Measuring the accuracy of particle position and force in optical tweezers using high-speed video microscopy

Accessing activity and viscoelastic properties of artificial and living systems from passive measurement

Living systems are complex dynamic entities that operate far from thermodynamic equilibrium. Their active, non-equilibrium behaviour requires energy to drive cellular organization and dynamics. Unfortunately, most statistical mechanics approaches are not valid in non-equilibrium situations, forcing researchers to use intricate and often invasive methods to study living processes. Here we experimentally demonstrate that an observable termed mean back relaxation quantifies the active mechanics of living cells from passively observed particle trajectories. The mean back relaxation represents the average trajectory of a particle after a recent motion and is calculated from three-point probabilities. We show that this parameter allows the detection of broken detailed balance in confined systems. We experimentally observe that it provides access to the non-equilibrium generating energy and viscoelastic properties of artificial bulk materials and living cells. These findings suggest that the mean back relaxation can function as a marker of non-equilibrium dynamics and is a non-invasive avenue to determine viscoelastic material properties from passive measurements.

Structured-light displacement detection method using split-waveplate for dual-beam optical tweezers

Structured-light displacement detection method is an innovative approach with extremely high sensitivity for measuring the displacement of a levitated particle. This scheme includes two key components, a split-waveplate (SWP) and a single-mode fiber. In this work, we further investigated the influence of SWP installation on this method regarding the sensitivity of displacement detection. The results indicate that the sensitivity increases with the expanding of SWP offset in the effective range. In addition, we found this method has a significant tolerance rate, with an extensive SWP offset effective range of 5%-25%. However, an excessive offset can render this method ineffective. More interestingly, we demonstrated the feasibility of rotating the SWP to detect displacement in different directions. Our research contributes to guiding the structured-light detection methods in practical applications and expanding their applications in fundamental physics.

Particle Localization Using Local Gradients and Its Application to Nanometer Stabilization of a Microscope

Particle localization plays a fundamental role in advanced biological techniques such as single-molecule tracking, superresolution microscopy, and manipulation by optical and magnetic tweezers. Such techniques require fast and accurate particle localization algorithms as well as nanometer-scale stability of the microscope. Here, we present a universal method for three-dimensional localization of single labeled and unlabeled particles based on local gradient calculation of particle images. The method outperforms state-of-the-art localization techniques in high-noise conditions, and it is capable of 3D nanometer accuracy localization of nano- and microparticles with sub-millisecond calculation time. By localizing a fixed particle as fiducial mark and running a feedback loop, we demonstrate its applicability for active drift correction in sensitive nanomechanical measurements such as optical trapping and superresolution imaging. A multiplatform open software package comprising a set of tools for local gradient calculation in brightfield, darkfield, and fluorescence microscopy is shared for ready use by the scientific community.

High-resolution Single-molecule Magnetic Tweezers

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

Graphene-Based Opto-Thermoelectric Tweezers

Since the discovery of graphene, its excellent physical properties have greatly improved the performance of optoelectronic devices and brought important technological advances to optical research and its applications. Here, graphene is introduced to the field of optical-tweezer technology and demonstrate a new graphene-based opto-thermoelectric tweezer. This technology not only reduces the incident light energy required by two orders of magnitude (compared with traditional optical tweezers), it also brings new advantages such as a much broader working bandwidth and a larger working area compared to those of widely researched gold-film-based opto-thermoelectric tweezers. Compared with gold film, graphene exhibits higher thermal conductivity and higher uniformity and is easier to process. Thus, it is found that even monolayer graphene provides stable trapping for particles in a broad bandwidth and that performance is enhanced as the number of graphene layers increases. Furthermore, parallel trap multiple particles as desired shapes can be easily generated with structured graphene patterns. This work demonstrates the enormous application potential of graphene in optical-tweezer technology and will promote their application to the trapping or concentration of cells and biomolecules as well as to microfluidics and biosensors.

