Recent Advances in Optical Tweezers

Optical chromatographic sample separation of hydrodynamically focused mixtures

Optical chromatography relies on the balance between the opposing optical and fluid drag forces acting on a particle. A typical configuration involves a loosely focused laser directly counter to the flow of particle-laden fluid passing through a microfluidic device. This equilibrium depends on the intrinsic properties of the particle, including size, shape, and refractive index. As such, uniquely fine separations are possible using this technique. Here, we demonstrate how matching the diameter of a microfluidic flow channel to that of the focusing laser in concert with a unique microfluidic platform can be used as a method to fractionate closely related particles in a mixed sample. This microfluidic network allows for a monodisperse sample of both polystyrene and poly(methyl methacrylate) spheres to be injected, hydrodynamically focused, and completely separated. To test the limit of separation, a mixed polystyrene sample containing two particles varying in diameter by less than 0.5 μm was run in the system. The analysis of the resulting separation sets the framework for continued work to perform ultra-fine separations.

Signal transduction: From the atomic age to the post-genomic era

We have come a long way in the 55 years since Edmond Fischer and the late Edwin Krebs discovered that the activity of glycogen phosphorylase is regulated by reversible protein phosphorylation. Many of the fundamental molecular mechanisms that operate in biological signaling have since been characterized and the vast web of interconnected pathways that make up the cellular signaling network has been mapped in considerable detail. Nonetheless, it is important to consider how fast this field is still moving and the issues at the current boundaries of our understanding. One must also appreciate what experimental strategies have allowed us to attain our present level of knowledge. We summarize here some key issues (both conceptual and methodological), raise unresolved questions, discuss potential pitfalls, and highlight areas in which our understanding is still rudimentary. We hope these wide-ranging ruminations will be useful to investigators who carry studies of signal transduction forward during the rest of the 21st century.

Simultaneous three-dimensional tracking of individual signals from multi-trap optical tweezers using fast and accurate photodiode detection

Multiple-beam optical traps facilitate advanced trapping geometries and exciting discoveries. However, the increased manipulation capabilities come at the price of more challenging position and force detection. Due to unrivaled bandwidth and resolution, photodiode based detection is preferred over camera based detection in most single/dual-beam optical traps assays. However, it has not been trivial to implement photodiode based detection for multiple-beam optical traps. Here, we present a simple and efficient method based on spatial filtering for parallel photodiode detection of multiple traps. The technique enables fast and accurate 3D force and distance detection of multiple objects simultaneously manipulated by multiple-beam optical tweezers.

Nanomechanical motion of Escherichia coli adhered to a surface

Nanomechanical motion of bacteria adhered to a chemically functionalized silicon surface is studied by means of a microcantilever. A non-specific binding agent is used to attach Escherichia coli (E. coli) to the surface of a silicon microcantilever. The microcantilever is kept in a liquid medium, and its nanomechanical fluctuations are monitored using an optical displacement transducer. The motion of the bacteria couples efficiently to the microcantilever well below its resonance frequency, causing a measurable increase in the microcantilever fluctuations. In the time domain, the fluctuations exhibit large-amplitude low-frequency oscillations. In corresponding frequency-domain measurements, it is observed that the mechanical energy is focused at low frequencies with a 1/f^α -type power law. A basic physical model is used for explaining the observed spectral distribution of the mechanical energy. These results lay the groundwork for understanding the motion of microorganisms adhered to surfaces and for developing micromechanical sensors for bacteria.

Direct single-molecule observation of calcium-dependent misfolding in human neuronal calcium sensor-1

Neurodegenerative disorders are strongly linked to protein misfolding, and crucial to their explication is a detailed understanding of the underlying structural rearrangements and pathways that govern the formation of misfolded states. Here we use single-molecule optical tweezers to monitor misfolding reactions of the human neuronal calcium sensor-1, a multispecific EF-hand protein involved in neurotransmitter release and linked to severe neurological diseases. We directly observed two misfolding trajectories leading to distinct kinetically trapped misfolded conformations. Both trajectories originate from an on-pathway intermediate state and compete with native folding in a calcium-dependent manner. The relative probability of the different trajectories could be affected by modulating the relaxation rate of applied force, demonstrating an unprecedented real-time control over the free-energy landscape of a protein. Constant-force experiments in combination with hidden Markov analysis revealed the free-energy landscape of the misfolding transitions under both physiological and pathological calcium concentrations. Remarkably for a calcium sensor, we found that higher calcium concentrations increased the lifetimes of the misfolded conformations, slowing productive folding to the native state. We propose a rugged, multidimensional energy landscape for neuronal calcium sensor-1 and speculate on a direct link between protein misfolding and calcium dysregulation that could play a role in neurodegeneration.

