Quantitative measurements of force and displacement using an optical trap.

We combined a single-beam gradient optical trap with a high-resolution photodiode position detector to show that an optical trap can be used to make quantitative measurements of nanometer displacements and piconewton forces with millisecond resolution. When an external force is applied to a micron-sized bead held by an optical trap, the bead is displaced from the center of the trap by an amount proportional to the applied force. When the applied force is changed rapidly, the rise time of the displacement is on the millisecond time scale, and thus a trapped bead can be used as a force transducer. The performance can be enhanced by a feedback circuit so that the position of the trap moves by means of acousto-optic modulators to exert a force equal and opposite to the external force applied to the bead. In this case the position of the trap can be used to measure the applied force. We consider parameters of the trapped bead such as stiffness and response time as a function of bead diameter and laser beam power and compare the results with recent ray-optic calculations.     

The stiffness of rabbit skeletal actomyosin cross-bridges determined with an optical tweezers transducer.

Muscle contraction is brought about by the cyclical interaction of myosin with actin coupled to the breakdown of ATP. The current view of the mechanism is that the bound actomyosin complex (or "cross-bridge") produces force and movement by a change in conformation. This process is known as the "working stroke." We have measured the stiffness and working stroke of a single cross-bridge (kappa xb, dxb, respectively) with an optical tweezers transducer. Measurements were made with the "three bead" geometry devised by Finer et al. (1994), in which two beads, supported in optical traps, are used to hold an actin filament in the vicinity of a myosin molecule, which is immobilized on the surface of a third bead. The movements and forces produced by actomyosin interactions were measured by detecting the position of both trapped beads. We measured, and corrected for, series compliance in the system, which otherwise introduces large errors. First, we used video image analysis to measure the long-range, force-extension property of the actin-to-bead connection (kappa con), which is the main source of "end compliance." We found that force-extension diagrams were nonlinear and rather variable between preparations, i.e., end compliance depended not only upon the starting tension, but also upon the F-actin-bead pair used. Second, we measured kappa xb and kappa con during a single cross-bridge attachment by driving one optical tweezer with a sinusoidal oscillation while measuring the position of both beads. In this way, the bead held in the driven optical tweezer applied force to the cross-bridge, and the motion of the other bead measured cross-bridge movement. Under our experimental conditions (at approximately 2 pN of pretension), connection stiffness (kappa con) was 0.26 +/- 0.16 pN nm-1. We found that rabbit heavy meromyosin produced a working stroke of 5.5 nm, and cross-bridge stiffness (kappa xb) was 0.69 +/- 0.47 pN nm-1.     

Construction and calibration of an optical trap on a fluorescence optical microscope

The application of optical traps has come to the fore in the last three decades. They provide a powerful, sterile and noninvasive tool for the manipulation of cells, single biological macromolecules, colloidal microparticles and nanoparticles. An optically trapped microsphere may act as a force transducer that is used to measure forces in the piconewton regime. By setting up a well-calibrated single-beam optical trap within a fluorescence microscope system, one can measure forces and collect fluorescence signals upon biological systems simultaneously. In this protocol, we aim to provide a clear exposition of the methodology of assembling and operating a single-beam gradient force trap (optical tweezers) on an inverted fluorescence microscope. A step-by-step guide is given for alignment and operation, with discussion of common pitfalls.     

Single-molecule DNA digestion by lambda-exonuclease.

We used a bead displacement sensor to determine the enzymatic shortening of individual molecules of unstained lambda-DNA attached to optically trapped beads. The setup has been described previously (Dapprich and Nicklaus: Bioimaging 6:25-32, 1998) and works by observing the change in position of a trapped bead depending on its viscous drag force during motion. The drag force of a naked bead increases with each attached DNA molecule to a characteristic level that depends on the length and the number of DNAs per bead. A single undigested DNA molecule on a bead will remain stable for extended periods and exhibit a constant drag force in flow. If lambda-exonuclease is added, the drag force decreases from the level for one strand of DNA on a bead to that of a naked bead in about 45 min. This result indicates that the digestion of native lambda-DNA by lambda-exonuclease occurs at an average rate of approximately 15-20 Hz.     

