Tired and stressed: direct holographic quasi-static stretching of aging echinocytes and discocytes in plasma using optical tweezers [Invited].

Red blood cells (RBCs) undergo a progressive morphological transformation from smooth biconcave discocytes into rounder echinocytes with spicules on their surface during cold storage. The echinocytic morphology impacts RBCs' ability to flow through narrow sections of the circulation and therefore transfusion of RBC units with a high echinocytic content are thought to have a reduced efficiency. We use an optical tweezers-based technique where we directly trap and measure linear stiffness of RBCs under stress without the use of attached spherical probe particles or microfluidic flow to induce shear. We study RBC deformability with over 50 days of storage performing multiple stretches in blood plasma (serum with cold agglutinins removed to eliminate clotting). In particular, we find that discocytes and echinocytes do not show significant changes in linear stiffness in the small strain limit (∼20% change in length) up to day 30 of the storage period, but do find differences between repeated stretches. By day 50 the linear stiffness of discocytes had increased to approximately that measured for echinocytes throughout the entire period of measurements. These changes in stiffness corresponded to recorded morphological changes in the discocytes as they underwent storage lesion. We believe our holographic trapping and direct measurement technique has applications to directly control and quantify forces that stretch other types of cells without the use of attached probes.

Far-Field Subwavelength Straight-Line Projection/Imaging by Means of a Novel Double-Near-Zero Index-Based Two-Layer Metamaterial.

In this paper, for the first time, tuned near-zero-index materials are used in a structure for the long-distance projection of very closely spaced objects with subwavelength separation. Near-zero-index materials have never been used for subwavelength projection/imaging. The proposed novel structure is composed of a two-layer slab that can project two slits with a subwavelength separation distance to a long distance without diverged/converged interference of the two imaged waves. The two-layer slab consists of a thin double-near-zero (DNZ) slab with an obtained tuned index of 0.05 and thickness of 0.04λ0 coupled with a high-index dielectric slab with specific thicknesses. Through a parametric study, the non-zero index of the DNZ layer is tuned to create a clear image when it is coupled with the high-index dielectric layer. The minimum size for the aperture of the proposed two-layer slab is 2λ0 to provide a clear projection of the two slits. The space between the slits is λ0/8, which is five times beyond the diffraction limit. It is shown that, through the conventional methods (e.g., only with high-index dielectric slabs, uncoupled with a DNZ layer), it is impossible to clearly project slits at a large distance (~λ0) due to the diffraction limit. An analytical analysis, as well as numerical results in a finite-element-based simulator, confirm the function of the proposed structure.

Optical-trapping of particles in air using parabolic reflectors and a hollow laser beam.

We present an advanced optical-trapping method that is capable of trapping arbitrary shapes of transparent and absorbing particles in air. Two parabolic reflectors were used to reflect the inner and outer parts of a single hollow laser beam, respectively, to form two counter-propagating conical beams and bring them into a focal point for trapping. This novel design demonstrated high trapping efficiency and strong trapping robustness with a simple optical configuration. Instead of using expensive microscope objectives, the parabolic reflectors can not only achieved large numerical aperture (N.A.) focusing, but were also able to focus the beam far away from optical surfaces to minimize optics contamination. This design also offered a large free space for flexible integration with other measuring techniques, such as optical-trapping Raman spectroscopy, for on-line single particle characterization.

Machine learning wall effects of eccentric spheres for convenient computation.

In confined systems, such as the inside of a biological cell, the outer boundary or wall can affect the dynamics of internal particles. In many cases of interest both the internal particle and outer wall are approximately spherical. Therefore, quantifying the wall effects from an outer spherical boundary on the motion of an internal eccentric sphere is very useful. However, when the two spheres are not concentric, the problem becomes nontrivial. In this paper we improve existing analytical methods to evaluate these wall effects and then train a feed-forward artificial neural network within a broader model. The final model generally performed with ∼0.001% error within the training domain and ∼0.05% when the outer spherical wall was extrapolated to an infinite plane. Through this model, the wall effects of an outer spherical boundary on the arbitrary motion of an internal sphere for all experimentally achievable configurations can now be conveniently and efficiently determined.

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.

Measuring local properties inside a cell-mimicking structure using rotating optical tweezers.

