Optical Tweezers Measurements Research Articles

Effects of non-Gaussian Brownian motion on direct force optical tweezers measurements of the electrostatic forces between pairs of colloidal particles.

Measurements of the electrostatic force with separation between a fixed and an optically trapped colloidal particle are examined with experiment, simulation and analytical calculation. Non-Gaussian Brownian motion is observed in the position of the optically trapped particle when particles are close and traps weak. As a consequence of this motion, a simple least squares parameterization of direct force measurements, in which force is inferred from the displacement of an optically trapped particle as separation is gradually decreased, contains forces generated by the rectification of thermal fluctuations in addition to those originating directly from the electrostatic interaction between the particles. Thus, when particles are close and traps weak, simply fitting the measured direct force measurement to DLVO theory extracts parameters with modified meanings when compared to the original formulation. In such cases, however, physically meaningful DLVO parameters can be recovered by comparing the measured non-Gaussian statistics to those predicted by solutions to Smoluchowski's equation for diffusion in a potential.

Testing Landscape Theory for Biomolecular Processes with Single Molecule Fluorescence Spectroscopy.

Although Kramers' theory for diffusive barrier crossing on a 1D free energy profile plays a central role in landscape theory for complex biomolecular processes, it has not yet been rigorously tested by experiment. Here we test this 1D diffusion scenario with single molecule fluorescence measurements of DNA hairpin folding. We find an upper bound of 2.5 μs for the average transition path time, consistent with the predictions by theory with parameters determined from optical tweezer measurements.

Fiber based optical tweezers for simultaneous in situ force exertion and measurements in a 3D polyacrylamide gel compartment.

Optical tweezers play an important role in biological applications. However, it is difficult for traditional optical tweezers based on objective lenses to work in a three-dimensional (3D) solid far away from the substrate. In this work, we develop a fiber based optical trapping system, namely inclined dual fiber optical tweezers, that can simultaneously apply and measure forces both in water and in a 3D polyacrylamide gel matrix. In addition, we demonstrate in situ, non-invasive characterization of local mechanical properties of polyacrylamide gel by measurements on an embedded bead. The fiber optical tweezers measurements agree well with those of atomic force microscopy (AFM). The inclined dual fiber optical tweezers provide a promising and versatile tool for cell mechanics study in 3D environments.

Specific Binding of the Nucleocapsid Protein Transforms the Folding Landscape of the HIV-1 TAR RNA Hairpin

Retroviral nucleocapsid (NC) proteins are nucleic acid chaperones that play a key role in the viral life cycle. During reverse transcription, HIV-1 NC destabilizes nucleic acids, including the transactivation response (TAR) hairpin to facilitate their structural re-arrangement into the lowest free energy conformations. By combining single molecule optical tweezers measurements with mfold-based free energy calculations of the unfolding landscape, we determine the equilibrium TAR stability and characterize the unfolding transition state in both the presence and absence of NC. Our results show that protein binding occurs specifically at guanines that border structural defects in the upper part of TAR hairpin. This results in preferential destabilization by NC of this part of TAR, thereby shifting the transition state closer to the bottom of the TAR stem, leading to a shorter critical unfolding length. Thus, NC facilitates TAR RNA annealing to its complementary DNA hairpin while having little effect on the stability of the final annealed duplexes. These results provide the first direct measurement of alterations in an RNA folding landscape that are induced by protein-RNA interactions, and are a novel case study of the effect of a protein that specifically destabilizes particular elements of the nucleic acid secondary structure.

A Novel Temperature Sensor Based on Optical Trapping Technology

We propose and fabricate a novel temperature sensor based on the optical trapping technology. The temperature sensing cell is constructed by putting a “test-micro-particle” enclosed in a space built by a quartz capillary tube and two opposite-inserted optical fibers. In order to make the temperature sensor have the ability of auto-ready and easy-reset, we design and fabricate the special concavities in the ends of two fibers. This ability of auto-ready and easy-reset makes the sensor convenient to be applied in industrial fields for long-term-use. These properties provide a new probably development direction in sensing research fields for the optical tweezers technology, and solve the optical tweezers measurement repeatability problems.