Detection and characterization of individual intermolecular bonds using optical tweezers

The development of scanning probe techniques has made it possible to examine protein-protein interactions at the level of individual molecular pairs. A calibrated optical tweezers, along with immunoglobulin G (IgG)-coated polystyrene microspheres, has been used to detect individual surface-linked Staphylococcus protein A (SpA) molecules and to characterize the strength of the noncovalent IgG-SpA bond. Microspheres containing, on average, less than one IgG per contact area were held in the optical trap while an SpA-coated substrate was scanned beneath them at a distance of approximately 50 nm. This geometry allows the trapped bead to make contact with the surface, from bond formation to rupture, and results in an enhancement of the force applied to a bond due to leverage supplied by the bead itself. Experiments yielded median single-bond rupture forces from 25 to 44 pN for IgG from four mammalian species, in general agreement with predictions based on free energies of association obtained from solution equilibrium constants.     

Localized dynamic light scattering: a new approach to dynamic measurements in optical microscopy.

We present a new approach to probing single-particle dynamics that uses dynamic light scattering from a localized region. By scattering a focused laser beam from a micron-size particle, we measure its spatial fluctuations via the temporal autocorrelation of the scattered intensity. We demonstrate the applicability of this approach by measuring the three-dimensional force constants of a single bead and a pair of beads trapped by laser tweezers. The scattering equations that relate the scattered intensity autocorrelation to the particle position correlation function are derived. This technique has potential applications for measurement of biomolecular force constants and probing viscoelastic properties of complex media.     

An automated two-dimensional optical force clamp for single molecule studies

We constructed a next-generation optical trapping instrument to study the motility of single motor proteins, such as kinesin moving along a microtubule. The instrument can be operated as a two-dimensional force clamp, applying loads of fixed magnitude and direction to motor-coated microscopic beads moving in vitro. Flexibility and automation in experimental design are achieved by computer control of both the trap position, via acousto-optic deflectors, and the sample position, using a three-dimensional piezo stage. Each measurement is preceded by an initialization sequence, which includes adjustment of bead height relative to the coverslip using a variant of optical force microscopy (to +/-4 nm), a two-dimensional raster scan to calibrate position detector response, and adjustment of bead lateral position relative to the microtubule substrate (to +/-3 nm). During motor-driven movement, both the trap and stage are moved dynamically to apply constant force while keeping the trapped bead within the calibrated range of the detector. We present details of force clamp operation and preliminary data showing kinesin motor movement subject to diagonal and forward loads.     

Quantitative measurement of changes in adhesion force involving focal adhesion kinase during cell attachment, spread, and migration

Focal adhesion kinase (FAK) is a critical protein for the regulation of integrin-mediated cellular functions and it can enhance cell motility in Madin-Darby canine kidney (MDCK) cells by hepatocyte growth factor (HGF) induction. We utilized optical trapping and cytodetachment techniques to measure the adhesion force between pico-Newton and nano-Newton (nN) for quantitatively investigating the effects of FAK on adhesion force during initial binding (5 s), beginning of spreading (30 min), spreadout (12 h), and migration (induced by HGF) in MDCK cells with overexpressed FAK (FAK-WT), FAK-related non-kinase (FRNK), as well as normal control cells. Optical tweezers was used to measure the initial binding force between a trapped cell and glass coverslide or between a trapped bead and a seeded cell. In cytodetachment, the commercial atomic force microscope probe with an appropriate spring constant was used as a cyto-detacher to evaluate the change of adhesion force between different FAK expression levels of cells in spreading, spreadout, and migrating status. The results demonstrated that FAK-WT significantly increased the adhesion forces as compared to FRNK cells throughout all the different stages of cell adhesion. For cells in HGF-induced migration, the adhesion force decreased to almost the same level (approximately 600 nN) regardless of FAK levels indicating that FAK facilitates cells to undergo migration by reducing the adhesion force. Our results suggest FAK plays a role of enhancing cell adhesive ability in the binding and spreading, but an appropriate level of adhesion force is required for HGF-induced cell migration.     