Tweezepy: A Python package for calibrating forces in single-molecule video-tracking experiments

Single-molecule force spectroscopy (SMFS) instruments (e.g., magnetic and optical tweezers) often use video tracking to measure the three-dimensional position of micron-scale beads under an applied force. The force in these experiments is calibrated by comparing the bead trajectory to a thermal motion-based model with the drag coefficient, γ, and trap spring constant, κ, as parameters. Estimating accurate parameters is complicated by systematic biases from spectral distortions, the camera exposure time, parasitic noise, and least-squares fitting methods. However, while robust calibration methods exist that correct for these biases, they are not always used because they can be complex to implement computationally. To address this barrier, we present Tweezepy: a Python package for calibrating forces in SMFS video-tracking experiments. Tweezepy uses maximum likelihood estimation (MLE) to estimate parameters and their uncertainties from a single bead trajectory via the power spectral density (PSD) and Allan variance (AV). It is well-documented, fast, easy to use, and accounts for most common sources of biases in SMFS video-tracking experiments. Here, we provide a comprehensive overview of Tweezepy's calibration scheme, including a review of the theory underlying thermal motion-based parameter estimates, a discussion of the PSD, AV, and MLE, and an explanation of their implementation.

Temperature Effects on Optical Trapping Stability

In recent years, optically trapped luminescent particles have emerged as a reliable probe for contactless thermal sensing because of the dependence of their luminescence on environmental conditions. Although the temperature effect in the optical trapping stability has not always been the object of study, the optical trapping of micro/nanoparticles above room temperature is hindered by disturbances caused by temperature increments of even a few degrees in the Brownian motion that may lead to the release of the particle from the trap. In this report, we summarize recent experimental results on thermal sensing experiments in which micro/nanoparticles are used as probes with the aim of providing the contemporary state of the art about temperature effects in the stability of potential trapping processes.

Multi-frequency passive and active microrheology with optical tweezers

Optical tweezers have attracted significant attention for microrheological applications, due to the possibility of investigating viscoelastic properties in vivo which are strongly related to the health status and development of biological specimens. In order to use optical tweezers as a microrheological tool, an exact force calibration in the complex system under investigation is required. One of the most promising techniques for optical tweezers calibration in a viscoelastic medium is the so-called active–passive calibration, which allows determining both the trap stiffness and microrheological properties of the medium with the least a-priori knowledge in comparison to the other methods. In this manuscript, we develop an optimization of the active–passive calibration technique performed with a sample stage driving, whose implementation is more straightforward with respect to standard laser driving where two different laser beams are required. We performed microrheological measurements over a broad frequency range in a few seconds implementing an accurate multi-frequency driving of the sample stage. The optical tweezers-based microrheometer was first validated by measuring water, and then exemplarily applied to more viscous medium and subsequently to a viscoelastic solution of methylcellulose in water. The described method paves the way to microrheological precision metrology in biological samples with high temporal- and spatial-resolution allowing for investigation of even short time-scale phenomena.

Plasmonic tweezers: for nanoscale optical trapping and beyond

Optical tweezers and associated manipulation tools in the far field have had a major impact on scientific and engineering research by offering precise manipulation of small objects. More recently, the possibility of performing manipulation with surface plasmons has opened opportunities not feasible with conventional far-field optical methods. The use of surface plasmon techniques enables excitation of hotspots much smaller than the free-space wavelength; with this confinement, the plasmonic field facilitates trapping of various nanostructures and materials with higher precision. The successful manipulation of small particles has fostered numerous and expanding applications. In this paper, we review the principles of and developments in plasmonic tweezers techniques, including both nanostructure-assisted platforms and structureless systems. Construction methods and evaluation criteria of the techniques are presented, aiming to provide a guide for the design and optimization of the systems. The most common novel applications of plasmonic tweezers, namely, sorting and transport, sensing and imaging, and especially those in a biological context, are critically discussed. Finally, we consider the future of the development and new potential applications of this technique and discuss prospects for its impact on science.

Displacement Detection Decoupling in Counter-Propagating Dual-Beams Optical Tweezers with Large-Sized Particle

As a kind of ultra-sensitive acceleration sensing platform, optical tweezers show a minimum measurable value inversely proportional to the square of the diameter of the levitated spherical particle. However, with increasing diameter, the coupling of the displacement measurement between the axes becomes noticeable. This paper analyzes the source of coupling in a forward-scattering far-field detection regime and proposes a novel method of suppression. We theoretically and experimentally demonstrated that when three variable irises are added into the detection optics without changing other parts of optical structures, the decoupling of triaxial displacement signals mixed with each other show significant improvement. A coupling detection ratio reduction of 49.1 dB and 22.9 dB was realized in radial and axial directions, respectively, which is principally in accord with the simulations. This low-cost and robust approach makes it possible to accurately measure three-dimensional mechanical quantities simultaneously and may be helpful to actively cool the particle motion in optical tweezers even to the quantum ground state in the future.