In Vitro Reconstitution of Transcellular Tunnels Closure

Several bacteria, such as Staphylococcus Aureus, are able to cross the endothelial barrier by inducing transcellular tunnels, called Transendothelial Macroapertures (TEM), in endothelial cells. The closure of these TEMs is critical to prevent endothelial permeability and cell death. Several proteins have been identified to play a role in this process. In particular, the I-BAR domain proteins MIM and ABBA have been shown to accumulate at the edge of the aperture shortly after the opening event. They subsequently recruit actin, followed by actin-rich membrane wave extension over the aperture. Interestingly, the related protein IRSp53, that unlike MIM and ABBA proteins does not have amphipathic alpha-helices on its I-BAR domain, has not been found at the edge of the TEM.The details of this mechanism remain unknown. Our objective is to characterize the physics underlying the first step in TEM closure. Our hypothesis is that MIM and ABBA have the ability to recognize the newly negatively-curved membrane at the edge of the TEM through their I-BAR domain. We use a minimal system where the protein is encapsulated in a giant unilamellar vesicle and can interact with the negatively-curved inner surface of a membrane tube that has been pulled out of the vesicle. We study protein-membrane interactions through fluorescence (confocal microscopy) and force (optical tweezers) measurements. By combining the two types of measurement, we quantify the affinity of the proteins for curved interfaces, ranging in radii of curvature from 10 to 100 nm, as well as their potential mechanical effect on the membrane. Our results show an original behavior where ABBA and IRSp53 are maximally enriched in membrane tubes of specific radii of curvature.

Timescales of water transport in viscous aerosol: measurements on sub-micron particles and dependence on conditioning history

Evaporation studies of single aqueous sucrose aerosol particles as a function of relative humidity (RH) are presented for coarse and fine mode particles down into the submicron size range (600 nm < r < 3.0 μm). These sucrose particles serve as a proxy for biogenic secondary organic aerosols that have been shown to exist, under ambient conditions, in an ultraviscous glassy state, which can affect the kinetics of water mass transport within the bulk phase and hinder particle response to changes in the gas phase water content. A counter-propagating Bessel beams (CPBBs) optical trapping setup is employed to monitor the real-time change in the particle radius with RH decreasing from 75% to 5%. The slow-down of the size change upon each RH step and the deviation from the theoretical equilibrium hygroscopic growth curve indicate the onset of glassy behavior in the RH range of 10-40%. Size-dependent effects were not observed within the uncertainty of the measurements. The influence of the drying time below the glass transition RH on the timescale of subsequent water condensation and re-equilibration for sucrose particles is explored by optical tweezers measurements of micron-sized particles (3 μm < r < 6 μm). The timescale for water condensation and re-equilibration is shown to increase with increasing drying time, i.e. the time over which a viscous particle is dried below 5% RH. These studies demonstrate the importance of the history of the particle conditioning on subsequent water condensation and re-equilibration dynamics of ultraviscous and glassy aerosol particles.

Single Molecule FRET Studies of DNA Hairpin Folding

Hairpins are the simplest structures for investigating fundamental aspects of nucleic acid folding mechanisms. For hairpins exhibiting two-state behavior, all of the mechanistic information is contained in the transition path, the rare event in single molecule trajectories when the free energy barrier between folded and unfolded states is actually crossed. The first step toward observing transition paths is to determine the transition path time. Average transition path times have recently been directly determined in proteins using the Gopich/Szabo maximum likelihood method (Gopich, Szabo J. Phys. Chem. B 2009) to analyze folding/unfolding photon trajectories in single molecule FRET experiments (Chung et al. Science 2012; Chung and Eaton Nature 2013), while the only experimental study of transition paths in nucleic acids used optical tweezer measurements to determine an upper bound of 50 μs in trajectories for a variety of structures (Neupane et al. Phys. Rev. Lett. 2012). Neupane et al. also reconstructed the free energy surface for an indirect determination of average transition path times from Szabo's analytical theory for diffusive barrier crossing. We use single molecule FRET to study a fast-folding DNA hairpin with 2 A-T and 2 G-C base pairs in the stem and 21 T's in the loop immobilized on a polyethylene glycol-coated glass surface via a biotin-streptavidin-biotin linkage. The folding time for this hairpin in 500mM NaCl is 530 μs. Maximum likelihood analysis of 780 transitions in photon trajectories with an average detection rate of 750 photons/ms yields an upper bound of 4 μs for the average transition path time, compared to the value of ∼3.6±0.8 μs predicted by Neupane et al. from hairpins with 9-30 base pair stems and 4 T's in the loop. Current experiments use viscogens to slow the transition path for directly determining the actual value.

