Simultaneous calibration of optical tweezers spring constant and position detector response

Food emulsions stabilized by proteins and emulsifiers: A review of the mechanistic explorations

The stability of food emulsions is the basis for other properties. During their production and processing, emulsions tend to become unstable due to their thermodynamic instability, and it is usually necessary to add emulsifiers and proteins to stabilize emulsions. It becomes crucial to study the intrinsic mechanisms of emulsifiers and proteins and their joint stabilization of food emulsions. This paper summarizes the research on intrinsic mechanisms of food emulsions stabilized by emulsifiers and proteins in recent years. The destabilization and stabilization of emulsions are related to the added surfactants. The properties, type, and concentration of emulsifiers determine the stability of emulsions, and the emulsifiers can be classified into different types (e.g., ionic or nonionic, solid or liquid) according to their properties and sources. The physicochemical properties of proteins (e.g., spatial conformation, hydrophobicity) and the composition of proteins can also determine the stability of emulsions, and emulsions stabilized by emulsifiers and proteins together not only depend on these factors but also have a great relationship with the mutual combination and competition between the two. The instability and stability of emulsions are related to factors such as interfacial interaction forces, the rheological nature of the interface, and the added surfactant.

Looking at Biomolecular Interactions through the Lens of Correlated Fluorescence Microscopy and Optical Tweezers

Understanding complex biological events at the molecular level paves the path to determine mechanistic processes across the timescale necessary for breakthrough discoveries. While various conventional biophysical methods provide some information for understanding biological systems, they often lack a complete picture of the molecular-level details of such dynamic processes. Studies at the single-molecule level have emerged to provide crucial missing links to understanding complex and dynamic pathways in biological systems, which are often superseded by bulk biophysical and biochemical studies. Latest developments in techniques combining single-molecule manipulation tools such as optical tweezers and visualization tools such as fluorescence or label-free microscopy have enabled the investigation of complex and dynamic biomolecular interactions at the single-molecule level. In this review, we present recent advances using correlated single-molecule manipulation and visualization-based approaches to obtain a more advanced understanding of the pathways for fundamental biological processes, and how this combination technique is facilitating research in the dynamic single-molecule (DSM), cell biology, and nanomaterials fields.

Enhanced Signal-to-Noise and Fast Calibration of Optical Tweezers Using Single Trapping Events

The trap stiffness us the key property in using optical tweezers as a force transducer. Force reconstruction via maximum-likelihood-estimator analysis (FORMA) determines the optical trap stiffness based on estimation of the particle velocity from statistical trajectories. Using a modification of this technique, we determine the trap stiffness for a two micron particle within 2 ms to a precision of ∼10% using camera measurements at 10 kfps with the contribution of pixel noise to the signal being larger the level Brownian motion. This is done by observing a particle fall into an optical trap once at a high stiffness. This type of calibration is attractive, as it avoids the use of a nanopositioning stage, which makes it ideal for systems of large numbers of particles, e.g., micro-fluidics or active matter systems.

Finding trap stiffness of optical tweezers using digital filters

Obtaining trap stiffness and calibration of the position detection system is the basis of a force measurement using optical tweezers. Both calibration quantities can be calculated using several experimental methods available in the literature. In most cases, stiffness determination and detection system calibration are performed separately, often requiring procedures in very different conditions, and thus confidence of calibration methods is not assured due to possible changes in the environment. In this work, a new method to simultaneously obtain both the detection system calibration and trap stiffness is presented. The method is based on the calculation of the power spectral density of positions through digital filters to obtain the harmonic contributions of the position signal. This method has the advantage of calculating both trap stiffness and photodetector calibration factor from the same dataset in situ. It also provides a direct method to avoid unwanted frequencies that could greatly affect calibration procedure, such as electric noise, for example.

In situ calibration of position detection in an optical trap for active microrheology in viscous materials

In optical trapping, accurate determination of forces requires calibration of the position sensitivity relating displacements to the detector readout via the V-nm conversion factor (β). Inaccuracies in measured trap stiffness (k) and dependent calculations of forces and material properties occur if β is assumed to be constant in optically heterogeneous materials such as tissue, necessitating calibration at each probe. For solid-like samples in which probes are securely positioned, calibration can be achieved by moving the sample with a nanopositioning stage and stepping the probe through the detection beam. However, this method may be applied to samples only under select circumstances. Here, we introduce a simple method to find β in any material by steering the detection laser beam while the probe is trapped. We demonstrate the approach in the yolk of living Danio rerio (zebrafish) embryos and measure the viscoelastic properties over an order of magnitude of stress-strain amplitude.

Exact Theory of Optical Tweezers and Its Application to Absolute Calibration

Optical tweezers have become a powerful tool for basic and applied research in cell biology. Here, we describe an experimentally verified theory for the trapping forces generated by optical tweezers based on first principles that allows absolute calibration. For pedagogical reasons, the steps that led to the development of the theory over the past 15 years are outlined. The results are applicable to a broad range of microsphere radii, from the Rayleigh regime to the ray optics one, for different polarizations and trapping heights, including all commonly employed parameter domains. Protocols for implementing absolute calibration are given, explaining how to measure all required experimental parameters, and including a link to an applet for stiffness calculations.

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.

