Trap Optical Tweezers Research Articles

Non-transverse electromagnetic fields in micro- and nano-fibers

We present an analytical and numerical study of electromagnetic modes in micro- and nano-fibers (MNFs) where the electric and magnetic fields of the modes are not necessarily orthogonal to each other. We first investigate these modes for different fiber structures including circular- and rectangular-core fibers as well as photonic crystal fibers. We then discuss two specific applications of these modes: (1) generation of hypothetical axions that are coupled to the electromagnetic fields through the dot product of electric and magnetic fields of a mode, E→⋅B→, and (2) a new type of optical trap (optical tweezers) for chiral atoms with magneto-electric cross coupling, where the confining potential again is proportional to E→⋅B→.

Studying fluctuating trajectories of optically confined passive tracers inside cells provides familiar active forces.

In recent years, there has been a growing interest in studying the trajectories of microparticles inside living cells. Among other things, such studies are useful in understanding the spatio-temporal properties of a cell. In this work, we study the stochastic trajectories of a passive microparticle inside a cell using experiments and theory. Our theory is based on modeling the microparticle inside a cell as an active particle in a viscoelastic medium. The activity is included in our model from an additional stochastic term with non-zero persistence in the Langevin equation describing the dynamics of the microparticle. Using this model, we are able to predict the power spectral density (PSD) measured in the experiment and compute active forces. This caters to the situation where a tracer particle is optically confined and then yields a PSD for positional fluctuations. The low frequency part of the PSD yields information about the active forces that the particle feels. The fit to the model extracts such active force. Thus, we can conclude that trapping the particle does not affect the values of the forces extracted from the active fits if accounted for appropriately by proper theoretical models. In addition, the fit also provides system properties and optical tweezers trap stiffness.

Collisional dynamics of a few atom quantum system with tunable interaction

The advent of single-atom trapping in optical tweezers and experimental evolution in control, isolation, and manipulation of cold atoms allows us to manifest the few-body physics and its connection with the many-body systems. In cold atom experiments, the universality of few-body physics is majorly governed by the scattering length which makes it an important parameter in determining theoretically calculated loss rates. Here, we numerically study the 3-body collisional dynamics for Cesium atoms using the atom loss model described by Born-Markov approximation. Using the Cs atoms provides us the freedom to vary the scattering length, a, as a function of the magnetic field through Feshbach resonances. We investigate the three-, two-, and one-particle processes in the repulsive interactions regime at different values for a. We find that the probability of one atom remaining in the trap is maximum at B = 26 G corresponding to a = 402.382a 0 and has the highest value amongst the probability of zero-, two-, and three-particle remaining in the trap at same magnetic field after the collision. Our findings leads to high fidelity single atom tweezers which have direct application in creating defect free arrays for quantum information processing purposes.

Use of Dual Optical Tweezers and Microfluidics for Single-Molecule Studies.

Visual biochemistry is a powerful technique for observing the stochastic properties of single enzymes or enzyme complexes that are obscured in the averaging that takes place in bulk-phase studies. To achieve visualization, dual optical tweezers, where one trap is fixed and the other is mobile, are focused into one channel of a multi-stream microfluidic chamber positioned on the stage of an inverted fluorescence microscope. The optical tweezers trap single molecules of fluorescently labeled DNA and fluid flow through the chamber and past the trapped beads, stretches the DNA to B-form (under minimal force, i.e., 0 pN) with the nucleic acid being observed as a white string against a black background. DNA molecules are moved from one stream to the next, by translating the stage perpendicular to the flow to enable the initiation of reactions in a controlled manner. To achieve success, microfluidic devices with optically clear channels are mated to glass syringes held in place in a syringe pump. Optimal results use connectors permanently bonded to the flow cell, tubing that is mechanically rigid and chemically resistant, and which is connected to switching valves that eliminate bubbles that prohibit laminar flow.

Implementation of 3D Multi-Color Fluorescence Microscopy in a Quadruple Trap Optical Tweezers System.

