Two-dimensional tracking of ncd motility by back focal plane interferometry

Kinesin-14 HSET and KlpA are non-processive microtubule motors with load-dependent power strokes

Accurate chromosome segregation during cell division relies on coordinated actions of microtubule (MT)-based motor proteins in the mitotic spindle. Kinesin-14 motors play vital roles in spindle assembly and maintenance by crosslinking antiparallel MTs at the spindle midzone and anchoring spindle MTs' minus ends at the poles. In this study, we investigate the force generation and motility of the Kinesin-14 motors HSET and KlpA. Our findings reveal that both motors are non-processive, producing single load-dependent power strokes per MT encounter, with estimated load-free power strokes of ~30 and ~35 nm, respectively. Each homodimeric motor generates forces of ~0.5 pN, but when assembled in teams, they cooperate to generate forces of 1 pN or more. Notably, the cooperative activity among multiple motors leads to increased MT-sliding velocities. These results quantitatively elucidate the structure-function relationship of Kinesin-14 motors and underscore the significance of cooperative behavior in their cellular functions.

Improving the multi-functionality of optical tweezers with FPGA integration

The development of optical tweezers aims to extend their operating function and pattern. However, excessive programming can lead to a decrease in the system's operating speed and introduce bugs or data transmission delays. In this study, we present a time-shared optical tweezers system that allows for parallel operation of multiple functions. To enable efficient data transmission, we employ a queue structure and a buffer. To assess the system's performance, we utilize a biological sample in conjunction with the optical tweezers system and scanning imaging technique. We quantify the trapping parameter while concurrently running power stabilization programs. As a result, the standard deviation of the measured stiffness is reduced by 60% in the x and y directions and 30% in the z direction, indicating a significant improvement in calibration precision. Throughout the program execution, the system maintains an operating rate of 110 kHz, and the data are continuously updated in real time on the host. The system's performance demonstrates its potential for quantification and morphological reconstruction of biological samples.

Kinesin-14 HSET and KlpA are non-processive microtubule motors with load-dependent power strokes

Accurate chromosome segregation during cell division relies on coordinated actions of microtubule (MT)-based motor proteins in the mitotic spindle. Kinesin-14 motors play vital roles in spindle assembly and maintenance by crosslinking antiparallel MTs at the spindle midzone and anchoring spindle MTs' minus ends at the poles. We investigate the force generation and motility of the Kinesin-14 motors HSET and KlpA, revealing that both motors function as non-processive motors under load, producing single power strokes per MT encounter. Each homodimeric motor generates forces of ∼0.5 pN, but when assembled in teams, they cooperate to generate forces of 1 pN or more. Importantly, cooperative activity among multiple motors leads to increased MT-sliding velocities. Our findings deepen our understanding of the structure-function relationship of Kinesin-14 motors and underscore the significance of cooperative behavior in their cellular functions.

Optical Tweezers to Force Information out of Biological and Synthetic Systems One Molecule at a Time

Over the last few decades, in vitro single-molecule manipulation techniques have enabled the use of force and displacement as controlled variables in biochemistry. Measuring the effect of mechanical force on the real-time kinetics of a biological process gives us access to the rates, equilibrium constants and free-energy landscapes of the mechanical steps of the reaction; this information is not accessible by ensemble assays. Optical tweezers are the current method of choice in single-molecule manipulation due to their versatility, high force and spatial and temporal resolutions. The aim of this review is to describe the contributions of our lab in the single-molecule manipulation field. We present here several optical tweezers assays refined in our laboratory to probe the dynamics and mechano-chemical properties of biological molecular motors and synthetic molecular devices at the single-molecule level.

Cell mediated remodeling of stiffness matched collagen and fibrin scaffolds

Cells are known to continuously remodel their local extracellular matrix (ECM) and in a reciprocal way, they can also respond to mechanical and biochemical properties of their fibrous environment. In this study, we measured how stiffness around dermal fibroblasts (DFs) and human fibrosarcoma HT1080 cells differs with concentration of rat tail type 1 collagen (T1C) and type of ECM. Peri-cellular stiffness was probed in four directions using multi-axes optical tweezers active microrheology (AMR). First, we found that neither cell type significantly altered local stiffness landscape at different concentrations of T1C. Next, rat tail T1C, bovine skin T1C and fibrin cell-free hydrogels were polymerized at concentrations formulated to match median stiffness value. Each of these hydrogels exhibited distinct fiber architecture. Stiffness landscape and fibronectin secretion, but not nuclear/cytoplasmic YAP ratio differed with ECM type. Further, cell response to Y27632 or BB94 treatments, inhibiting cell contractility and activity of matrix metalloproteinases, respectively, was also dependent on ECM type. Given differential effect of tested ECMs on peri-cellular stiffness landscape, treatment effect and cell properties, this study underscores the need for peri-cellular and not bulk stiffness measurements in studies on cellular mechanotransduction.

