Optical force on a pair of concentric spheres in a focused laser beam: ray-optics regime

Sang Bok Kim, Kyung Heon Lee, Sang Soo Kim, and Hyung Jin Sung

The photon stream method is used to derive the optical force on a pair of concentric spheres in a focused beam. The effects of the differences in refractive index and relative size between the inner and outer spheres on the optical force are evaluated. In addition, the effects of total internal reflection at the interface between the inner and outer spheres are examined. Computational results are compared with previous findings. The present method can be applied to arbitrary intensity distributions of the laser beam.

DOI

Stability and rewiring of nematic braids in chiral nematic colloids

Simon Čopar , Tine Porenta , V. S. R. Jampani , Igor Muševič and Slobodan Žumer

Disclination lines in chiral nematic liquid crystals exhibit larger geometrical diversity than their counterparts in ordinary nematics and form rich entangled structures in systems with dispersed colloidal inclusions. Numerous metastable and stable states separated by low energy barriers allow for simple rewiring of the braids. Introducing a new visualization scheme where variations in splay, bend and twist deformations are followed separately allows us to display the effect of chirality on the director profile of the disclinations, and to uncover the mechanism of their rewiring. We demonstrate the richness of structures by performing a survey of all possible disclination structures that entangle a pair of homeotropic silica microspheres in a π-twisted cholesteric cell using numerical free-energy minimization and laser tweezers assisted microscopy. We analyze their stability against spontaneous rewiring and trace the stability differences to the local effects of chiral environment. We compare the predictions to the experimental results and discuss the differences between both approaches.

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Optical trapping using cascade conical refraction of light

D. P. O’Dwyer, K. E. Ballantine, C. F. Phelan, J. G. Lunney, and J. F. Donegan

Cascade conical refraction occurs when a beam of light travels through two or more biaxial crystals arranged in series. The output beam can be altered by varying the relative azimuthal orientation of the two biaxial crystals. For two identical crystals, in general the output beam comprises a ring beam with a spot at its centre. The relative intensities of the spot and ring can be controlled by varying the azimuthal angle between the refracted cones formed in each crystal. We have used this beam arrangement to trap one microsphere within the central spot and a second microsphere on the ring. Using linearly polarized light, we can rotate the microsphere on the ring with respect to the central sphere. Finally, using a half wave-plate between the two crystals, we can create a unique beam profile that has two intensity peaks on the ring, and thereby trap two microspheres on diametrically opposite points on the ring and rotate them around the central sphere. Such a versatile optical trap should find application in optical trapping setups.

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Optical trapping of metal-dielectric nanoparticle clusters near photonic crystal microcavities

Camilo A. Mejia, Ningfeng Huang, and Michelle L. Povinelli

We predict the formation of optically trapped, metal-dielectric nanoparticle clusters above photonic crystal microcavities. We determine the conditions on particle size and position for a gold particle to be trapped above the microcavity. We then show that strong field redistribution and enhancement near the trapped gold nanoparticle results in secondary trapping sites for a pair of dielectric nanoparticles.

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Scattering of inhomogeneous circularly polarized optical field and mechanical manifestation of the internal energy flows

A. Ya. Bekshaev, O. V. Angelsky, S. G. Hanson, and C. Yu. Zenkova

Based on the Mie theory and on the incident beam model via superposition of two plane waves, we analyze numerically the momentum flux of the field scattered by a spherical, nonmagnetic microparticle placed within the spatially inhomogeneous circularly polarized paraxial light beam. The asymmetry between the forward- and backward-scattered momentum fluxes in the Rayleigh scattering regime appears due to the spin part of the internal energy flow in the incident beam. The transverse ponderomotive forces exerted on dielectric and conducting particles of different sizes are calculated and special features of the mechanical actions produced by the spin and orbital parts of the internal energy flow are recognized. In particular, the transverse orbital flow exerts the transverse force that grows as a3 for conducting and as a6 for dielectric subwavelength particle with radius a, in compliance with the dipole mechanism of the field-particle interaction; the force associated with the spin flow behaves as a8 in both cases, which testifies for the nondipole mechanism. The results can be used for experimental identification and separate investigation of the spin and orbital parts of the internal energy flow in light fields.

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Raman Spectroscopy of Circulating Single Red Blood Cells in Microvessels in vivo

Jingwei Shao, Huilu Yao, LingJing Meng, YongQing Li, ManMan Lin, Xue li, JunXian Liu, Jianpin Liang

Raman tweezers have been used to study single blood cells in vivo without requiring invasive procedures. In the present study, we use optical tweezers to capture single blood cells(RBCs) in the microvessel of a mouse ear. Without the use of any invasive procedures, we were able to obtain the Raman spectra of single red blood cells from a mouse ear. An analysis of these spectra indicated that RBCs in arterioles are oxygenated, while those in the capillaries of venules are deoxygenated, those in vitro are similar to that in venules. In addition, hemoglobin in vivo was observed to be more concentrated than that in vitro. By studying the change of the band at 1604 cm−1, we concluded that the pH in arterioles is higher than that in venules. The information gained from the single RBCs in vivo is important for the understanding of the reaction of RBCs to changes in their environment and may have many applications in the diagnosis and treatment of red blood cell disorders.

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Single-Molecule Stochastic Resonance

K. Hayashi, S. de Lorenzo, M. Manosas, J. M. Huguet, and F. Ritort

Stochastic resonance (SR) is a well-known phenomenon in dynamical systems. It consists of the amplification and optimization of the response of a system assisted by stochastic (random or probabilistic) noise. Here we carry out the first experimental study of SR in single DNA hairpins which exhibit cooperatively transitions from folded to unfolded configurations under the action of an oscillating mechanical force applied with optical tweezers. By varying the frequency of the force oscillation, we investigate the folding and unfolding kinetics of DNA hairpins in a periodically driven bistable free-energy potential. We measure several SR quantifiers under varied conditions of the experimental setup such as trap stiffness and length of the molecular handles used for single-molecule manipulation. We find that a good quantifier of the SR is the signal-to-noise ratio (SNR) of the spectral density of measured fluctuations in molecular extension of the DNA hairpins. The frequency dependence of the SNR exhibits a peak at a frequency value given by the resonance-matching condition. Finally, we carry out experiments on short hairpins that show how SR might be useful for enhancing the detection of conformational molecular transitions of low SNR.

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Proposed Nonlinear Resonance Laser Technique for Manipulating Nanoparticles

Tetsuhiro Kudo and Hajime Ishihara
We propose nonlinear resonant laser manipulation, a technique that drastically enhances the number of degrees of freedom when manipulating nano-objects. Considering the high laser intensity required to trap single molecules, we calculate the radiation force exerted on a molecule in a focused laser beam by solving the density matrix equations using the nonperturbative method. The results coherently elucidate certain recently reported puzzling phenomena that contradict the conventional understanding of laser trapping. Further, we demonstrate unconventional forms of laser manipulations using “stimulated recoil force” and “subwavelength laser manipulation.”

