Microrheology of solutions of semiflexible biopolymer filaments using laser tweezers interferometry

Microrheology and structural quantification of hypercoagulable clots

Hypercoagulability is a pathology that remains difficult to explain today in most cases. It is likely due to a modification of the conditions of polymerization of the fibrin, the main clot component. Using passive microrheology, we measured the mechanical properties of clots and correlated them under the same conditions with structural information obtained with confocal microscopy. We tested our approach with known alterations: an excess of fibrinogen and of coagulation Factor VIII. We observed simultaneously a rigidification and densification of the fibrin network, showing the potential of microrheology for hypercoagulability diagnosis.

Micro-mechanical response and power-law exponents from the longitudinal fluctuations of F-actin solutions

We investigate the local fluctuations of filamentous actin (F-actin), with a focus on the skeletal thin filament, using single-particle optical trapping interferometry. This experimental technique allows us to detect the Brownian motion of a tracer bead immersed in a complex fluid with nanometric resolution at the microsecond time-scale. The mean square displacement, loss modulus, and velocity autocorrelation function (VAF) of the trapped microprobes in the fluid follow power-law behaviors, whose exponents can be determined in the short-time/high-frequency regime over several decades. We obtain 7/8 subdiffusive power-law exponents for polystyrene depleted microtracers at low optical trapping forces. Microrheologically, the elastic modulus of these suspensions is observed to be constant up to the limit of high frequencies, confirming that the origin of this subdiffusive exponent is the local longitudinal fluctuations of the polymers. Deviations from this value are measured and discussed in relation to the characteristic length scales of these F-actin networks and probes' properties, and also in connection with the different power-law exponents detected in the VAFs. Finally, we observed that the thin filament, composed of tropomyosin (Tm) and troponin (Tn) coupled to F-actin in the presence of Ca2+, shows exponent values less dispersed than that of F-actin alone, which we interpret as a micro-measurement of the filament stabilization.

Line optical tweezers as controllable micromachines: techniques and emerging trends

In the past three decades, the technology of optical tweezers has made significant contributions in various scientific areas, including optics, photonics, and nanosciences. Breakthroughs include manipulating particles in both static and dynamic ways, particle sorting, and constructing controllable micromachines. Advances in shaping and controlling the laser beam profile enable control over the position and location of the trap, which has many possible applications. A line optical tweezer (LOT) can be created by rapidly moving a spot optical tweezer using a tool such as a galvanometer mirror or an acousto-optic modulator. By manipulating the intensity profile along the beam line to be asymmetric or non-uniform, the technique can be adapted to various specific applications. Among the many exciting applications of line optical tweezers, in this work, we discuss in detail applications of LOT, including probing colloidal interactions, transporting and sorting of colloidal microspheres, self-propelled motions, trapping anisotropic particles, exploring colloidal interactions at fluid-fluid interfaces, and building optical thermal ratchets. We further discuss prospective applications in each of these areas of soft matter, including polymeric and biological soft materials.

Dynamics of undulatory fluctuations of semiflexible filaments in a network

We study the dynamics of a single semiflexible filament coupled to a Hookean spring at its boundary. The spring produces a fluctuating tensile force on the filament, the value of which depends on the filament's instantaneous end-to-end length. The spring thereby introduces a nonlinearity, which mixes the undulatory normal modes of the filament and changes their dynamics. We study these dynamics using the Martin-Siggia-Rose-Janssen-De Dominicis formalism, and compute the time-dependent correlation functions of transverse undulations and of the filament's end-to-end distance. The relaxational dynamics of the modes below a characteristic wavelength sqrt[κ/τ_{R}], set by the filament's bending modulus κ and spring-renormalized tension τ_{R}, are changed by the boundary spring. This occurs near the crossover frequency between tension- and bending-dominated modes of the system. The boundary spring can be used to represent the linear elastic compliance of the rest of the filament network to which the filament is cross linked. As a result, we predict that this nonlinear effect will be observable in the dynamical correlations of constituent filaments of networks and in the networks' collective shear response. The system's dynamic shear modulus is predicted to exhibit the well-known crossover with increasing frequency from ω^{1/2} to ω^{3/4}, but the inclusion of the network's compliance in the analysis of the individual filament dynamics shifts this transition to a higher frequency.

Equilibrium fluctuations of a semiflexible filament cross linked into a network

We examine the equilibrium fluctuation spectrum of a semiflexible filament segment in a network. The effect of this cross linking is to modify the mechanical boundary conditions at the end of the filament. We consider the effect of both tensile stress in the network and its elastic compliance. Most significantly, the network's compliance introduces a nonlinear term into the filament Hamiltonian even in the small-bending approximation. We analyze the effect of this nonlinearity upon the filament's fluctuation profile. We also find that there are three principal fluctuation regimes dominated by one of the following: (i) network tension, (ii) filament bending stiffness, or (iii) network compliance. This work provides the theoretical framework necessary to analyze activity microrheology, which uses the observed filament fluctuations as a noninvasive probe of tension in the network.

