Interferometric 3D tracking of several particles in a scanning laser focus

Towards non-blind optical tweezing by finding 3D refractive index changes through off-focus interferometric tracking

In modern 3D microscopy, holding and orienting arbitrary biological objects with optical forces instead of using coverslips and gel cylinders is still a vision. Although optical trapping forces are strong enough and related photodamage is acceptable, the precise (re-) orientation of large specimen with multiple optical traps is difficult, since they grab blindly at the object and often slip off. Here, we present an approach to localize and track regions with increased refractive index using several holographic optical traps with a single camera in an off-focus position. We estimate the 3D grabbing positions around several trapping foci in parallel through analysis of the beam deformations, which are continuously measured by defocused camera images of cellular structures inside cell clusters. Although non-blind optical trapping is still a vision, this is an important step towards fully computer-controlled orientation and feature-optimized laser scanning of sub-mm sized biological specimen for future 3D light microscopy.

3D calibration of microsphere position in optical tweezers using the back-focal-plane interferometry method

This paper presents a method to directly calibrate the position of a trapped micro-sphere in optical tweezers utilizing its interference pattern formed at the back focal plane (BFP). Through finite difference time domain (FDTD) and scalar diffraction theorem, the scattering field complex amplitude of the near and far fields can be simulated after interference between the trapped sphere and focus Gaussian beam. The position of the trapped sphere can be recovered and calibrated based on a back focal plane interferometry (BFPI) algorithm. Theoretical results demonstrate that optical tweezers with a larger numerical aperture (NA) Gaussian beam will yield a better detection sensitivity but with a smaller linear range. These results were experimentally validated by trapping a microsphere in a single beam optical tweezer. We used an extra focused laser to manipulate the trapped sphere and then compared its position in the images and that obtained using the BFP method. The interference pattern from simulation and experiments showed good agreement, implying that the calibration factor can be deduced from simulation and requires no intermediate calculation process. These results provide a pathway to obtain the calibration factor, enable a faster and direct measurement of the sphere position, and show possibilities for adjusting the crosstalk and nonlinearity inside an optical trap.

Optical Tweezers with Integrated Multiplane Microscopy (OpTIMuM): a new tool for 3D microrheology

We introduce a novel 3D microrheology system that combines for the first time Optical Tweezers with Integrated Multiplane Microscopy (OpTIMuM). The system allows the 3D tracking of an optically trapped bead, with ~ 20 nm accuracy along the optical axis. This is achieved without the need for a high precision z-stage, separate calibration sample, nor a priori knowledge of either the bead size or the optical properties of the suspending medium. Instead, we have developed a simple yet effective in situ spatial calibration method using image sharpness and exploiting the fact we image at multiple planes simultaneously. These features make OpTIMuM an ideal system for microrheology measurements, and we corroborate the effectiveness of this novel microrheology tool by measuring the viscosity of water in three dimensions, simultaneously.

Measuring Stepwise Binding of Thermally Fluctuating Particles to Cell Membranes without Fluorescence

Thermal motions enable a particle to probe the optimal interaction state when binding to a cell membrane. However, especially on the scale of microseconds and nanometers, position and orientation fluctuations are difficult to observe with common measurement technologies. Here, we show that it is possible to detect single binding events of immunoglobulin-G-coated polystyrene beads, which are held in an optical trap near the cell membrane of a macrophage. Changes in the spatial and temporal thermal fluctuations of the particle were measured interferometrically, and no fluorophore labeling was required. We demonstrate both by Brownian dynamic simulations and by experiments that sequential stepwise increases in the force constant of the bond between a bead and a cell of typically 20 pN/μm are clearly detectable. In addition, this technique provides estimates about binding rates and diffusion constants of membrane receptors. The simple approach of thermal noise tracking points out new strategies in understanding interactions between cells and particles, which are relevant for a large variety of processes, including phagocytosis, drug delivery, and the effects of small microplastics and particulates on cells.