Exploring the rheological properties of intracellular materials is essential for understanding cellular and subcellular processes. Optical traps have been widely used for physical manipulation of micro and nano objects within fluids enabling studies of biological systems. However, experiments remain challenging as it is unclear how the probe particle's mobility is influenced by the nearby membranes and organelles. We use liposomes (unilamellar lipid vesicles) as a simple biomimetic model of living cells, together with a trapped particle rotated by optical tweezers to study mechanical and rheological properties inside a liposome both theoretically and experimentally. Here, we demonstrate that this system has the capacity to predict the hydrodynamic interaction between three-dimensional spatial membranes and internal probe particles within submicron distances, and it has the potential to aid in the design of high resolution optical micro/nanorheology techniques to be used inside living cells.

Calibration of force detection for arbitrarily shaped particles in optical tweezers.

Force measurement with an optical trap requires calibration of it. With a suitable detector, such as a position-sensitive detector (PSD), it is possible to calibrate the detector so that the force can be measured for arbitrary particles and arbitrary beams without further calibration; such a calibration can be called an "absolute calibration". Here, we present a simple method for the absolute calibration of a PSD. Very often, paired position and force measurements are required, and even if synchronous measurements are possible with the position and force detectors used, knowledge of the force-position curve for the particle in the trap can be highly beneficial. Therefore, we experimentally demonstrate methods for determining the force-position curve with and without synchronous force and position measurements, beyond the Hookean (linear) region of the trap. Unlike the absolute calibration of the force and position detectors, the force-position curve depends on the particle and the trapping beam, and needs to be determined in each individual case. We demonstrate the robustness of our absolute calibration by measuring optical forces on microspheres as commonly trapped in optical tweezers, and other particles such a birefringent vaterite microspheres, red blood cells, and a deformable "blob".

Impact of complex surfaces on biomicrorheological measurements using optical tweezers.

The characterisation of physical properties in biologically relevant processes and the development of novel microfluidic devices for this purpose are experiencing a great resurgence at present. In many of measurements of this type where a probe in a fluid is used, the strong influence of the boundaries of the volume used is a serious problem. In these geometries the proximity of a probe to a wall can severely influence the measurement. However, although much knowledge has been gained about flat walls, to date, the effect of non-planar surfaces at microscopic scale on rotational motion of micro-objects has not been studied. Here we present for the first time both experimental measurements and numerical computations which aim to study the drag torque on optically trapped rotating particles moving near 3D-printed conical and cylindrical walls on-chip. These results are essential for quantifying how curved walls can effect the torque on particles, and thus enable accurate hydrodynamic simulations at the micron-scale. This opens the potential for new sensing approaches under more complex conditions, allowing both dynamic and microrheological studies of biological systems and lab-on-chip devices.

Active rotational and translational microrheology beyond the linear spring regime.

Active particle tracking microrheometers have the potential to perform accurate broadband measurements of viscoelasticity within microscopic systems. Generally, their largest possible precision is limited by Brownian motion and low frequency changes to the system. The signal to noise ratio is usually improved by increasing the size of the driven motion compared to the Brownian as well as averaging over repeated measurements. New theory is presented here whereby error in measurements of the complex shear modulus can be significantly reduced by analyzing the motion of a spherical particle driven by nonlinear forces. In some scenarios error can be further reduced by applying a variable transformation which linearizes the equation of motion. This enables normalization that eliminates error introduced by low frequency drift in the particle's equilibrium position. Our measurements indicate that this can further resolve an additional decade of viscoelasticity at high frequencies. Using this method will easily increase the signal strength enough to significantly reduce the measurement time for the same error. Thus the method is more conducive to measuring viscoelasticity in slowly changing microscopic systems, such as a living cell.

Escape forces and trajectories in optical tweezers and their effect on calibration.

Whether or not an external force can make a trapped particle escape from optical tweezers can be used to measure optical forces. Combined with the linear dependence of optical forces on trapping power, a quantitative measurement of the force can be obtained. For this measurement, the particle is at the edge of the trap, away from the region near the equilbrium position where the trap can be described as a linear spring. This method provides the ability to measure higher forces for the same beam power, compared with using the linear region of the trap, with lower risk of optical damage to trapped specimens. Calibration is typically performed by using an increasing fluid flow to exert an increasing force on a trapped particle until it escapes. In this calibration technique, the particle is usually assumed to escape along a straight line in the direction of fluid-flow. Here, we show that the particle instead follows a curved trajectory, which depends on the rate of application of the force (i.e., the acceleration of the fluid flow). In the limit of very low acceleration, the particle follows the surface of zero axial optical force during the escape. The force required to produce escape depends on the trajectory, and hence the acceleration. This can result in variations in the escape force of a factor of two. This can have a major impact on calibration to determine the escape force efficiency. Even when calibration measurements are all performed in the low acceleration regime, variations in the escape force efficiency of 20% or more can still occur. We present computational simulations using generalized Lorenz-Mie theory and experimental measurements to show how the escape force efficiency depends on rate of increase of force and trapping power, and discuss the impact on calibration.