Recent advances in the design and measurement capabilities of optical tweezers instruments, and especially the combination with multi-color fluorescence detection, have accommodated a dramatic increase in the versatility of optical trapping. Quadruple (Q)-trap optical tweezers are an excellent example of such an advance, by providing three-dimensional control over two constructs and thereby enabling for example DNA-DNA braiding. However, the implementation of fluorescence detection in such a Q-trapping system poses several challenges: (1) since typical samples span a distance in the order of tens of micrometers, it requires imaging of a large field of view, (2) in order to capture fast molecular dynamics, fast imaging with single-molecule sensitivity is desired, (3) in order to study three-dimensional objects, it could be needed to detect emission light at different axial heights while keeping the objective lens and thus the optically trapped microspheres in a fixed position. In this chapter, we describe design guidelines for a fluorescence imaging module on a Q-trap system that overcomes these challenges and provide a step-by-step description for construction and alignment of such a system. Finally, we present detailed instructions for proof-of-concept experiments that can be used to validate and highlight the capabilities of the instruments.

Mathematical Model of a Nanosensor Based on Optical Tweezers

The paper considers the conditions for capturing a dielectric nanoparticle in a liquid by an optical tweezers trap. It is shown that the displacement of a nanoparticle from the equilibrium position under the action of a local physical field not associated with a laser trap shaper can be used to create a nanosensor for fields of physical or chemical origin.

Enhancing Dipolar Interactions between Molecules Using State-Dependent Optical Tweezer Traps.

We show how state-dependent optical potentials can be used to trap a pair of molecules in different internal states at a separation much smaller than the wavelength of the trapping light. This close spacing greatly enhances the dipole-dipole interaction and we show how it can be used to implement two-qubit gates between molecules that are 100 times faster than existing protocols and than rotational coherence times already demonstrated. We analyze complications due to hyperfine structure, tensor light shifts, photon scattering, and collisional loss, and conclude that none is a barrier to implementing the scheme.

Studying the rigidity of red blood cells induced by Plasmodium falciparum infection

We study the effect of different chemical moieties on the rigidity of red blood cells (RBCs) induced by Plasmodium falciparum infection, and the bystander effect previously found. The infected cells are obtained from a culture of parasite-infected RBCs grown in the laboratory. The rigidity of RBCs is measured by looking at the Brownian fluctuations of individual cells in an optical-tweezers trap. The results point towards increased intracellular cyclic adenosine monophosphate (cAMP) levels as being responsible for the increase in rigidity.

Raman sideband cooling of a single atom in an optical dipole trap: Toward a theoretical optimum in a three-dimensional regime

We clarify the optimal conditions for the protocol of Raman sideband cooling (RSC) of a single atom confined with a tightly focused far-off-resonant optical dipole trap (optical tweezers). The protocol ultimately pursues cooling to a three-dimensional ground state of the confining potential. We show that the RSC protocol has to fulfil a set of critical requirements for the parameters of cooling beams and the excitation geometry to be effective in a most general three-dimensional confguration and for an atom, having initial temperature between the recoil and the Doppler bounds. We perform a numerical simulation of the Raman passage for an example of an $^{85}$Rb atom taking into account the full level structure and all possible transition channels.

Optical Force Sensing with Cylindrical Microcontainers

AbstractQuantitative force sensing reveals essential information for the study of biological systems. Forces on molecules, cells, and tissues uncover functioning conditions and pathways. To analyze such forces, spherical particles are trapped and controlled inside an optical tweezers (OT) trap. Although these spherical particles are well‐established sensors in biophysics, elongated probes are envisioned for remote force sensing reducing heat damage caused by OT. There is thus a growing demand for force metrology with OT using complexly shaped objects, e.g., sac‐like organelles or rod‐like bacteria. Here, the employment of Zeolite‐L crystals as cylindrical force sensing probes inside a single optical trap is investigated. It is shown that cylindrical objects can be used as force probes since existing calibration assays can be performed with suitable corrections. Forces of active driving assays are compared with passive calibration methods. Finally, the investigations are extended to direct force measurements based on momentum calibration, in which the influence of rotation due to torque in a single optical trap is unveiled. Simulations reveal the relation between torque and the position of equilibrium in the trap. The results highlight the functionality of Zeolite‐L crystals as probes for force sensing, while opening perspectives for enhanced, accurate force metrology in biophotonics.