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Design and Optical Trapping of a Biocompatible Propeller-like Nanoscale Hybrid

Jaekwon Do , Robert Schreiber , Andrey A. Lutich , Tim Liedl , Jessica Rodríguez-Fernández , and Jochen Feldmann

Designing nanoscale objects with the potential to perform externally-controlled motion in biological environments is one of the most sought-after objectives in nanotechnology. Different types of chemically and physically-powered motors have been prepared at the macro- and microscale. However, the preparation of nanoscale objects with a complex morphology, and the potential for light-driven motion has remained elusive to date. Here, we go a step forward by designing a nanoscale hybrid with a propeller-resembling shape, which can be controlled by focused light under biological conditions. Our hybrid, hereafter ‘Au@DNA-origami’, consists of a spherical gold nanoparticle with self-assembled, biocompatible, two-dimensional DNA sheets on its surface. As a first step towards the potential utilization of these nanoscale objects as light-driven assemblies in biological environments, we show that they can be optically trapped, and hence translated and deposited on-demand, and that under realistic trapping conditions the thermally-induced dehybridization of the DNA sheets can be avoided.

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Ribosomal protein S1 unwinds double-stranded RNA in multiple steps

Xiaohui Qu, Laura Lancaster, Harry F. Noller, Carlos Bustamante, and Ignacio Tinoco, Jr.

The sequence and secondary structure of the 5′-end of mRNAs regulate translation by controlling ribosome initiation on the mRNA. Ribosomal protein S1 is crucial for ribosome initiation on many natural mRNAs, particularly for those with structured 5′-ends, or with no or weak Shine-Dalgarno sequences. Besides a critical role in translation, S1 has been implicated in several other cellular processes, such as transcription recycling, and the rescuing of stalled ribosomes by tmRNA. The mechanisms of S1 functions are still elusive but have been widely considered to be linked to the affinity of S1 for single-stranded RNA and its corresponding destabilization of mRNA secondary structures. Here, using optical tweezers techniques, we demonstrate that S1 promotes RNA unwinding by binding to the single-stranded RNA formed transiently during the thermal breathing of the RNA base pairs and that S1 dissociation results in RNA rezipping. We measured the dependence of the RNA unwinding and rezipping rates on S1 concentration, and the force applied to the ends of the RNA. We found that each S1 binds 10 nucleotides of RNA in a multistep fashion implying that S1 can facilitate ribosome initiation on structured mRNA by first binding to the single strand next to an RNA duplex structure (“stand-by site”) before subsequent binding leads to RNA unwinding. Unwinding by multiple small substeps is much less rate limited by thermal breathing than unwinding in a single step. Thus, a multistep scheme greatly expedites S1 unwinding of an RNA structure compared to a single-step mode.

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The Ndc80 kinetochore complex directly modulates microtubule dynamics

Neil T. Umbreit, Daniel R. Gestaut, Jerry F. Tien, Breanna S. Vollmar, Tamir Gonen, Charles L. Asbury, and Trisha N. Davis

The conserved Ndc80 complex is an essential microtubule-binding component of the kinetochore. Recent findings suggest that the Ndc80 complex influences microtubule dynamics at kinetochores in vivo. However, it was unclear if the Ndc80 complex mediates these effects directly, or by affecting other factors localized at the kinetochore. Using a reconstituted system in vitro, we show that the human Ndc80 complex directly stabilizes the tips of disassembling microtubules and promotes rescue (the transition from microtubule shortening to growth). In vivo, an N-terminal domain in the Ndc80 complex is phosphorylated by the Aurora B kinase. Mutations that mimic phosphorylation of the Ndc80 complex prevent stable kinetochore-microtubule attachment, and mutations that block phosphorylation damp kinetochore oscillations. We find that the Ndc80 complex with Aurora B phosphomimetic mutations is defective at promoting microtubule rescue, even when robustly coupled to disassembling microtubule tips. This impaired ability to affect dynamics is not simply because of weakened microtubule binding, as an N-terminally truncated complex with similar binding affinity is able to promote rescue. Taken together, these results suggest that in addition to regulating attachment stability, Aurora B controls microtubule dynamics through phosphorylation of the Ndc80 complex.

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Optical forces on submicron particles induced by full Poincaré beams

Li-Gang Wang

In this paper, we have considered the optical forces acting on submicron particles induced by arbitrary-order full Poincaré (FP) beams. Different from the traditional scalar beams, the optical forces of the FP beams include three contributions: the scattering, gradient, and curl forces. The last contribution is due to both the vectorial properties of the FP beams’ polarization and the rotating phase structure of the FP beams. We analytically derive all components of the optical forces of the FP beams acting on Rayleigh particles. The numerical results show that the optical curl force is very significant to the absorbing Rayleigh particles, and it has the same order with the scattering force. The total vortex force fields and their trapping effects of different order FP beams on the absorbing dielectric and metallic Rayleigh particles are discussed in detail. Our results may stimulate further investigations on the trapping effect of various vector-vortex beams on submicron or nanometer sized objects.

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Myosin IC generates power over a range of loads via a new tension-sensing mechanism

Michael J. Greenberg, Tianming Lin, Yale E. Goldman, Henry Shuman, and E. Michael Ostap

Myosin IC (myo1c), a widely expressed motor protein that links the actin cytoskeleton to cell membranes, has been associated with numerous cellular processes, including insulin-stimulated transport of GLUT4, mechanosensation in sensory hair cells, endocytosis, transcription of DNA in the nucleus, exocytosis, and membrane trafficking. The molecular role of myo1c in these processes has not been defined, so to better understand myo1c function, we utilized ensemble kinetic and single-molecule techniques to probe myo1c’s biochemical and mechanical properties. Utilizing a myo1c construct containing the motor and regulatory domains, we found the force dependence of the actin-attachment lifetime to have two distinct regimes: a force-independent regime at forces < 1 pN, and a highly force-dependent regime at higher loads. In this force-dependent regime, forces that resist the working stroke increase the actin-attachment lifetime. Unexpectedly, the primary force-sensitive transition is the isomerization that follows ATP binding, not ADP release as in other slow myosins. This force-sensing behavior is unique amongst characterized myosins and clearly demonstrates mechanochemical diversity within the myosin family. Based on these results, we propose that myo1c functions as a slow transporter rather than a tension-sensitive anchor.