Mechanisms of cellular proteostasis: insights from single-molecule approaches

Cells employ a variety of strategies to maintain proteome homeostasis. Beginning during protein biogenesis, the translation machinery and a number of molecular chaperones promote correct de novo folding of nascent proteins even before synthesis is complete. Another set of molecular chaperones helps to maintain proteins in their functional, native state. Polypeptides that are no longer needed or pose a threat to the cell, such as misfolded proteins and aggregates, are removed in an efficient and timely fashion by ATP-dependent proteases. In this review, we describe how applications of single-molecule manipulation methods, in particular optical tweezers, are shedding new light on the molecular mechanisms of quality control during the life cycles of proteins.

Optical forces and torques on realistic plasmonic nanostructures: a surface integral approach

We develop a novel formalism to calculate the optical forces and torques on complex and realistic nanostructures by combining the surface integral equation (SIE) technique with Maxwell's stress tensor. The optical force is calculated directly on the scatterer surface from the currents obtained from the SIE, which does not require an additional surface to evaluate Maxwell's stress tensor; this is especially useful for intricate geometries such as plasmonic antennas. SIE enables direct evaluation of forces from the surface currents very efficiently and accurately for complex systems. As a proof of concept, we establish the accuracy of the model by comparing the results with the calculations from the Mie theory. The flexibility of the method is demonstrated by simulating a realistic plasmonic system with intricate geometry.

Acoustic devices for particle and cell manipulation and sensing

An emerging demand for the precise manipulation of cells and particles for applications in cell biology and analytical chemistry has driven rapid development of ultrasonic manipulation technology. Compared to the other manipulation technologies, such as magnetic tweezing, dielectrophoresis and optical tweezing, ultrasonic manipulation has shown potential in a variety of applications, with its advantages of versatile, inexpensive and easy integration into microfluidic systems, maintenance of cell viability, and generation of sufficient forces to handle particles, cells and their agglomerates. This article briefly reviews current practice and reports our development of various ultrasonic standing wave manipulation devices, including simple devices integrated with high frequency (>20 MHz) ultrasonic transducers for the investigation of biological cells and complex ultrasonic transducer array systems to explore the feasibility of electronically controlled 2-D and 3-D manipulation. Piezoelectric and passive materials, fabrication techniques, characterization methods and possible applications are discussed. The behavior and performance of the devices have been investigated and predicted with computer simulations, and verified experimentally. Issues met during development are highlighted and discussed. To assist long term practical adoption, approaches to low-cost, wafer level batch-production and commercialization potential are also addressed.

Probing the micro-rheological properties of aerosol particles using optical tweezers

The use of optical trapping techniques to manipulate probe particles for performing micro-rheological measurements on a surrounding fluid is well-established. Here, we review recent advances made in the use of optical trapping to probe the rheological properties of trapped particles themselves. In particular, we review observations of the continuous transition from liquid to solid-like viscosity of sub-picolitre supersaturated solution aerosol droplets using optical trapping techniques. Direct measurements of the viscosity of the particle bulk are derived from the damped oscillations in shape following coalescence of two particles, a consequence of the interplay between viscous and surface forces and the capillary driven relaxation of the approximately spheroidal composite particle. Holographic optical tweezers provide a facile method for the manipulation of arrays of particles allowing coalescence to be controllably induced between two micron-sized aerosol particles. The optical forces, while sufficiently strong to confine the composite particle, are several orders of magnitude weaker than the capillary forces driving relaxation. Light, elastically back-scattered by the particle, is recorded with sub-100 ns resolution allowing measurements of fast relaxation (low viscosity) dynamics, while the brightfield image can be used to monitor the shape relaxation extending to times in excess of 1000 s. For the slowest relaxation dynamics studied (particles with the highest viscosity) the presence and line shape of whispering gallery modes in the cavity enhanced Raman spectrum can be used to infer the relaxation time while serving the dual purpose of allowing the droplet size and refractive index to be measured with accuracies of ±0.025% and ±0.1%, respectively. The time constant for the damped relaxation can be used to infer the bulk viscosity, spanning from the dilute solution limit to a value approaching that of a glass, typically considered to be >10(12) Pa s, whilst the frequencies of the normal modes of the oscillations of the particle can be used to infer surface properties. We will review the use of optical tweezers for studying the viscosity of aerosol particles and discuss the potential use of this micro-rheological tool for probing the fundamental concepts of phase, thermodynamic equilibrium and metastability.

