Measuring storage and loss moduli using optical tweezers: broadband microrheology

Exploiting Matrix Stiffness to Overcome Drug Resistance

Drug resistance is arguably one of the biggest challenges facing cancer research today. Understanding the underlying mechanisms of drug resistance in tumor progression and metastasis are essential in developing better treatment modalities. Given the matrix stiffness affecting the mechanotransduction capabilities of cancer cells, characterization of the related signal transduction pathways can provide a better understanding for developing novel therapeutic strategies. In this review, we aimed to summarize the recent advancements in tumor matrix biology in parallel to therapeutic approaches targeting matrix stiffness and its consequences in cellular processes in tumor progression and metastasis. The cellular processes governed by signal transduction pathways and their aberrant activation may result in activating the epithelial-to-mesenchymal transition, cancer stemness, and autophagy, which can be attributed to drug resistance. Developing therapeutic strategies to target these cellular processes in cancer biology will offer novel therapeutic approaches to tailor better personalized treatment modalities for clinical studies.

Fundamental Aspects of Phase-Separated Biomolecular Condensates

Biomolecular condensates, formed through phase separation, are upending our understanding in much of molecular, cell, and developmental biology. There is an urgent need to elucidate the physicochemical foundations of the behaviors and properties of biomolecular condensates. Here we aim to fill this need by writing a comprehensive, critical, and accessible review on the fundamental aspects of phase-separated biomolecular condensates. We introduce the relevant theoretical background, present the theoretical basis for the computation and experimental measurement of condensate properties, and give mechanistic interpretations of condensate behaviors and properties in terms of interactions at the molecular and residue levels.

Optical Halo: A Proof of Concept for a New Broadband Microrheology Tool

Microrheology, the study of material flow at micron scales, has advanced significantly since Robert Brown's discovery of Brownian motion in 1827. Mason and Weitz's seminal work in 1995 established the foundation for microrheology techniques, enabling the measurement of viscoelastic properties of complex fluids using light-scattering particles. However, existing techniques face limitations in exploring very slow dynamics, crucial for understanding biological systems. Here, we present a proof of concept for a novel microrheology technique called "Optical Halo", which utilises a ring-shaped Bessel beam created by optical tweezers to overcome existing limitations. Through numerical simulations and theoretical analysis, we demonstrate the efficacy of the Optical Halo in probing viscoelastic properties across a wide frequency range, including low-frequency regimes inaccessible to conventional methods. This innovative approach holds promise for elucidating the mechanical behaviour of complex biological fluids.

Enzymatic cleaving of entangled DNA rings drives scale-dependent rheological trajectories

DNA, which naturally occurs in linear, ring, and supercoiled topologies, frequently undergoes enzyme-driven topological conversion and fragmentation in vivo, enabling it to perform a variety of functions within the cell. In vitro, highly concentrated DNA polymers form entanglements that yield viscoelastic properties dependent on the topologies and lengths of the DNA. Enzyme-driven alterations of DNA size and shape therefore offer a means of designing active materials with programmable viscoelastic properties. Here, we incorporate multi-site restriction endonucleases into dense DNA solutions to linearize and fragment circular DNA molecules. We pair optical tweezers microrheology with differential dynamic microscopy and single-molecule tracking to measure the linear and nonlinear viscoelastic response and transport properties of entangled DNA solutions over a wide range of spatiotemporal scales throughout the course of enzymatic digestion. We show that, at short timescales, relative to the relaxation timescales of the polymers, digestion of these 'topologically-active' fluids initially causes an increase in elasticity and relaxation times followed by a gradual decrease. Conversely, for long timescales, linear viscoelastic moduli exhibit signatures of increasing elasticity. DNA diffusion, likewise, becomes increasingly slowed, in direct opposition to the short-time behavior. We hypothesize that this scale-dependent rheology arises from the population of small DNA fragments, which increases as digestion proceeds, driving self-association of larger fragments via depletion interactions, giving rise to slow relaxation modes of clusters of entangled chains, interspersed among shorter unentangled fragments. While these slow modes likely dominate at long times, they are presumably frozen out in the short-time limit, which instead probes the faster relaxation modes of the unentangled population.