Comparative study of methods to calibrate the stiffness of a single-beam gradient-force optical tweezers over various laser trapping powers

Optical tweezers have become an important instrument in force measurements associated with various physical, biological, and biophysical phenomena. Quantitative use of optical tweezers relies on accurate calibration of the stiffness of the optical trap. Using the same optical tweezers platform operating at 1064 nm and beads with two different diameters, we present a comparative study of viscous drag force, equipartition theorem, Boltzmann statistics, and power spectral density (PSD) as methods in calibrating the stiffness of a single beam gradient force optical trap at trapping laser powers in the range of 0.05 to 1.38 W at the focal plane. The equipartition theorem and Boltzmann statistic methods demonstrate a linear stiffness with trapping laser powers up to 355 mW, when used in conjunction with video position sensing means. The PSD of a trapped particle's Brownian motion or measurements of the particle displacement against known viscous drag forces can be reliably used for stiffness calibration of an optical trap over a greater range of trapping laser powers. Viscous drag stiffness calibration method produces results relevant to applications where trapped particle undergoes large displacements, and at a given position sensing resolution, can be used for stiffness calibration at higher trapping laser powers than the PSD method.

Calibrating optical tweezers with Bayesian inference

We present a new method for calibrating an optical-tweezer setup that does not depend on input parameters and is less affected by systematic errors like drift of the setup. It is based on an inference approach that uses Bayesian probability to infer the diffusion coefficient and the potential felt by a bead trapped in an optical or magnetic trap. It exploits a much larger amount of the information stored in the recorded bead trajectory than standard calibration approaches. We demonstrate that this method outperforms the equipartition method and the power-spectrum method in input information required (bead radius and trajectory length) and in output accuracy.

Scanning a DNA molecule for bound proteins using hybrid magnetic and optical tweezers

The functional state of the genome is determined by its interactions with proteins that bind, modify, and move along the DNA. To determine the positions and binding strength of proteins localized on DNA we have developed a combined magnetic and optical tweezers apparatus that allows for both sensitive and label-free detection. A DNA loop, that acts as a scanning probe, is created by looping an optically trapped DNA tether around a DNA molecule that is held with magnetic tweezers. Upon scanning the loop along the λ-DNA molecule, EcoRI proteins were detected with ∼17 nm spatial resolution. An offset of 33±5 nm for the detected protein positions was found between back and forwards scans, corresponding to the size of the DNA loop and in agreement with theoretical estimates. At higher applied stretching forces, the scanning loop was able to remove bound proteins from the DNA, showing that the method is in principle also capable of measuring the binding strength of proteins to DNA with a force resolution of 0.1 pN/. The use of magnetic tweezers in this assay allows the facile preparation of many single-molecule tethers, which can be scanned one after the other, while it also allows for direct control of the supercoiling state of the DNA molecule, making it uniquely suitable to address the effects of torque on protein-DNA interactions.

Optimizing bead size reduces errors in force measurements in optical traps

Optical traps are used to measure force (F) over a wide range (0.01 to 1,000 pN). Variations in bead radius (r) hinder force precision since trap stiffness (k(trap)) varies as r3 when r is small. Prior work has shown k(trap) is maximized when r is approximately equal to the beam waist (w0), which on our instrument was ~400 nm when trapping with a 1064-nm laser. In this work, we show that by choosing r ≈w0, we improved the force precision by 2.8-fold as compared to a smaller bead (250 nm). This improvement in force precision was verified by pulling on a canonical DNA hairpin. Thus, by using an optimum bead size, one can simultaneously maximize k(trap) while minimizing errors in F.

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.

High-resolution detection of Brownian motion for quantitative optical tweezers experiments

We have developed an in situ method to calibrate optical tweezers experiments and simultaneously measure the size of the trapped particle or the viscosity of the surrounding fluid. The positional fluctuations of the trapped particle are recorded with a high-bandwidth photodetector. We compute the mean-square displacement, as well as the velocity autocorrelation function of the sphere, and compare it to the theory of Brownian motion including hydrodynamic memory effects. A careful measurement and analysis of the time scales characterizing the dynamics of the harmonically bound sphere fluctuating in a viscous medium directly yields all relevant parameters. Finally, we test the method for different optical trap strengths, with different bead sizes and in different fluids, and we find excellent agreement with the values provided by the manufacturers. The proposed approach overcomes the most commonly encountered limitations in precision when analyzing the power spectrum of position fluctuations in the region around the corner frequency. These low frequencies are usually prone to errors due to drift, limitations in the detection, and trap linearity as well as short acquisition times resulting in poor statistics. Furthermore, the strategy can be generalized to Brownian motion in more complex environments, provided the adequate theories are available.

Measurement of probe displacement to the thermal resolution limit in photonic force microscopy using a miniature quadrant photodetector

A photonic force microscope comprises of an optically trapped micro-probe and a position detection system to track the motion of the probe. Signal collection for motion detection is often carried out using the backscattered light off the probe-however, this mode has problems of low S/N due to the small backscattering cross sections of the micro-probes typically used. The position sensors often used in these cases are quadrant photodetectors. To ensure maximum sensitivity of such detectors, it would help if the detector size matched with the detection beam radius after the condenser lens (which for backscattered detection would be the trapping objective itself). To suit this condition, we have used a miniature displacement sensor whose dimensions makes it ideal to work with 1:1 images of micrometer-sized trapped probes in the backscattering detection mode. The detector is based on the quadrant photo-integrated chip in the optical pick-up head of a compact disc player. Using this detector, we measured absolute displacements of an optically trapped 1.1 μm probe with a resolution of ∼10 nm for a bandwidth of 10 Hz at 95% significance without any sample or laser stabilization. We characterized our optical trap for different sized probes by measuring the power spectrum for each probe to 1% accuracy, and found that for 1.1 μm diameter probes, the noise in our position measurement matched the thermal resolution limit for averaging times up to 10 ms. We also achieved a linear response range of around 385 nm with cross talk between axes ≃4% for 1.1 μm diameter probes. The detector has extremely high bandwidth (few MHz) and low optical power threshold-other factors that can lead to its widespread use in photonic force microscopy.