Trapping of single nano-objects in dynamic temperature fields

In this article we explore the dynamics of a Brownian particle in a feedback-free dynamic thermophoretic trap. The trap contains a focused laser beam heating a circular gold structure locally and creating a repulsive thermal potential for a Brownian particle. In order to confine a particle the heating beam is steered along the circumference of the gold structure leading to a non-trivial motion of the particle. We theoretically find a stability condition by switching to a rotating frame, where the laser beam is at rest. Particle trajectories and stable points are calculated as a function of the laser rotation frequency and are experimentally confirmed. Additionally, the effect of Brownian motion is considered. The present study complements the dynamic thermophoretic trapping with a theoretical basis and will enhance the applicability in micro- and nanofluidic devices.

Double nanohole optical tweezers visualize protein p53 suppressing unzipping of single DNA-hairpins

Here we report on the use of double-nanohole (DNH) optical tweezers as a label-free and free-solution single-molecule probe for protein-DNA interactions. Using this approach, we demonstrate the unzipping of individual 10 base pair DNA-hairpins, and quantify how tumor suppressor p53 protein delays the unzipping. From the Arrhenius behavior, we find the energy barrier to unzipping introduced by p53 to be 2 × 10(-20) J, whereas cys135ser mutant p53 does not show suppression of unzipping, which gives clues to its functional inability to suppress tumor growth. This transformative approach to single molecule analysis allows for ultra-sensitive detection and quantification of protein-DNA interactions to revolutionize the fight against genetic diseases.

Nanophotonic trapping for precise manipulation of biomolecular arrays

Optical trapping is a powerful manipulation and measurement technique widely used in the biological and materials sciences. Miniaturizing optical trap instruments onto optofluidic platforms holds promise for high-throughput lab-on-a-chip applications. However, a persistent challenge with existing optofluidic devices has been achieving controlled and precise manipulation of trapped particles. Here, we report a new class of on-chip optical trapping devices. Using photonic interference functionalities, an array of stable, three-dimensional on-chip optical traps is formed at the antinodes of a standing-wave evanescent field on a nanophotonic waveguide. By employing the thermo-optic effect via integrated electric microheaters, the traps can be repositioned at high speed (∼30 kHz) with nanometre precision. We demonstrate sorting and manipulation of individual DNA molecules. In conjunction with laminar flows and fluorescence, we also show precise control of the chemical environment of a sample with simultaneous monitoring. Such a controllable trapping device has the potential to achieve high-throughput precision measurements on chip.

Coil-bridge transition in a single polymer chain as an unconventional phase transition: theory and simulation

The coil-bridge transition in a self-avoiding lattice chain with one end fixed at height H above the attractive planar surface is investigated by theory and Monte Carlo simulation. We focus on the details of the first-order phase transition between the coil state at large height H ⩾ Htr and a bridge state at H ⩽ Htr, where Htr corresponds to the coil-bridge transition point. The equilibrium properties of the chain were calculated using the Monte Carlo pruned-enriched Rosenbluth method in the moderate adsorption regime at (H/Na)tr ⩽ 0.27 where N is the number of monomer units of linear size a. An analytical theory of the coil-bridge transition for lattice chains with excluded volume interactions is presented in this regime. The theory provides an excellent quantitative description of numerical results at all heights, 10 ⩽ H/a ⩽ 320 and all chain lengths 40 < N < 2560 without free fitting parameters. A simple theory taking into account the effect of finite extensibility of the lattice chain in the strong adsorption regime at (H/Na)tr ⩾ 0.5 is presented. We discuss some unconventional properties of the coil-bridge transition: the absence of phase coexistence, two micro-phases involved in the bridge state, and abnormal behavior in the microcanonical ensemble.