Scattering of Sculpted Light in Intact Brain Tissue, with implications for Optogenetics.

Optogenetics uses light to control and observe the activity of neurons, often using a focused laser beam. As brain tissue is a scattering medium, beams are distorted and spread with propagation through neural tissue, and the beam's degradation has important implications in optogenetic experiments. To address this, we present an analysis of scattering and loss of intensity of focused laser beams at different depths within the brains of zebrafish larvae. Our experimental set-up uses a 488 nm laser and a spatial light modulator to focus a diffraction-limited spot of light within the brain. We use a combination of experimental measurements of back-scattered light in live larvae and computational modelling of the scattering to determine the spatial distribution of light. Modelling is performed using the Monte Carlo method, supported by generalised Lorenz-Mie theory in the single-scattering approximation. Scattering in areas rich in cell bodies is compared to that of regions of neuropil to identify the distinct and dramatic contributions that cell nuclei make to scattering. We demonstrate the feasibility of illuminating individual neurons, even in nucleus-rich areas, at depths beyond 100 µm using a spatial light modulator in combination with a standard laser and microscope optics.

Forces due to pulsed beams in optical tweezers: linear effects.

We present a method for the precise calculation of optical forces due to a tightly-focused pulsed laser beam using generalized Lorenz-Mie theory or the T-matrix method. This method can be used to obtain the fields as a function of position and time, allowing the approximate calculation of weak non-linear effects, and provides a reference calculation for validation of calculations including non-linear effects. We calculate forces for femtosecond pulses of various widths, and compare with forces due to a continuous wave (CW) beam. The forces are similar enough so that the continuous beam case provides a useful approximation for the pulsed case, with trap parameters such as the radial spring constant usually differing by less than 1% for pulses of 100 fs or longer. For large high-index (e.g., polystyrene, with n = 1.59) particles, the difference can be as large as 3% for 100 fs pulses, and up to 8% for 25 fs pulses. A weighted average of CW forces for individual spectral components of the pulsed beam provides a simple improved approximation, which we use to illustrate the physical principles responsible for the differences between pulsed and CW beams.

Determination of motility forces on isolated chromosomes with laser tweezers.

Quantitative determination of the motility forces of chromosomes during cell division is fundamental to understanding a process that is universal among eukaryotic organisms. Using an optical tweezers system, isolated mammalian chromosomes were held in a 1064 nm laser trap. The minimum force required to move a single chromosome was determined to be ≈ 0.8-5 pN. The maximum transverse trapping efficiency of the isolated chromosomes was calculated as ≈ 0.01-0.02. These results confirm theoretical force calculations of ≈ 0.1-12 pN to move a chromosome on the mitotic or meiotic spindle. The verification of these results was carried out by calibration of the optical tweezers when trapping microspheres with a diameter of 4.5-15 µm in media with 1-7 cP viscosity. The results of the chromosome and microsphere trapping experiments agree with optical models developed to simulate trapping of cylindrical and spherical specimens.

Driving corrugated donut rotors with Laguerre-Gauss beams.

Tightly-focused laser beams that carry angular momentum have been used to trap and rotate microrotors. In particular, a Laguerre-Gauss mode laser beam can be used to transfer its orbital angular momentum to drive microrotors. We increase the torque efficiency by a factor of about 2 by designing the rotor such that its geometry is compatible with the driving beam, when driving the rotation with the optimum beam, rather than beams of higher or lower orbital angular momentum. Based on Floquet's theorem, the order of discrete rotational symmetry of the rotor can be made to couple with the azimuthal mode of the Laguerre-Gauss beam. We design corrugated donut rotors, that have a flat disc-like profile, with the help of the discrete dipole approximation and the T-matrix methods in parallel with experimental demonstrations of stable trapping and torque measurement. We produce and test such a rotor using two-photon photopolymerization. With a rotor that has 8-fold discrete rotational symmetry, an outer radius of 1.85 µm and a hollow core radius of 0.5 µm, we were able to transfer approximately 0.3 h̄ per photon of the orbital angular momentum from an LG04 beam.