Broken detailed balance and non-equilibrium dynamics in living systems: a review

Living systems operate far from thermodynamic equilibrium. Enzymatic activity can induce broken detailed balance at the molecular scale. This molecular scale breaking of detailed balance is crucial to achieve biological functions such as high-fidelity transcription and translation, sensing, adaptation, biochemical patterning, and force generation. While biological systems such as motor enzymes violate detailed balance at the molecular scale, it remains unclear how non-equilibrium dynamics manifests at the mesoscale in systems that are driven through the collective activity of many motors. Indeed, in several cellular systems the presence of non-equilibrium dynamics is not always evident at large scales. For example, in the cytoskeleton or in chromosomes one can observe stationary stochastic processes that appear at first glance thermally driven. This raises the question how non-equilibrium fluctuations can be discerned from thermal noise. We discuss approaches that have recently been developed to address this question, including methods based on measuring the extent to which the system violates the fluctuation-dissipation theorem. We also review applications of this approach to reconstituted cytoskeletal networks, the cytoplasm of living cells, and cell membranes. Furthermore, we discuss a more recent approach to detect actively driven dynamics, which is based on inferring broken detailed balance. This constitutes a non-invasive method that uses time-lapse microscopy data, and can be applied to a broad range of systems in cells and tissue. We discuss the ideas underlying this method and its application to several examples including flagella, primary cilia, and cytoskeletal networks. Finally, we briefly discuss recent developments in stochastic thermodynamics and non-equilibrium statistical mechanics, which offer new perspectives to understand the physics of living systems.

Effects of finite and discrete sampling and blur on microrheology experiments

The frequency-dependent viscous and elastic properties of fluids can be determined from measurements of the thermal fluctuations of a micron-sized particle trapped by optical tweezers. Finite bandwidth and other instrument limitations lead to systematic errors in measurement of the fluctuations. In this work, we numerically represented power spectra of bead position measurements as if collected by two different measurement devices: a quadrant photodiode, which measures the deflection of the trapping laser; and a high-speed camera, which images the trapped bead directly. We explored the effects of aliasing, camera blur, sampling frequency, and measurement time. By comparing the power spectrum, complex response function, and the complex shear modulus with the ideal values, we found that the viscous and elastic properties inferred from the data are affected by the instrument limitations of each device. We discuss how these systematic effects might affect experimental results from microrheology measurements and suggest approaches to reduce discrepancies.

Intact Telopeptides Enhance Interactions between Collagens

Collagen is the fundamental structural component of a wide range of connective tissues and of the extracellular matrix. It undergoes self-assembly from individual triple-helical proteins into well-ordered fibrils, a process that is key to tissue development and homeostasis, and to processes such as wound healing. Nucleation of this assembly is known to be slowed considerably by pepsin removal of short nonhelical regions that flank collagen's triple helix, known as telopeptides. Using optical tweezers to perform microrheology measurements, we explored the changes in viscoelasticity of solutions of collagen with and without intact telopeptides. Our experiments reveal that intact telopeptides contribute a significant frequency-dependent enhancement of the complex shear modulus. An analytical model of polymers associating to establish chemical equilibrium among higher-order species shows trends in G' and G″ consistent with our experimental observations, including a concentration-dependent crossover in G″/c around 300 Hz. This work suggests that telopeptides facilitate transient intermolecular interactions between collagen proteins, even in the acidic conditions used here.

Tube Concept for Entangled Stiff Fibers Predicts Their Dynamics in Space and Time

We study dynamically crowded solutions of stiff fibers deep in the semidilute regime, where the motion of a single constituent becomes increasingly confined to a narrow tube. The spatiotemporal dynamics for wave numbers resolving the motion in the confining tube becomes accessible in Brownian dynamics simulations upon employing a geometry-adapted neighbor list. We demonstrate that in such crowded environments the intermediate scattering function, characterizing the motion in space and time, can be predicted quantitatively by simulating a single freely diffusing phantom needle only, yet with very unusual diffusion coefficients.

Measurements of fluid viscosity using a miniature ball drop device

This paper describes measurement of fluid viscosity using a small ball drop device. It requires as little as 100 μl of fluid. Each measurement can be performed in seconds. The experiment is designed to yield reliable viscosity values by operating at properly chosen tilt angles and with calibration using well-characterized Newtonian fluids such as mixtures of glycerol and water. It also yields dynamical viscosity of non-Newtonian fluids at moderate shear rates. The device is easy to assemble and it allows for the measurement of viscosity even when the fluid samples are too small to measure using most commercial viscometers or rheometers. Therefore, the technique is particularly useful in characterizing biological fluids such as solutions of proteins, DNA, and polymers frequently used in biomaterial applications.