Optical Sorting at the Single-Particle Level with Single-Nanometer Precision Using Coordinated Intensity and Phase Gradient Forces

Position-controlled sorting of colloidal nanoparticles (NPs) at the single-particle level is a challenge in nanoscience. Optofluidic potential wells can partially address this challenge, but they have limited flexibility, reconfigurability, and precision. Here we introduce a strategy by feedback-controlled manipulation of NPs using reconfigurable optical traps with designed intensity and phase gradient. Spatiotemporal patterns of these optical traps coordinatively manipulate the NPs based on machine vision of their positions and differentiated scattering intensities. The NPs are always kept inside the optical field during the manipulation and stably trapped once the sorting is accomplished. To substantiate the key advantages of our approach, we present position-controlled optical sorting of single Ag and Au NPs of the same size (150 nm diameter) and ordering of monodisperse Au NPs (80 ± 9 nm diameter) according to their sub-10 nm radius variation, which can hardly be done via other approaches.

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.

Coherent oscillations of a levitated birefringent microsphere in vacuum driven by nonconservative rotation-translation coupling

We demonstrate an effect whereby stochastic, thermal fluctuations combine with nonconservative optical forces to break detailed balance and produce increasingly coherent, apparently deterministic motion for a vacuum-trapped particle. The particle is birefringent and held in a linearly polarized Gaussian optical trap. It undergoes oscillations that grow rapidly in amplitude as the air pressure is reduced, seemingly in contradiction to the equipartition of energy. This behavior is reproduced in direct simulations and captured in a simplified analytical model, showing that the underlying mechanism involves nonsymmetric coupling between rotational and translational degrees of freedom. When parametrically driven, these self-sustained oscillators exhibit an ultranarrow linewidth of 2.2 μHz and an ultrahigh mechanical quality factor in excess of 2 × 10⁸ at room temperature. Last, nonequilibrium motion is seen to be a generic feature of optical vacuum traps, arising for any system with symmetry lower than that of a perfect isotropic microsphere in a Gaussian trap.

Relaxing constraints on data acquisition and position detection for trap stiffness calibration in optical tweezers

Optical tweezers find applications in various fields, ranging from biology to physics. One of the fundamental steps necessary to perform quantitative measurements using trapped particles is the calibration of the tweezer's spring constant. This can be done through power spectral density analysis, from forward scattering detection of the particle's position. In this work we propose and experimentally test simplifications to such measurement procedure, aimed at reducing post-processing of recorded data and dealing with acquisition devices that have frequency-dependent electronic noise. In the same line of simplifying the tweezer setup we also present a knife-edge detection scheme that can substitute standard position sensitive detectors.

Trapping metallic particles using focused Bloch surface waves

Metallic particles are promising for applications in various areas, including optical sensing, imaging and electric field enhancement-induced optical and thermal effects. The ability to trap or transport these particles stably will be important in these applications. However, while traditional optical tweezers can trap metallic Rayleigh particles easily, it is difficult to trap metallic mesoscopic/Mie particles because of the strong scattering forces that come from the far-field trapping laser beam. Here we demonstrate that metallic particles can be trapped stably using focused Bloch surface waves that propagate in the near-field region of a dielectric multilayer structure with a photonic band gap. Focused Bloch surface waves can be excited efficiently using an annular beam with azimuthal polarization and a high-numerical-aperture objective. Numerical simulations were performed to calculate the optical forces loaded on a gold particle by focused Bloch surface waves and the results were consistent with those of the experimental observations.

The mechanism of DNA unwinding by the eukaryotic replicative helicase

Accurate DNA replication is tightly regulated in eukaryotes to ensure genome stability during cell division and is performed by the multi-protein replisome. At the core an AAA+ hetero-hexameric complex, Mcm2-7, together with GINS and Cdc45 form the active replicative helicase Cdc45/Mcm2-7/GINS (CMG). It is not clear how this replicative ring helicase translocates on, and unwinds, DNA. We measure real-time dynamics of purified recombinant Drosophila melanogaster CMG unwinding DNA with single-molecule magnetic tweezers. Our data demonstrates that CMG exhibits a biased random walk, not the expected unidirectional motion. Through building a kinetic model we find CMG may enter up to three paused states rather than unwinding, and should these be prevented, in vivo fork rates would be recovered in vitro. We propose a mechanism in which CMG couples ATP hydrolysis to unwinding by acting as a lazy Brownian ratchet, thus providing quantitative understanding of the central process in eukaryotic DNA replication.