Shining Light in Mechanobiology: Optical Tweezers, Scissors, and Beyond

Mechanobiology helps us to decipher cell and tissue functions by looking at changes in their mechanical properties that contribute to development, cell differentiation, physiology, and disease. Mechanobiology sits at the interface of biology, physics and engineering. One of the key technologies that enables characterization of properties of cells and tissue is microscopy. Combining microscopy with other quantitative measurement techniques such as optical tweezers and scissors, gives a very powerful tool for unraveling the intricacies of mechanobiology enabling measurement of forces, torques and displacements at play. We review the field of some light based studies of mechanobiology and optical detection of signal transduction ranging from optical micromanipulation-optical tweezers and scissors, advanced fluorescence techniques and optogenentics. In the current perspective paper, we concentrate our efforts on elucidating interesting measurements of forces, torques, positions, viscoelastic properties, and optogenetics inside and outside a cell attained when using structured light in combination with optical tweezers and scissors. We give perspective on the field concentrating on the use of structured light in imaging in combination with tweezers and scissors pointing out how novel developments in quantum imaging in combination with tweezers and scissors can bring to this fast growing field.

Fully angularly resolved 3D microrheology with optical tweezers

Microrheology with optical tweezers (MOT) is an all-optical technique that allows the user to investigate a materials' viscoelastic properties at microscopic scales, and is particularly useful for those materials that feature complex microstructures, such as biological samples. MOT is increasingly being employed alongside 3D imaging systems and particle tracking methods to generate maps showing not only how properties may vary between different points in a sample but also how at a single point the viscoelastic properties may vary with direction. However, due to the diffraction limited shape of focussed beams, optical traps are inherently anisotropic in 3D. This can result in a significant overestimation of the fluids' viscosity in certain directions. As such, the rheological properties can only be accurately probed along directions parallel or perpendicular to the axis of trap beam propagation. In this work, a new analytical method is demonstrated to overcome this potential artefact. This is achieved by performing principal component analysis on 3D MOT data to characterise the trap, and then identify the frequency range over which trap anisotropy influences the data. This approach is initially applied to simulated data for a Newtonian fluid where the trap anisotropy induced maximum error in viscosity is reduced from ~ 150% to less than 6%. The effectiveness of the method is corroborated by experimental MOT measurements performed with water and gelatine solutions, thus confirming that the microrheology of a fluid can be extracted reliably across a wide frequency range and in any arbitrary direction. This work opens the door to fully spatially and angularly resolved 3D mapping of the rheological properties of soft materials over a broad frequency range.

Living cells as a biological analog of optical tweezers - a non-invasive microrheology approach

Microrheology, the study of fluids on micron length-scales, promises to reveal insights into cellular biology, including mechanical biomarkers of disease and the interplay between biomechanics and cellular function. Here a minimally-invasive passive microrheology technique is applied to individual living cells by chemically binding a bead to the surface of a cell, and observing the mean squared displacement of the bead at timescales ranging from milliseconds to 100s of seconds. Measurements are repeated over the course of hours, and presented alongside analysis to quantify changes in the cells' low-frequency elastic modulus, G0', and the cell's dynamics over the time window ∼10-2 s to 10 s. An analogy to optical trapping allows verification of the invariant viscosity of HeLa S3 cells under control conditions and after cytoskeletal disruption. Stiffening of the cell is observed during cytoskeletal rearrangement in the control case, and cell softening when the actin cytoskeleton is disrupted by Latrunculin B. These data correlate with conventional understanding that integrin binding and recruitment triggers cytoskeletal rearrangement. This is, to our knowledge, the first time that cell stiffening has been measured during focal adhesion maturation, and the longest time over which such stiffening has been quantified by any means. STATEMENT OF SIGNIFICANCE: Here, we present an approach for studying mechanical properties of live cells without applying external forces or inserting tracers. Regulation of cellular biomechanics is crucial to healthy cell function. For the first time in literature, we can non-invasively and passively quantify cell mechanics during interactions with functionalised surface. Our method can monitor the maturation of adhesion sites on the surface of individual live cells without disrupting the cell mechanics by applying forces to the cell. We observe a stiffening response in cells over tens of minutes after a bead chemically binds. This stiffening reduces the deformation rate of the cytoskeleton, although the internal force generation increases. Our method has potential for applications to study mechanics during cell-surface and cell-vesicle interactions.