DNA driven self-assembly of micron-sized rods using DNA-grafted bacteriophage fd virions

We have functionalized the sides of fd bacteriophage virions with oligonucleotides to induce DNA hybridization driven self-assembly of high aspect ratio filamentous particles. Potential impacts of this new structure range from an entirely new building block in DNA origami structures, inclusion of virions in DNA nanostructures and nanomachines, to a new means of adding thermotropic control to lyotropic liquid crystal systems. A protocol for producing the virions in bulk is reviewed. Thiolated oligonucleotides are attached to the viral capsid using a heterobifunctional chemical linker. A commonly used system is utilized, where a sticky, single-stranded DNA strand is connected to an inert double-stranded spacer to increase inter-particle connectivity. Solutions of fd virions carrying complementary strands are mixed, annealed, and their aggregation is studied using dynamic light scattering (DLS), fluorescence microscopy, and atomic force microscopy (AFM). Aggregation is clearly observed on cooling, with some degree of local order, and is reversible when temperature is cycled through the DNA hybridization transition.

The mechanical properties of early Drosophila embryos measured by high-speed video microrheology

In early development, Drosophila melanogaster embryos form a syncytium, i.e., multiplying nuclei are not yet separated by cell membranes, but are interconnected by cytoskeletal polymer networks consisting of actin and microtubules. Between division cycles 9 and 13, nuclei and cytoskeleton form a two-dimensional cortical layer. To probe the mechanical properties and dynamics of this self-organizing pre-tissue, we measured shear moduli in the embryo by high-speed video microrheology. We recorded position fluctuations of injected micron-sized fluorescent beads with kHz sampling frequencies and characterized the viscoelasticity of the embryo in different locations. Thermal fluctuations dominated over nonequilibrium activity for frequencies between 0.3 and 1000 Hz. Between the nuclear layer and the yolk, the cytoplasm was homogeneous and viscously dominated, with a viscosity three orders of magnitude higher than that of water. Within the nuclear layer we found an increase of the elastic and viscous moduli consistent with an increased microtubule density. Drug-interference experiments showed that microtubules contribute to the measured viscoelasticity inside the embryo whereas actin only plays a minor role in the regions outside of the actin caps that are closely associated with the nuclei. Measurements at different stages of the nuclear division cycle showed little variation.

Active one-particle microrheology of an unentangled polymer melt studied by molecular dynamics simulation

We present molecular dynamics simulations for active one-particle microrheology of an unentangled polymer melt. The tracer particle is forced to oscillate by an oscillating harmonic potential, which models an experiment using optical tweezers. The amplitude and phase shift of this oscillation are related to the complex shear modulus of the polymer melt. In the linear response regime at low frequencies, the active microrheology gives the same result as the passive microrheology, where the thermal motion of a tracer particle is related to the complex modulus. We expand the analysis to include full hydrodynamic effects instead of stationary Stokes friction only, and show that different approaches suggested in the literature lead to completely different results, and that none of them improves on the description using the stationary Stokes friction.

Passive one-particle microrheology of an unentangled polymer melt studied by molecular dynamics simulation

We present a molecular dynamics simulation study of the possibility of performing a microrheological analysis of a polymer melt by following the Brownian motion of a dispersed nanoparticle. We study the influence of the size of the nanoparticle, taken to be comparable to the radius of gyration of the chains, and of the strength of the interaction between the nanoparticle and the repeat units of the polymer chains. The influence of the presence of the nanoparticle on the melt mechanical behavior is analyzed, and the importance of effects of different levels of hydrodynamic analysis on the frequency-dependent dynamic shear modulus derived from the particle motion is worked out.

Microrheological characterization of collagen systems: from molecular solutions to fibrillar gels

Collagen is the most abundant protein in the extracellular matrix (ECM), where its structural organization conveys mechanical information to cells. Using optical-tweezers-based microrheology, we investigated mechanical properties both of collagen molecules at a range of concentrations in acidic solution where fibrils cannot form and of gels of collagen fibrils formed at neutral pH, as well as the development of microscale mechanical heterogeneity during the self-assembly process. The frequency scaling of the complex shear modulus even at frequencies of ∼10 kHz was not able to resolve the flexibility of collagen molecules in acidic solution. In these solutions, molecular interactions cause significant transient elasticity, as we observed for 5 mg/ml solutions at frequencies above ∼200 Hz. We found the viscoelasticity of solutions of collagen molecules to be spatially homogeneous, in sharp contrast to the heterogeneity of self-assembled fibrillar collagen systems, whose elasticity varied by more than an order of magnitude and in power-law behavior at different locations within the sample. By probing changes in the complex shear modulus over 100-minute timescales as collagen self-assembled into fibrils, we conclude that microscale heterogeneity appears during early phases of fibrillar growth and continues to develop further during this growth phase. Experiments in which growing fibrils dislodge microspheres from an optical trap suggest that fibril growth is a force-generating process. These data contribute to understanding how heterogeneities develop during self-assembly, which in turn can help synthesis of new materials for cellular engineering.