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Protein sliding and DNA denaturation are essential for DNA organization by human mitochondrial transcription factor A

Géraldine Farge, Niels Laurens, Onno D. Broekmans, Siet M.J.L. van den Wildenberg, Linda C.M. Dekker, Martina Gaspari, Claes M. Gustafsson, Erwin J.G. Peterman, Maria Falkenberg & Gijs J.L. Wuite

Mitochondria organize their genome in protein–DNA complexes called nucleoids. The mitochondrial transcription factor A (TFAM), a protein that regulates mitochondrial transcription, is abundant in these nucleoids. TFAMis believed to be essential for mitochondrial DNA compaction, yet the exact mechanism has not been resolved. Here we use a combination of single-molecule manipulation and fluorescence microscopy to show the nonspecific DNA-binding dynamics and compaction by TFAM. We observe that singleTFAM proteins diffuse extensively over DNA (sliding) and, by collisions, form patches on DNA in a cooperative manner. Moreover, we demonstrate thatTFAM induces compaction by changing the flexibility of the DNA, which can be explained by local denaturation of the DNA (melting). Both sliding of TFAM and DNA melting are also necessary characteristics for effective, specific transcription regulation by TFAM. This apparent connection between transcription and DNA organization clarifies how TFAM can accomplish two complementary roles in the mitochondrial nucleoid at the same time.

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Energy landscape analysis of native folding of the prion protein yields the diffusion constant, transition path time, and rates

Hao Yua, Amar Nath Guptaa, Xia Liua, Krishna Neupane, Angela M. Brigley, Iveta Sosova, and Michael T. Woodside

Protein folding is described conceptually in terms of diffusion over a configurational free-energy landscape, typically reduced to a one-dimensional profile along a reaction coordinate. In principle, kinetic properties can be predicted directly from the landscape profile using Kramers theory for diffusive barrier crossing, including the folding rates and the transition time for crossing the barrier. Landscape theory has been widely applied to interpret the time scales for protein conformational dynamics, but protein folding rates and transition times have not been calculated directly from experimentally measured free-energy profiles. We characterized the energy landscape for native folding of the prion protein using force spectroscopy, measuring the change in extension of a single protein molecule at high resolution as it unfolded/refolded under tension. Key parameters describing the landscape profile were first recovered from the distributions of unfolding and refolding forces, allowing the diffusion constant for barrier crossing and the transition path time across the barrier to be calculated. The full landscape profile was then reconstructed from force-extension curves, revealing a double-well potential with an extended, partially unfolded transition state. The barrier height and position were consistent with the previous results. Finally, Kramers theory was used to predict the folding rates from the landscape profile, recovering the values observed experimentally both under tension and at zero force in ensemble experiments. These results demonstrate how advances in single-molecule theory and experiment are harnessing the power of landscape formalisms to describe quantitatively the mechanics of folding.

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Direct laser trapping for measuring the behavior of transfused erythrocytes in a sickle cell anemia patient

Aline Pellizzaro, Gabriel Welker, David Scott, Rance Solomon, James Cooper, Anthony Farone, Mary Farone, Robert S. Mushi, Maria del Pilar Aguinaga, and Daniel Erenso

Using a laser trap, we have studied the properties of erythrocytes from a sickle cell anemia patient (SCA) after receiving an intravenous blood transfusion, and a normal adult individual carrying normal adult hemoglobin. The hemoglobin type and quantitation assessment was carried out by high performance liquid chromatography (HPLC). We conducted an analysis of the size distributions of the cells. By targeting those erythrocytes in the overlapping regions of size distributions, we have investigated their properties when the cells are trapped and released. The efficacy of the transfusion treatment is also studied by comparing the relative changes in deformation and the relaxation-time of the cells in the two samples.

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Back-focal-plane position detection with extended linear range for photonic force microscopy

Ignacio A. Martínez and Dmitri Petrov

In photonic force microscopes, the position detection with high temporal and spatial resolution is usually implemented by a quadrant position detector placed in the back focal plane of a condenser. An objective with high numerical aperture (NA) for the optical trap has also been used to focus a detection beam. In that case the displacement of the probe at a fixed position of the detector produces a unique and linear response only in a restricted region of the probe displacement, usually several hundred nanometers. There are specific experiments where the absolute position of the probe is a relevant measure together with the probe position relative the optical trap focus. In our scheme we introduce the detection beam into the condenser with low NA through a pinhole with tunable size. This combination permits us to create a wide detection spot and to achieve the linear range of several micrometers by the probe position detection without reducing the trapping force.

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Single Reconstituted Neuronal SNARE Complexes Zipper in Three Distinct Stages

Ying Gao, Sylvain Zorman, Gregory Gundersen, Zhiqun Xi, Lu Ma, George Sirinakis, James E. Rothman, Yongli Zhang

SNARE proteins drive membrane fusion by assembling into a four-helix bundle in a zippering process. Here, we used optical tweezers to observe in a cell-free reconstitution experiment in real time a long-sought SNARE assembly intermediate in which only the membrane-distal N-terminal half of the bundle is assembled. Our findings support the zippering hypothesis, but suggest that zippering proceeds through three sequential binary switches, not continuously, in the N- and C-terminal halves of the bundle and the linker domain. The half-zippered intermediate was stabilized by externally applied force that mimicked the repulsion between apposed membranes being forced to fuse. This intermediate then rapidly and forcefully zippered, delivering free energy of 36 kBT to mediate fusion.

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Controlling the Position and Orientation of Single Silver Nanowires on a Surface Using Structured Optical Fields

Zijie Yan, Julian Sweet, Justin E. Jureller, Mason J. Guffey, Matthew Pelton, and Norbert F. Scherer

We demonstrate controlled trapping and manipulation of single silver (Ag) nanowires in two dimensions at a surface using structured light fields generated with a spatial light modulator. The Ag nanowires are attracted toward the regions of maximal optical intensity along the surface when the trapping laser light is linearly polarized and are repelled toward the minima of optical intensity when the light is circularly polarized. For linearly polarized light, stably trapped nanowires are oriented perpendicular to the polarization direction due to a torque induced by an asymmetrical response of the nanowire to the electric field. The attractive interactions with linearly polarized trapping laser light, which is at 800 nm for all measurements, enable stable trapping and translation of Ag nanowires in the antinodes of optical gratings and in zero-order Bessel beams. Trapped nanowires can be positioned and oriented on a transparent dielectric substrate, making possible the nonmechanical assembly of plasmonic nanostructures for particular functions.