Advanced Mechanical Testing Technologies at the Cellular Level: The Mechanisms and Application in Tissue Engineering

Mechanics, as a key physical factor which affects cell function and tissue regeneration, is attracting the attention of researchers in the fields of biomaterials, biomechanics, and tissue engineering. The macroscopic mechanical properties of tissue engineering scaffolds have been studied and optimized based on different applications. However, the mechanical properties of the overall scaffold materials are not enough to reveal the mechanical mechanism of the cell-matrix interaction. Hence, the mechanical detection of cell mechanics and cellular-scale microenvironments has become crucial for unraveling the mechanisms which underly cell activities and which are affected by physical factors. This review mainly focuses on the advanced technologies and applications of cell-scale mechanical detection. It summarizes the techniques used in micromechanical performance analysis, including atomic force microscope (AFM), optical tweezer (OT), magnetic tweezer (MT), and traction force microscope (TFM), and analyzes their testing mechanisms. In addition, the application of mechanical testing techniques to cell mechanics and tissue engineering scaffolds, such as hydrogels and porous scaffolds, is summarized and discussed. Finally, it highlights the challenges and prospects of this field. This review is believed to provide valuable insights into micromechanics in tissue engineering.

Correlating microscopic viscoelasticity and structure of an aging colloidal gel using active microrheology and cryogenic scanning electron microscopy

Optical tweezers (OTs) can detect pico-Newton range forces operating on a colloidal particle trapped in a medium and have been successfully utilized to investigate complex systems with internal structures. LAPONITE® clay particles in an aqueous medium self-assemble to form microscopic networks over time as electrostatic interactions between the particles gradually evolve in a physical aging process. We investigate the forced movements of an optically trapped micron-sized colloidal probe particle, suspended in an aging LAPONITE® suspension, as the underlying LAPONITE® microstructures gradually develop. Our OT-based oscillatory active microrheology experiments allow us to investigate the mechanical responses of the evolving microstructures in aging aqueous clay suspensions of concentrations ranging from 2.5% w/v to 3.0% w/v and at several aging times between 90 and 150 minutes. We repeat such oscillatory measurements for a range of colloidal probe particle diameters and investigate the effect of probe size on the microrheology of the aging suspensions. Using cryogenic field emission scanning electron microscopy (cryo-FESEM), we examine the average pore areas of the LAPONITE® suspension microstructures for various sample concentrations and aging times. By combining our OT and cryo-FESEM data, we report here for the first time to the best of our knowledge, an inverse correlation between the crossover modulus and the average pore diameter of the aging suspension microstructures for the different suspension concentrations and probe particle sizes studied here.