Effective-medium theory of a filamentous triangular lattice

We present an effective-medium theory that includes bending as well as stretching forces, and we use it to calculate the mechanical response of a diluted filamentous triangular lattice. In this lattice, bonds are central-force springs, and there are bending forces between neighboring bonds on the same filament. We investigate the diluted lattice in which each bond is present with a probability p. We find a rigidity threshold p(b) which has the same value for all positive bending rigidity and a crossover characterizing bending, stretching, and bend-stretch coupled elastic regimes controlled by the central-force rigidity percolation point at p(CF)=/~2/3 of the lattice when fiber bending rigidity vanishes.

The specificity of the interaction between αB-crystallin and desmin filaments and its impact on filament aggregation and cell viability

CRYAB (αB-crystallin) is expressed in many tissues and yet the R120G mutation in CRYAB causes tissue-specific pathologies, namely cardiomyopathy and cataract. Here, we present evidence to demonstrate that there is a specific functional interaction of CRYAB with desmin intermediate filaments that predisposes myocytes to disease caused by the R120G mutation. We use a variety of biochemical and biophysical techniques to show that plant, animal and ascidian small heat-shock proteins (sHSPs) can interact with intermediate filaments. Nevertheless, the mutation R120G in CRYAB does specifically change that interaction when compared with equivalent substitutions in HSP27 (R140G) and into the Caenorhabditis elegans HSP16.2 (R95G). By transient transfection, we show that R120G CRYAB specifically promotes intermediate filament aggregation in MCF7 cells. The transient transfection of R120G CRYAB alone has no significant effect upon cell viability, although bundling of the endogenous intermediate filament network occurs and the mitochondria are concentrated into the perinuclear region. The combination of R120G CRYAB co-transfected with wild-type desmin, however, causes a significant reduction in cell viability. Therefore, we suggest that while there is an innate ability of sHSPs to interact with and to bind to intermediate filaments, it is the specific combination of desmin and CRYAB that compromises cell viability and this is potentially the key to the muscle pathology caused by the R120G CRYAB.

Optical tweezers with fluorescence detection for temperature-dependent microrheological measurements

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

Python algorithms in particle tracking microrheology

BACKGROUND

Particle tracking passive microrheology relates recorded trajectories of microbeads, embedded in soft samples, to the local mechanical properties of the sample. The method requires intensive numerical data processing and tools allowing control of the calculation errors.

RESULTS

We report the development of a software package collecting functions and scripts written in Python for automated and manual data processing, to extract viscoelastic information about the sample using recorded particle trajectories. The resulting program package analyzes the fundamental diffusion characteristics of particle trajectories and calculates the frequency dependent complex shear modulus using methods published in the literature. In order to increase conversion accuracy, segmentwise, double step, range-adaptive fitting and dynamic sampling algorithms are introduced to interpolate the data in a splinelike manner.

CONCLUSIONS

The presented set of algorithms allows for flexible data processing for particle tracking microrheology. The package presents improved algorithms for mean square displacement estimation, controlling effects of frame loss during recording, and a novel numerical conversion method using segmentwise interpolation, decreasing the conversion error from about 100% to the order of 1%.

Stochastic optical active rheology

We demonstrate a stochastic based method for performing active rheology using optical tweezers. By monitoring the displacement of an embedded particle in response to stochastic optical forces, a rapid estimate of the frequency dependent shear moduli of a sample is achieved in the range of 10(-1)-10(3) Hz. We utilize the method to probe linear viscoelastic properties of hydrogels at varied cross-linker concentrations. Combined with fluorescence imaging, our method demonstrates non-linear changes of bond strength between T cell receptors and an antigenic peptide due to force-induced cell activation.