Single-atom trapping and transport in DMD-controlled optical tweezers

We demonstrate the trapping and manipulation of single neutral atoms in reconfigurable arrays of optical tweezers. Our approach offers unparalleled speed by using a Texas instruments digital micro-mirror device as a holographic amplitude modulator with a frame rate of 20 000 per second. We show the trapping of static arrays of up to 20 atoms, as well as transport of individually selected atoms over a distance of 25 μm with laser cooling and 4 μm without. We discuss the limitations of the technique and the scope for technical improvements.

Diagnosis of malarial infection using change in properties of optically trapped red blood cells

BackgroundIn previous work studying the properties of red blood cells (RBCs) held in an optical tweezers trap, we observed an increase in the spectrum of Brownian fluctuations for RBCs from a Plasmodium falciparum culture—due to increased rigidity of the cells—compared to normal RBCs. We wanted to extend the study to patient samples, since the earlier work was done with cultures grown in the lab. MethodsIndividual RBCs were held in an optical-tweezers trap. Its position fluctuations were measured and the power spectrum determined. The corner frequency (fc) of the spectrum gave a quantitative measurement of the spectrum. ResultsThe value of fc was 25 Hz for normal cells, which increased to 29 Hz for infected cells—both for P. falciparum and Plasmodium vivax infections. ConclusionThe technique of measuring fc can be used as a screening tool for malaria in patients with fever, since RBCs not carrying the parasite will also show the change due to the bystander effect, irrespective of whether it is caused by P. falciparum or P. vivax.

Nucleosomal arrangement affects single-molecule transcription dynamics

In eukaryotes, gene expression depends on chromatin organization. However, how chromatin affects the transcription dynamics of individual RNA polymerases has remained elusive. Here, we use dual trap optical tweezers to study single yeast RNA polymerase II (Pol II) molecules transcribing along a DNA template with two nucleosomes. The slowdown and the changes in pausing behavior within the nucleosomal region allow us to determine a drift coefficient, χ, which characterizes the ability of the enzyme to recover from a nucleosomal backtrack. Notably, χ can be used to predict the probability to pass the first nucleosome. Importantly, the presence of a second nucleosome changes χ in a manner that depends on the spacing between the two nucleosomes, as well as on their rotational arrangement on the helical DNA molecule. Our results indicate that the ability of Pol II to pass the first nucleosome is increased when the next nucleosome is turned away from the first one to face the opposite side of the DNA template. These findings help to rationalize how chromatin arrangement affects Pol II transcription dynamics.

Fast and Accurate Photodiode-Based Detection of Multiple Trap Optical Tweezers with Crosstalk-Elimination