Simultaneous Analysis of the Equilibrium Hygroscopicity and Water Transport Kinetics of Liquid Aerosol

We demonstrate that the equilibrium hygroscopic response of an aerosol droplet and the kinetics of water condensation and evaporation can be retrieved with high accuracy, even close to saturation, through comparative measurements of probe and sample aerosol droplets. The experimental methodology is described and is based on an electrodynamic balance with a newly designed trapping chamber. Through use of a probe aerosol, composed of either pure water or a sodium chloride solution of known concentration, the gas-phase relative humidity (RH) can be accurately measured with an uncertainty of typically <0.005. By fast manipulation of the airflows into the chamber, a step-change in RH over a time scale of <0.5 s can be achieved. Using this approach, the kinetics of mass transfer are studied using the comparative procedure, and results are compared to theoretical mass flux predictions. The time-dependent measured mass fluxes for sodium chloride, ammonium sulfate, sorbitol, and galactose are used to calculate droplet water activities as a function of the droplet growth factor, allowing retrieval of a hygroscopic growth curve in a matter of seconds. Comparisons with both new and established thermodynamic predictions of hygroscopicity, as well as to optical tweezers measurements, are presented, demonstrating good agreement within the experimental uncertainties.

Predicting the disorder–order transition of dielectrophoretic colloidal assembly with dielectric spectroscopy

The dielectrophoretic assembly of colloidal suspensions into crystalline arrays is described by a master scaling that collapses the disorder-order transition as a function of field strength, frequency, and particle size. This master scaling has been verified for particle diameters ranging from 2a = 200 nm to 3 μm by light scattering (Lumsdon et al., Langmuir 2004, 20, 2108-2116; McMullan and Wagner, Langmuir 2012, 28, 4123-4130), optical laser tweezer measurements (Mittal et al., J. Chem. Phys. 2008, 129, 064513), and small-angle neutron scattering (McMullan and Wagner, Soft Matter 2010, 6, 5443-5450). In this work, we reconcile the empirical phase diagram with direct measurements of the colloid polarizability using dielectric spectroscopy. Dielectric spectroscopy confirms the origin of the order-disorder transition frequency dependence, including its quadratic scaling with particle radius, a(2), and provides an alternative method to search for optimal self-assembly conditions.

Optical tweezers with fluorescence detection for temperature-dependent microrheological measurements

We introduce a setup of optical tweezers, capable of carrying out temperature-dependent rheological measurements of soft materials. In our setup, the particle displacement is detected by imaging a bright spot due to fluorescence emitted from a dye-labeled particle against a dark background onto a quadrant photodiode. This setup has a relatively wide space around the sample that allows us to further accessorize the optical tweezers by a temperature control unit. The applicability of the setup was examined on the basis of the rheological measurements using a typical viscoelastic system, namely a worm-like micelle solution. The temperature and frequency dependences of the local viscoelastic functions of the worm-like micelle solution obtained by this setup were in good accordance with those obtained by a conventional oscillatory rheometer, confirming the capability of the optical tweezers as a tool for the local rheological measurements of soft materials. Since the optical tweezers measurements only require a tiny amount of sample (~40 μL), the rheological measurements using our setup should be useful for soft materials of which the available amount is limited.

Kinetics and Thermodynamics of Phenotype: Unwinding and Rewinding the Nucleosome

Chromatin "remodeling" is widely accepted as the mechanism that permits access to DNA by the transcription machinery. To date, however, there has been no experimental measurement of the changes in the kinetics and thermodynamics of the DNA-histone octamer association that are required to remodel chromatin so that transcription may occur. Here, we present the results of optical tweezer measurements that compare the kinetic and thermodynamic properties of nucleosomes composed of unmodified histones with those of nucleosomes that contain a mutant histone H4 (H4-R45H), which has been shown to allow SWI/SNF remodeling factor-independent transcription from the yeast HO promoter in vivo. Our measurements, carried out in a force-clamp mode, determine the force-dependent unwinding and rewinding rates of the nucleosome inner turn. At each force studied, nucleosomes containing H4-R45H unwind more rapidly and rewind more slowly than nucleosomes containing unmodified H4, indicating that the latter are the more stable. Extrapolation to forces at which the winding and unwinding rates are equal determines the absolute free energy of the nucleosome inner turn to be -32k(B)T for nucleosomes containing unmodified H4 and -27k(B)T for nucleosomes containing H4-R45H. Thus, the "loosening" or "remodeling" caused by this point mutation, which is demonstrated to be sufficient to allow transcriptional machinery access to the HO promoter (in the absence of other remodeling factors), is 5k(B)T. The correlation between the free energy of the nucleosome inner turn and the sin (SWI/SNF-independent) transcription suggests that, beyond partial unwinding, complete histone unwinding may play a role in transcriptional activation.