Construction of multiphasic membraneless organelles towards spontaneous spatial segregation and directional flow of biochemical reactions

Many intracellular membraneless organelles (MLOs) appear to adapt a hierarchical multicompartment organization for efficient coordination of highly complex reaction networks. Recapitulating such an internal architecture in biomimetic platforms is, therefore, an important step to facilitate the functional understanding of MLOs and to enable the design of advanced microreactors. Herein, we present a modular bottom-up approach for building synthetic multiphasic condensates using a set of engineered multivalent polymer-oligopeptide hybrids. These hybrid constructs exhibit dynamic phase separation behaviour generating membraneless droplets with a subdivided interior featuring distinct chemical and physical properties, whereby a range of functional biomolecules can be spontaneously enriched and spatially segregated. The platform also attains separated confinement of transcription and translation reactions in proximal compartments, while allowing inter-compartment communication via a directional flow of reactants. With advanced structural and functional features attained, this system can be of great value as a MLO model and as a cell-free system for multiplex chemical biosynthesis.

Mucus from human bronchial epithelial cultures: rheology and adhesion across length scales

Mucus is a viscoelastic aqueous fluid that participates in the protective barrier of many mammals' epithelia. In the airways, together with cilia beating, mucus rheological properties are crucial for lung mucociliary function, and, when impaired, potentially participate in the onset and progression of chronic obstructive pulmonary disease (COPD). Samples of human mucus collected in vivo are inherently contaminated and are thus poorly characterized. Human bronchial epithelium (HBE) cultures, differentiated from primary cells at an air-liquid interface, are highly reliable models to assess non-contaminated mucus. In this paper, the viscoelastic properties of HBE mucus derived from healthy subjects, patients with COPD and from smokers are measured. Hallmarks of shear-thinning and elasticity are obtained at the macroscale, whereas at the microscale mucus appears as a heterogeneous medium showing an almost Newtonian behaviour in some extended regions and an elastic behaviour close to boundaries. In addition, we developed an original method to probe mucus adhesion at the microscopic scale using optical tweezers. The measured adhesion forces and the comparison with mucus-simulants rheology as well as mucus imaging collectively support a structure composed of a network of elastic adhesive filaments with a large mesh size, embedded in a very soft gel.

Programmable viscoelasticity in protein-RNA condensates with disordered sticker-spacer polypeptides

Liquid-liquid phase separation of multivalent proteins and RNAs drives the formation of biomolecular condensates that facilitate membrane-free compartmentalization of subcellular processes. With recent advances, it is becoming increasingly clear that biomolecular condensates are network fluids with time-dependent material properties. Here, employing microrheology with optical tweezers, we reveal molecular determinants that govern the viscoelastic behavior of condensates formed by multivalent Arg/Gly-rich sticker-spacer polypeptides and RNA. These condensates behave as Maxwell fluids with an elastically-dominant rheological response at shorter timescales and a liquid-like behavior at longer timescales. The viscous and elastic regimes of these condensates can be tuned by the polypeptide and RNA sequences as well as their mixture compositions. Our results establish a quantitative link between the sequence- and structure-encoded biomolecular interactions at the microscopic scale and the rheological properties of the resulting condensates at the mesoscale, enabling a route to systematically probe and rationally engineer biomolecular condensates with programmable mechanics.

Effect of shear flow on the hydrodynamic drag force of a spherical particle near a wall evaluated using optical tweezers and microfluidics

The hydrodynamic drag force on a spherical particle in shear flow near-wall is investigated using optical tweezers and microfluidics. Simple shear flow is applied using a microfluidic channel at different volumetric flow rates. The hydrodynamic drag force exerted on the particle is detected from the displacement of the trapped particle. The effect of the wall is obtained from the force balance of the trapping and hydrodynamic drag force employing the exact solution of the theoretical model using the lubrication theory for a sphere near the wall. Here, we report the experimentally obtained hydrodynamic drag force coefficient under the influence of shear flow. The drag correction factor increases with decreasing distance from the wall due to the effect of the wall surface. We found that the calculated hydrodynamic drag force coefficient is in quantitative comparison with the theoretical prediction for a shear flow past a sphere near-wall. This study provides a straightforward investigation of the effect of the shear flow on the hydrodynamic drag force coefficient on a particle near the wall. Furthermore, these pieces of information can be used in various applications, particularly in optimizing microfluidic designs for mixing and separations of particles or exploiting the formation of the concentration gradient of particles perpendicular to flow directions caused by the non-linear hydrodynamic interactions.