Rheology and DWS microrheology of concentrated suspensions of the semiflexible filamentous fd virus

Microrheology measurements were performed on suspensions of bacteriophage fd with diffusive wave spectroscopy in the concentrated regime, at different values of ionic strength. Viscosity vs. shear rate was also measured, and the effect of bacteriophage concentration and salt addition on shear thinning was determined, as well as on the peaks in the viscosity vs. shear curves corresponding to a transition from tumbling to wagging flow. The influence of concentration and salt addition on the mean square displacement of microspheres embedded in the suspensions was determined, as well as on their viscoelastic moduli up to high angular frequencies. Our results were compared with another microrheology technique previously reported where the power spectral density of thermal fluctuations of embedded micron-sized particles was evaluated. Although both results in general agree, the diffusive wave spectroscopy results are much less noisy and can reach larger frequencies. A comparison was made between measured and calculated shear modulus. Calculations were made employing the theory for highly entangled isotropic solutions of semiflexible polymers using a tube model, where various ways of calculating the needed parameters were used. Although some features are captured by the model, it is far from the experimental results mainly at high frequencies.

A DUAL OPTICAL TWEEZER FOR MICRORHEOLOGY OF BACTERIAL SUSPENSIONS

A dual optical tweezer has been built around an inverted microscope with high numerical aperture objective (N.A 1.4). The setup is versatile and can be used both as a single and a dual tweezer, and in the dual mode, enables us to optically trap two micron-sized latex beads within a few microns from each other in solution. Using this setup, we report measurements of the microrheological parameters of Pseudomonas fluorescens and Bacillus subtilis bacterial suspensions. We study the variation of viscoelastic moduli of these bacterial suspensions as a function of their cell count in solution. A comparison with inactive bacteria of corresponding cell count enables us to characterize the activity of the bacterial samples in terms of an average force that the bacteria exerts on the trapped bead. This work paves way for studies of interesting nonlinear rheological phenomena at small length scales.

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

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

High-throughput ballistic injection nanorheology to measure cell mechanics

High-throughput ballistic injection nanorheology is a method for the quantitative study of cell mechanics. Cell mechanics are measured by ballistic injection of submicron particles into the cytoplasm of living cells and tracking the spontaneous displacement of the particles at high spatial resolution. The trajectories of the cytoplasm-embedded particles are transformed into mean-squared displacements, which are subsequently transformed into frequency-dependent viscoelastic moduli and time-dependent creep compliance of the cytoplasm. This method allows for the study of a wide range of cellular conditions, including cells inside a 3D matrix, cell subjected to shear flows and biochemical stimuli, and cells in a live animal. Ballistic injection lasts <1 min and is followed by overnight incubation. Multiple particle tracking for one cell lasts <1 min. Forty cells can be examined in <1 h.

High- and low-frequency mechanical properties of living starfish oocytes

We studied the mechanical properties of living starfish oocytes belonging to two species, Astropecten Auranciacus and Asterina pectinifera, over a wide range of timescales. We monitored the Brownian motion of microspheres injected in the cytoplasm using laser particle-tracking (LPT) and video multiple-particle-tracking (MPT) techniques, to explore high- and low-frequency response ranges, respectively. The analysis of the mean-square-displacements (MSD) allowed us to characterize the samples on different timescales. The MSD behavior is explained by three power-law exponents: for short times (τ < 1 ms) it reflects the semiflexible behavior of the actin network; for intermediate timescales (1 ms < τ < 1 s) it is similar to that of a soft-glass material; finally for long times (τ > 1 s) it behaves mainly like a viscous medium. We computed and compared the viscoelastic moduli using a recently proposed model describing the frequency response of the cell material. The large fluctuations found in the MSD over hundreds of trajectories indicate and confirm the significant cytoplasm heterogeneity.

Surface adsorption and hopping cause probe-size-dependent microrheology of actin networks

A network of filaments formed primarily by the abundant cytoskeletal protein actin gives animal cells their shape and elasticity. The rheological properties of reconstituted actin networks have been studied by tracking micron-sized probe beads embedded within the networks. We investigate how microrheology depends on surface properties of probe particles by varying the stickiness of their surface. For this purpose, we chose carboxylate polystyrene (PS) beads, silica beads, bovine serum albumin (BSA) -coated PS beads, and polyethylene glycol (PEG) -grafted PS beads, which show descending stickiness to actin filaments, characterized by confocal imaging and microrheology. Probe size dependence of microrheology is observed for all four types of beads. For the slippery PEG beads, particle-tracking microrheology detects weaker networks using smaller beads, which tend to diffuse through the network by hopping from one confinement "cage" to another. This trend is reversed for the other three types of beads, for which microrheology measures stiffer networks for smaller beads due to physisorption of nearby filaments to the bead surface. We explain the probe size dependence with two simple models. We also evaluate depletion effect near nonadsorption bead surface using quantitative image analysis and discuss the possible impact of depletion on microrheology. Analysis of these effects is necessary in order to accurately define the actin network rheology both in vitro and in vivo.