Flagellar rotational features of an optically confined bacterium at high frequency and temporal resolution reveal the microorganism's response to changes in the fluid environment

Rotations of the flagella control the movement of a peritrichous (multiflagellar) bacterium in fluids, the run and tumble events being caused through modulations in the flagella's collective rotation speed and pattern. Observing such modulations is a challenge in free swimming bacteria. In this work, we present a setup to measure the collective flagellar rotational features of an optically confined Bacillus subtilis bacterium. We adopt a Continuous Wavelet Technique (CWT) while monitoring the rotational patterns in frequency and time, thus achieving optimal resolution in both the domains. This enables in marking the events wherein subtle changes in the flagellar rotational pattern occur. These studies unravel a fact, hitherto unknown, that variations in swimming speed that are seen in pure run sequences are also caused by modulations in the rotating flagella. Further, we have monitored the flagellar rotation for durations over a minute and observe a gradual slowing down of the rotation before ceasing completely due to the trapping laser induced photodamage. We have observed a significant alteration in the rate of rotational fall off in real time with changes in pH or the nutrient concentration in the fluid. This work serves to demonstrate the advantage of optical confinement of a bacterium in its pristine form for carrying out such studies and can serve as a marker for work that assesses membrane photodamage in active matter. Details on the role of flagella in propulsion and on other factors influencing the rotations, can be of significance in the design of artificial microswimmers.

Patterned photocrosslinking to establish stiffness anisotropies in fibrous 3D hydrogels

Cells are known to constantly interact with their local extracellular matrix (ECM) and respond to a variety of biochemical and mechanical cues received from the ECM. Nonetheless, comprehensive understanding of cell-ECM interactions has been elusive. Many studies rely on analysis of cell behavior on 2D substrates, which do not reflect a natural cell environment. Further, lack of dynamic control over local stiffness anisotropies and fiber alignment hinders progress in studies in naturally derived fibrous 3D cultures. Here, we present a cell-safe method of patterned photocrosslinking, which can aid in studying biological hypotheses related to mechanotransduction in 3D hydrogels. As previously described by our group, ruthenium-catalyzed photocrosslinking (RCP) of selected ECM regions promotes localized increase in stiffness mediated by focused blue laser light in a confocal microscope. In this study, we further demonstrate that RCP can induce localized strain stiffening and fiber alignment outside of the selected crosslinked region and induce stiffness anisotropy biased towards the direction of fiber alignment. MDA-MB-231 cells are shown to respond to RCP-induced changes in local ECM architecture and display directional bias towards the direction of fiber alignment, as compared to control cells. Further, the effect of patterned crosslinking on a stiffness landscape is measured using multi-axes optical tweezers active microrheology (AMR) with backscattered laser beam illumination. AMR validates RCP as a suitable tool for creating distinct stiffness anisotropies which promote directed migration of cells, further underscoring the usefulness of RCP in cell-ECM studies. STATEMENT OF SIGNIFICANCE: Studies on cell-ECM interactions in 3D cultures have often been hindered by the lack of available tools to dynamically alter local ECM stiffness and fiber alignment. Here, we present a non-invasive, cell-safe and easily applicable method of patterned photocrosslinking, which can aid in studying biological hypotheses in fibrous 3D hydrogels. Ruthenium-catalyzed crosslinking (RCP) of selected fibrin ECM regions promotes localized increase in stiffness and creates distinct stiffness anisotropies in the presence of the focused blue laser light. Outside of the crosslinked region, RCP causes fiber alignment and strain stiffening in the ECM, verified using multi-axes optical tweezers active microrheology (AMR). Following RCP, human breast cancer MDA-MB-231 exhibit directed cell migration, validating usefulness of this method in cell-ECM studies.

Particle Classification through the Analysis of the Forward Scattered Signal in Optical Tweezers

The ability to select, isolate, and manipulate micron-sized particles or small clusters has made optical tweezers one of the emergent tools for modern biotechnology. In conventional setups, the classification of the trapped specimen is usually achieved through the acquired image, the scattered signal, or additional information such as Raman spectroscopy. In this work, we propose a solution that uses the temporal data signal from the scattering process of the trapping laser, acquired with a quadrant photodetector. Our methodology rests on a pre-processing strategy that combines Fourier transform and principal component analysis to reduce the dimension of the data and perform relevant feature extraction. Testing a wide range of standard machine learning algorithms, it is shown that this methodology allows achieving accuracy performances around 90%, validating the concept of using the temporal dynamics of the scattering signal for the classification task. Achieved with 500 millisecond signals and leveraging on methods of low computational footprint, the results presented pave the way for the deployment of alternative and faster classification methodologies in optical trapping technologies.

Optical tweezers in single-molecule biophysics

Optical tweezers have become the method of choice in single-molecule manipulation studies. In this Primer, we first review the physical principles of optical tweezers and the characteristics that make them a powerful tool to investigate single molecules. We then introduce the modifications of the method to extend the measurement of forces and displacements to torques and angles, and to develop optical tweezers with single-molecule fluorescence detection capabilities. We discuss force and torque calibration of these instruments, their various modes of operation and most common experimental geometries. We describe the type of data obtained in each experimental design and their analyses. This description is followed by a survey of applications of these methods to the studies of protein-nucleic acid interactions, protein/RNA folding and molecular motors. We also discuss data reproducibility, the factors that lead to the data variability among different laboratories and the need to develop field standards. We cover the current limitations of the methods and possible ways to optimize instrument operation, data extraction and analysis, before suggesting likely areas of future growth.

