Acoustic tweezers for the life sciences.

Acoustic tweezers are a versatile set of tools that use sound waves to manipulate bioparticles ranging from nanometer-sized extracellular vesicles to millimeter-sized multicellular organisms. Over the past several decades, the capabilities of acoustic tweezers have expanded from simplistic particle trapping to precise rotation and translation of cells and organisms in three dimensions. Recent advances have led to reconfigured acoustic tweezers that are capable of separating, enriching, and patterning bioparticles in complex solutions. Here, we review the history and fundamentals of acoustic-tweezer technology and summarize recent breakthroughs.

Simple way to correct the drift in surface-coupled optical tweezers using the laser reflection pattern.

The surface-coupled optical tweezers are widely used to resolve small units of motion in biology. However, such motions could readily be interfered by the drift between the trap and surface. We present a simple and low-cost method to correct the drift both actively and passively based on video tracking the distance between the laser reflection pattern and the reference bead. As a result, we achieved sub-nanometer resolution and stability for the stuck bead over a broad range of averaging time (0.002-100 s) as demonstrated by the Allan deviation analysis. The sub-nanometer resolution was further manifested with step measurement. Finally, in double-stranded DNA and DNA hairpin stretching experiments, an extension resolution of 1-2 nm with the stability over 120 s has been demonstrated under a constant force. This work thus provides an easy way to bring the benefit of nanometer resolution and long-term stability to the surface-coupled optical tweezers.

Calibration of optical traps by dual trapping of one bead.

We introduce a method for optical trap calibration that is suitable for viscoelastic material. The method is designed for use on experimental setups with two optical tweezers and is based on pulling a trapped particle with one trap while holding it with the other. No piezo stage is needed, and only one optical trap must be movable with galvo mirrors, piezo mirrors, or acousto-optical deflectors. The method combines advantages of commonly known PSD-fitting and fast-sweeping methods, allowing calibration of a completely fixed trap in a fluid of unknown viscosity/viscoelasticity. A detailed method description, a theoretical derivation, and an experimental comparison to other methods are reported.

Measuring red blood cell aggregation forces using double optical tweezers.

Classic immunohematology approaches, based on agglutination techniques, have been used in manual and automated immunohematology laboratory routines. Red blood cell (RBC) agglutination depends on intermolecular attractive forces (hydrophobic bonds, Van der Walls, electrostatic forces and hydrogen bonds) and repulsive interactions (zeta potential). The aim of this study was to measure the force involved in RBC aggregation using double optical tweezers, in normal serum, in the presence of erythrocyte antibodies and associated to agglutination potentiator solutions (Dextran, low ionic strength solution [LISS] and enzymes). The optical tweezers consisted of a neodymium:yattrium aluminium garnet (Nd:YAG) laser beam focused through a microscope equipped with a minicam, which registered the trapped cell image in a computer where they could be analyzed using a software. For measuring RBC aggregation, a silica bead attached to RBCs was trapped and the force needed to slide one RBC over the other, as a function of the velocities, was determined. The median of the RBC aggregation force measured in normal serum (control) was 1 × 10(-3) (0.1-2.5) poise.cm. The samples analyzed with anti-D showed 2 × 10(-3) (1.0-4.0) poise.cm (p < 0.001). RBC diluted in potentiator solutions (Dextran 0.15%, Bromelain and LISS) in the absence of erythrocyte antibodies, did not present agglutination. High adherence was observed when RBCs were treated with papain. Results are in agreement with the imunohematological routine, in which non-specific results are not observed when using LISS, Dextran and Bromelain. Nevertheless, false positive results are frequently observed in manual and automated microplate analyzer using papain enzyme. The methodology proposed is simple and could provide specific information with the possibility of meansuration regarding RBC interaction.

Simultaneous calibration of optical tweezers spring constant and position detector response.

We demonstrate a fast and direct calibration method for systems using a single laser for optical tweezers and particle position detection. The method takes direct advantage of back-focal-plane interferometry measuring not an absolute but a differential position, i.e. the position of the trapped particle relative to the center of the optical tweezers. Therefore, a fast step-wise motion of the optical tweezers yields the impulse response of the trapped particle. Calibration parameters such as the detector's spatial and temporal response and the spring constant of the optical tweezers then follow readily from fitting the measured impulse response.