Optical trapping and manipulation of plasmonic nanoparticles: fundamentals, applications, and perspectives

This feature article discusses the optical trapping and manipulation of plasmonic nanoparticles, an area of current interest with potential applications in nanofabrication, sensing, analytics, biology and medicine. We give an overview over the basic theoretical concepts relating to optical forces, plasmon resonances and plasmonic heating. We discuss fundamental studies of plasmonic particles in optical traps and the temperature profiles around them. We place a particular emphasis on our own work employing optically trapped plasmonic nanoparticles towards nanofabrication, manipulation of biomimetic objects and sensing.

Enhancing optofluidic actuation of micro-objects by tagging with plasmonic nanoparticles

We report experimentally and theoretically on the significant exaltation of optical forces on microparticles when they are partially coated by metallic nanodots and shined with laser light within the surface plasmon resonance. Optical forces on both pure silica particles and silica-gold raspberries are characterized using an optical chromatography setup to measure the variations of the Stokes drag versus laser beam power. Results are compared to the Mie theory prediction for both pure dielectric particles and core-shell ones with a shell described as a continuous dielectric-metal composite of dielectric constant determined from the Maxwell-Garnett approach. The observed quantitative agreement demonstrates that radiation pressure forces are directly related to the metal concentration on the microparticle surface and that metallic nanodots increase the magnitude of optical forces compared to pure dielectric particles of the same overall size, even at very low metal concentration. Behaving as "micro-sized nanoparticles", the benefit of microparticles coated with metallic nanodots is thus twofold: it significantly enhances optofluidic manipulation and motion at the microscale, and brings nanometric optical, chemical or biological capabilities to the microscale.

Accurate measurement of force and displacement with optical tweezers using DNA molecules as metrology standards

Optical tweezers facilitate measurement of piconewton-level forces and nanometer-level displacements and have broad applications in biophysics and soft matter physics research. We have shown previously that DNA molecules can be used as metrology standards to define such measurements. Force-extension measurements on two DNA molecules of different lengths can be used to determine four necessary measurement parameters. Here, we show that the accuracy of determining these parameters can be improved by more than 7-fold by incorporating measurements of the DNA overstretching transition and using a multi-step data analysis procedure. This method results in very robust and precise fitting of DNA force-extension measurements to the worm-like chain model. We verify the accuracy through independent measurements of DNA stretching, DNA unzipping, and microsphere contact forces.

Probing the force-induced dissociation of aptamer-protein complexes

Aptamers are emerging as powerful synthetic bioreceptors for fundamental research, diagnostics, and therapeutics. For further advances, it is important to gain a better understanding of how aptamers interact with their targets. In this work, we have used magnetic force-induced dissociation experiments to study the dissociation process of two different aptamer-protein complexes, namely for hIgE and Ara h 1. The measurements show that both complexes exhibit dissociation with two distinct regimes: the dissociation rate depends weakly on the applied force at high forces but depends stronger on force at low forces. We attribute these observations to the existence of at least one intermediate state and at least two energy barriers in the aptamer-protein interaction. The measured spontaneous dissociation rate constants were validated with SPR using both Biacore and fiber optic technology. This work demonstrates the potential of the magnetic force-induced dissociation approach for an in-depth study of the dissociation kinetics of aptamer-protein bonds, which is not possible with SPR technologies. The results will help in the development and expansion of aptamers as bioaffinity probes.