Cutting-Edge Single-Molecule Technologies Unveil New Mechanics in Cellular Biochemistry

Single-molecule technologies have expanded our ability to detect biological events individually, in contrast to ensemble biophysical technologies, where the result provides averaged information. Recent developments in atomic force microscopy have not only enabled us to distinguish the heterogeneous phenomena of individual molecules, but also allowed us to view up to the resolution of a single covalent bond. Similarly, optical tweezers, due to their versatility and precision, have emerged as a potent technique to dissect a diverse range of complex biological processes, from the nanomechanics of ClpXP protease-dependent degradation to force-dependent processivity of motor proteins. Despite the advantages of optical tweezers, the time scales used in this technology were inconsistent with physiological scenarios, which led to the development of magnetic tweezers, where proteins are covalently linked with the glass surface, which in turn increases the observation window of a single biomolecule from minutes to weeks. Unlike optical tweezers, magnetic tweezers use magnetic fields to impose torque, which makes them convenient for studying DNA topology and topoisomerase functioning. Using modified magnetic tweezers, researchers were able to discover the mechanical role of chaperones, which support their substrate proteinsby pulling them during translocation and assist their native folding as a mechanical foldase. In this article, we provide a focused review of many of these new roles of single-molecule technologies, ranging from single bond breaking to complex chaperone machinery, along with the potential to design mechanomedicine, which would be a breakthrough in pharmacological interventions against many diseases.

Force-Induced Formation of Twisted Chiral Ribbons

We demonstrate that an achiral stretching force transforms disk-shaped colloidal membranes composed of chiral rods into twisted ribbons with handedness opposite the preferred twist of the rods. Using an experimental technique that enforces torque-free boundary conditions we simultaneously measure the force-extension curve and the ribbon shape. An effective theory that accounts for the membrane bending energy and uses geometric properties of the edge to model the internal liquid crystalline degrees of freedom explains both the measured force-extension curve and the force-induced twisted shape.

Single-Molecule Studies of Protein Folding with Optical Tweezers

Manipulation of individual molecules with optical tweezers provides a powerful means of interrogating the structure and folding of proteins. Mechanical force is not only a relevant quantity in cellular protein folding and function, but also a convenient parameter for biophysical folding studies. Optical tweezers offer precise control in the force range relevant for protein folding and unfolding, from which single-molecule kinetic and thermodynamic information about these processes can be extracted. In this review, we describe both physical principles and practical aspects of optical tweezers measurements and discuss recent advances in the use of this technique for the study of protein folding. In particular, we describe the characterization of folding energy landscapes at high resolution, studies of structurally complex multidomain proteins, folding in the presence of chaperones, and the ability to investigate real-time cotranslational folding of a polypeptide.

Trap stiffness modification of an optically trapped microsphere through directed motion of nanoparticles

We report an enhancement in the corner frequency of an optically trapped non-magnetic microsphere in the plane perpendicular to the laser propagation direction on addition of ferrofluid to the suspension medium. We conjecture that a directed motion of the nanoparticles toward the trap in this plane is responsible for the augmentation. Changes in the corner frequency in the presence of external magnetic field gradients lend credence to this conjecture. Corner frequency augmentation is also observed when zinc oxide nanoparticles are used. Here, however, no further changes are seen in the presence of magnetic field gradients.

Structured Back Focal Plane Interferometry (SBFPI)

Back focal plane interferometry (BFPI) is one of the most straightforward and powerful methods for achieving sub-nanometer particle tracking precision at high speed (MHz). BFPI faces technical challenges that prohibit tunable expansion of linear detection range with minimal loss to sensitivity, while maintaining robustness against optical aberrations. In this paper, we devise a tunable BFPI combining a structured beam (conical wavefront) and structured detection (annular quadrant photodiode). This technique, which we termed Structured Back Focal Plane Interferometry (SBFPI), possesses three key novelties namely: extended tracking range, low loss in sensitivity, and resilience to spatial aberrations. Most importantly, the conical wavefront beam preserves the axial Gouy phase shift and lateral beam waist that can then be harnessed in a conventional BFPI system. Through a series of experimental results, we were able to tune detection sensitivity and detection range over the SBFPI parameter space. We also identified a figure of merit based on the experimental optimum that allows us to identify optimal SBPFI configurations that balance both range and sensitivity. In addition, we also studied the resilience of SBFPI against asymmetric spatial aberrations (astigmatism of up to 0.8 λ) along the lateral directions. The simplicity and elegance of SBFPI will accelerate its dissemination to many associated fields in optical detection, interferometry and force spectroscopy.

Miniaturized Metalens Based Optical Tweezers on Liquid Crystal Droplets for Lab-on-a-Chip Optical Motors

Surfaces covered with layers of ultrathin nanoantenna structures—so called metasurfaces have recently been proven capable of completely controlling phase of light. Metalenses have emerged from the advance in the development of metasurfaces providing a new basis for recasting traditional lenses into thin, planar optical components capable of focusing light. The lens made of arrays of plasmonic gold nanorods were fabricated on a glass substrate by using electron beam lithography. A 1064 nm laser was used to create a high intensity circularly polarized light focal spot through metalens of focal length 800 µm, N.A. = 0.6 fabricated based on Pancharatnam-Berry phase principle. We demonstrated that optical rotation of birefringent nematic liquid crystal droplets trapped in the laser beam was possible through this metalens. The rotation of birefringent droplets convinced that the optical trap possesses strong enough angular momentum of light from radiation of each nanostructure acting like a local half waveplate and introducing an orientation-dependent phase to light. Here, we show the success in creating a miniaturized and robust metalens based optical tweezers system capable of rotating liquid crystals droplets to imitate an optical motor for future lab-on-a-chip applications.

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.