Multiple trap optical tweezers have proven instrumental for a variety of exciting biophysical discoveries, e.g., from shedding light on molecular motor mechanisms to revealing intricate details of DNA-protein interactions. This ‘second’ generation of optical tweezers allows for advanced trapping geometries beyond single traps, however, these increased manipulation capabilities typically come at the price of more challenging position and force detection. The accuracy of position and force measurements is often compromised by crosstalk between the detected signals, this crosstalk leading to systematic and significant errors on the measured forces and distances. We developed an easy-to-implement simple method that enables simultaneous three-dimensional tracking of several individual objects in dual trap optical tweezers [1] and multi-trap holographic optical tweezers [2,3]. The method is based on spatial filtering and is highly compatible with standard back-focal-plane photodiode-based detection offering unrivaled temporal and spatial resolution with minimal crosstalk. This fast and accurate photodiode-based detection offers distinct advantages over camera-based solutions and opens the possibility for a variety of new biophysical assays. The reported technique significantly improves the accuracy of force-distance measurements, e.g., of single molecules, and hence provides much more scientific value for the experimental efforts.Publications:[1] D. Ott, S.N.S. Reihani, & L.B. Oddershede, “Crosstalk elimination in the detection of dual-beam optical tweezers by spatial filtering,” Review of Scientific Instruments,(2014).[2] D. Ott, S.N.S. Reihani, & L.B. Oddershede, “Simultaneous three-dimensional tracking of individual signals from multi-trap optical tweezers using fast and accurate photodiode detection,” Optics Express (2014).Filed Patent:[3] L.B. Oddershede, D. Ott, S.N.S. Reihani, “A detection system for an optical manipulation system for manipulating micro-particles or nano-particles of a sample by means of at least two optical traps,” PA 2014 70097, Denmark.

Counter-propagating dual-trap optical tweezers based on linear momentum conservation

We present a dual-trap optical tweezers setup which directly measures forces using linear momentum conservation. The setup uses a counter-propagating geometry, which allows momentum measurement on each beam separately. The experimental advantages of this setup include low drift due to all-optical manipulation, and a robust calibration (independent of the features of the trapped object or buffer medium) due to the force measurement method. Although this design does not attain the high-resolution of some co-propagating setups, we show that it can be used to perform different single molecule measurements: fluctuation-based molecular stiffness characterization at different forces and hopping experiments on molecular hairpins. Remarkably, in our setup it is possible to manipulate very short tethers (such as molecular hairpins with short handles) down to the limit where beads are almost in contact. The setup is used to illustrate a novel method for measuring the stiffness of optical traps and tethers on the basis of equilibrium force fluctuations, i.e., without the need of measuring the force vs molecular extension curve. This method is of general interest for dual trap optical tweezers setups and can be extended to setups which do not directly measure forces.

The bystander effect in optically trapped red blood cells due to Plasmodium falciparum infection

In a previous study of the properties of red blood cells (RBC) trapped in an optical tweezers trap, an increase in the spectrum of Brownian fluctuations for RBCs from a Plasmodium falciparum culture (due to increased rigidity) compared with normal RBCs was measured. A bystander effect was observed, whereby RBCs actually hosting the parasite had an effect on the physical properties of remaining non-hosting RBCs. The distribution of corner frequency (fc) in the power spectrum of single RBCs held in an optical tweezers trap was studied. Two tests were done to confirm the bystander effect. In the first, RBCs from an infected culture were separated into hosting and non-hosting RBCs. In the second, all RBCs were removed from the infected culture, and normal RBCs were incubated in the spent medium. The trapping environment was the same for all measurements so only changes in the properties of RBCs were measured. In the first experiment, a similar and statistically significant increase was measured both for hosting and non-hosting RBCs. In the second experiment, normal RBCs incubated in spent medium started to become rigid after a few hours and showed complete changes (comparable with RBCs from the infected culture) after 24 h. These experiments provide direct evidence of medium-induced changes in the properties of RBCs in an infected culture, regardless of whether the RBCs actually host the parasite.

Force Mapping during the Formation and Maturation of Cell Adhesion Sites with Multiple Optical Tweezers