Real-time in situ calibration of an optically trapped probing system.

We present real-time in situ calibration of an optically trapped probing system. In the probing system, a micro/nanobead is stably trapped around the minimum of the field potential to serve as the measurement probe, whereas the random thermal force tends to destabilize it and causes Brownian motion around the equilibrium. The weighted recursive least-squares algorithm is applied to recursively update the system's parameters, such as the state transition coefficient, and to estimate specific system response and the unknown variance of the Gaussian white noise in real time according to the probe's motion. The real-time recursive algorithm was first applied to real-time calibration of measurement sensitivity and trapping stiffness for the case that the local temperature and the damping coefficient of the probe are known. It was then applied to estimate the probe's local temperature in real time. Two experiments were designed to illustrate the applicability of the real-time calibration method. The experimental results show that the recursive algorithm is able to real-time calibrate the trapping stiffness of the probing system and the measurement sensitivity of the back-focal-plane interferometry employed for position measurement. The experimental results also show that the method can estimate the probe's local temperature in real time.

An adaptive system identification approach to optical trap calibration.

A method of adaptive system identification for the modeling of an optical trap's system dynamics is presented. The system dynamics can be used to locate the corner frequency for trapping stiffness calibration using the power spectral method. The method is based on an adaptive least-mean-square (LMS) algorithm, which adjusts weights of a tapped delay line filter using a gradient descent method. The identified model is the inverse of the high order finite impulse response (FIR) filter. The model order is reduced using balanced model reduction, giving the corner frequency which can be used to calibrate the trapping stiffness. This method has an advantage over other techniques in that it is quick, does not explicitly require operator interaction, and can be acquired in real time. It is also a necessary step for an adaptive controller that can automatically update the controller for changes in the trap (e.g., power fluctuations) and for particles of different sizes and refractive indices.

Multiple holographic optical tweezers parallel calibration with optical potential well characterization.

We report the extension to a multi-axes exploration of the potential well reconstruction method against drag force to simultaneously characterize the potential wells of several trapping sites generated with holographic optical tweezers. The final result is a robust, fast and automatic procedure we use to characterize holographic tweezers. We mainly focus on the reliability of the method and its application to address the dependence of the diffraction efficiency with the trap position in a given holographic traps pattern.

Calibration of dynamic holographic optical tweezers for force measurements on biomaterials.

Holographic optical tweezers (HOTs) enable the manipulation of multiple traps independently in three dimensions in real time. Application of this technique to force measurements requires calibration of trap stiffness and its position dependence. Here, we determine the trap stiffness of HOTs as they are steered in two dimensions. To do this, we trap a single particle in a multiple-trap configuration and analyze the power spectrum of the laser deflection on a position-sensitive photodiode. With this method, the relative trap strengths can be determined independent of exact particle size, and high stiffnesses can be probed because of the high bandwidth of the photodiode. We find a trap stiffness for each of three HOT traps of kappa approximately 26 pN/microm per 100 mW of laser power. Importantly, we find that this stiffness remains constant within +/- 4% over 20 microm displacements of a trap. We also investigate the minimum step size achievable when steering a trap with HOTs, and find that traps can be stepped and detected within approximately 2 nm in our instrument, although there is an underlying position modulation of the traps of comparable scale that arises from SLM addressing. The independence of trap stiffness on steering angle over wide ranges and the nanometer positioning accuracy of HOTs demonstrate the applicability of this technique to quantitative study of force response of extended biomaterials such as cells or elastomeric protein networks.

Correction-free force calibration for magnetic tweezers experiments.

Magnetic tweezers are a powerful technique to perform high-throughput and high-resolution force spectroscopy experiments at the single-molecule level. The camera-based detection of magnetic tweezers enables the observation of hundreds of magnetic beads in parallel, and therefore the characterization of the mechanochemical behavior of hundreds of nucleic acids and enzymes. However, magnetic tweezers experiments require an accurate force calibration to extract quantitative data, which is limited to low forces if the deleterious effect of the finite camera open shutter time (τsh) is not corrected. Here, we provide a simple method to perform correction-free force calibration for high-throughput magnetic tweezers at low image acquisition frequency (fac). By significantly reducing τsh to at least 4-fold the characteristic times of the tethered magnetic bead, we accurately evaluated the variance of the magnetic bead position along the axis parallel to the magnetic field, estimating the force with a relative error of ~10% (standard deviation), being only limited by the bead-to-bead difference. We calibrated several magnets - magnetic beads configurations, covering a force range from ~50 fN to ~60 pN. In addition, for the presented configurations, we provide a table with the mathematical expressions that describe the force as a function of the magnets position.