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Filopodium retraction is controlled by adhesion to its tip

Stephane Romero, Alessia Quatela, Thomas Bornschlögl, Stéphanie Guadagnini, Patricia Bassereau and Guy Tran Van Nhieu

Filopodia are thin cell extensions sensing the environment. They play an essential role during cell migration, cell-cell or cell-matrix adhesion, by initiating contacts and conveying signals to the cell cortex. Pathogenic microorganisms can hijack filopodia to invade cells by inducing their retraction towards the cell body. Because their dynamics depend on a discrete number of actin filaments, filopodia provide a model of choice to study elementary events linked to adhesion and downstream signaling. However, the determinants controlling filopodial sensing are not well characterized. Here, we have used beads functionalized with different ligands that triggered filopodial retraction when contacting filopodia of epithelial cells. With optical tweezers (OTs), we were able to measure forces stalling the retraction of a single filopodium. We found that the filopodial stall force depends on the coating of the bead. Stall forces reached 8 pN for beads coated with the β1- integrin ligand Yersinia Invasin, while retraction was stopped with a higher force of 15 pN when beads were functionalized with carboxyl groups. In all cases, stall forces increased in correlation with the density of ligands contacting filopodial tips and were independent of the optical trap stiffness. Unexpectedly, a discrete and small number of Shigella type three secretion systems induced stall forces of 10 pN. These results suggest that the number of receptor-ligand interactions at the filopodial tip determines the maximal retraction force exerted by filopodia but a discrete number of clustered receptors is sufficient to induce high retraction stall forces.

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Mathieu Function Solutions for the Photoacoustic Effect in Two- and Three-Dimensional Structures and Optical Traps

Binbin Wu and Gerald J. Diebold

The wave equation for the photoacoustic effect in a three-dimensional spherically symmetric, or two-dimensional structure where the compressibility or density varies sinusoidally in space reduces to an inhomogeneous Mathieu equation. As such, exact solutions for the photoacoustic pressure can be found in terms of either Mathieu functions, integer order Mathieu functions, or fractional order Mathieu functions, the last of these being of importance for problems pertaining to structures of finite dimensions. Here, frequency domain solutions are given for a spherical structure with material properties varying radially, and a two-dimensional structure with material variations in one direction. Solutions for the acoustic pressure are found that give closed form expressions for the resonance frequencies. It is also shown that Mathieu functions give solutions for the motion of an optically levitated sphere trapped in an intensity modulated, Gaussian laser beam. By determining the frequencies at which the motions of the sphere are largest, that is, where the Mathieu functions become unstable, it is shown that the trap can act to determine the radiation force relative to the gravitational force on the sphere.

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Plasmonic tweezers—The strength of surface plasmons

Romain Quidant

Enhanced and confined optical fields near metallic nanostructures, supporting surface plasmon (SP) resonances, make it possible to enhance the interaction of light with tiny amounts of matter, down to the molecular level. Such capability has been extensively exploited in the framework of optical spectroscopy, nonlinear optics, imaging and integrated optics, among others. Here we discuss the use of plasmonics for optical trapping. Plasmon-based trapping addresses key limitations of conventional optical tweezers formed at the focus of a diffraction-limited laser beam. Beyond permitting trapping of smaller objects, down to the true nanometer scale, they enable parallel trapping from a single beam and can be easily integrated on a chip. SP-based trapping opens new perspectives in a wide range of fields from biology to quantum optics.

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Plasmonics: Metal-worthy methods and materials in nanophotonics

Jennifer A. Dionne and Harry A. Atwater

Electrons and photons can coexist as a single entity called a surface plasmon—an elementary excitation found at the interface between a conductor and an insulator. Because of their hybrid electric and photonic nature, plasmons allow photons to be precisely controlled on the nanoscale. Plasmons are evident in the vivid hues of rose windows, which derive their color from small metallic nanoparticles embedded in the glass. They also provide the basis for color-changing biosensors (such as home pregnancy tests), photothermal cancer treatments, improved photovoltaic cell efficiencies, and nanoscale lasers. While surface plasmons were first identified nearly 55 years ago, many of their exciting applications are yet to come. This issue of MRS Bulletin reviews the progress and promise of plasmonics—from the characterization tools that have allowed nanometer-scale probing of plasmons to the new materials that may enable low-loss, active, and quantum plasmonics. Within reach are applications ranging from integrated plasmonic circuits for nanophotonic computation to plasmonic optical tweezers for manipulation of nano-sized particles and proteins.

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Resolving two-dimensional kinetics of the integrin αIIbβ3-fibrinogen interactions using Binding-Unbinding Correlation Spectroscopy

Rustem I. Litvinov, Andrey Mekler, Henry Shuman, Joel S. Bennett,Valeri Barsegov and John W. Weisel

Using a combined experimental and theoretical approach named Binding-Unbinding Correlation Spectroscopy (BUCS), we describe the 2D kinetics of interactions between fibrinogen and the integrin αIIbβ3, the ligand-receptor pair essential for platelet function during hemostasis and thrombosis. The methodology uses the optical trap to probe force-free association of individual surface-attached fibrinogen and αIIbβ3 molecules and forced dissociation of an αIIbβ3-fibrinogen complex. This novel approach combines force-clamp measurements of bond lifetimes with the binding mode to quantify the dependence of the binding probability on the interaction time. We found that fibrinogen-reactive αIIbβ3 pre-exists in at least two states that differ in their zero-force on-rates (kon1=1.4x10-4 and kon2=2.3x10-4 μm2/s), off-rates (koff1=2.42 and koff2=0.60 s-1) and dissociation constants (Kd1=1.7x104 andKd2=2.6x103 1/μm2). The integrin activator Mn2+ changed the on-rates and affinities (Kd1=5x104 and Kd2=0.3x103 1/μm2) but did not affect the off-rates. The strength of αIIbβ3-fibrinogen interactions was time-dependent due to progressive increase in the fraction of the high-affinity state of the αIIbβ3-fibrinogen complex characterized by a faster on-rate. Upon Mn2+-induced integrin activation, the force-dependent off-rates decrease while the complex undergoes a conformational transition from a lower- to higher-affinity state. The results obtained provide quantitative estimates of the 2D kinetic rates for the low- and high-affinity αIIbβ3 and fibrinogen interactions at the single-molecule level, and offer direct evidence for the time- and force-dependent changes in αIIbβ3 conformation and ligand-binding activity, underlying the dynamics of fibrinogen-mediated platelet adhesion and aggregation.

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Polarization-induced stiffness asymmetry of optical tweezers

Ebrahim Madadi, Akbar Samadi, Mojtaba Cheraghian, and S. Nader S. Reihani

A tightly focused, linearly polarized laser beam, so-called optical tweezers, is proven to be a useful micromanipulation tool. It is known that there is a stiffness asymmetry in the direction perpendicular to the optical axis inherited from the polarization state of the laser. In this Letter, we report our experimental results of stiffness asymmetry for different bead sizes measured at the optimal trapping condition. We also provide the results of our generalized Lorenz–Mie based calculations, which are in good agreement with our experimental results. We also compare our results with previous reports.

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Optical tweezers: a light touch

MICHAEL P. LEE, MILES J. PADGETT

Optical tweezers use focused laser light to manipulate microscopic particles. We discuss the underlying physics of the technique in terms of a gradient force exerted by the light on the particles. The versatility of optical tweezers is highlighted, in particular, we explain how spatial light modulators and various imaging methods have greatly enhanced their range of applications.