The mechanical properties of kinesin-1: a holistic approach

During the last 25?years, a vast amount of research has gone into understanding the mechanochemical cycle of kinesin-1 and similar processive motor proteins. An experimental method that has been widely used to this effect is the in vitro study of kinesin-1 molecules moving along microtubules while pulling a bead, the position of which is monitored optically while trapped in a laser focus. Analysing results from such experiments, in which thermally excited water molecules are violently buffeting the system components, can be quite difficult. At low loads, the effect of the mechanical properties of the entire molecule must be taken into account, as stalk compliance means the bead position recorded is only weakly coupled to the movement of the motor domains, the sites of ATP hydrolysis and microtubule binding. In the present review, findings on the mechanical and functional properties of the various domains of full-length kinesin-1 molecules are summarized and a computer model is presented that uses this information to simulate the motion of a bead carried by a kinesin molecule along a microtubule, with and without a weak optical trap present. A video sequence made from individual steps of the simulation gives a three-dimensional visual insight into these types of experiment at the molecular level.     

A high-resolution magnetic tweezer for single-molecule measurements

Magnetic tweezers (MT) are single-molecule manipulation instruments that utilize a magnetic field to apply force to a biomolecule-tethered magnetic bead while using optical bead tracking to measure the biomolecule’s extension. While relatively simple to set up, prior MT implementations have lacked the resolution necessary to observe sub-nanometer biomolecular configuration changes. Here, we demonstrate a reflection-interference technique for bead tracking, and show that it has much better resolution than traditional diffraction-based systems. We enhance the resolution by fabricating optical coatings on all reflecting surfaces that optimize the intensity and contrast of the interference image, and we implement feedback control of the focal position to remove drift. To test the system, we measure the length change of a DNA hairpin as it undergoes a folding/unfolding transition.     

On-chip manipulation and detection of magnetic particles for functional biosensors

We demonstrate the real-time on-chip detection and manipulation of single 1 microm superparamagnetic particles in solution, with the aim to develop a biosensor that can give information on biological function. Our chip-based sensor consists of micro-fabricated current wires and giant magneto resistance (GMR) sensors. The current wires serve to apply force on the particles as well as to magnetize the particles for on-chip detection. The sensitivity profile of the sensor was reconstructed by simultaneously measuring the sensor signal and the position of an individual particle crossing the sensor. A single-dipole model reproduces the measured sensitivity curve for a 1 microm bead. For a 2.8 microm bead the model shows deviations, which we attribute to the fact that the particle size becomes comparable to the sensor width. In the range between 1 and 10 particles, we observed a linear relationship between the number of beads and the sensor signal. The real-time detection and manipulation of individual particles opens the possibility to perform on-chip high-parallel single-particle assays.     

Unfolding individual nucleosomes by stretching single chromatin fibers with optical tweezers.

Single chromatin fibers were assembled directly in the flow cell of an optical tweezers setup. A single lambda phage DNA molecule, suspended between two polystyrene beads, was exposed to a Xenopus laevis egg extract, leading to chromatin assembly with concomitant apparent shortening of the DNA molecule. Assembly was force-dependent and could not take place at forces exceeding 10 pN. The assembled single chromatin fiber was subjected to stretching by controlled movement of one of the beads with the force generated in the molecule continuously monitored with the second bead trapped in the optical trap. The force displayed discrete, sudden drops upon fiber stretching, reflecting discrete opening events in fiber structure. These opening events were quantized at increments in fiber length of approximately 65 nm and are attributed to unwrapping of the DNA from around individual histone octamers. Repeated stretching and relaxing of the fiber in the absence of egg extract showed that the loss of histone octamers was irreversible. The forces measured for individual nucleosome disruptions are in the range of 20-40 pN, comparable to forces reported for RNA- and DNA-polymerases.     