New Detector Sensitivity Calibration and the Calculation of the Interaction Force between Particles Using an Optical Tweezer

We propose a new approach to calculate the sensitivity factor of the detector in optical tweezers. In this work, we used a charge-coupled device (CCD) camera and a quadrant photodiode (QPD) for the extraction of the various positions occupied by the trapped object (in this case, silica beads of different diameters). Image-J software and the Boltzmann statistical method were then used to estimate the sensitivity of the detector. Silica beads of diameter 0.8 µm, 2 µm, a system of 2 µm bead stuck to 4.5 µm one and another system of 2 µm beads stuck to 2 µm one, were studied. This work contributes significantly to making better calibration of the detector without taking into account the geometry of the object imprisoned in the optical trap. We further developed an approach to calculate the interaction force between two microbeads. This approach does not require any knowledge of solvent viscosity and works for all types of samples.

Real-time identification of the singleness of a trapped bead in optical tweezers

Beads trapped in optical tweezers are aligned along the optical propagation direction, which makes it difficult to determine the number of beads with bright-field microscopy. This problem also dramatically influences the measurement of the optical trapping based single-molecule force spectroscopy. Here, we propose a video processing approach to count the number of trapped micro-objects in real time. The approach uses a normalized cross-correlation algorithm and image enhancement techniques to amplify a slight change of the image induced by the entry of an exotic object. As tested, this method introduces a ∼10% change per bead to the image similarity, and up to four beads, one-by-one falling into the trap, are identified. Moreover, the feasibility of the above analysis in a moving trap is investigated. A movement of the trap leads to a fluctuation of less than 2% for the similarity signal and can be ignored in most cases. The experimental results prove that image similarity measurement is a sensitive way to monitor the interruption, which is very useful, especially during experiments. In addition, the approach is easy to apply to an existing optical tweezers system.

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.

Objective-lens-free Fiber-based Position Detection with Nanometer Resolution in a Fiber Optical Trapping System

Position detection with high accuracy is crucial for force calibration of optical trapping systems. Most existing position detection methods require high-numerical-aperture objective lenses, which are bulky, expensive, and difficult to miniaturize. Here, we report an affordable objective-lens-free, fiber-based position detection scheme with 2 nm spatial resolution and 150 MHz bandwidth. This fiber based detection mechanism enables simultaneous trapping and force measurements in a compact fiber optical tweezers system. In addition, we achieved more reliable signal acquisition with less distortion compared with objective based position detection methods, thanks to the light guiding in optical fibers and small distance between the fiber tips and trapped particle. As a demonstration of the fiber based detection, we used the fiber optical tweezers to apply a force on a cell membrane and simultaneously measure the cellular response.

Back-focal-plane displacement detection using side-scattered light in dual-beam fiber-optic traps

In optical traps the position of a trapped bead is usually determined by measuring the intensity distribution of the forward-scattered light and the back-scattered light. In this paper we demonstrate that this position can be determined using the side-scattered light. A quadrant photodiode is used to monitor the position of an optically trapped object in a dual-beam fiber-optic trap by measurement of intensity shifts in the back focal plane of the objective that is perpendicular to the propagating beam. An approximated model based on ray optics is presented with numerical results that describe the use of the side-scattered light for position detection. The influences of system parameters, including fiber separations, the numerical apertures (NA), and the radii of microspheres, are discussed in details. We find out that the displacement sensitivity of the detector is null for some critical radii and numerical apertures. In addition, the noises in laser powers are analyzed, and one power difference regime is proposed to weaken the influences.

Achiral symmetry breaking and positive Gaussian modulus lead to scalloped colloidal membranes

In the presence of a nonadsorbing polymer, monodisperse rod-like particles assemble into colloidal membranes, which are one-rod-length-thick liquid-like monolayers of aligned rods. Unlike 3D edgeless bilayer vesicles, colloidal monolayer membranes form open structures with an exposed edge, thus presenting an opportunity to study elasticity of fluid sheets. Membranes assembled from single-component chiral rods form flat disks with uniform edge twist. In comparison, membranes composed of a mixture of rods with opposite chiralities can have the edge twist of either handedness. In this limit, disk-shaped membranes become unstable, instead forming structures with scalloped edges, where two adjacent lobes with opposite handedness are separated by a cusp-shaped point defect. Such membranes adopt a 3D configuration, with cusp defects alternatively located above and below the membrane plane. In the achiral regime, the cusp defects have repulsive interactions, but away from this limit we measure effective long-ranged attractive binding. A phenomenological model shows that the increase in the edge energy of scalloped membranes is compensated by concomitant decrease in the deformation energy due to Gaussian curvature associated with scalloped edges, demonstrating that colloidal membranes have positive Gaussian modulus. A simple excluded volume argument predicts the sign and magnitude of the Gaussian curvature modulus that is in agreement with experimental measurements. Our results provide insight into how the interplay between membrane elasticity, geometrical frustration, and achiral symmetry breaking can be used to fold colloidal membranes into 3D shapes.

Direct measurement of cortical force generation and polarization in a living parasite

Apicomplexa is a large phylum of intracellular parasites that are notable for the diseases they cause, including toxoplasmosis, malaria, and cryptosporidiosis. A conserved motile system is critical to their life cycles and drives directional gliding motility between cells, as well as invasion of and egress from host cells. However, our understanding of this system is limited by a lack of measurements of the forces driving parasite motion. We used a laser trap to measure the function of the motility apparatus of living Toxoplasma gondii by adhering a microsphere to the surface of an immobilized parasite. Motion of the microsphere reflected underlying forces exerted by the motile apparatus. We found that force generated at the parasite surface begins with no preferential directionality but becomes directed toward the rear of the cell after a period of time. The transition from nondirectional to directional force generation occurs on spatial intervals consistent with the lateral periodicity of structures associated with the membrane pellicle and is influenced by the kinetics of actin filament polymerization and cytoplasmic calcium. A lysine methyltransferase regulates both the magnitude and polarization of the force. Our work provides a novel means to dissect the motile mechanisms of these pathogens.