High-speed transverse and axial optical force measurements using amplitude filter masks

Direct optical force measurement is a versatile method used in optical tweezers experiments, providing accurate measurements of forces for a wide range of particles and trapping beams. It is based on the detection of the change of the momentum of light scattered by a trapped object. A digital micromirror device can be used to selectively reflect light in different directions using an appropriately defined mask. We have developed position-sensitive masked detection (PSMD) for measuring transverse (radial) and axial forces. The method is comparable in performance to the fastest split detectors, while maintaining the linearity and customizability similar to duo-lateral position-sensitive detectors (PSD) and cameras. We show an order of magnitude increase in the bandwidth compared to a conventional PSD for radial forces. We measure axial force and verify the measurement using the Stokes drag for the particle. Combining both detectors (PSMD and PSD), we can perform full 3-D optical force measurements in real time.

Indirect optical trapping using light driven micro-rotors for reconfigurable hydrodynamic manipulation

Optical tweezers are a highly versatile tool for exploration of the mesoscopic world, permitting non-contact manipulation of nanoscale objects. However, direct illumination with intense lasers restricts their use with live biological specimens, and limits the types of materials that can be trapped. Here we demonstrate an indirect optical trapping platform which circumvents these limitations by using hydrodynamic forces to exert nanoscale-precision control over aqueous particles, without directly illuminating them. Our concept is based on optically actuated micro-robotics: closed-loop control enables highly localised flow-fields to be sculpted by precisely piloting the motion of optically-trapped micro-rotors. We demonstrate 2D trapping of absorbing particles which cannot be directly optically trapped, stabilise the position and orientation of yeast cells, and demonstrate independent control over multiple objects simultaneously. Our work expands the capabilities of optical tweezers platforms, and represents a new paradigm for manipulation of aqueous mesoscopic systems.

Optical tweezing with intense lasers can be harmful to biological specimens and limits the types of materials that can be trapped. Here, the authors demonstrate an indirect optical trapping approach which uses hydrodynamic forces to exert nanoscale-precision control over aqueous particles, without directly illuminating them.

All-fiber interferometer for displacement and velocity measurement of a levitated particle in fiber-optic traps

We propose an all-fiber interferometer based on laser Doppler velocimetry in a dual-beam fiber-optic trap to measure the displacement and velocity of a trapped particle. ABCD matrices are used to compute the contrast ratio of the interference. The influence of the reflectivity of the fiber end face is discussed. We have designed an optimized reflectivity based on the parameters of our setup. The antireflective coatings on the fiber end face are employed to achieve the given reflectivity. The displacement and velocity of the trapped microparticle are successfully measured by the period and frequency of the interference signal, respectively. The sensitivity of the displacement detection is 368 nm. By describing the miniaturization of the detection system, this paper provides a simple and practical scheme to achieve the integration of the entire optical trapping setup.

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

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

Micro-Dumbbells-A Versatile Tool for Optical Tweezers

Manipulation of micro- and nano-sized objects with optical tweezers is a well-established, albeit still evolving technique. While many objects can be trapped directly with focused laser beam(s), for some applications indirect manipulation with tweezers-operated tools is preferred. We introduce a simple, versatile micro-tool operated with holographic optical tweezers. The 40 µm long dumbbell-shaped tool, fabricated with two-photon laser 3D photolithography has two beads for efficient optical trapping and a probing spike on one end. We demonstrate fluids viscosity measurements and vibration detection as examples of possible applications.

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.

Effect of red light on optically trapped spermatozoa

Successful artificial insemination relies on the use of high quality spermatozoa. One measure of sperm quality is swimming force. Increased swimming force has been correlated with higher sperm swimming speeds and improved reproductive success. It is hypothesized that by increasing sperm swimming speed, one can increase swimming force. Previous studies have shown that red light irradiation causes an increase in sperm swimming speed. In the current study, 633nm red light irradiation is shown to increase mean squared displacement in trapped sperm. The methodology allows for comparison of relative swimming forces between irradiated and non-irradiated samples.

Extending calibration-free force measurements to optically-trapped rod-shaped samples

Optical trapping has become an optimal choice for biological research at the microscale due to its non-invasive performance and accessibility for quantitative studies, especially on the forces involved in biological processes. However, reliable force measurements depend on the calibration of the optical traps, which is different for each experiment and hence requires high control of the local variables, especially of the trapped object geometry. Many biological samples have an elongated, rod-like shape, such as chromosomes, intracellular organelles (e.g., peroxisomes), membrane tubules, certain microalgae, and a wide variety of bacteria and parasites. This type of samples often requires several optical traps to stabilize and orient them in the correct spatial direction, making it more difficult to determine the total force applied. Here, we manipulate glass microcylinders with holographic optical tweezers and show the accurate measurement of drag forces by calibration-free direct detection of beam momentum. The agreement between our results and slender-body hydrodynamic theoretical calculations indicates potential for this force-sensing method in studying protracted, rod-shaped specimens.