Novel detection system for biomolecules using nano-sized bacterial magnetic particles and magnetic force microscopy

A system for streptavidin detection using biotin conjugated to nano-sized bacterial magnetic particles (BMPs) has been developed. BMPs, isolated from magnetic bacteria, were used as magnetic markers for magnetic force microscopy (MFM) imaging. The magnetic signal was obtained from a single particle using MFM without application of an external magnetic field. The number of biotin conjugated BMPs (biotin-BMPs) bound to streptavidin immobilized on the glass slides increased with streptavidin concentrations up to 100 pg/ml. The minimum streptavidin detection limit using this technique is 1 pg/ml, which is 100 times more sensitive than a conventional fluorescent detection system. This is the first report using single domain nano-sized magnetic particles as magnetic markers for biosensing. This assay system can be used for immunoassay and DNA detection with high sensitivities.     

Analyzing the Movement of the Nauplius 'Artemia salina' by Optical Tracking of Plasmonic Nanoparticles

We demonstrate how optical tweezers may provide a sensitive tool to analyze the fluidic vibrations generated by the movement of small aquatic organisms. A single gold nanoparticle held by an optical tweezer is used as a sensor to quantify the rhythmic motion of a Nauplius larva (Artemia salina) in a water sample. This is achieved by monitoring the time dependent displacement of the trapped nanoparticle as a consequence of the Nauplius activity. A Fourier analysis of the nanoparticle''s position then yields a frequency spectrum that is characteristic to the motion of the observed species. This experiment demonstrates the capability of this method to measure and characterize the activity of small aquatic larvae without the requirement to observe them directly and to gain information about the position of the larvae with respect to the trapped particle. Overall, this approach could give an insight on the vitality of certain species found in an aquatic ecosystem and could expand the range of conventional methods for analyzing water samples.     

Laser-Induced Heating in Optical Traps

In an optical tweezers experiment intense laser light is tightly focused to intensities of MW/cm² in order to apply forces to submicron particles or to measure mechanical properties of macromolecules. It is important to quantify potentially harmful or misleading heating effects due to the high light intensities in biophysical experiments. We present a model that incorporates the geometry of the experiment in a physically correct manner, including heat generation by light absorption in the neighborhood of the focus, balanced by outward heat flow, and heat sinking by the glass surfaces of the sample chamber. This is in contrast to the earlier simple models assuming heat generation in the trapped particle only. We find that in the most common experimental circumstances, using micron-sized polystyrene or silica beads, absorption of the laser light in the solvent around the trapped particle, not in the particle itself, is the most important contribution to heating. To validate our model we measured the spectrum of the Brownian motion of trapped beads in water and in glycerol as a function of the trapping laser intensity. Heating both increases the thermal motion of the bead and decreases the viscosity of the medium. We measured that the temperature in the focus increased by 34.2 ± 0.1 K/W with 1064-nm laser light for 2200-nm-diameter polystyrene beads in glycerol, 43.8 ± 2.2 K/W for 840-nm polystyrene beads in glycerol, 41.1 ± 0.7 K/W for 502-nm polystyrene beads in glycerol, and 7.7 ± 1.2 K/W for 500-nm silica beads and 8.1 ± 2.1 K/W for 444-nm silica beads in water. Furthermore, we observed that in glycerol the heating effect increased when the bead was trapped further away from the cover glass/glycerol interface as predicted by the model. We show that even though the heating effect in water is rather small it can have non-negligible effects on trap calibration in typical biophysical experimental circumstances and should be taken into consideration when laser powers of more than 100 mW are used.     

Detection of forces and displacements along the axial direction in an optical trap

We present measurements of the forces on, and displacements of, an optically trapped bead along the propagation direction of the trapping laser beam (the axial direction). In a typical experimental configuration, the bead is trapped in an aqueous solution using an oil-immersion, high-numerical-aperture objective. This refractive index mismatch complicates axial calibrations due to both a shift of the trap center along the axial direction and spherical aberrations. In this work, a known DNA template was unzipped along the axial direction and its characteristic unzipping force-extension data were used to determine 1), the location of the trap center along the axial direction; 2), the axial displacement of the bead from the trap center; and 3), the axial force exerted on the bead. These axial calibrations were obtained for trap center locations up to approximately 4 microm into the aqueous solution and with axial bead displacements up to approximately 600 nm from the trap center. In particular, the axial trap stiffness decreased substantially when the trap was located further into the aqueous solution. This approach, together with conventional lateral calibrations, results in a more versatile optical trapping instrument that is accurately calibrated in all three dimensions.     