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.

Biophysical properties of human β-cardiac myosin with converter mutations that cause hypertrophic cardiomyopathy

Hypertrophic cardiomyopathy (HCM) affects 1 in 500 individuals and is an important cause of arrhythmias and heart failure. Clinically, HCM is characterized as causing hypercontractility, and therapies are aimed toward controlling the hyperactive physiology. Mutations in the β-cardiac myosin comprise ~40% of genetic mutations associated with HCM, and the converter domain of myosin is a hotspot for HCM-causing mutations; however, the underlying primary effects of these mutations on myosin's biomechanical function remain elusive. We hypothesize that these mutations affect the biomechanical properties of myosin, such as increasing its intrinsic force and/or its duty ratio and therefore the ensemble force of the sarcomere. Using recombinant human β-cardiac myosin, we characterize the molecular effects of three severe HCM-causing converter domain mutations: R719W, R723G, and G741R. Contrary to our hypothesis, the intrinsic forces of R719W and R723G mutant myosins are decreased compared to wild type and unchanged for G741R. Actin and regulated thin filament gliding velocities are ~15% faster for R719W and R723G myosins, whereas there is no change in velocity for G741R. Adenosine triphosphatase activities and the load-dependent velocity change profiles of all three mutant proteins are very similar to those of wild type. These results indicate that the net biomechanical properties of human β-cardiac myosin carrying these converter domain mutations are very similar to those of wild type or are even slightly hypocontractile, leading us to consider an alternative mechanism for the clinically observed hypercontractility. Future work includes how these mutations affect protein interactions within the sarcomere that increase the availability of myosin heads participating in force production.

Introduction to Optical Tweezers

Thirty years after their invention by Arthur Ashkin and colleagues at Bell Labs in 1986 [1], optical tweezers (or traps) have become a versatile tool to address numerous biological problems. Put simply, an optical trap is a highly focused laser beam that is capable of holding and applying forces to micron-sized dielectric objects. However, their development over the last few decades has converted these tools from boutique instruments into highly versatile instruments of molecular biophysics. This introductory chapter intends to give a brief overview of the field, highlight some important scientific achievements, and demonstrate why optical traps have become a powerful tool in the biological sciences. We introduce a typical optical setup, describe the basic theoretical concepts of how trapping forces arise, and present the quantitative position and force measurement techniques that are most widely used today.

Advances in the microrheology of complex fluids

New developments in the microrheology of complex fluids are considered. Firstly the requirements for a simple modern particle tracking microrheology experiment are introduced, the error analysis methods associated with it and the mathematical techniques required to calculate the linear viscoelasticity. Progress in microrheology instrumentation is then described with respect to detectors, light sources, colloidal probes, magnetic tweezers, optical tweezers, diffusing wave spectroscopy, optical coherence tomography, fluorescence correlation spectroscopy, elastic- and quasi-elastic scattering techniques, 3D tracking, single molecule methods, modern microscopy methods and microfluidics. New theoretical techniques are also reviewed such as Bayesian analysis, oversampling, inversion techniques, alternative statistical tools for tracks (angular correlations, first passage probabilities, the kurtosis, motor protein step segmentation etc), issues in micro/macro rheological agreement and two particle methodologies. Applications where microrheology has begun to make some impact are also considered including semi-flexible polymers, gels, microorganism biofilms, intracellular methods, high frequency viscoelasticity, comb polymers, active motile fluids, blood clots, colloids, granular materials, polymers, liquid crystals and foods. Two large emergent areas of microrheology, non-linear microrheology and surface microrheology are also discussed.

Measurement of Elastic Modulus of Collagen Type I Single Fiber

Collagen fibers are the main components of the extra cellular matrix and the primary contributors to the mechanical properties of tissues. Here we report a novel approach to measure the longitudinal component of the elastic moduli of biological fibers under conditions close to those found in vivo and apply it to type I collagen from rat tail tendon. This approach combines optical tweezers, atomic force microscopy, and exploits Euler-Bernoulli elasticity theory for data analysis. This approach also avoids drying for measurements or visualization, since samples are freshly extracted. Importantly, strains are kept below 0.5%, which appear consistent with the linear elastic regime. We find, surprisingly, that the longitudinal elastic modulus of type I collagen cannot be represented by a single quantity but rather is a distribution that is broader than the uncertainty of our experimental technique. The longitudinal component of the single-fiber elastic modulus is between 100 MPa and 360 MPa for samples extracted from different rats and/or different parts of a single tail. Variations are also observed in the fibril-bundle/fibril diameter with an average of 325±40 nm. Since bending forces depend on the diameter to the fourth power, this variation in diameter is important for estimating the range of elastic moduli. The remaining variations in the modulus may be due to differences in composition of the fibril-bundles, or the extent of the proteoglycans constituting fibril-bundles, or that some single fibrils may be of fibril-bundle size.