Advances in the microrheology of complex fluids

New developments in the microrheology of complex fluids are considered. Firstly the requirements for a simple modern particle tracking microrheology experiment are introduced, the error analysis methods associated with it and the mathematical techniques required to calculate the linear viscoelasticity. Progress in microrheology instrumentation is then described with respect to detectors, light sources, colloidal probes, magnetic tweezers, optical tweezers, diffusing wave spectroscopy, optical coherence tomography, fluorescence correlation spectroscopy, elastic- and quasi-elastic scattering techniques, 3D tracking, single molecule methods, modern microscopy methods and microfluidics. New theoretical techniques are also reviewed such as Bayesian analysis, oversampling, inversion techniques, alternative statistical tools for tracks (angular correlations, first passage probabilities, the kurtosis, motor protein step segmentation etc), issues in micro/macro rheological agreement and two particle methodologies. Applications where microrheology has begun to make some impact are also considered including semi-flexible polymers, gels, microorganism biofilms, intracellular methods, high frequency viscoelasticity, comb polymers, active motile fluids, blood clots, colloids, granular materials, polymers, liquid crystals and foods. Two large emergent areas of microrheology, non-linear microrheology and surface microrheology are also discussed.

A one-piece 3D printed flexure translation stage for open-source microscopy

Open source hardware has the potential to revolutionise the way we build scientific instruments; with the advent of readily available 3D printers, mechanical designs can now be shared, improved, and replicated faster and more easily than ever before. However, printed parts are typically plastic and often perform poorly compared to traditionally machined mechanisms. We have overcome many of the limitations of 3D printed mechanisms by exploiting the compliance of the plastic to produce a monolithic 3D printed flexure translation stage, capable of sub-micron-scale motion over a range of 8 × 8 × 4 mm. This requires minimal post-print clean-up and can be automated with readily available stepper motors. The resulting plastic composite structure is very stiff and exhibits remarkably low drift, moving less than 20 μm over the course of a week, without temperature stabilisation. This enables us to construct a miniature microscope with excellent mechanical stability, perfect for time-lapse measurements in situ in an incubator or fume hood. The ease of manufacture lends itself to use in containment facilities where disposability is advantageous and to experiments requiring many microscopes in parallel. High performance mechanisms based on printed flexures need not be limited to microscopy, and we anticipate their use in other devices both within the laboratory and beyond.

'Lissajous-like' trajectories in optical tweezers

When a microscopic particle moves through a low Reynolds number fluid, it creates a flow-field which exerts hydrodynamic forces on surrounding particles. In this work we study the 'Lissajous-like' trajectories of an optically trapped 'probe' microsphere as it is subjected to time-varying oscillatory hydrodynamic flow-fields created by a nearby moving particle (the 'actuator'). We show a breaking of time-reversal symmetry in the motion of the probe when the driving motion of the actuator is itself time-reversal symmetric. This symmetry breaking results in a fluid-pumping effect, which arises due to the action of both a time-dependent hydrodynamic flow and a position-dependent optical restoring force, which together determine the trajectory of the probe particle. We study this situation experimentally, and show that the form of the trajectories observed is in good agreement with Stokesian dynamics simulations. Our results are related to the techniques of active micro-rheology and flow measurement, and also highlight how the mere presence of an optical trap can perturb the environment it is in place to measure.

Three-dimensional motion detection of a 20-nm gold nanoparticle using twilight-field digital holography with coherence regulation

In the twilight-field method for obtaining interference fringes with high contrast in in-line digital holography, only the intensity of the reference light is regulated to be close to the intensity of the object light, which is the ultra-weak scattered light from a nanoparticle, by using a low-frequency attenuation filter. Coherence of the light also strongly affects the contrast of the interference fringes. High coherence causes a lot of undesired coherent noise, which masks the fringes derived from the nanoparticles. Too-low coherence results in fringes with low contrast and a correspondingly low signal-to-noise ratio. Consequently, proper regulation of the coherence of the light source, in this study the spectral width, improves the minimum detectable size in holographic three-dimensional position measurement of nanoparticles. By using these methods, we were able to measure the position of a gold nanoparticle with a minimum diameter of 20 nm.