Introducing Memory in Coarse-Grained Molecular Simulations

Preserving the correct dynamics at the coarse-grained (CG) level is a pressing problem in the development of systematic CG models in soft matter simulation. Starting from the seminal idea of simple time-scale mapping, there have been many efforts over the years toward establishing a meticulous connection between the CG and fine-grained (FG) dynamics based on fundamental statistical mechanics approaches. One of the most successful attempts in this context has been the development of CG models based on the Mori-Zwanzig (MZ) theory, where the resulting equation of motion has the form of a generalized Langevin equation (GLE) and closely preserves the underlying FG dynamics. In this Review, we describe some of the recent studies in this regard. We focus on the construction and simulation of dynamically consistent systematic CG models based on the GLE, both in the simple Markovian limit and the non-Markovian case. Some recent studies of physical effects of memory are also discussed. The Review is aimed at summarizing recent developments in the field while highlighting the major challenges and possible future directions.

Bayesian inference of the viscoelastic properties of a Jeffrey's fluid using optical tweezers

Bayesian inference is a conscientious statistical method which is successfully used in many branches of physics and engineering. Compared to conventional approaches, it makes highly efficient use of information hidden in a measured quantity by predicting the distribution of future data points based on posterior information. Here we apply this method to determine the stress-relaxation time and the solvent and polymer contributions to the frequency dependent viscosity of a viscoelastic Jeffrey's fluid by the analysis of the measured trajectory of an optically trapped Brownian particle. When comparing the results to those obtained from the auto-correlation function, mean-squared displacement or the power spectrum, we find Bayesian inference to be much more accurate and less affected by systematic errors.

Inverse integral transformation method to derive local viscosity distribution measured by optical tweezers

Complex fluids have a non-uniform local inner structure; this is enhanced under deformation, inducing a characteristic flow, such as an abrupt increase in extensional viscosity and drag reduction. However, it is challenging to derive and quantify the non-uniform local structure of a low-concentration solution. In this study, we attempted to characterize the non-uniformity of dilute and semi-dilute polymer and worm-like micellar solutions using the local viscosity at the micro scale. The power spectrum density (PSD) of the particle displacement, measured using optical tweezers, was analyzed to calculate the local viscosity, and two methods were compared. One is based on the PSD roll-off method, which yields a single representative viscosity of the solution. The other is based on our proposed method, called the inverse integral transformation method (IITM), for deriving the local viscosity distribution. The distribution obtained through the IITM reflects the non-uniformity of the solutions at the micro scale, i.e., the distribution widens above the entanglement concentrations of the polymer or viscoelastic worm-like micellar solutions.

Colloidal Probes of PNIPAM-Grafted SiO2 in Studying the Microrheology of Thermally Sensitive Microgel Suspensions

The complex rheology and the phase behavior of thermally sensitive poly(N-isopropylacrylamide) (PNIPAM) microgels have been investigated in both the swollen and collapsed states by using microrheology. To avoid the interactions between the tracer probes and the PNIPAM microgels, such as the adsorption or the depletion effect, the probes of silica (SiO2) particles have been grafted with PNIPAM chains (SiO2-PNIPAM) and characterized with Fourier transform infrared spectroscopy (FTIR). The successful preparation of SiO2-PNIPAM has also been proved by the investigation of the particle size and morphology with dynamic light scattering (DLS) and transmission electron microscope (TEM) below and beyond the phase transition temperature of PNIPAM. The microrheology of the PNIPAM microgel suspension has been investigated by using the prepared SiO2-PNIPAM particles as microrheological probes, and the results show that the diffusive coefficient of the probes in the swollen state is one-fifth of that in the collapsed state, and the viscosity of the PNIPAM microgel suspension in the swollen state is four times higher than that in the collapsed state, indicating SiO2-PNIPAM is a good probe in the microrheological study of PNIPAM microgel suspensions.