Gold rotor bead tracking for high-speed measurements of DNA twist, torque and extension

Simultaneous measurements of DNA twist and extension have been used to measure physical properties of the double helix and to characterize structural dynamics and mechanochemistry in nucleoprotein complexes. However, the spatiotemporal resolution of twist measurements has been limited by the use of angular probes with large rotational drags, preventing the detection of short-lived intermediates or small angular steps. Here we introduce AuRBT, demonstrating a >100X improvement in time resolution over previous techniques. AuRBT employs gold nanoparticles as bright low-drag rotational and extensional probes, relying on instrumentation that combines magnetic tweezers with objective-side evanescent darkfield microscopy. In an initial application to molecular motor mechanism, we have examined the high-speed structural dynamics of DNA gyrase, revealing an unanticipated transient intermediate. AuRBT also enables direct measurements of DNA torque with >50X shorter integration times than previous techniques; here we demonstrate high-resolution torque spectroscopy by mapping the conformational landscape of a Z-forming DNA sequence.

Two steps forward, one step back: determining XPD helicase mechanism by single-molecule fluorescence and high-resolution optical tweezers

XPD-like helicases constitute a prominent DNA helicase family critical for many aspects of genome maintenance. These enzymes share a unique structural feature, an auxiliary domain stabilized by an iron-sulphur (FeS) cluster, and a 5'-3' polarity of DNA translocation and duplex unwinding. Biochemical analyses alongside two single-molecule approaches, total internal reflection fluorescence microscopy and high-resolution optical tweezers, have shown how the unique structural features of XPD helicase and its specific patterns of substrate interactions tune the helicase for its specific cellular function and shape its molecular mechanism. The FeS domain forms a duplex separation wedge and contributes to an extended DNA binding site. Interactions within this site position the helicase in an orientation to unwind the duplex, control the helicase rate, and verify the integrity of the translocating strand. Consistent with its cellular role, processivity of XPD is limited and is defined by an idiosyncratic stepping kinetics. DNA duplex separation occurs in single base pair steps punctuated by frequent backward steps and conformational rearrangements of the protein-DNA complex. As such, the helicase in isolation mainly stabilizes spontaneous base pair opening and exhibits a limited ability to unwind stable DNA duplexes. The presence of a cognate ssDNA binding protein converts XPD into a vigorous helicase by destabilizing the upstream dsDNA as well as by trapping the unwound strands. Remarkably, the two proteins can co-exist on the same DNA strand without competing for binding. The current model of the XPD unwinding mechanism will be discussed along with possible modifications to this mechanism by the helicase interacting partners and unique features of such bio-medically important XPD-like helicases as FANCJ (BACH1), RTEL1 and CHLR1 (DDX11).

Emergent collective phenomena in a mixture of hard shapes through active rotation

We investigate collective phenomena with rotationally driven spinners of concave shape. Each spinner experiences a constant internal torque in either a clockwise or counterclockwise direction. Although the spinners are modeled as hard, otherwise noninteracting rigid bodies, their active motion induces an effective interaction that favors rotation in the same direction. With increasing density and activity, phase separation occurs via spinodal decomposition, as well as self-organization into rotating crystals. We observe the emergence of cooperative, superdiffusive motion along interfaces, which can transport inactive test particles. Our results demonstrate novel phase behavior of actively rotated particles that is not possible with linear propulsion or in nondriven, equilibrium systems of identical hard particles.

Folding a stable RNA pseudoknot through rearrangement of two hairpin structures

Folding messenger RNA into specific structures is a common regulatory mechanism involved in translation. In Escherichia coli, the operator of the rpsO gene transcript folds into a pseudoknot or double-hairpin conformation. S15, the gene product, binds only to the pseudoknot, thereby repressing its own synthesis when it is present in excess in the cell. The two RNA conformations have been proposed to exist in equilibrium. However, it remained unclear how structural changes can be achieved between these two topologically distinct conformations. We used optical tweezers to study the structural dynamics and rearrangements of the rpsO operator RNA at the single-molecule level. We discovered that the two RNA structures can be interchanged spontaneously and the pseudoknot can exist in conformations that exhibit various levels of stability. Conversion from the double hairpin to a pseudoknot through potential hairpin–hairpin interactions favoured the high-stability conformation. By contrast, mutations that blocked the formation of a hairpin typically resulted in alternative low-stability pseudoknots. These results demonstrate that specific tertiary interactions of RNA can be established and modulated based on the interactions and rearrangements between secondary structural components. Our findings provide new insight into the RNA folding pathway that leads to a regulatory conformation for target protein binding.