All-optical constant-force laser tweezers

Optical tweezers are a powerful tool for the study of single biomolecules. Many applications require that a molecule be held under constant tension while its extension is measured. We present two schemes based on scanning-line optical tweezers to accomplish this, providing all-optical alternatives to force-clamp traps that rely on electronic feedback to maintain constant-force conditions for the molecule. In these schemes, a laser beam is rapidly scanned along a line in the focal plane of the microscope objective, effectively creating an extended one-dimensional optical potential over distances of up to 8 microm. A position-independent lateral force acting on a trapped particle is created by either modulating the laser beam intensity during the scan or by using an asymmetric beam profile in the back focal plane of the microscope objective. With these techniques, forces of up to 2.69 pN have been applied over distances of up to 3.4 microm with residual spring constants of <26.6 fN/microm. We used these techniques in conjunction with a fast position measurement scheme to study the relaxation of lambda-DNA molecules against a constant external force with submillisecond time resolution. We compare the results to predictions from the wormlike chain model.     

Colored noise in the fluctuations of an extended DNA molecule detected by optical trapping

We studied fluctuations of an optically trapped bead connected to a single DNA molecule anchored between the bead and a cover glass or between two optically trapped beads. Power spectral densities of the bead position for different extensions of the molecule were compared with the power spectral density of the position fluctuations of the same bead without the molecule attached. Experiments showed that the fluctuations of the DNA molecule extended up to 80% by a force of 3 pN include the colored noise contribution with spectral dependence 1/f ^α with α ∼ 0.75.     

Adhesion energy of receptor-mediated interaction measured by elastic deformation

We investigated the role of receptor binding affinity in surface adhesion. A sensitive technique was developed to measure the surface energy of receptor-mediated adhesion. The experimental system involved a functionalized elastic agarose bead resting on a functionalized glass coverslip. Attractive intersurface forces pulled the two surfaces together, deforming the bead to produce an enlarged contact area. The Johnson-Kendall-Roberts (JKR) model was used to relate the surface energy of the interaction to the elasticity of the bead and the area of contact. The surface energies for different combinations of modified surfaces in solution were obtained from reflection interference contrast microscopy (RICM) measurements of the contact area formed by the bead and the coverslip. Studies with surfaces functionalized with ligand-receptor pairs showed that the relationship between surface energy and the association constant of the ligand binding has two regimes. At low binding affinity, surface energy increased linearly with the association constant, while surface energy increased logarithmically with the association constant in the high affinity regime.     

Counter-propagating optical trapping system for size and refractive index measurement of microparticles

We propose and demonstrate a novel approach to measure the size and refractive index of microparticles based on two beam optical trapping, where forward scattered light is detected to give information about the particle. The counter-propagating optical trap measurement (COTM) system exploits the capability of optical traps to measure pico-Newton forces for microparticles' refractive index and size characterization. Different from the current best technique for microparticles' refractive index measurement, refractometry, a bulk technique requiring changing the fluid composition of the sample, our optical trap technique works with any transparent fluid and enables single particle analysis without the use of biological markers. A ray-optics model is used to explore the physical operation of the COTM system, predict system performance and aid system design. Experiments demonstrate the accuracy of refractive index measurement of Deltan=0.013 and size measurement of 3% of diameter with 2% standard deviation. Present performance is instrumentation limited, and a potential improvement by more than two orders of magnitude can be expected in the future. With further development in parallelism and miniaturization, the system offers advantages for cell manipulation and bioanalysis compatible with lab-on-a-chip systems.