Complex fluids: probing mechanical properties of biological systems with optical tweezers

The mechanical properties of cells are crucial for cell sensing and reaction to mechanical environments. This review describes the basic principles of optical tweezers and their use as force sensors for studying the mechanical properties of biological systems. It covers experiments of four groups of biological systems arranged by increasing complexity: (a) packaging DNA into viral capsids by bacteriophage portal motors and the dynamical stiffness of DNA upon protein binding, (b) actin-coated giant vesicles and the myosin-II embedded actin polymer network, (c) suspension cells, and (d) adhesion cells. These examples demonstrate how optical tweezers have been used to improve the understanding of the mechanical properties of biological systems at subcellular and molecular levels.

Characterization of hydrogel microstructure using laser tweezers particle tracking and confocal reflection imaging

Hydrogels are commonly used as extracellular matrix mimetics for applications in tissue engineering and increasingly as cell culture platforms with which to study the influence of biophysical and biochemical cues on cell function in 3D. In recent years, a significant number of studies have focused on linking substrate mechanical properties to cell function using standard methodologies to characterize the bulk mechanical properties of the hydrogel substrates. However, current understanding of the correlations between the microstructural mechanical properties of hydrogels and cell function in 3D is poor, in part because of a lack of appropriate techniques. Here we have utilized a laser tracking system, based on passive optical microrheology instrumentation, to characterize the microstructure of viscoelastic fibrin clots. Trajectories and mean square displacements were observed as bioinert PEGylated (PEG: polyethylene glycol) microspheres (1, 2 or 4.7 μm in diameter) diffused within confined pores created by the protein phase of fibrin hydrogels. Complementary confocal reflection imaging revealed microstructures comprised of a highly heterogeneous fibrin network with a wide range of pore sizes. As the protein concentration of fibrin gels was increased, our quantitative laser tracking measurements showed a corresponding decrease in particle mean square displacements with greater resolution and sensitivity than conventional imaging techniques. This platform-independent method will enable a more complete understanding of how changes in substrate mechanical properties simultaneously influence other microenvironmental parameters in 3D cultures.

Passive and active microrheology for cross-linked F-actin networks in vitro

Actin filament (F-actin) is one of the dominant structural constituents in the cytoskeleton. Orchestrated by various actin-binding proteins (ABPs), F-actin is assembled into higher-order structures such as bundles and networks that provide mechanical support for the cell and play important roles in numerous cellular processes. Although mechanical properties of F-actin networks have been extensively studied, the underlying mechanisms for network elasticity are not fully understood, in part because different measurements probe different length and force scales. Here, we developed both passive and active microrheology techniques using optical tweezers to estimate the mechanical properties of F-actin networks at a length scale comparable to cells. For the passive approach we tracked the motion of a thermally fluctuating colloidal sphere to estimate the frequency-dependent complex shear modulus of the network. In the active approach, we used an optical trap to oscillate an embedded microsphere and monitored the response in order to obtain network viscoelasticity over a physiologically relevant force range. While both active and passive measurements exhibit similar results at low strain, the F-actin network subject to high strain exhibits non-linear behavior which is analogous to the strain-hardening observed in macroscale measurements. Using confocal and total internal reflection fluorescent microscopy, we also characterize the microstructure of reconstituted F-actin networks in terms of filament length, mesh size and degree of bundling. Finally, we propose a model of network connectivity by investigating the effect of filament length on the mechanical properties and structure.

Blinking Optical Tweezers for microrheology measurements of weak elasticity complex fluids

Optical tweezers have become a powerful tool to explore the viscoelasticity of complex fluids at micrometric scale. In the experiments, the Brownian trajectories of optically confined microparticles are properly analysed to provide the viscous and elastic moduli G' and G'. Nevertheless, the elastic response of the medium is inherently superimposed on the trap stiffness itself. Usually, this drawback is removed by subtracting the elastic trap contribution from the measured medium response. However, it is clear that when trap and medium elasticity become comparable this procedure is no longer reliable. Still, there exists a wide class of complex fluids that exhibit a low elasticity (diluted biopolymers, Boger fluids, etc) for which alternative experimental approaches would be desirable. Herein we propose a new method based on blinking optical tweezers. It makes use of two independent laser beams: the first is used to trap a single bead while the second one, of very weak power, acts as probe to monitor its position with a quadrant photodiode. The trap laser intensity is modulated on-off: when the laser is off the bead follows a free diffusion trajectory that, hence, leads to an estimation of G' and G' free of the influence of the trap. We have successfully applied this technique to highly-diluted hyaluronic acid solutions (c < 0.1 mg/ml) reaching to measure very weak G' modulus ( approximately 0.01 Pa) in a wide range of frequencies.