Contractility parameters of human β-cardiac myosin with the hypertrophic cardiomyopathy mutation R403Q show loss of motor function

Hypertrophic cardiomyopathy (HCM) is the most frequently occurring inherited cardiovascular disease. It is caused by mutations in genes encoding the force-generating machinery of the cardiac sarcomere, including human β-cardiac myosin. We present a detailed characterization of the most debated HCM-causing mutation in human β-cardiac myosin, R403Q. Despite numerous studies, most performed with nonhuman or noncardiac myosin, there is no consensus about the mechanism of action of this mutation on the function of the enzyme. We use recombinant human β-cardiac myosin and new methodologies to characterize in vitro contractility parameters of the R403Q myosin compared to wild type. We extend our studies beyond pure actin filaments to include the interaction of myosin with regulated actin filaments containing tropomyosin and troponin. We find that, with pure actin, the intrinsic force generated by R403Q is ~15% lower than that generated by wild type. The unloaded velocity is, however, ~10% higher for R403Q myosin, resulting in a load-dependent velocity curve that has the characteristics of lower contractility at higher external loads compared to wild type. With regulated actin filaments, there is no increase in the unloaded velocity and the contractility of the R403Q myosin is lower than that of wild type at all loads. Unlike that with pure actin, the actin-activated adenosine triphosphatase activity for R403Q myosin with Ca(2+)-regulated actin filaments is ~30% lower than that for wild type, predicting a lower unloaded duty ratio of the motor. Overall, the contractility parameters studied fit with a loss of human β-cardiac myosin contractility as a result of the R403Q mutation.

Calibrating oscillation response of a piezo-stage using optical tweezers

In optical tweezers, a piezo-stage (PZT) is widely used to precisely position samples for force clamp, calibrating optical trap and stretching DNA. For a trapped bead in solution, the oscillation response of PZT is vital for all kinds of applications. A coupling ratio, actual amplitude to nominal amplitude, can be calibrated by power spectral density during sinusoidal oscillations. With oscillation frequency increasing, coupling ratio decreases in both x- and y-directions, which is also confirmed by the calibration with light scattering of scanning two aligned beads on slide. Those oscillation responses are related with deformability of chamber and the intrinsic characteristics of PZT. If we take nominal amplitude as actual amplitude for sinusoidal oscillations at 50 Hz, the amplitude is overestimated ~2 times in x-direction and ~3 times in y-direction. That will lead to huge errors for subsequent calibrations.

Origins of Escherichia coli growth rate and cell shape changes at high external osmolality

In Escherichia coli, a sudden increase in external concentration causes a pressure drop across the cell envelope, followed by an active recovery. After recovery, and if the external osmolality remains high, cells have been shown to grow more slowly, smaller, and at reduced turgor pressure. Despite the fact that the active recovery is a key stress response, the nature of these changes and how they relate to each other is not understood. Here, we use fluorescence imaging of single cells during hyperosmotic shocks, combined with custom made microfluidic devices, to show that cells fully recover their volume to the initial, preshock value and continue to grow at a slower rate immediately after the recovery. We show that the cell envelope material properties do not change after hyperosmotic shock, and that cell shape recovers along with cell volume. Taken together, these observations indicate that the turgor pressure recovers to its initial value so that reduced turgor is not responsible for the reduced growth rate observed immediately after recovery. To determine the point at which the reduction in cell size and turgor pressure occurs after shock, we measured the volume of E. coli cells at different stages of growth in bulk cultures. We show that cell volume reaches the same maximal level irrespective of the osmolality of the media. Based on these measurements, we propose that turgor pressure is used as a feedback variable for osmoregulatory pumps instead of being directly responsible for the reduction in growth rates. Reestablishment of turgor to its initial value might ensure correct attachment of the inner membrane and cell wall needed for cell wall biosynthesis.

Pushing the limit: investigation of hydrodynamic forces on a trapped particle kicked by a laser pulse

We introduce a new optical technique where a train of short optical pulses is utilized to disturb a trapped microscopic particle. Using fast (250 kHz) and accurate (nm) detection of the position of the particle, accurately synchronized to the repetition rate of the laser pulses, we can coherently superimpose the displacement caused by each individual laser pulse. Thereby we are able to both bypass the influence from the Brownian motion of the trapped particle and to simultaneously increase the ability to localize its average trajectory by √n, where n is the number of repetitive pulses. In the results presented here we utilize a train of 1200 pulses to kick a 5 μm polystyrene sphere and obtain a spatial resolution corresponding to 0.09 nm and a time resolution of 4 μs. The magnitude of the optical force pushing the particle corresponds to ∼ 10(4)g and enables an investigation of both the hydrodynamical drag and the inertial effects caused by the particle and the surrounding liquid. Our results enables a more accurate testing of the existing extended models for the hydrodynamic drag and we discuss the observed agreement between experiments and theory.

Extracting physical chemistry from mechanics: a new approach to investigate DNA interactions with drugs and proteins in single molecule experiments

In this review we focus on the idea of establishing connections between the mechanical properties of DNA–ligand complexes and the physical chemistry of DNA–ligand interactions.

Interrogating biology with force: single molecule high-resolution measurements with optical tweezers

Single molecule force spectroscopy methods, such as optical and magnetic tweezers and atomic force microscopy, have opened up the possibility to study biological processes regulated by force, dynamics of structural conformations of proteins and nucleic acids, and load-dependent kinetics of molecular interactions. Among the various tools available today, optical tweezers have recently seen great progress in terms of spatial resolution, which now allows the measurement of atomic-scale conformational changes, and temporal resolution, which has reached the limit of the microsecond-scale relaxation times of biological molecules bound to a force probe. Here, we review different strategies and experimental configurations recently developed to apply and measure force using optical tweezers. We present the latest progress that has pushed optical tweezers' spatial and temporal resolution down to today's values, discussing the experimental variables and constraints that are influencing measurement resolution and how these can be optimized depending on the biological molecule under study.

