angular trapping frequency of the external confinement. Our extrapolated zero-range energies are estimated to have uncertainties of 0.1$%$ or smaller. The $(2,2)$ and $(3,1)$ energies are used to determine the fourth-order virial coefficient of the trapped unitary two-component Fermi gas in the low-temperature regime. Our results are compared with recent predictions for the fourth-order virial coefficient of the homogeneous system. We also calculate small portions of the energy spectra of the $(3,2)$ and $(4,1)$ systems at unitarity.

Passive Torque Wrench and Angular Position Detection Using a Single Beam Optical Trap

The recent advent of angular optical trapping techniques has allowed for rotational control and direct torque measurement on biological substrates. Here we present a novel method that increases the versatility and flexibility of these techniques. We demonstrate that a single beam with a rapidly rotating linear polarization can be utilized to apply a constant controllable torque to a trapped particle without active feedback while simultaneously measuring the particle's angular position. In addition, this device can rapidly switch between a torque wrench and an angular trap. These features should make possible torsional measurements across a wide range of biological systems.

Passive torque wrench and angular position detection using a single-beam optical trap

The recent advent of angular optical trapping techniques has allowed for rotational control and direct torque measurement on biological substrates. Here we present a method that increases the versatility and flexibility of these techniques. We demonstrate that a single beam with a rapidly rotating linear polarization can be utilized to apply a constant controllable torque to a trapped particle without active feedback, while simultaneously measuring the particle angular position. In addition, this device can rapidly switch between a torque wrench and an angular trap. These features should make possible torsional measurements across a wide range of biological systems.

An Optical Torque Wrench For Studying Kinesin Dynamics

We constructed an optical tweezers instrument capable of exerting torque and measuring the angular motions of small trapped particles, based on the rotation of linear polarization of the trapping laser beam. To change polarization, we employed an electro-optic modulator (EOM), which allows for a much simpler setup than a previous design (La Porta, A. and Wang, M.D. 2004. Optical torque wrench: angular trapping, rotation, and torque detection of quartz microparticles. Phys. Rev. Lett. 19:190801). Torque is monitored by measuring the difference between circularly left-handed and right-handed components of the transmitted beam: constant torque is implemented by feeding this angular signal back into a custom-designed electronic servo loop. The limited dynamic range of the EOM (±180°) is extended by monitoring the drive signal with a microcontroller, which triggers a switch to flip the output polarization by ±180° once a pre-set threshold is reached (within 10 μs). These features enable us to maintain constant torque over unlimited rotations at high bandwidth (∼100 kHz). In addition, we developed optically birefringent, non-spherical particles suitable for this instrument using nanofabrication techniques. The polarization-sensitive method employed by the apparatus precludes the use of Wollaston prisms to perform differential interference contrast (DIC) imaging. However, by exploiting conventional video-enhancement techniques (including background subtraction, contrast enhancement, and frame averaging), we report that individual microtubules (∼25 nm in diameter) can be visualized without DIC optics at ∼5 frames per second. Altogether, our instrument allows for the simultaneous application of force and torque to the study of macromolecules of interest. We are presently extending our previous studies (Gutierrez-Medina, B., et al. 2339-Pos. Torsional properties of kinesin. Biophys. J. 2008. 94:2339-Pos) on the torsional properties of the molecular motor kinesin to investigate the effect of torque on its stepwise motion.

Viscous Drag Torque on a Rotating Nanofabricated Cylinder Near an Infinite Plane Boundary

Microrheological and single molecule biological measurements often involve the use of a microscopic probe particle near a surface. On such systems a precise understanding of the hydrodynamic interactions between the particle and the surface is required. Recently nanofabricated nearly cylindrical quartz particles have been used as ideal trapping particles for an angular optical trap. Here the rotational viscous drag torque imposed on a nanofabricated quartz cylinder near a surface is measured with the angular optical trap. The deviation of torque from the Stokes drag relation in solution is measured as a function of distance from the plane surface of a microscope cover glass. The surface effect is found to be significant for distances on the order of the characteristic dimension of the cylinder. These findings will allow for more accurate and quantitative torsional measurements of angular trapping systems.

Nanofabricated quartz cylinders for angular trapping: DNA supercoiling torque detection

We designed and created nanofabricated quartz cylinders well suited for torque application and detection in an angular optical trap. We made the cylinder axis perpendicular to the extraordinary axis of the quartz crystal and chemically functionalized only one end of each cylinder for attachment to a DNA molecule. We directly measured the torque on a single DNA molecule as it underwent a phase transition from B-form to supercoiled P-form.

Optical torque wrench: angular trapping, rotation, and torque detection of quartz microparticles.

We describe an apparatus that can measure the instantaneous angular displacement and torque applied to a quartz particle which is angularly trapped. Torque is measured by detecting the change in angular momentum of the transmitted trap beam. The rotational Brownian motion of the trapped particle and its power spectral density are used to determine the angular trap stiffness. The apparatus features a feedback control that clamps torque or other rotational quantities. The torque sensitivity demonstrated is ideal for the study of known biological molecular motors.