Viscoelastic response of a model endothelial glycocalyx

Many cells cover themselves with a multifunctional polymer coat, the pericellular matrix (PCM), to mediate mechanical interactions with the environment. A particular PCM, the endothelial glycocalyx (EG), is formed by vascular endothelial cells at their luminal side, forming a mechanical interface between the flowing blood and the endothelial cell layer. The glycosaminoglycan (GAG) hyaluronan (HA) is involved in the main functions of the EG, mechanotransduction of fluid shear stress and molecular sieving. HA, due to its length, is the only GAG in the EG or any other PCM able to form an entangled network. The mechanical functions of the EG are, however, impaired when any one of its components is removed. We here used microrheology to measure the effect of the EG constituents heparan sulfate, chondroitin sulfate, whole blood plasma and albumin on the high-bandwidth mechanical properties of a HA solution. Furthermore, we probed the effect of the hyaldherin aggrecan, a constituent of the PCM of chondrocytes, and very similar to versican (present in the PCM of various cells, and possibly in the EG). We show that components directly interacting with HA (chondroitin sulfate and aggrecan) can increase the viscoelastic shear modulus of the polymer composite.

Light at work: the use of optical forces for particle manipulation, sorting, and analysis

We review the combinations of optical micro-manipulation with other techniques and their classical and emerging applications to non-contact optical separation and sorting of micro- and nanoparticle suspensions, compositional and structural analysis of specimens, and quantification of force interactions at the microscopic scale. The review aims at inspiring researchers, especially those working outside the optical micro-manipulation field, to find new and interesting applications of these methods.

Precision optical trapping via a programmable direct-digital-synthesis-based controller for acousto-optic deflectors

We describe a simple-to-construct programmable direct-digital-synthesis-based controller for use with acousto-optic deflectors. Our controller corrects for nonlinear diffraction efficiency versus diffraction angle, provides superior stability, functionality, and configurability, and costs a fraction of commercially available systems. Using this instrument, we move a 1 mum diameter bead by 1-nm-sized steps and resolve these steps.

High-bandwidth viscoelastic properties of aging colloidal glasses and gels

We report measurements of the frequency-dependent shear moduli of aging colloidal systems that evolve from a purely low-viscosity liquid to a predominantly elastic glass or gel. Using microrheology, we measure the local complex shear modulus G;{*}(omega) over a very wide range of frequencies (from 1Hzto100kHz ). The combined use of one- and two-particle microrheology allows us to differentiate between colloidal glasses and gels-the glass is homogenous, whereas the colloidal gel shows a considerable degree of heterogeneity on length scales larger than 0.5microm . Despite this characteristic difference, both systems exhibit similar rheological behaviors which evolve in time with aging, showing a crossover from a single-power-law frequency dependence of the viscoelastic modulus to a sum of two power laws. The crossover occurs at a time t_{0} , which defines a mechanical transition point. We found that the data acquired during the aging of different samples can be collapsed onto a single master curve by scaling the aging time with t_{0} . This raises questions about the prior interpretation of two power laws in terms of a superposition of an elastic network embedded in a viscoelastic background.

Counterion-dependent microrheological properties of F-actin solutions across the isotropic-nematic phase transition

We studied microrheological properties of F-actin across the isotropic-nematic phase transition region by video particle tracking (VPT) and by laser deflection particle tracking (LDPT). Both methods track the motion of thermally driven micron-sized beads, and convert the temporal mean square displacement (MSD) to shear moduli. The two methods give consistent results for the elastic modulus G' and less so for the loss modulus G'' . As the nematic order parameter increases with actin concentration, G'|| (measured parallel to the nematic director) and G' perpendicular (perpendicular to the director) grow apart, with G' perpendicular larger than G'||. The moduli scale with actin concentration as G'|| approximately c 0.54+/-0.13 and G' perpendicular approximately c 1.38+/-0.15. Furthermore, G' and G'' dependence on [Mg2+] were measured and compared for 1mg/ml isotropic and 4 mg/ml nematic F-actin solutions, respectively. In the isotropic phase, G' increases with [Mg2+] up to 6mM and then plateaus. In the nematic phase, G' perpendicular is larger than G'||, and both G' perpendicular and G'|| increase with [Mg2+] progressively up to 16 mM , above which F-actin form large bundles. In both isotropic and nematic phases, G'' only weakly depends on [Mg2+] . In conclusion, particle tracking microrheology reveals rich rheological features of F-actin affected by the isotropic-nematic phase transition and by tuning weak electrostatic interactions among the protein filaments.