Investigating biomolecular recognition at the cell surface using atomic force microscopy

Probing the interaction forces that drive biomolecular recognition on cell surfaces is essential for understanding diverse biological processes. Force spectroscopy has been a widely used dynamic analytical technique, allowing measurement of such interactions at the molecular and cellular level. The capabilities of working under near physiological environments, combined with excellent force and lateral resolution make atomic force microscopy (AFM)-based force spectroscopy a powerful approach to measure biomolecular interaction forces not only on non-biological substrates, but also on soft, dynamic cell surfaces. Over the last few years, AFM-based force spectroscopy has provided biophysical insight into how biomolecules on cell surfaces interact with each other and induce relevant biological processes. In this review, we focus on describing the technique of force spectroscopy using the AFM, specifically in the context of probing cell surfaces. We summarize recent progress in understanding the recognition and interactions between macromolecules that may be found at cell surfaces from a force spectroscopy perspective. We further discuss the challenges and future prospects of the application of this versatile technique.

Modeling stochastic kinetics of molecular machines at multiple levels: from molecules to modules

A molecular machine is either a single macromolecule or a macromolecular complex. In spite of the striking superficial similarities between these natural nanomachines and their man-made macroscopic counterparts, there are crucial differences. Molecular machines in a living cell operate stochastically in an isothermal environment far from thermodynamic equilibrium. In this mini-review we present a catalog of the molecular machines and an inventory of the essential toolbox for theoretically modeling these machines. The tool kits include 1), nonequilibrium statistical-physics techniques for modeling machines and machine-driven processes; and 2), statistical-inference methods for reverse engineering a functional machine from the empirical data. The cell is often likened to a microfactory in which the machineries are organized in modular fashion; each module consists of strongly coupled multiple machines, but different modules interact weakly with each other. This microfactory has its own automated supply chain and delivery system. Buoyed by the success achieved in modeling individual molecular machines, we advocate integration of these models in the near future to develop models of functional modules. A system-level description of the cell from the perspective of molecular machinery (the mechanome) is likely to emerge from further integrations that we envisage here.

Microfluidics and Raman microscopy: current applications and future challenges

Raman microscopy systems are becoming increasingly widespread and accessible for characterising chemical species. Microfluidic systems are also progressively finding their way into real world applications. Therefore, it is anticipated that the integration of Raman systems with microfluidics will become increasingly attractive and practical. This review aims to provide an overview of Raman microscopy-microfluidics integrated systems for researchers who are actively interested in utilising these tools. The fundamental principles and application strengths of Raman microscopy are discussed in the context of microfluidics. Various configurations of microfluidics that incorporate Raman microscopy methods are presented, with applications highlighted. Data analysis methods are discussed, with a focus on assisting the interpretation of Raman-microfluidics data from complex samples. Finally, possible future directions of Raman-microfluidic systems are presented.

The platelet and the biophysical microenvironment: lessons from cellular mechanics

While the role of platelets in hemostasis is well characterized from a biological perspective, the biophysical interactions between platelets and their mechanical microenvironment are relatively unstudied. The field of cellular mechanics has developed a number of approaches to study the effects of extracellular matrix (ECM)-derived mechanical forces on various cells, and has elucidated that integrin-cytoskeleton-mediated force transduction governs many cellular processes. As platelets adhere and spread via molecular machinery that is similar to that which enables other cells to mechanosense and mechanotransduce forces from their biophysical microenvironment, platelets too are likely governed by the same overarching mechanisms. Indeed, recent platelet mechanobiology studies have revealed that key aspects of platelet physiology and activation are regulated by the mechanical and spatial properties of the ECM microenvironment. At the same time, there are also key differences that make platelets unique in the world of cells-- their size, origin as megakaryocyte fragments, and unique αIIbβ3 integrin-- render their mechanosensing activities particularly interesting. The structurally "simple," anucleate nature of platelets coupled with their high actin concentration (20% of total protein) and integrin density [1] seem to make them ideal for mechanical force generation and transmission. Further studies will enhance our understanding of the role of platelet mechanobiology in hemostasis and thrombosis, potentially leading to new categories of diagnostics that investigate the mechanical properties of clots to determine bleeding risk, as well as therapies that target the mechanotransduction signaling pathway to alter the stability of clots.