Back-focal-plane interferometric detection of nanoparticles in spatially confined microfluidic channels

Nanoparticles are important in several areas of modern biomedical research. However, detection and characterization of nanoparticles is challenging due to their small size. Back-focal-plane interferometry (BFPI) is a highly sensitive technique that has been used in laser tweezers for quantitative measurement of force and displacement. The utility of BFPI for detection and characterization of nanoparticles, however, has not yet been achieved. Here we show that BFPI can be used for rapid probing of a suspension of nanoparticles in a spatially confined microfluidic channel. We show that the Gaussian Root-mean-squared noise of the BFPI signal is highly sensitive to the nanoparticle size and can be used as a parameter for rapid detection of nanoparticles at a single-particle level and characterization of particle heterogeneities in a suspension. By precisely aligning the optical trap relative to the channel boundaries, individual polystyrene particles with a diameter as small as 63 nm can be detected using BFPI with a high signal-to-noise ratio.

Single microtubules and small networks become significantly stiffer on short time-scales upon mechanical stimulation

The transfer of mechanical signals through cells is a complex phenomenon. To uncover a new mechanotransduction pathway, we study the frequency-dependent transport of mechanical stimuli by single microtubules and small networks in a bottom-up approach using optically trapped beads as anchor points. We interconnected microtubules to linear and triangular geometries to perform micro-rheology by defined oscillations of the beads relative to each other. We found a substantial stiffening of single filaments above a characteristic transition frequency of 1–30 Hz depending on the filament’s molecular composition. Below this frequency, filament elasticity only depends on its contour and persistence length. Interestingly, this elastic behavior is transferable to small networks, where we found the surprising effect that linear two filament connections act as transistor-like, angle dependent momentum filters, whereas triangular networks act as stabilizing elements. These observations implicate that cells can tune mechanical signals by temporal and spatial filtering stronger and more flexibly than expected.

Measuring Local Viscosities near Plasma Membranes of Living Cells with Photonic Force Microscopy

The molecular processes of particle binding and endocytosis are influenced by the locally changing mobility of the particle nearby the plasma membrane of a living cell. However, it is unclear how the particle's hydrodynamic drag and momentum vary locally and how they are mechanically transferred to the cell. We have measured the thermal fluctuations of a 1 μm-sized polystyrene sphere, which was placed in defined distances to plasma membranes of various cell types by using an optical trap and fast three-dimensional (3D) interferometric particle tracking. From the particle position fluctuations on a 30 μs timescale, we determined the distance-dependent change of the viscous drag in directions perpendicular and parallel to the cell membrane. Measurements on macrophages, adenocarcinoma cells, and epithelial cells revealed a significantly longer hydrodynamic coupling length of the particle to the membrane than those measured at giant unilamellar vesicles (GUVs) or a plane glass interface. In contrast to GUVs, there is also a strong increase in friction and in mean first passage time normal to the cell membrane. This hydrodynamic coupling transfers a different amount of momentum to the interior of living cells and might serve as an ultra-soft stimulus triggering further reactions.

Interaction dynamics of two diffusing particles: contact times and influence of nearby surfaces

Interactions of diffusing particles are governed by hydrodynamics on different length and timescales. The local hydrodynamics can be influenced substantially by simple interfaces. Here, we investigate the interaction dynamics of two micron-sized spheres close to plane interfaces to mimic more complex biological systems or microfluidic environments. Using scanned line optical tweezers and fast 3D interferometric particle tracking, we are able to track the motion of each bead with precisions of a few nanometers and at a rate of 10 kilohertz. From the recorded trajectories, all spatial and temporal information is accessible. This way, we measure diffusion coefficients for two coupling particles at varying distances h to one or two glass interfaces. We analyze their coupling strength and length by cross-correlation analysis relative to h and find a significant decrease in the coupling length when a second particle diffuses nearby. By analysing the times the particles are in close contact, we find that the influence of nearby surfaces and interaction potentials reduce the diffusivity strongly, although we found that the diffusivity hardly affects the contact times and the binding probability between the particles. All experimental results are compared to a theoretical model, which is based on the number of possible diffusion paths following the Catalan numbers and a diffusion probability, which is biased by the spheres' surface potential. The theoretical and experimental results agree very well and therefore enable a better understanding of hydrodynamically coupled interaction processes.