Entangled dynamics of a stiff polymer

Entangled networks of stiff biopolymers exhibit complex dynamic response, emerging from the topological constraints that neighboring filaments impose upon each other. We propose a class of reference models for entanglement dynamics of stiff polymers and provide a quantitative foundation of the tube concept for stiff polymers. For an infinitely thin needle exploring a planar course of point obstacles, we have performed large-scale computer simulations proving the conjectured scaling relations from the fast transverse equilibration to the slowest process of orientational relaxation. We determine the rotational diffusion coefficient of the tracer, its angular confinement, the tube diameter, and the orientational correlation functions.

Combined macro- and microrheometer for use with Langmuir monolayers

A Langmuir monolayer trough that is equipped for simultaneous microrheology and standard rheology measurements has been constructed. The central elements are the trough itself with a full range of optical tools accessing the air-water interface from below the trough and a portable knife-edge torsion pendulum that can access the interface from above. The ability to simultaneously measure the mechanical response of Langmuir monolayers on very different length scales is an important step for our understanding of the mechanical response of two-dimensional viscoelastic networks.

Twin optical traps for two-particle cross-correlation measurements: eliminating cross-talk

The correlated motions of two micron-sized particles reflect the (micro-) rheological properties of a fluid and can be conveniently detected using two optical traps in combination with interferometric displacement detection. When the correlations become small, cross-talk between the two beams becomes important. We have used dual optical traps created by either two orthogonally polarized laser beams derived from one laser source, or by two independent lasers of different wavelengths for microrheology experiments. High numerical aperture lenses (objective and condenser) in the optical path can introduce depolarization, and polarizing beam splitters are not perfect, both of which can lead to optical cross-talk. We have characterized the cross-talk in our setup and demonstrate that the use of two independent laser eliminates cross-talk entirely.

Optical tweezers as a probe for oligodeoxyribonucleotide structuration

The aim of this work is to investigate if the optical tweezers (OT) are suitable as a diagnostic tool for monitoring the oligodeoxyribonucleotide (ODN) structural behavior in solution. Preliminary experiments, performed on the quadruplex formed by the ODN sequence TGGGGT, showed that the OT can be used as a probe for ODN structuration by monitoring the medium viscosity changes associated with ODN folding-unfolding processes.

Colloid dynamics in semiflexible polymer solutions

We investigate the dynamics of monodisperse colloidal polystyrene particles suspended in solutions of the semiflexible polymer filamentous actin, over a range of filament lengths that either exceed or are substantially less than the particle radius. The filament length is controlled by the capping protein gelsolin, and particle surface chemistries that minimize the adsorption of filaments are used. The particle dynamics are measured on short time scales using diffusing wave spectroscopy. A sharp transition in the initial particle diffusivity marks the expected shift from a dilute to a tightly entangled polymer network as the filament average length increases. In both the dilute and entangled regimes, the measured particle dynamics are compared with the theories of rodlike and semiflexible polymer solution rheology using the generalized Stokes-Einstein relationship. In the dilute limit, the particle dynamics are in good agreement with theory. However, in the tightly entangled regime, the particle response is consistent with polymer depleted near the surfaces of the particles. The magnitude of the depletion layer thickness depends strongly on particle size and weakly on filament length. This behavior is in agreement with nonlocal entropic repulsions and the loss of conformational entropy associated with rodlike molecules near impenetrable particles. These results illustrate the use of microrheology as a method to investigate local structure and dynamics in colloid-polymer solutions.

Correlated fluctuations of microparticles in viscoelastic solutions: quantitative measurement of material properties by microrheology in the presence of optical traps

The Brownian motions of microscopic particles in viscous or viscoelastic fluids can be used to measure rheological properties. This is the basis of recently developed one- and two-particle microrheology techniques. For increased temporal and spatial resolution, some microrheology techniques employ optical traps, which introduce additional forces on the particles. We have systematically studied the effect that confinement of particles by optical traps has on their auto- and cross-correlated fluctuations. We show that trapping causes anticorrelations in the motion of two particles at low frequencies. We demonstrate how these anticorrelations depend on trap strength and the shear modulus of viscoelastic media. We present a method to account for the effects of optical traps, which permits the quantitative measurement of viscoelastic properties in one- and two-particle microrheology over an extended frequency range in a variety of viscous and viscoelastic media.

Characterization of optically driven fluid stress fields with optical tweezers

We present a controlled stress microviscometer with applications to complex fluids. It generates and measures microscopic fluid velocity fields, based on dual beam optical tweezers. This allows an investigation of bulk viscous properties and local inhomogeneities at the probe particle surface. The accuracy of the method is demonstrated in water. In a complex fluid model (hyaluronic acid), we observe a strong deviation of the flow field from classical behavior. Knowledge of the deviation together with an optical torque measurement is used to determine the bulk viscosity. Furthermore, we model the observed deviation and derive microscopic parameters.