Loop 2 of myosin is a force-dependent inhibitor of the rigor bond

Myosin's actin-binding loop (loop 2) carries a charge opposite to that of its binding site on actin and is thought to play an important role in ionic interactions between the two molecules during the initial binding step. However, no subsequent role has been identified for loop 2 in actin-myosin binding. We used an optical trap to measure bond formation and bond rupture between actin and rigor heavy meromyosin when loaded perpendicular to the filament axis. We studied HMM with intact or proteolytically cleaved loop 2 at low and physiologic ionic strength. Here we show that the presence of intact loop 2 allows actomyosin bonds to form quickly and that they do so in a short-lived bound state. Increasing tensile load causes the transition to a long-lived state-the distinguishing behavior of a catch bond. When loop 2 was cleaved catch bond behavior was abrogated leaving only a long-lived state. These data suggest that in addition to its role in locating binding sites on actin, loop 2 is also a force-dependent inhibitor of the long-lived actomyosin complex. This may be important for reducing the duty ratio and increasing the shortening velocity of actomyosin at low forces.

Plasmolysis and cell shape depend on solute outer-membrane permeability during hyperosmotic shock in E. coli

The concentration of chemicals inside the bacterial cytoplasm generates an osmotic pressure, termed turgor, which inflates the cell and is necessary for cell growth and survival. In Escherichia coli, a sudden increase in external concentration causes a pressure drop across the cell envelope that drives changes in cell shape, such as plasmolysis, where the inner and outer membranes separate. Here, we use fluorescence imaging of single cells during hyperosmotic shock with a time resolution on the order of seconds to examine the response of cells to a range of different conditions. We show that shock using an outer-membrane impermeable solute results in total cell volume reduction with no plasmolysis, whereas a shock caused by outer-membrane permeable ions causes plasmolysis immediately upon shock. Slowly permeable solutes, such as sucrose, which cross the membrane in minutes, cause plasmolysis to occur gradually as the chemical potential equilibrates. In addition, we quantify the detailed morphological changes to cell shape during osmotic shock. Nonplasmolyzed cells shrink in length with an additional lateral size reduction as the magnitude of the shock increases. Quickly plasmolyzing cells shrink largely at the poles, whereas gradually plasmolyzing cells invaginate along the cell cylinder. Our results give a comprehensive picture of the initial response of E. coli to hyperosmotic shock and offer explanations for seemingly opposing results that have been reported previously.

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.

An improved optical tweezers assay for measuring the force generation of single kinesin molecules

Numerous microtubule-associated molecular motors, including several kinesins and cytoplasmic dynein, produce opposing forces that regulate spindle and chromosome positioning during mitosis. The motility and force generation of these motors are therefore critical to normal cell division, and dysfunction of these processes may contribute to human disease. Optical tweezers provide a powerful method for studying the nanometer motility and piconewton force generation of single motor proteins in vitro. Using kinesin-1 as a prototype, we present a set of step-by-step, optimized protocols for expressing a kinesin construct (K560-GFP) in Escherichia coli, purifying it, and studying its force generation in an optical tweezers microscope. We also provide detailed instructions on proper alignment and calibration of an optical trapping microscope. These methods provide a foundation for a variety of similar experiments.

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.

A high-speed vertical optical trap for the mechanical testing of living cells at piconewton forces

Although atomic force microscopy is often the method of choice to probe the mechanical response of (sub)micrometer sized biomaterials, the lowest force that can be reliably controlled is limited to ≈0.1 nN. For soft biological samples, like cells, such forces can already lead to a strain large enough to enter the non-elastic deformation regime. To be able to investigate the response of single cells at lower forces we developed a vertical optical trap. The force can be controlled down to single piconewtons and most of the advantages of atomic force microscopy are maintained, such as the symmetrical application of forces at a wide range of loading rates. Typical consequences of moving the focus in the vertical direction, like the interferometric effect between the bead and the coverslip and a shift of focus, were quantified and found to have negligible effects on our measurements. With a fast responding force feedback loop we can achieve deformation rates as high as 50 μm/s, which allow the investigation of the elastic and viscous components of very soft samples. The potential of the vertical optical trap is demonstrated by measuring the linearity of the response of single cells at very low forces and a high bandwidth of deformation rates.

Differential interference contrast microscopy using light-emitting diode illumination in conjunction with dual optical traps

Differential interference contrast (DIC) microscopy is a common mode of biological light microscopy used to achieve maximal resolution and contrast with label-free, weakly absorbing specimens such as cells. Maintaining the polarization state of the illuminating light is essential for the technique, and this requirement can conflict with optical trapping. We describe how to optimize DIC imaging using a light-emitting diode illumination source in a microscope while integrating a dual optical trap into the set up. Every time a polarized light beam reflects off or transmits through a dichroic mirror in the beam path, its polarization state will change if it is not polarized exactly parallel (p) or perpendicular (s) to the plane of incidence. We observe wavelength-dependent optical rotation and depolarization effects in our illumination light upon reflection from/transmission through dichroic mirrors in the beam path, resulting in significant degradation of image quality. We describe a method to compensate for these effects by introducing quarter-waveplates and a laser clean-up filter into the imaging pathway. We show that this approach achieves a full recovery of image quality.