Microrheology with optical tweezers: measuring the relative viscosity of solutions 'at a glance'

We present a straightforward method for measuring the relative viscosity of fluids via a simple graphical analysis of the normalised position autocorrelation function of an optically trapped bead, without the need of embarking on laborious calculations. The advantages of the proposed microrheology method are evident when it is adopted for measurements of materials whose availability is limited, such as those involved in biological studies. The method has been validated by direct comparison with conventional bulk rheology methods, and has been applied both to characterise synthetic linear polyelectrolytes solutions and to study biomedical samples.

Precision assembly of complex cellular microenvironments using holographic optical tweezers

The accurate study of cellular microenvironments is limited by the lack of technologies that can manipulate cells in 3D at a sufficiently small length scale. The ability to build and manipulate multicellular microscopic structures will facilitate a more detailed understanding of cellular function in fields such as developmental and stem cell biology. We present a holographic optical tweezers based technology to accurately generate bespoke cellular micro-architectures. Using embryonic stem cells, 3D structures of varying geometries were created and stabilized using hydrogels and cell-cell adhesion methods. Control of chemical microenvironments was achieved by the temporal release of specific factors from polymer microparticles positioned within these constructs. Complex co-culture micro-environmental analogues were also generated to reproduce structures found within adult stem cell niches. The application of holographic optical tweezers-based micromanipulation will enable novel insights into biological microenvironments by allowing researchers to form complex architectures with sub-micron precision of cells, matrices and molecules.

Label-free free-solution nanoaperture optical tweezers for single molecule protein studies

Recent advances in nanoaperture optical tweezers have enabled studies of single nanoparticles like proteins in label-free, free-solution environments.

Toward optical-tweezers-based force microscopy for airborne microparticles

Optical tweezers have found widespread application in biological and colloidal physics for the measurement of pN forces over nanometer to micrometer length scales. Similar aerosol-phase measurements of interparticle force have not been reported in spite of the potential to better resolve particle coagulation kinetics. Various refractive index mismatches in the beam path as well as the need to explicitly account for gravity and inertial particle motion provide a number of challenges that must be overcome to make such measurements tractable. In this regard, we demonstrate schemes by which the particle position and trap stiffness may be unambiguously measured using bright-field microscopy with resolution comparable with analogous condensed-phase measurements. Moreover, some of the challenges of working with highly dynamic aqueous particles are introduced and exploited to observe size-dependent phenomena in aerosol optical tweezers. Notably, when combined with cavity-enhanced Raman spectroscopy, this provides a unique opportunity to explore trapping forces over a continuum of particle size and refractive index. It is expected that the methods developed will provide a basis for the measurement of pairwise interaction forces in aerosol optical tweezers while providing a probe of fundamental airborne particle trapping dynamics.

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

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

Simultaneous three-dimensional tracking of individual signals from multi-trap optical tweezers using fast and accurate photodiode detection

Multiple-beam optical traps facilitate advanced trapping geometries and exciting discoveries. However, the increased manipulation capabilities come at the price of more challenging position and force detection. Due to unrivaled bandwidth and resolution, photodiode based detection is preferred over camera based detection in most single/dual-beam optical traps assays. However, it has not been trivial to implement photodiode based detection for multiple-beam optical traps. Here, we present a simple and efficient method based on spatial filtering for parallel photodiode detection of multiple traps. The technique enables fast and accurate 3D force and distance detection of multiple objects simultaneously manipulated by multiple-beam optical tweezers.

Probing the micro-rheological properties of aerosol particles using optical tweezers

The use of optical trapping techniques to manipulate probe particles for performing micro-rheological measurements on a surrounding fluid is well-established. Here, we review recent advances made in the use of optical trapping to probe the rheological properties of trapped particles themselves. In particular, we review observations of the continuous transition from liquid to solid-like viscosity of sub-picolitre supersaturated solution aerosol droplets using optical trapping techniques. Direct measurements of the viscosity of the particle bulk are derived from the damped oscillations in shape following coalescence of two particles, a consequence of the interplay between viscous and surface forces and the capillary driven relaxation of the approximately spheroidal composite particle. Holographic optical tweezers provide a facile method for the manipulation of arrays of particles allowing coalescence to be controllably induced between two micron-sized aerosol particles. The optical forces, while sufficiently strong to confine the composite particle, are several orders of magnitude weaker than the capillary forces driving relaxation. Light, elastically back-scattered by the particle, is recorded with sub-100 ns resolution allowing measurements of fast relaxation (low viscosity) dynamics, while the brightfield image can be used to monitor the shape relaxation extending to times in excess of 1000 s. For the slowest relaxation dynamics studied (particles with the highest viscosity) the presence and line shape of whispering gallery modes in the cavity enhanced Raman spectrum can be used to infer the relaxation time while serving the dual purpose of allowing the droplet size and refractive index to be measured with accuracies of ±0.025% and ±0.1%, respectively. The time constant for the damped relaxation can be used to infer the bulk viscosity, spanning from the dilute solution limit to a value approaching that of a glass, typically considered to be >10(12) Pa s, whilst the frequencies of the normal modes of the oscillations of the particle can be used to infer surface properties. We will review the use of optical tweezers for studying the viscosity of aerosol particles and discuss the potential use of this micro-rheological tool for probing the fundamental concepts of phase, thermodynamic equilibrium and metastability.