Active cell mechanics: Measurement and theory

Living cells are active mechanical systems that are able to generate forces. Their structure and shape are primarily determined by biopolymer filaments and molecular motors that form the cytoskeleton. Active force generation requires constant consumption of energy to maintain the nonequilibrium activity to drive organization and transport processes necessary for their function. To understand this activity it is necessary to develop new approaches to probe the underlying physical processes. Active cell mechanics incorporates active molecular-scale force generation into the traditional framework of mechanics of materials. This review highlights recent experimental and theoretical developments towards understanding active cell mechanics. We focus primarily on intracellular mechanical measurements and theoretical advances utilizing the Langevin framework. These developing approaches allow a quantitative understanding of nonequilibrium mechanical activity in living cells. This article is part of a Special Issue entitled: Mechanobiology.

How to calibrate an object-adapted optical trap for force sensing and interferometric shape tracking of asymmetric structures

Optical traps have shown to be a flexible and powerful tool for 3D manipulations on the microscale. However, when it comes to sensitive measurements of particle displacements and forces thorough calibration procedures are required, which can be already demanding for trapped spheres. For asymmetric structures, with more complicated shapes, such as helical bacteria, novel calibration schemes need to be established. The paper describes different methods of how to extract various calibration parameters of a tiny helical bacterium, which is trapped and tracked in shape by scanning line optical tweezers. Tiny phase differences of the light scattered at each slope of the bacterium are measured by back focal plane interferometry, providing precise and high bandwidth information about fast deformations of the bacterium. A simplified theoretical model to estimate the optical forces on a chain like structure is presented. The methods presented here should be of interest to people that investigate optical trapping and tracking of asymmetric particles.

Induced phagocytic particle uptake into a giant unilamellar vesicle

Phagocytosis, the uptake and ingestion of solid particles into living cells, is a central mechanism of our immune system. Due to the complexity of the uptake mechanism, the different forces involved in this process are only partly understood. Therefore the usage of a giant unilamellar vesicle (GUV) as the simplest biomimetic model for a cell allows one to investigate the influence of the lipid membrane on the energetics of the uptake process. Here, a photonic force microscope (PFM) is used to approach an optically trapped 1 μm latex bead to an immobilized GUV to finally insert the particle into the GUV. By analysing the mean displacement and the position fluctuations of the trapped particle during the uptake process in 3D with nanometre precision, we are able to record force and energy profiles, as well as changes in the viscous drag and the stiffness. After observing a global followed by a local deformation of the GUV, we measured uptake energies of 2000 kT to 5500 kT and uptake forces of 4 pN to 16 pN for Egg-PC GUVs with sizes of 18-26 μm and varying membrane tension. The measured energy profiles, which are compared to a Helfrich energy model for local and global deformation, show good coincidence with the theoretical results. Our proof-of-principle study opens the door to a large number of similar experiments with GUVs containing more biochemical components and complexity. This bottom-up strategy should allow for a better understanding of the physics of phagocytosis.

5D-Tracking of a nanorod in a focused laser beam--a theoretical concept

Back-focal plane (BFP) interferometry is a very fast and precise method to track the 3D position of a sphere within a focused laser beam using a simple quadrant photo diode (QPD). Here we present a concept of how to track and recover the 5D state of a cylindrical nanorod (3D position and 2 tilt angles) in a laser focus by analyzing the interference of unscattered light and light scattered at the cylinder. The analytical theoretical approach is based on Rayleigh-Gans scattering together with a local field approximation for an infinitely thin cylinder. The approximated BFP intensities compare well with those from a more rigorous numerical approach. It turns out that a displacement of the cylinder results in a modulation of the BFP intensity pattern, whereas a tilt of the cylinder results in a shift of this pattern. We therefore propose the concept of a local QPD in the BFP of a detection lens, where the QPD center is shifted by the angular coordinates of the cylinder tilt.

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.

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.