Comparison of the Accuracy of Aerosol Refractive Index Measurements from Single Particle and Ensemble Techniques

The ability of two techniques, aerosol cavity ring down spectroscopy (A-CRDS) and optical tweezers, to retrieve the refractive index of atmospherically relevant aerosol was compared through analysis of supersaturated sodium nitrate at a range of relative humidities. Accumulation mode particles in the diameter range 300-600 nm were probed using A-CRDS, with optical tweezer measurements performed on coarse mode particles several micrometers in diameter. A correction for doubly charged particles was applied in the A-CRDS measurements. Both techniques were found to retrieve refractive indices in good agreement with previously published results from Tang and Munkelwitz, with a precision of ±0.0012 for the optical tweezers and ±0.02 for the A-CRDS technique. The coarse mode optical tweezer measurements agreed most closely with refractive index predictions made using a mass-weighted linear mixing rule. The uncertainty in the refractive index retrieved by the A-CRDS technique prevented discrimination between predictions using both mass-weighted and volume-weighted linear mixing rules. No efflorescence or kinetic limitations on water transport between the particle and the gas phase were observed at relative humidities down to 14%. The magnitude of the uncertainty in refractive index retrieved using the A-CRDS technique reflects the challenges in determining particle optical properties in the accumulation mode, where the extinction efficiency varies steeply with particle size.

Probing Functional Motifs and Regions in the Phage Lambda DNA Packaging Motor by Mutagenesis and Single-Molecule Optical Tweezers Measurements

A key step in the assembly of many viruses is the packaging of DNA into preformed procapsids by an ATP-powered molecular motor. To shed light on the motor mechanism we used optical tweezers measurements to study the effect on DNA translocation dynamics of amino acid changes in the large terminase subunit (gpA) of the phage lambda packaging motor. Observed changes in motor velocity, processivity, and/or velocity-force dependence provide evidence supporting the assignment of a Walker A-like phosphate-binding motif, an adenine binding Q motif analogous to that recently identified in RNA helicases, and a C motif that couples ATP hydrolysis to DNA translocation. In addition, we found that a residue change T194M in a predicted loop-helix-loop region outside any previously described motifs, caused a dramatic 8-fold reduction in motor velocity without changing processivity or force-dependence. T194 lies in a loop-helix-loop region that is predicted to position key residues of Walker B and C catalytic motifs and appears to regulate DNA translocation rate in both the lambda DNA packaging motor and the homologous B. Subtilis SpoIIIE chromosome segregation motor.

Observation of Bacterial Type I Pili Extension under Fluid Flow

Type I pili which mediate bacterial adhesion of E coli, are thought to help bacteria resist drag forces caused by fluid flow. The mechanical properties of these pili have already been studied by AFM force spectroscopy: They were found to elongate significantly at forces above ∼50pN and contract at forces below ∼25pN due to uncoiling and coiling of the quaternary structure of pili. It was speculated that these coiling forces could help bacteria move in opposition to the direction of fluid flow. We show here that pili extend when E coli bacteria are exposed to physiological shear stresses in a flow chamber. Moreover, we observe that pili can indeed help bacteria move against flow. We compare the results obtained in the flow chamber with those obtained by AFM and optical tweezers measurements using the Goldman formula to relate shear stress with force acting on a bacterium. The changes in bacterial position caused by changes in fluid flow are smaller than the changes in length obtained in the AFM experiments, suggesting bacteria bind to the flow chamber surface through more than one pilus. We measure bacterial displacements with sub-micrometric precision by tracking their centers, and conclude that these displacements are consistent with the coiling and uncoiling of pili observed by AFM measurements but not with bacterial or pili deformation.

Anisotropic Hydrodynamic Mean-Field Theory for Semiflexible Polymers under Tension

We introduce an anisotropic mean-field approach for the dynamics of semiflexible polymers under intermediate tension, the force range where a chain is partially extended but not in the asymptotic regime of a nearly straight contour. The theory is designed to exactly reproduce the lowest order equilibrium averages of a stretched polymer, and it treats the full complexity of the problem: the resulting dynamics include the coupled effects of long-range hydrodynamic interactions, backbone stiffness, and large-scale polymer contour fluctuations. Validated by Brownian hydrodynamics simulations and comparison to optical tweezer measurements on stretched DNA, the theory is highly accurate in the intermediate tension regime over a broad dynamical range, without the need for additional dynamic fitting parameters.