Towards absolute calibration of optical tweezers.

Aiming at absolute force calibration of optical tweezers, following a critical review of proposed theoretical models, we present and test the results of Mie-Debye-spherical aberration (MDSA) theory, an extension of a previous (MD) model, taking account of spherical aberration at the glass-water interface. This first-principles theory is formulated entirely in terms of experimentally accessible parameters (none adjustable). Careful experimental tests of the MDSA theory, undertaken at two laboratories, with very different setups, are described. A detailed description is given of the procedures employed to measure laser beam waist, local beam power at the transparent microspheres trapped by the tweezers, microsphere radius, and the trap transverse stiffness, as a function of radius and height in the (inverted microscope) sample chamber. We find generally very good agreement with MDSA theory predictions, for a wide size range, from the Rayleigh domain to large radii, including the values most often employed in practice, and at different chamber heights, both with objective overfilling and underfilling. The results asymptotically approach geometrical optics in the mean over size intervals, as they should, and this already happens for size parameters not much larger than unity. MDSA predictions for the trapping threshold, position of stiffness peak, stiffness variation with height, multiple equilibrium points, and "hopping" effects among them are verified. Remaining discrepancies are ascribed to focus degradation, possibly arising from objective aberrations in the infrared, not yet included in MDSA theory.

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.

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.

DNA translocation of ATP-dependent chromatin remodeling factors revealed by high-resolution optical tweezers.

ATP-dependent chromatin remodeling complexes (remodelers) use the energy of ATP hydrolysis to regulate chromatin structures by repositioning and reconfiguring nucleosomes. Ensemble experiments have suggested that remodeler ATPases are DNA translocases, molecular motors capable of processively moving along DNA. This concept of DNA translocation has become a foundation for understanding the molecular mechanisms of ATP-dependent chromatin remodeling and its biological functions. However, quantitative characterizations of DNA translocation by representative remodelers are rare. Furthermore, it is unclear how a unified theory of chromatin remodeling is built upon this foundation. To address these problems, high-resolution optical tweezers have been applied to investigate remodeler translocation on bare DNA and nucleosomal DNA substrates at a single-molecule level. Our strategy is to hold two ends of a single DNA molecule and measure remodeler translocation by detecting the end-to-end extension and tension changes of the DNA molecule in response to chromatin remodeling. These single-molecule assays can reveal detailed kinetics of remodeler translocation, including velocity, processivity, stall force, pauses, direction changes, and even step size. Here we describe instruments, reagents, sample preparations, and detailed protocols for the single-molecule experiments. We show that optical tweezer force microscopy is a powerful and friendly tool for studies of chromatin structures and remodeling.

Unzipping single DNA molecules to study nucleosome structure and dynamics.

DNA unzipping is a powerful tool to study protein-DNA interactions at the single-molecule level. In this chapter, we provide a detailed and practical guide to performing this technique with an optical trap, using nucleosome studies as an example. We detail protocols for preparing an unzipping template, constructing and calibrating the instrument, and acquiring, processing, and analyzing unzipping data. We also summarize major results from utilization of this technique for the studies of nucleosome structure, dynamics, positioning, and remodeling.

Exploring mechanochemical processes in the cell with optical tweezers.

Force and torque, stress and strain or work are examples of mechanical and elastic actions which are intimately linked to chemical reactions in the cell. Optical tweezers are a light-based method which allows the real-time manipulation of single molecules and cells to measure their interactions. We describe the technique, briefly reviewing the operating principles and the potential capabilities to the study of biological processes. Additional emphasis is given to the importance of fluctuations in biology and how single-molecule techniques allow access to them. We illustrate the applications by addressing experimental configurations and recent progresses in molecular and cell biology.