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Traceable assembly of microparts using optical tweezers

Jung-Dae Kim, Sun-Uk Hwang and Yong-Gu Lee

Assembly of components with a size in the order of tens of micrometers or less is difficult because the gravitational forces become smaller than weak forces such as capillary, electrostatic and van der Waals forces. As such, the picked-up components commonly adhere to the manipulator, making the release operation troublesome, and the repeatable supply of components cannot be guaranteed because the magazining and bunkering scheme available in conventional scale assembly cannot be extended to these small objects. Moreover, there are also no effective ways known to deliver the finalized assembly externally. In this paper, we present the manipulation and assembly of microparts using optical tweezers, which by nature do not have stiction problems. Techniques allowing bunkering and finalizing the assembly for exporting are also presented. Finally, we demonstrate an exemplary microassembly formed by assembling two microparts: a movable microring and a microrod fixed on a glass substrate. We believe this traceable microassembly to be an important step forward for micro- and nano-manufacturing.

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Measurement of interaction force between RGD-peptide and Hela cell surface by optical tweezers

Mincheng Zhong, Guosheng Xue, Jinhua Zhou, Ziqiang Wang and Yinmei Li

Since RGD peptides (R: arginine; G: glycine; D: aspartic acid) are found to promote cell adhesion, they are modified at numerous materials surface for medical applications such as drug delivery and regenerative medicine. Peptide-cell surface interactions play a key role in the above applications. In this letter, we study the adhesion force between the RGD-coated bead and Hela cell surface by optical tweezes. The adhesion is dominated by the binding of \alpha5\beta1 and RGD-peptide with higher adhesion probability and stronger adhesion strength compared with the adhesion of bare bead and cell surface. The binding force for a single \alpha5\beta1-GRGDSP pair is determined to be 16.8 pN at a loading rate of 1.5 nN/s. The unstressed off-rate is 1.65 \times 10-2 s-1 and the distance of transition state for the rigid binding model is 3.0 nm.

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Nonlinear optical effects of near-IR femtosecond laser radiation on the morphology and structure of a nerve cell in the field of an optical trap

Yu. V. Barbashov, A. D. Zalesskii, M. A. Berezutskaya, G. V. Maksimov, A. B. Rubin, O. M. Sarkisov and V. A. Nadtochenko

Changes in the morphology and structure of a neuron cell in the process of manipulating it with an femtosecond laser tweezers operating at a wavelength of 800 nm are examined. The changes in the morphology and structure are caused by the nonlinear optical absorption and multiphoton excitation of cell biomacromolecules by femtosecond pulses of light. The cell nucleus is demonstrated to be destroyed by focused femtosecond laser radiation (FLR). Changes in the state of the cytoplasmic nucleoproteins and the hydrophobicity of the plasmatic membrane under the action of FLR focused inside the cell are observed. By the example of the simultaneous displacement of the neuron with a cw laser and cutting of a neuron with FLR, the operation of holographic optical manipulator and a scalpel based on the use of femtosecond and cw lasers is considered. The possibility of the simultaneous microsurgical operation with several optical foci of FLR is demonstrated.

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Modeling of optical trapping using double negative index fishnet metamaterials

T. Cao and M. J. Cryan

We calculate the optical force exerted on the nanoparticle close proximity to the surface of fishnet metamaterials based on metal/dielectric/metal films when irradiated at near infrared wavelength. These forces show the resonant frequencies similar to the magnetic resonant frequencies in the double negative index fishnet metamaterial. We also present that the optical force can be enhanced by optimizing the geometry of the fishnet to provide a stronger magnetic resonant dipole. In contrast to the other plasmonic nanostructure always obtaining trapping force using electrical resonant dipole, our presented structure utilizes the magnetic resonance to provide a gradient force, which is suitable for the optical trapping of the nanoscale particles at illumination intensities of just 1 mW/μm2, the optical force is sufficient to overcome the Earth's gravitational pull.

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Analysis of the Raman spectra of Ca2+-dipicolinic acid alone and in the bacterial spore core in both aqueous and dehydrated environments

Lingbo Kong , Peter Setlow and Yong-qing Li

The core of dormant bacterial spores suspended in water contains a large depot of dipicolinic acid (DPA) chelated with divalent cations, predominantly Ca2+ (CaDPA), and surrounded by water molecules. Since the intensities of the vibration bands of CaDPA molecules depend significantly on the water content in the CaDPA's environment, the Raman spectra of CaDPA in spores may allow the determination of the spore core's hydration state. We have measured Raman spectra of single spores of three Bacillus species in different hydration states including the spores suspended in water, air-dried and vacuum-dried. As a comparison, we also measured the Raman spectra of CaDPA and DPA in different forms including in aqueous solution, and as amorphous powder and crystalline form. We also monitored changes in Raman spectra of an individual spore during dehydration under vacuum. The results indicated that (1) the state of CaDPA in the core of a spore suspended in water is close to an amorphous solid or a glassy state, but still mixed with water molecules; (2) the ratio of intensities of Raman bands at 1575 and 1017 cm−1 (I1575/I1017) is sensitive to the water content in the CaDPA's environment; (3) variations in I1575/I1017 are small (4%) in a population of dormant Bacillusspores suspended in water; and (4) the I1575/I1017 ratio increases significantly during dehydration under vacuum. Consequently, measurement of the I1575/I1017 ratio of CaDPA in spores may allow a qualitative estimation of the degree of hydration of the bacterial spore's core.

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Size-dependent partitioning of nano/micro-particles mediated by membrane lateral heterogeneity

Tsutomu Hamada , Masamune Morita , Makiyo Miyakawa , Ryoko Sugimoto , Ai Hatanaka ,Mun'delanji C. Vestergaard , and Masahiro Takagi

It is important that we understand the physical, chemical and biological mechanisms that govern the interaction between nanoparticles (NPs) and heterogeneous cellular surfaces because of the possible cytotoxicity of engineered nanomaterials. In this study, we investigated the lateral localization of nano/micro-particles within a biomimetic heterogeneous membrane interface using cell-sized two-phase liposomes. We found that lateral heterogeneity in the membrane mediates the partitioning of nano/micro-particles in a size-dependent manner: small particles with a diameter of ≤ 200 nm were localized in an ordered phase, while large particles preferred a fluidic disordered phase. This partitioning behavior was verified by temperature-controlled membrane miscibility transition and laser-trapping of associated particles. In terms of the membrane elastic energy, we present a physical model that explains this localization preference of nano/micro-particles. The calculated threshold diameter of particles that separates the particle-partitioning phase was 260 nm, which is in close agreement with our observation (200 nm). These findings may lead to a better understanding of the basic mechanisms that underlie the association of nanomaterials within a cell surface.