Kinesin KIFC1 actively transports bare double-stranded DNA

During the past years, exogenous DNA molecules have been used in gene and molecular therapy. At present, it is not known how these DNA molecules reach the cell nucleus. We used an in cell single-molecule approach to observe the motion of exogenous short DNA molecules in the cytoplasm of eukaryotic cells. Our observations suggest an active transport of the DNA along the cytoskeleton filaments. We used an in vitro motility assay, in which the motion of single-DNA molecules along cytoskeleton filaments in cell extracts is monitored; we demonstrate that microtubule-associated motors are involved in this transport. Precipitation of DNA-bound proteins and mass spectrometry analyses reveal the preferential binding of the kinesin KIFC1 on DNA. Cell extract depletion of kinesin KIFC1 significantly decreases DNA motion, confirming the active implication of this molecular motor in the intracellular DNA transport.

Differential interferometric particle tracking on the subnanometer- and submillisecond-scale

We describe an interferometric method to measure the movement of a subwavelength probe particle relative to an immobilized reference particle with high spatial (Δx = 0.9nm) and temporal (Δt = 200μs) resolution. The differential method eliminates microscope stage drift. An upright microscope is equipped with laser dark field illumination (λ(0) = 532nm, P(0) = 30mW) and a compact modified Mach-Zehnder interferometer is mounted on the camera exit of the microscope, where the beams of scattered light of both particles are combined. The resulting interferograms provide in two channels subnanometer information about the motion of the probe particle relative to the reference particle. The interferograms are probed with two avalanche photodiodes. We applied this method to measuring the movement of kinesin along microtubules and were able to resolve the generic 8-nm steps at high ATP concentrations without external forces.

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.

Fast, multiphase volume adaptation to hyperosmotic shock by Escherichia coli

All living cells employ an array of different mechanisms to help them survive changes in extra cellular osmotic pressure. The difference in the concentration of chemicals in a bacterium's cytoplasm and the external environment generates an osmotic pressure that inflates the cell. It is thought that the bacterium Escherichia coli use a number of interconnected systems to adapt to changes in external pressure, allowing them to maintain turgor and live in surroundings that range more than two-hundred-fold in external osmolality. Here, we use fluorescence imaging to make the first measurements of cell volume changes over time during hyperosmotic shock and subsequent adaptation on a single cell level in vivo with a time resolution on the order of seconds. We directly observe two previously unseen phases of the cytoplasmic water efflux upon hyperosmotic shock. Furthermore, we monitor cell volume changes during the post-shock recovery and observe a two-phase response that depends on the shock magnitude. The initial phase of recovery is fast, on the order of 15–20 min and shows little cell-to-cell variation. For large sucrose shocks, a secondary phase that lasts several hours adds to the recovery. We find that cells are able to recover fully from shocks as high as 1 Osmol/kg using existing systems, but that for larger shocks, protein synthesis is required for full recovery.

High-resolution microrheology in the pericellular matrix of prostate cancer cells

Many cells express a membrane-coupled external mechanical layer, the pericellular matrix (PCM), which often contains long-chain polymers. Its role and properties are not entirely known, but its functions are believed to include physical protection, mechanosensing, chemical signalling or lubrication. The viscoelastic response of the PCM, with polysaccharides as the main structural components, is therefore crucial for the understanding of its function. We have here applied microrheology, based on optically trapped micrometre-sized colloids, to the PCM of cultured PC3 prostate cancer cells. This technology allowed us to measure the extremely soft response of the PCM, with approximately 1 µm height resolution. Exogenously added aggrecan, a hyaluronan-binding proteoglycan, caused a remarkable increase in thickness of the viscoelastic layer and also triggered filopodia-like protrusions. The viscoelastic response of the PCM, however, did not change significantly.

Plasmonic coherent drive of an optical trap

We demonstrate that optical trapping can be driven by delocalized surface plasmon modes resonantly excited within a standing wave trap. Dynamical modifications are shown to be determined by the near-field symmetry of the plasmonic modes with negligible thermal effect. With low trapping powers and polarization control, remarkable stiffness enhancements are recorded, the larger the smaller the particle. The results can be simply modeled accounting for a coherent interaction between the plasmon field and the Gaussian standing wave of the trap.

Extending vaterite microviscometry to ex vivo blood vessels by serial calibration

The endothelial glycocalyx layer is a ~2 µm thick glycosaminoglycan rich pericellular matrix expressed on the luminal surface of vascular endothelial cells, which has implications in vessel mechanics and mechanotransduction. Despite its role in vascular physiology, no direct measurement has of yet been made of vessel glycocalyx material properties. Vaterite microviscometry is a laser tweezers based microrheological method, which has been previously utilized to measure the viscosity of linear and complex fluids under flow. This form of microrheology has until now relied on complete recollection of the forward scattered light. Here we present a novel method to extend vaterite microviscometry to relatively thick samples. We validate our method and its assumptions and measure the apparent viscosity as a function of distance from the vascular endothelium. We observe a differential response in conditions designed to preserve the EGL in comparison to those designed to collapse it.

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.

Digital holographic tracking of microprobes for multipoint viscosity measurements

Digital holographic microscopy provides an ideal tool for 3D tracking of microspheres while simultaneously allowing a full and accurate characterization of their main physical properties such as: radius and refractive index. We demonstrate that the combination of high resolution multipoint tracking and accurate optical sizing of tracers provides an ideal tool for precise multipoint viscosity measurements. We also report a detailed evaluation of the technique's accuracy and precision in relation to the primary sources of error.