Cytoskeletal actin networks in motile cells are critically self-organized systems synchronized by mechanical interactions

Growing networks of actin fibers are able to organize into compact, stiff two-dimensional structures inside lamellipodia of crawling cells. We put forward the hypothesis that the growing actin network is a critically self-organized system, in which long-range mechanical stresses arising from the interaction with the plasma membrane provide the selective pressure leading to organization. We show that a simple model based only on this principle reproduces the stochastic nature of lamellipodia protrusion (growth periods alternating with fast retractions) and several of the features observed in experiments: a growth velocity initially insensitive to the external force; the capability of the network to organize its orientation; a load-history-dependent growth velocity. Our model predicts that the spectrum of the time series of the height of a growing lamellipodium decays with the inverse of the frequency. This behavior is a well-known signature of self-organized criticality and is confirmed by unique optical tweezer measurements performed in vivo on neuronal growth cones.

VEGF internalization is not required for VEGFR-2 phosphorylation in bioengineered surfaces with covalently linked VEGF

Vascular endothelial growth factor (VEGF) is known to activate proliferation, migration, and survival pathways in endothelial cells through phosphorylation of VEGF receptor-2 (VEGFR-2). VEGF has been incorporated into biomaterials through encapsulation, electrostatic sequestration, and covalent attachment, but the effect of these immobilization strategies on VEGF signaling has not been thoroughly investigated. Further, although growth factor internalization along with the receptor generally occurs in a physiological setting, whether this internalization is needed for receptor phosphorylation is not entirely clear. Here we show that VEGF covalently bound through a modified heparin molecule elicits an extended response of pVEGFR-2 in human umbilical vein endothelial cells (HUVECs) and that the covalent linkage reduces internalization of the growth factor during receptor endocytosis. Optical tweezer measurements show that the rupture force required to disrupt the heparin-VEGF-VEGFR-2 interaction increases from 3-8 pN to 6-12 pN when a covalent bond is introduced between VEGF and heparin. Importantly, by covalently binding VEGF to a heparin substrate, the stability (half-life) of VEGF is extended over three-fold. Here, mathematical models support the biological conclusions, further suggesting that VEGF internalization is significantly reduced when covalently bound, and indicating that VEGF is available for repeated phosphorylation events.

The Q motif of a viral packaging motor governs its force generation and communicates ATP recognition to DNA interaction

A key step in the assembly of many viruses is the packaging of DNA into preformed procapsids by an ATP-powered molecular motor. To shed light on the motor mechanism we used single-molecule optical tweezers measurements to study the effect of mutations in the large terminase subunit in bacteriophage lambda on packaging motor dynamics. A mutation, K84A, in the putative ATPase domain driving DNA translocation was found to decrease motor velocity by approximately 40% but did not change the force dependence or decrease processivity substantially. These findings support the hypothesis that a deviant "Walker A-like" phosphate-binding motif lies adjacent to residue 84. Another mutation, Y46F, was also found to decrease motor velocity by approximately 40% but also increase slipping during DNA translocation by >10-fold. These findings support the hypothesis that viral DNA packaging motors contain an adenine-binding motif that regulates ATP hydrolysis and substrate affinity analogous to the "Q motif" recently identified in DEAD-box RNA helicases. We also find impaired force generation for the Y46F mutant, which shows that the Q motif plays an important role in determining the power and efficiency of the packaging motor.

Statistically optimal analysis of samples from multiple equilibrium states

We present a new estimator for computing free energy differences and thermodynamic expectations as well as their uncertainties from samples obtained from multiple equilibrium states via either simulation or experiment. The estimator, which we call the multistate Bennett acceptance ratio estimator (MBAR) because it reduces to the Bennett acceptance ratio estimator (BAR) when only two states are considered, has significant advantages over multiple histogram reweighting methods for combining data from multiple states. It does not require the sampled energy range to be discretized to produce histograms, eliminating bias due to energy binning and significantly reducing the time complexity of computing a solution to the estimating equations in many cases. Additionally, an estimate of the statistical uncertainty is provided for all estimated quantities. In the large sample limit, MBAR is unbiased and has the lowest variance of any known estimator for making use of equilibrium data collected from multiple states. We illustrate this method by producing a highly precise estimate of the potential of mean force for a DNA hairpin system, combining data from multiple optical tweezer measurements under constant force bias.