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Probing of pair interaction of magnetic microparticles with optical tweezers

M. N. Skryabina, E. V. Lyubin, M. D. Khokhlova and A. A. Fedyanin

Magnetic interaction of paramagnetic Brownian submicron-sized particles is studied by optical tweezers technique. Correlation analysis allows one to extract magnetic interaction of two particles 0.4 μm in size, which are optically trapped at the distance of 3 μm one from each other and placed in a static magnetic field of 30 Oe, from the background of their Brownian motion. The magnetic interaction force is estimated to be of approximately 100 fN. Two configurations of the mutual orientation of the magnetic field vector and the line connecting two centers of optical traps are used in the experiment. For field vector orientation parallel/perpendicular to this line, the magnetic interaction is detected by the cross-correlation function increase/decrease in comparison with the absence of magnetic field on the time scales of 1 ms.

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Measuring Molecular Motor Forces In Vivo: Implications for Tug-of-War Models of Bidirectional Transport

Christina Leidel, Rafael A. Longoria, Franciso Marquez Gutierrez, George T. Shubeita

Molecular motor proteins use the energy released from ATP hydrolysis to generate force and haul cargoes along cytoskeletal filaments. Thus, measuring the force motors generate amounts to directly probing their function. We report on optical trapping methodology capable of making precise in vivo stall-force measurements of individual cargoes hauled by molecular motors in their native environment. Despite routine measurement of motor forces in vitro, performing and calibrating such measurements in vivo has been challenging. We describe the methodology recently developed to overcome these difficulties, and used to measure stall forces of both kinesin-1 and cytoplasmic dynein-driven lipid droplets in Drosophila embryos. Critically, by measuring the cargo dynamics in the optical trap, we find that there is memory: it is more likely for a cargo to resume motion in the same direction—rather than reverse direction—after the motors transporting it detach from the microtubule under the force of the optical trap. This suggests that only motors of one polarity are active on the cargo at any instant in time and is not consistent with the tug-of-war models of bidirectional transport where both polarity motors can bind the microtubules at all times. We further use the optical trap to measure in vivo the detachment rates from microtubules of kinesin-1 and dynein-driven lipid droplets. Unlike what is commonly assumed, we find that dynein’s but not kinesin’s detachment time in vivo increases with opposing load. This suggests that dynein’s interaction with microtubules behaves like a catch bond.

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Binding and Translocation ofTermination Factor RhoStudiedat the Single-Molecule Level

Daniel J. Koslover, Furqan M. Fazal, Rachel A. Mooney, Robert Landick, Steven M. Block

Rho termination factor is an essential hexameric helicase responsible for terminating 20–50% of all mRNA synthesis in E. coli. We used single-molecule force spectroscopy to investigate Rho-RNA binding interactions at the Rho-utilization (rut) site of the λtR1 terminator. Our results are consistent with Rhocomplexes adopting two states, one that binds 57 ± 2 nucleotides of RNA across all six of the Rho primary binding sites, and another that binds 85 ± 2 nucleotides at the six primary sitesplus a single secondary site situated at the center of the hexamer. The single-molecule data serve to establish that Rho translocates 5′-to-3′ towards RNA polymerase (RNAP) by a tethered-tracking mechanism, looping out the intervening RNA between the rut site and RNAP. These findings lead to a general model forRho binding and translocation, and establish a novel experimental approach that should facilitate additional single-molecule studies of RNA-binding proteins.

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

Matthias Grimm, Thomas Franosch, and Sylvia Jeney

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.

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Influenza virus binds its host cell using multiple dynamic interactions

Christian Sieben, Christian Kappel, Rong Zhu, Anna Wozniak, Christian Rankl, Peter Hinterdorfer, Helmut Grubmüller, and Andreas Herrmann

Influenza virus belongs to a wide range of enveloped viruses. The major spike protein hemagglutinin binds sialic acid residues of glycoproteins and glycolipids with dissociation constants in the millimolar range [Sauter NK, et al. (1992)Biochemistry 31:9609–9621], indicating a multivalent binding mode. Here, we characterized the attachment of influenza virus to host cell receptors using three independent approaches. Optical tweezers and atomic force microscopy-based single-molecule force spectroscopy revealed very low interaction forces. Further, the observation of sequential unbinding events strongly suggests a multivalent binding mode between virus and cell membrane. Molecular dynamics simulations reveal a variety of unbinding pathways that indicate a highly dynamic interaction between HA and its receptor, allowing rationalization of influenza virus–cell binding quantitatively at the molecular level.

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Observation of the Binary Coalescence and Equilibration of Micrometer-Sized Droplets of Aqueous Aerosol in a Single-Beam Gradient-Force Optical Trap

Rory Power , Jonathan Philip Reid , Suman Anand ,David McGloin , Abdullah Almohammedi , Nilesh Mistry , and Andrew James Hudson

The binary coalescence of aqueous droplets has been observed in a single-beam gradient-force optical trap. By measuring the time-dependent intensity for elastic scattering of light from the trapping laser, the dynamics of binary coalescence have been examined and the timescale for equilibration of a composite droplet to ambient conditions has been determined. These data are required for modeling the agglomeration of aqueous droplets in dense sprays and atmospheric aerosol. Elastic-light scattering from optically-trapped particles has not been used before to study the time-resolved dynamics of mixing. It is shown to offer a unique opportunity to characterize the binary coalescence of aqueous droplets with radii from 1 to 6 m. The study of this size regime, which cannot be achieved by conventional imaging methods, is critical for understanding the interactions of droplets in the environment of dense sprays.

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Intrinsic fluctuations lead to broad range of transduced forces in tethered-bead single-molecule experiments

Shafigh Mehraeen and Andrew J. Spakowitz

We build a theoretical platform for predicting the behavior of tethered-bead single-molecule experiments, accounting for bead translational and rotational fluctuations, the specific type of experimental setup, and the detailed application of tension to the tether molecule. Within this framework, the external force applied to the bead is distinguished from the instantaneous force transduced to the tether molecule, resulting in a distinction between the observable response of the bead and the underlying force fluctuations felt by the tether that directly affect the biomolecular processes being studied. Our theoretical model indicates that the spread of the distribution of tether forces increases with applied external force, resulting in substantial deviations between the external and tether forces. We find that the impact of rotational and translational fluctuations of the bead motion is larger in magnetic tweezers than optical tweezers. However, this distinction diminishes at large external forces, and our asymptotic expressions offer a simple route for experimental analyses. Overall, our theory demonstrates that fluctuations in the tether molecule due to bead rotation and translation lead to a broad range of tether forces.

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

Bernard J. Mason, Simon-John King, Rachael E.H. Miles, Katherine M Manfred, Andrew M.J. Rickards, Jin Kim, Jonathan Philip Reid, and Andrew Orr-Ewing

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 to 600 nm were probed using A-CRDS, with optical tweezers measurements performed on coarse mode particles several microns 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 tweezers 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.