Optically trapped bacteria pairs reveal discrete motile response to control aggregation upon cell-cell approach

Aggregation of bacteria plays a key role in the formation of many biofilms. The critical first step is cell-cell approach, and yet the ability of bacteria to control the likelihood of aggregation during this primary phase is unknown. Here, we use optical tweezers to measure the force between isolated Bacillus subtilis cells during approach. As we move the bacteria towards each other, cell motility (bacterial swimming) initiates the generation of repulsive forces at bacterial separations of ~3 μm. Moreover, the motile response displays spatial sensitivity with greater cell-cell repulsion evident as inter-bacterial distances decrease. To examine the environmental influence on the inter-bacterial forces, we perform the experiment with bacteria suspended in Tryptic Soy Broth, NaCl solution and deionised water. Our experiments demonstrate that repulsive forces are strongest in systems that inhibit biofilm formation (Tryptic Soy Broth), while attractive forces are weak and rare, even in systems where biofilms develop (NaCl solution). These results reveal that bacteria are able to control the likelihood of aggregation during the approach phase through a discretely modulated motile response. Clearly, the force-generating motility we observe during approach promotes biofilm prevention, rather than biofilm formation.

Theoretical analysis for the optical deformation of emulsion droplets

We propose a theoretical framework to predict the three-dimensional shapes of optically deformed micron-sized emulsion droplets with ultra-low interfacial tension. The resulting shape and size of the droplet arises out of a balance between the interfacial tension and optical forces. Using an approximation of the laser field as a Gaussian beam, working within the Rayleigh-Gans regime and assuming isotropic surface energy at the oil-water interface, we numerically solve the resulting shape equations to elucidate the three-dimensional droplet geometry. We obtain a plethora of shapes as a function of the number of optical tweezers, their laser powers and positions, surface tension, initial droplet size and geometry. Experimentally, two-dimensional droplet silhouettes have been imaged from above, but their full side-on view has not been observed and reported for current optical configurations. This experimental limitation points to ambiguity in differentiating between droplets having the same two-dimensional projection but with disparate three-dimensional shapes. Our model elucidates and quantifies this difference for the first time. We also provide a dimensionless number that indicates the shape transformation (ellipsoidal to dumbbell) at a value ≈ 1.0, obtained by balancing interfacial tension and laser forces, substantiated using a data collapse.

Dynamic stereo microscopy for studying particle sedimentation

We demonstrate a new method for measuring the sedimentation of a single colloidal bead by using a combination of optical tweezers and a stereo microscope based on a spatial light modulator. We use optical tweezers to raise a micron-sized silica bead to a fixed height and then release it to observe its 3D motion while it sediments under gravity. This experimental procedure provides two independent measurements of bead diameter and a measure of Faxén's correction, where the motion changes due to presence of the boundary.

Quantification of high-efficiency trapping of nanoparticles in a double nanohole optical tweezer

We measure the dynamics of 20 nm polystyrene particles in a double nanohole trap to determine the trap stiffness for various laser powers. Both the autocorrelation analysis of Brownian fluctuations and the trapping transient analysis provide a consistent value of ∼ 0.2 fN/nm stiffness for 2 mW of laser power, which is similar to theoretical calculations for aperture trapping. As expected, the stiffness increases linearly with laser power. This is comparable to the stiffness obtained for conventional optical traps for trapping, but for ten times smaller dielectric particles and less power. This approach will allow us to quantitatively evaluate future aperture-based optical traps, with the goal of studying the folding dynamics of smaller proteins (∼ 10 kDa) and small-molecule interactions.