Optimization of probe-laser focal offsets for single-particle tracking

In optical tweezers applications, tracking a trapped particle is essential for force measurement. One of the most popular techniques for single-particle tracking is achieved by analyzing the forward and backward light pattern, scattered by the target particle trapped by a trap laser beam, of an additional probe-laser beam with different wavelength whose focus is slightly apart from the trapping center. However, the optimized focal offset has never been discussed. In this paper, we investigate the tracking range and sensitivity as a function of the focal offset between the trapping and the probe-laser beams. As a result, the optimized focal offsets are a 3.3-fold radius ahead and a 2.0-fold radius behind the trapping laser focus in the forward tracking and the backward tracking, respectively. The experimental result agrees well with a theoretical prediction using the Mie scattering theory.

Interaction dynamics of two colloids in a single optical potential

The interaction of two diffusing particles is strongly influenced by their hydrodynamic coupling. At a tracking rate of 10 kHz we are able to measure the 3D trajectories of two colloidal spheres in a single harmonic potential, which was generated by scanning line optical tweezers. This common potential enables tilting, rotational, and translational dynamics of the spheres, which we analyzed via the spheres position cross-correlations C(τ) over a time range of 10(-4)-2 s. We found that the dynamic interaction of the colloids is controlled by short-range surface forces F(s), which are attractive in one direction and repulsive in the other two directions. This unexpected behavior is supported by a theoretical model using two Langevin equations, which decouple for linear F(s), allowing a description with autocorrelation functions for collective and relative motions. We further demonstrate that variations in salt concentration and reaction volumes significantly influence C(τ) and the mean contact times between the particles, which may offer new insights into biological particle interaction.

Dark-field digital holographic microscopy for 3D-tracking of gold nanoparticles

We present a new technique that combines off-axis Digital Holography and Dark Field Microscopy to track 100nm gold particles diffusing in water. We show that a single hologram is sufficient to localize several particles in a thick sample with a localization accuracy independent of the particle position. From our measurements we reconstruct the trajectories of the particles and derive their 3D diffusion coefficient. Our results pave the way for quantitative studies of the motion of single nanoparticle in complex media.

Fast parallel interferometric 3D tracking of numerous optically trapped particles and their hydrodynamic interaction

Multi-dimensional, correlated particle tracking is a key technology to reveal dynamic processes in living and synthetic soft matter systems. In this paper we present a new method for tracking micron-sized beads in parallel and in all three dimensions - faster and more precise than existing techniques. Using an acousto-optic deflector and two quadrant-photo-diodes, we can track numerous optically trapped beads at up to tens of kHz with a precision of a few nanometers by back-focal plane interferometry. By time-multiplexing the laser focus, we can calibrate individually all traps and all tracking signals in a few seconds and in 3D. We show 3D histograms and calibration constants for nine beads in a quadratic arrangement, although trapping and tracking is easily possible for more beads also in arbitrary 2D arrangements. As an application, we investigate the hydrodynamic coupling and diffusion anomalies of spheres trapped in a 3 × 3 arrangement.

Holographic optical tweezers and their relevance to lab on chip devices

During the last decade, optical tweezers have been transformed by the combined availability of spatial light modulators and the speed of low-cost computing to drive them. Holographic optical tweezers can trap and move many objects simultaneously and their compatibility with other optical techniques, particularly microscopy, means that they are highly appropriate to lab-on-chip systems to enable optical manipulation, actuation and sensing.

Particle tracking stereomicroscopy in optical tweezers: control of trap shape

We present an optical system capable of generating stereoscopic images to track trapped particles in three dimensions. Two-dimensional particle tracking on each image yields three dimensional position information. Our approach allows the use of a high numerical aperture (NA=1.3) objective and large separation angle, such that particles can be tracked axially with resolution of 3 nm at 340 Hz. Spatial Light Modulators (SLMs), the diffractive elements used to steer and split laser beams in Holographic Optical Tweezers, are also capable of more general operations. We use one here to vary the ratio of lateral to axial trap stiffness by changing the shape of the beam at the back aperture of the microscope objective. Beams which concentrate their optical power at the extremes of the back aperture give rise to much more efficient axial trapping. The flexibility of using an SLM allows us to create multiple traps with different shapes.