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Analysis of radiation pressure force exerted on a biological cell induced by high-order Bessel beams using Debye series

Renxian Li, Kuan Fang Ren, Xiang'e Han, Zhensen Wu, Lixin Guo, Shuxi Gong

Debye series expansion (DSE) is employed to the analysis of radiation pressure force (RPF) exerted on biological cells induced by high-order Bessel beams (BB). The Beam Shape Coefficients (BSCs) for high-order Bessel beams are calculated using analytical expressions obtained by the Integral Localized Approximation (ILA). Different types of cells, including a real Chinese Hamster Ovary cell (CHO) and a lymphocyte which are respectively modeled by a coated and five-layered sphere, are considered. The RPF induced by high-order Bessel beams is compared with that by Gaussian beams and zeroth-order Bessel beams, and the effect of different scattering processes on RPF is studied. Numerical calculations show that high-order Bessel beams with zero central intensity can also transversely trap particle in the beam center, and some scattering processes can provide longitudinal pulling force.

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Optical trapping of nanotubes with cylindrical vector beams

M. G. Donato, S. Vasi, R. Sayed, P. H. Jones, F. Bonaccorso, A. C. Ferrari, P. G. Gucciardi, and O. M. Maragò

We use laser beams with radial and azimuthal polarization to optically trap carbon nanotubes. We measure force constants and trap parameters as a function of power showing improved axial trapping efficiency with respect to linearly polarized beams. The analysis of the thermal fluctuations highlights a significant change in the optical trapping potential when using cylindrical vector beams. This enables the use of polarization states to shape optical traps according to the particle geometry, as well as paving the way to nanoprobe-based photonic force microscopy with increased performance compared to a standard linearly polarized configuration.

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Measurement of the trapping efficiency of an elliptical optical trap with rigid and elastic objects

Antti Kauppila, Matti Kinnunen, Artashes Karmenyan, and Risto Myllylä

Optical tweezers and their various modifications offer a sophisticated way to perform noncontact cell manipulation. In this paper, we quantify forces existing in an elliptical trap formed by two cylindrical lenses and compare the results with a point optical trap case. The trapping efficiency of point and elliptical traps was analyzed by measuring the Q values of both traps. Polystyrene microspheres and red blood cells (RBCs) were used as samples. Stretching of the RBC was taken into account in the Q value measurements. Although the Q value of a point optical trap is larger than that of an elliptical trap when measured for a single RBC, we can manipulate the orientation of an RBC in a point trap with the elliptical trap and can also trap several RBCs simultaneously in the elliptical trap far from the cuvette surfaces by using a long-working-distance water immersion objective. This opens new possibilities for studying light–matter interactions at the cellular level.

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Transition Path Times for Nucleic Acid Folding Determined from Energy-Landscape Analysis of Single-Molecule Trajectories

Krishna Neupane, Dustin B. Ritchie, Hao Yu, Daniel A. N. Foster, Feng Wang, and Michael T. Woodside

The duration of structural transitions in biopolymers is only a fraction of the time spent searching diffusively over the configurational energy landscape. We found the transition time, τTP, and the diffusion constant, D, for DNA and RNA folding using energy landscapes obtained from single-molecule trajectories under tension in optical traps. DNA hairpins, RNA pseudoknots, and a riboswitch all had τTP∼10  μs and D∼10-13–14  m2/s, despite widely differing unfolding rates. These results show how energy-landscape analysis can be harnessed to characterize brief but critical events during folding reactions.

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Mechanical and kinetic properties of β-cardiac/slow skeletal muscle myosin

Bernhard Brenner, Nils Hahn, Eva Hanke, Faramarz Matinmehr, Tim Scholz, Walter Steffen and Theresia Kraft

We aimed to establish reference parameters to identify functional effects of familial hypertrophic cardiomyopathy-related point mutations in the β-cardiac/slow skeletal muscle myosin heavy chain (β-cardiac/MyHC-1). We determined mechanical and kinetic parameters of the β-cardiac/MyHC-1 using human soleus muscle fibers that express the same myosin heavy chain (MyHC-1) as ventricular myocardium (β-cardiac). The observed parameters are compared to previously reported data for rabbit psoas muscle fibers. We found all of the examined kinetic parameters to be slower in soleus fibers than in rabbit psoas muscle. Somewhat surprisingly, however, we also found that the stiffness of the β-cardiac/MyHC-1 head domain is more than 3-fold lower than the stiffness of the fast isoform of psoas fibers. Furthermore, and different from rabbit psoas muscle, in human soleus fibers both the occupancy of force-generating cross-bridge states as well as the elastic extension of force-generating heads increase with temperature. Thus, a myosin head in the force generating states makes an increasing contribution to force with temperature. We support some of our fiber data by data from in vitro motility and optical trapping assays. Initial findings with FHC-related point mutations in the converter imply that the differences in stiffness of the head domain between the slow and fast isoform may well be due to particular differences in the amino acid sequence of the converter. We show that the slower kinetics may be linked to a larger flexibility of the β-cardiac/MyHC-1 isoform compared to fast MyHC isoforms.

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Parametrization of trapping forces on microbubbles in scanning optical tweezers

P H Jones, O M Maragó and E P J Stride

We present the results of experiments to parametrize the trapping forces on microbubbles held in scanning optical tweezers. We determine the dependence on microbubble and trap dimensions of the maximum axial trapping force, and the dependence on bubble size of the maximum transverse drag force for which the bubble remains trapped. We have also determined the spring constant of the optical trap in the radial direction, which is the first measurement of this important parameter for a low refractive index particle, or for any object in a time-averaged optical potential.

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Experimental free-energy measurements of kinetic molecular states using fluctuation theorems

Anna Alemany, Alessandro Mossa, Ivan Junier & Felix Ritort

Recent advances in non-equilibrium statistical mechanics and single-molecule technologies have made it possible to use irreversible work measurements to extract free-energy differences associated with the mechanical (un)folding of molecules. To date, free-energy recovery has been focused on native (or equilibrium) molecular states, but free-energy measurements of kinetic states have remained unexplored. Kinetic states are metastable, finite-lifetime states that are generated dynamically, and play important roles in diverse physical processes. In biophysics, there are many examples in which these states determine the fate of molecular reactions, including protein binding, enzymatic reactions, as well as the formation of transient intermediate states during molecular-folding processes. Here we demonstrate that it is possible to obtain free energies of kinetic states by applying extended fluctuation relations, using optical tweezers to mechanically unfold and refold deoxyribonucleic acid (DNA) structures exhibiting intermediate and misfolded kinetic states.