Single and dual fiber nano-tip optical tweezers: trapping and analysis

An original optical tweezers using one or two chemically etched fiber nano-tips is developed. We demonstrate optical trapping of 1 micrometer polystyrene spheres at optical powers down to 2 mW. Harmonic trap potentials were found in the case of dual fiber tweezers by analyzing the trapped particle position fluctuations. The trap stiffness was deduced using three different models. Consistent values of up to 1 fN/nm were found. The stiffness linearly decreases with decreasing light intensity and increasing fiber tip-to-tip distance.

Holographic optical tweezers combined with back-focal-plane displacement detection

A major problem with holographic optical tweezers (HOTs) is their incompatibility with laser-based position detection methods, such as back-focal-plane interferometry (BFPI). The alternatives generally used with HOTs, like high-speed video tracking, do not offer the same spatial and temporal bandwidths. This has limited the use of this technique in precise quantitative experiments. In this paper, we present an optical trap design that combines digital holography and back-focal-plane displacement detection. We show that, with a particularly simple setup, it is possible to generate a set of multiple holographic traps and an additional static non-holographic trap with orthogonal polarizations and that they can be, therefore, easily separated for measuring positions and forces with the high positional and temporal resolutions of laser-based detection. We prove that measurements from both polarizations contain less than 1% crosstalk and that traps in our setup are harmonic within the typical range. We further tested the instrument in a DNA stretching experiment and we discuss an interesting property of this configuration: the small drift of the differential signal between traps.

Invited article: a review of haptic optical tweezers for an interactive microworld exploration

This paper is the first review of haptic optical tweezers, a new technique which associates force feedback teleoperation with optical tweezers. This technique allows users to explore the microworld by sensing and exerting picoNewton-scale forces with trapped microspheres. Haptic optical tweezers also allow improved dexterity of micromanipulation and micro-assembly. One of the challenges of this technique is to sense and magnify picoNewton-scale forces by a factor of 10(12) to enable human operators to perceive interactions that they have never experienced before, such as adhesion phenomena, extremely low inertia, and high frequency dynamics of extremely small objects. The design of optical tweezers for high quality haptic feedback is challenging, given the requirements for very high sensitivity and dynamic stability. The concept, design process, and specification of optical tweezers reviewed here are focused on those intended for haptic teleoperation. In this paper, two new specific designs as well as the current state-of-the-art are presented. Moreover, the remaining important issues are identified for further developments. The initial results obtained are promising and demonstrate that optical tweezers have a significant potential for haptic exploration of the microworld. Haptic optical tweezers will become an invaluable tool for force feedback micromanipulation of biological samples and nano- and micro-assembly parts.

Using optical tweezers for the characterization of polyelectrolyte solutions with very low viscoelasticity

Recently, optical tweezing has been used to provide a method for microrheology addressed to measure the rheological properties of small volumes of samples. In this work, we corroborate this emerging field of microrheology by using these optical methods for the characterization of polyelectrolyte solutions with very low viscoelasticity. The influence of polyelectrolyte (i.e., polyacrylamide, PAM) concentration, specifically its aging, of the salt concentration is shown. The close agreement of the technique with classical bulk rheological measurements is demonstrated, illustrating the advantages of the technique.

Pushing, pulling and twisting liquid crystal systems: exploring new directions with laser manipulation

Optical tweezers are exciting tools with which to explore liquid crystal (LC) systems; the motion of particles held in laser traps through LCs is perhaps the only approach that allows a low Ericksen number regime to be accessed. This offers a new method of studying the microrheology associated with micrometre-sized particles suspended in LC media--and such hybrid systems are of increasing importance as novel soft-matter systems. This paper describes the microrheology experiments that are possible in nematic materials and discusses the sometimes unexpected results that ensue. It also presents observations made in the inverse system; micrometre-sized droplets of LC suspended in an isotropic medium.

Optical trapping and binding

The phenomenon of light's momentum was first observed in the laboratory at the beginning of the twentieth century, and its potential for manipulating microscopic particles was demonstrated by Ashkin some 70 years later. Since that initial demonstration, and the seminal 1986 paper where a single-beam gradient-force trap was realized, optical trapping has been exploited as both a rich example of physical phenomena and a powerful tool for sensitive measurement. This review outlines the underlying theory of optical traps, and explores many of the physical observations that have been made in such systems. These phenomena include 'optical binding', where trapped objects interact with one another through the trapping light field. We also discuss a number of the applications of 'optical tweezers' across the physical and life sciences, as well as covering some of the issues involved in constructing and using such a tool.