Electrode-embedded nanopores for label-free single-molecule sequencing by electric currents

Electrode-embedded nanopores have been developed to realize label-free, low-cost, and high-throughput DNA sequencers.

Mechanosensing in developing lymphatic vessels

The lymphatic vasculature is responsible for fluid homeostasis, transport of immune cells, inflammatory molecules, and dietary lipids. It is composed of a network of lymphatic capillaries that drain into collecting lymphatic vessels and ultimately bring fluid back to the blood circulation. Lymphatic endothelial cells (LECs) that line lymphatic capillaries present loose overlapping intercellular junctions and anchoring filaments that support fluid drainage. When interstitial fluid accumulates within tissues, the extracellular matrix (ECM) swells and pulls the anchoring filaments. This results in opening of the LEC junctions and permits interstitial fluid uptake. The absorbed fluid is then transported within collecting lymphatic vessels, which exhibit intraluminal valves that prevent lymph backflow and smooth muscle cells that sequentially contract to propel lymph.Mechanotransduction involves translation of mechanical stimuli into biological responses. LECs have been shown to sense and respond to changes in ECM stiffness, fluid pressure-induced cell stretch, and fluid flow-induced shear stress. How these signals influence LEC function and lymphatic vessel growth can be investigated by using different mechanotransduction assays in vitro and to some extent in vivo.In this chapter, we will focus on the mechanical forces that regulate lymphatic vessel expansion during embryonic development and possibly secondary lymphedema. In mouse embryos, it has been recently shown that the amount of interstitial fluid determines the extent of lymphatic vessel expansion via a mechanosensory complex formed by β1 integrin and vascular endothelial growth factor receptor-3 (VEGFR3). This model might as well apply to secondary lymphedema.

Measuring two at the same time: combining magnetic tweezers with single-molecule FRET

Molecular machines are the workhorses of the cell that efficiently convert chemical energy into mechanical motion through conformational changes. They can be considered powerful machines, exerting forces and torque on the molecular level of several piconewtons and piconewton-nanometer, respectively. For studying translocation and conformational changes of these machines, fluorescence methods, like FRET, as well as "mechanical" methods, like optical and magnetic tweezers, have proven well suited over the past decades. One of the current challenges in the field of molecular machines is gaining maximal information from single-molecule experiments by simultaneously measuring translocation, conformational changes, and forces exerted by these machines. In this chapter, we describe the combination of magnetic tweezers with single-molecule FRET for orthogonal simultaneous readout to maximize the information gained in single-molecule experiments.

Joining forces: integrating the mechanical and optical single molecule toolkits

Combining single molecule force measurements with fluorescence detection opens up exciting new possibilities for the characterization of mechanoresponsive molecules in Biology and Materials Science.

Optically controlled thermophoretic trapping of single nano-objects

Brownian motion is driven by thermal fluctuations and becoming more efficient for decreasing size and elevated temperatures. Here, we show that despite the increased fluctuations local temperature fields can be used to localize and control single nano-objects in solution. By creating strong local temperature gradients in a liquid using optically heated gold nanostructures, we are able to trap single colloidal particles. The trapping is thermophoretic in nature, and thus no restoring body force is involved. The simplicity of the setup allows for an easy integration and scalability to large arrays of traps.

Calibrating optical tweezers with Bayesian inference

We present a new method for calibrating an optical-tweezer setup that does not depend on input parameters and is less affected by systematic errors like drift of the setup. It is based on an inference approach that uses Bayesian probability to infer the diffusion coefficient and the potential felt by a bead trapped in an optical or magnetic trap. It exploits a much larger amount of the information stored in the recorded bead trajectory than standard calibration approaches. We demonstrate that this method outperforms the equipartition method and the power-spectrum method in input information required (bead radius and trajectory length) and in output accuracy.