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Nano-inside-micro: Disease-responsive microgels with encapsulated nanoparticles for intracellular drug delivery to the deep lung

Prinda Wanakule, Gary W. Liu, Asha T. Fleury, Krishnendu Roy

It is well appreciated that delivery of therapeutic agents through the pulmonary route could provide significant improvement in patient compliance and reduce systemic toxicity for a variety of diseases. Many inhalable drug formulations suffer from low respirable fractions, rapid clearance by alveolar macrophages, target non-specificity, and difficulty in combining aerodynamic properties with efficient cellular uptake. To overcome these challenges, we developed an enzyme-responsive, nanoparticle-in-microgel delivery system. This system is designed to provide optimal aerodynamic carrier size for deep lung delivery, improved residence time of carriers in the lungs by avoiding rapid clearance by macrophages, and reduction of side effects and toxicity by releasing encapsulated therapeutics in response to disease-specific stimuli. This unique carrier system is fabricated using a new Michael addition during (water-in-oil) emulsion (MADE) method, especially suitable for biologic drugs due to its gentle fabrication conditions. The resulting microgels have a highly porous internal structure and an optimal aerodynamic diameter for effective deep lung delivery. They also exhibit triggered release of various nanoparticles and biologics in the presence of physiological levels of enzyme. In addition, the nanoparticle-carrying microgels showed little uptake by macrophages, indicating potential for increased lung residence time and minimal clearance by alveolar macrophages. Collectively, this system introduces a rationally designed, disease-specific, multi-tiered delivery system for use as an improved, pulmonary carrier for biologic drugs.

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In situ observation of azobenzene isomerization along with photo-induced swelling of cross-linked vesicles by laser-trapping Raman spectroscopy

Guangyong Shen , Guosheng Xue , Jun Cai , Gang Zou , Yinmei Li , Mincheng Zhong and Qijin Zhang

Laser-trapping Raman spectroscopy (LTRS) is adopted to detect the photo-induced isomerization of azobenzene in the cross-linked membrane of a single vesicle, which is self-assembled first by an amphiphilic copolymer, poly(N-isopropylacrylamide)-block-poly{6-[4-(4-pyridyazo)phenoxy]hexylmethacrylate} (PNIPAM-b-PAzPy6), and then cross-linked by reaction between 1,3-dibromopropane and pyridine groups in the copolymer chain. A series of polymer vesicles with different cross-linking degrees were made to meet the need of vesicles with different softness during this research work. Vesicles with 0.0% and 18.7% cross-linking degrees have characteristic photo-induced swelling–shrinking, others with higher cross-linking degrees do not. The isomerization of azobenzene is observed in situ by LTRS along with photo-induced swelling of single vesicles with different cross-linking degrees. Results from analysis of the obtained Raman spectra show that photo-induced isomerization of azobenzene is a trigger of the photo-induced swelling process and the swelling degree is mainly dependent on the degree of cross-linking, namely, the softness of the polymer vesicle. The former result is different from that obtained by analysis of UV-Vis spectroscopy for vesicle solutions and shows that photo-induced swelling–shrinking vesicles can be constructed by amphiphilic copolymers bearing azobenzene units in the minority.

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Extended Kramers-Moyal analysis applied to optical trapping

Christoph Honisch, Rudolf Friedrich, Florian Hörner, and Cornelia Denz

The Kramers-Moyal analysis is a well-established approach to analyze stochastic time series from complex systems. If the sampling interval of a measured time series is too low, systematic errors occur in the analysis results. These errors are labeled as finite time effects in the literature. In the present article, we present some new insights about these effects and discuss the limitations of a previously published method to estimate Kramers-Moyal coefficients at the presence of finite time effects. To increase the reliability of this method and to avoid misinterpretations, we extend it by the computation of error estimates for estimated parameters using a Monte Carlo error propagation technique. Finally, the extended method is applied to a data set of an optical trapping experiment yielding estimations of the forces acting on a Brownian particle trapped by optical tweezers. We find an increased Markov-Einstein time scale of the order of the relaxation time of the process, which can be traced back to memory effects caused by the interaction of the particle and the fluid. Above the Markov-Einstein time scale, the process can be very well described by the classical overdamped Markov model for Brownian motion.

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Interaction dynamics of two colloids in a single optical potential

Benjamin Tränkle, Michael Speidel, and Alexander Rohrbach
The interaction of two diffusing particles is strongly influenced by their hydrodynamic coupling. At a tracking rate of 10 kHz we are able to measure the 3D trajectories of two colloidal spheres in a single harmonic potential, which was generated by scanning line optical tweezers. This common potential enables tilting, rotational, and translational dynamics of the spheres, which we analyzed via the spheres position cross-correlations C(τ) over a time range of 10−4–2 s. We found that the dynamic interaction of the colloids is controlled by short-range surface forces Fs, which are attractive in one direction and repulsive in the other two directions. This unexpected behavior is supported by a theoretical model using two Langevin equations, which decouple for linear Fs, allowing a description with autocorrelation functions for collective and relative motions. We further demonstrate that variations in salt concentration and reaction volumes significantly influence C(τ) and the mean contact times between the particles, which may offer new insights into biological particle interaction.

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Optimization of probe-laser focal offsets for single-particle tracking

Ai-Tang Chang, Yi-Ren Chang, Sien Chi, and Long Hsu

In optical tweezers applications, tracking a trapped particle is essential for force measurement. One of the most popular techniques for single-particle tracking is achieved by analyzing the forward and backward light pattern, scattered by the target particle trapped by a trap laser beam, of an additional probe-laser beam with different wavelength whose focus is slightly apart from the trapping center. However, the optimized focal offset has never been discussed. In this paper, we investigate the tracking range and sensitivity as a function of the focal offset between the trapping and the probe-laser beams. As a result, the optimized focal offsets are a 3.3-fold radius ahead and a 2.0-fold radius behind the trapping laser focus in the forward tracking and the backward tracking, respectively. The experimental result agrees well with a theoretical prediction using the Mie scattering theory.

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Single-Molecule Study of G-Quadruplex Disruption Using Dynamic Force Spectroscopy

Michel de Messieres, Jen-Chien Chang, Barbara Brawn-Cinani, and Arthur La Porta

Guanine-rich sequences in nucleic acids can fold into G quadruplexes, in which four guanines on a single strand combine to form G-tetrad planes stabilized by metallic ions. Sequence motifs which are predicted to form a G quadruplex are found throughout the genome and are believed to regulate a variety of biological processes. Detailed knowledge of the kinetics of G-quadruplex folding and unfolding would provide critical insight into these processes. To probe its structural stability, we used optical tweezers to disrupt single molecules of a single-stranded DNA G4 quadruplex. Dynamic force spectroscopy was employed, in which the distribution of rupture forces was measured for different loading rates and used to infer the nature of the transition state barrier for unfolding of the structure. The distance and height of the energy barriers were extracted for two observed conformations. The energy barrier was found to be close to the folded conformation, resulting in a high disruption force despite the relatively low energy barrier height.

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