Focal contacts act as mechanosensors allowing cells to respond to their biomechanical environment. Force transmission through newly formed contact sites is a highly dynamic process requiring a stable link between the intracellular cytoskeleton and the extracellular environment. To simultaneously investigate cellular traction forces in several individual maturing adhesion sites within the same cell, we established a custom-built multiple trap optical tweezers setup. Beads functionalized with fibronectin or RGD-peptides were placed onto the apical surface of a cell and trapped with a maximum force of 160 pN. Cells form adhesion contacts around the beads as demonstrated by vinculin accumulation and start to apply traction forces after 30 seconds. Force transmission was found to strongly depend on bead size, surface density of integrin ligands and bead location on the cell surface. Highest traction forces were measured for beads positioned on the leading edge. For mouse embryonic fibroblasts, traction forces acting on single beads are in the range of 80 pN after 5 minutes. If two beads were positioned parallel to the leading edge and with a center-to-center distance less than 10 µm, traction forces acting on single beads were reduced by 40%. This indicates a spatial and temporal coordination of force development in closely related adhesion sites. We also used our setup to compare traction forces, retrograde transport velocities, and migration velocities between two cell lines (mouse melanoma and fibroblasts) and primary chick fibroblasts. We find that maximal force development differs considerably between the three cell types with the primary cells being the strongest. In addition, we observe a linear relation between force and retrograde transport velocity: a high retrograde transport velocity is associated with strong cellular traction forces. In contrast, migration velocity is inversely related to traction forces and retrograde transport velocity.

Cytoskeletal strains in modeled optohydrodynamically stressed healthy and diseased biological cells.

Controlled external chemomechanical stimuli have been shown to influence cellular and tissue regeneration/degeneration, especially with regards to distinct disease sequelae or health maintenance. Recently, a unique three-dimensional stress state was mathematically derived to describe the experimental stresses applied to isolated living cells suspended in an optohydrodynamic trap (optical tweezers combined with microfluidics). These formulae were previously developed in two and three dimensions from the fundamental equations describing creeping flows past a suspended sphere. The objective of the current study is to determine the full-field cellular strain response due to the applied three-dimensional stress environment through a multiphysics computational simulation. In this investigation, the multiscale cytoskeletal structures are modeled as homogeneous, isotropic, and linearly elastic. The resulting computational biophysics can be directly compared with experimental strain measurements, other modeling interpretations of cellular mechanics including the liquid drop theory, and biokinetic models of biomolecule dynamics. The described multiphysics computational framework will facilitate more realistic cytoskeletal model interpretations, whose intracellular structures can be distinctly defined, including the cellular membrane substructures, nucleus, and organelles.

Force Spectroscopy with Dual-Trap Optical Tweezers: Molecular Stiffness Measurements and Coupled Fluctuations Analysis

Dual-trap optical tweezers are often used in high-resolution measurements in single-molecule biophysics. Such measurements can be hindered by the presence of extraneous noise sources, the most prominent of which is the coupling of fluctuations along different spatial directions, which may affect any optical tweezers setup. In this article, we analyze, both from the theoretical and the experimental points of view, the most common source for these couplings in dual-trap optical-tweezers setups: the misalignment of traps and tether. We give criteria to distinguish different kinds of misalignment, to estimate their quantitative relevance and to include them in the data analysis. The experimental data is obtained in a, to our knowledge, novel dual-trap optical-tweezers setup that directly measures forces. In the case in which misalignment is negligible, we provide a method to measure the stiffness of traps and tether based on variance analysis. This method can be seen as a calibration technique valid beyond the linear trap region. Our analysis is then employed to measure the persistence length of dsDNA tethers of three different lengths spanning two orders of magnitude. The effective persistence length of such tethers is shown to decrease with the contour length, in accordance with previous studies.

Studying Single Red Blood Cells Under a Tunable External Force by Combining Passive Microrheology with Raman Spectroscopy

The dynamic micromechanical and structural properties of single human red blood cells are studied using a combination of dual trap optical tweezers and confocal Raman spectroscopy. Such a combination permits us to show a direct relationship between the rheological properties and chemical structure conformation. The frequency dependence of the complex stiffness of the cells was measured using both one and two probe response functions under identical experimental conditions. Both the microrheology and Raman measurements were performed at different stretching forces applied to the cell. A detailed analysis of the auto- and cross-correlated probe motions allows exploring the local and overall viscoelastic properties of the cells over a controlled range of the deformations. The observed growth of the cell viscoelasticity with stretching was associated with structural changes in the cell membrane monitored via the Raman spectroscopy.