Comparison of T-matrix calculation methods for scattering by cylinders in optical tweezers.

The T-matrix method, or the T-matrix formulation of scattering, is a framework for mathematically describing the scattering properties of an object as a linear relationship between expansion coefficients of the incident and scattering fields in a basis of vector spherical wave functions (VSWFs). A variety of methods can be used to calculate the T-matrix. We explore the applicability of the extended boundary condition method (EBCM) and point matching (PM) method to calculate the T-matrix for scattering by cylinders in optical tweezers and hence the optical force acting on them. We compare both methods with the discrete-dipole approximation (DDA) to measure their accuracy for different sizes and aspect ratios (ARs) for Rayleigh and wavelength-size cylinders. We determine range of sizes and ARs giving errors below 1% and 10%. These results can help researchers choose the most efficient method to calculate the T-matrix for nonspherical particles with acceptable accuracy.

Mapping organelle motion reveals a vesicular conveyor belt spatially replenishing secretory vesicles in stimulated chromaffin cells.

How neurosecretory cells spatially adjust their secretory vesicle pools to replenish those that have fused and released their hormonal content is currently unknown. Here we designed a novel set of image analyses to map the probability of tracked organelles undergoing a specific type of movement (free, caged or directed). We then applied our analysis to time-lapse z-stack confocal imaging of secretory vesicles from bovine Chromaffin cells to map the global changes in vesicle motion and directionality occurring upon secretagogue stimulation. We report a defined region abutting the cortical actin network that actively transports secretory vesicles and is dissipated by actin and microtubule depolymerizing drugs. The directionality of this "conveyor belt" towards the cell surface is activated by stimulation. Actin and microtubule networks therefore cooperatively probe the microenvironment to transport secretory vesicles to the periphery, providing a mechanism whereby cells globally adjust their vesicle pools in response to secretagogue stimulation.

Calibration of nonspherical particles in optical tweezers using only position measurement.

Nonspherical probe particles are an attractive choice for optically-trapped scanning probe microscopy. We show that it is possible to calibrate a trap with a nonspherical particle using only position measurements, without requiring measurement of orientation, using a pseudopotential based on the position occupation probability. It is not necessary to assume the force is linear with displacement.

Equilibrium orientations and positions of non-spherical particles in optical traps.

Dynamic simulation is a powerful tool to observe the behavior of arbitrary shaped particles trapped in a focused laser beam. Here we develop a method to find equilibrium positions and orientations using dynamic simulation. This general method is applied to micro- and nano-cylinders as a demonstration of its predictive power. Orientation landscapes for particles trapped with beams of differing polarisation are presented. The torque efficiency of micro-cylinders at equilibrium in a plane is also calculated as a function of tilt angle. This systematic investigation elucidates in both the function and properties of micro- and nano-cylinders trapped in optical tweezers.

Highly birefringent vaterite microspheres: production, characterization and applications for optical micromanipulation.

This paper reports on a simple synthesis and characterization of highly birefringent vaterite microspheres, which are composed of 20-30 nm sized nanocrystalls. Scanning electron microscopy shows a quite disordered assembly of nanocrystals within the microspheres. However, using optical tweezers, the effective birefringence of the microspheres was measured to be Deltan = 0.06, which compares to Deltan = 0.1 of vaterite single crystals. This suggests a very high orientation of the nanocrystals within the microspheres. A hyperbolic model of the direction of the optical axis throughout the vaterite spherulite best fits the experimental data. Results from polarized light microscopy further confirm the hyperbolic model.

Synthesis and surface modification of birefringent vaterite microspheres.

This paper reports on the synthesis of birefringent vaterite microspheres with narrow size distribution using a seeded growth method. In a post-treatment the microspheres were stabilized and functionalized through coating with a combination of organosilica and silica. The coating vastly enhanced the stability of the vaterite microspheres in biological buffers and allowed the attachment of biomolecules such as DNA or proteins. As an example, streptavidin was attached to the surface of the functionalized microspheres. These results pave the way for the use of birefringent vaterite particles for the micromanipulation of single biological molecules such as DNA or specific proteins in an optical trap capable of exerting and measuring torques. The stabilized birefringent microspheres may also find use for biosensor and biological screening applications.