Holographic optical tweezers combined with back-focal-plane displacement detection

A major problem with holographic optical tweezers (HOTs) is their incompatibility with laser-based position detection methods, such as back-focal-plane interferometry (BFPI). The alternatives generally used with HOTs, like high-speed video tracking, do not offer the same spatial and temporal bandwidths. This has limited the use of this technique in precise quantitative experiments. In this paper, we present an optical trap design that combines digital holography and back-focal-plane displacement detection. We show that, with a particularly simple setup, it is possible to generate a set of multiple holographic traps and an additional static non-holographic trap with orthogonal polarizations and that they can be, therefore, easily separated for measuring positions and forces with the high positional and temporal resolutions of laser-based detection. We prove that measurements from both polarizations contain less than 1% crosstalk and that traps in our setup are harmonic within the typical range. We further tested the instrument in a DNA stretching experiment and we discuss an interesting property of this configuration: the small drift of the differential signal between traps.

Motor proteins and molecular motors: how to operate machines at the nanoscale

Several classes of biological molecules that transform chemical energy into mechanical work are known as motor proteins or molecular motors. These nanometer-sized machines operate in noisy stochastic isothermal environments, strongly supporting fundamental cellular processes such as the transfer of genetic information, transport, organization and functioning. In the past two decades motor proteins have become a subject of intense research efforts, aimed at uncovering the fundamental principles and mechanisms of molecular motor dynamics. In this review, we critically discuss recent progress in experimental and theoretical studies on motor proteins. Our focus is on analyzing fundamental concepts and ideas that have been utilized to explain the non-equilibrium nature and mechanisms of molecular motors.

Extracting signal from noise: kinetic mechanisms from a Michaelis-Menten-like expression for enzymatic fluctuations

Enzyme-catalyzed reactions are naturally stochastic, and precision measurements of these fluctuations, made possible by single-molecule methods, promise to provide fundamentally new constraints on the possible mechanisms underlying these reactions. We review some aspects of statistical kinetics: a new field with the goal of extracting mechanistic information from statistical measures of fluctuations in chemical reactions. We focus on a widespread and important statistical measure known as the randomness parameter. This parameter is remarkably simple in that it is the squared coefficient of variation of the cycle completion times, although it places significant limits on the minimal complexity of possible enzymatic mechanisms. Recently, a general expression has been introduced for the substrate dependence of the randomness parameter that is for rate fluctuations what the Michaelis-Menten expression is for the mean rate of product generation. We discuss the information provided by the new kinetic parameters introduced by this expression and demonstrate that this expression can simplify the vast majority of published models.

The ClpXP protease unfolds substrates using a constant rate of pulling but different gears

ATP-dependent proteases are vital to maintain cellular protein homeostasis. Here, we study the mechanisms of force generation and intersubunit coordination in the ClpXP protease from E. coli to understand how these machines couple ATP hydrolysis to mechanical protein unfolding. Single-molecule analyses reveal that phosphate release is the force-generating step in the ATP-hydrolysis cycle and that ClpXP translocates substrate polypeptides in bursts resulting from highly coordinated conformational changes in two to four ATPase subunits. ClpXP must use its maximum successive firing capacity of four subunits to unfold stable substrates like GFP. The average dwell duration between individual bursts of translocation is constant, regardless of the number of translocating subunits, implying that ClpXP operates with constant "rpm" but uses different "gears."

Mechanical unzipping and rezipping of a single SNARE complex reveals hysteresis as a force-generating mechanism

Formation of the soluble N-ethylmaleimide-sensitive factor attachment protein receptor (SNARE) complex provides mechanical thrust for membrane fusion, but its molecular mechanism is still unclear. Here using magnetic tweezers, we observe mechanical responses of a single neuronal SNARE complex under constant pulling force. Single SNARE complexes may be unzipped with 34 pN force. When rezipping is induced by lowering the force to 11 pN, only a partially assembled state results, with the C-terminal half of the SNARE complex remaining disassembled. Reassembly of the C-terminal half occurs only when the force is further lowered below 11 pN. Thus, mechanical hysteresis, characterized by the unzipping and rezipping cycle of a single SNARE complex, produces the partially assembled state. In this metastable state, unzipping toward the N-terminus is suppressed while zippering toward the C-terminus is initiated as a steep function of force. This ensures the directionality of SNARE-complex formation, making the SNARE complex a robust force-generating machine.

Interactions between (SNARE) proteins on vesicle and target membranes provide the force necessary to drive membrane fusion. By applying piconewton forces to single SNARE complexes, the authors identify a partially assembled intermediate state that reveals how force is generated in a consistent direction.