Single-shot phase-sensitive wideband active microrheology of viscoelastic fluids using pulse-scanned optical tweezers

We present a fast phase sensitive active microrheology technique exploring the phase response of a microscopic probe particle trapped in a linear viscoelastic fluid using optical tweezers under an external perturbation. Thus, we experimentally determine the cumulative response of the probe to an entire repertoire of sinusoidal excitations simultaneously by applying a spatial square pulse as an excitation to the trapped probe. The square pulse naturally contains the fundamental sinusoidal frequency component and higher odd harmonics, so that we measure the phase response of the probe over a wide frequency band in a single shot, with the band being tunable over the spectrum by choosing suitable experimental parameters. We then determine the responses to individual harmonics using a lock-in algorithm, and compare the phase shifts to those obtained theoretically by solving the equation of motion of the probe particle confined in a harmonic potential in the fluid in the presence of a sinusoidal perturbation. We go on to relate the phase response of the probe to the complex shear modulus [Formula: see text], and proceed to verify our technique in a mixture of polyacrylamide and water, which we compare with known values in literature and obtain very good agreement. Our method increases the robustness of active microrheology in general and ensures that any drifts in time are almost entirely ruled out from the data, with the added advantage of high speed and ease of use.

A quantitative analysis of memory effects in the viscously coupled dynamics of optically trapped Brownian particles

We provide a quantitative description of the memory effects existing in the apparently random Markovian dynamics of a pair of optically trapped colloidal microparticles in water. The particles are trapped in very close proximity to each other such that the resultant hydrodynamic interactions lead to non-Markovian signatures manifested by the double exponential auto-correlation function for the Brownian motion of each particle. In connection with the memory effects, we quantify the storage of energy in terms of various system parameters and demonstrate that a pair of Markovian particles - confined in individual optical traps in a viscous fluid - can be described in the framework of a single Brownian particle in a viscoelastic medium. We define and quantify the equivalent storage and loss moduli of the two-particle system, and show experimentally that the memory effects are maximized at a certain trap stiffness ratio, and reduce with increasing particle separation. The technique can be generally used to determine the effective viscoelastic parameters of any such fluid-particle systems, and can thus help understand the interactions between active particles mediated by simple or complex fluids.

Dynamics of hydrodynamically coupled Brownian harmonic oscillators in a Maxwell fluid

It has been shown recently that the coupled dynamics of micro-particles in a viscous fluid has many interesting aspects including motional resonance which can be used to perform two-point micro-rheology. However, it is expected that this phenomenon in a viscoelastic fluid is much more interesting due to the presence of the additional frequency-dependent elasticity of the medium. Thus, a theory describing the equilibrium dynamics of two hydrodynamically coupled Brownian harmonic oscillators in a viscoelastic Maxwell fluid has been derived which appears with new and impressive characteristics. Initially, the response functions have been calculated and then the fluctuation-dissipation theorem has been used to calculate the correlation functions between the coloured noises present on the concerned particles placed in a Maxwell fluid due to the thermal motions of the fluid molecules. These correlation functions appear to be in a linear relationship with the delta-correlated noises in a viscous fluid. Consequently, this reduces the statistical description of a simple viscoelastic fluid to the statistical representation for an extended dynamical system subjected to delta-correlated random forces. Thereupon, the auto and cross-correlation functions in the time domain and frequency domain and the mean-square displacement functions of the particles have been calculated which are perfectly consistent with their corresponding established forms in a viscous fluid and emerge with exceptional features.

Synergistic Interactions Between DNA and Actin Trigger Emergent Viscoelastic Behavior

Composites of flexible and rigid polymers are ubiquitous in biology and industry alike, yet the physical principles determining their mechanical properties are far from understood. Here, we couple force spectroscopy with large-scale Brownian dynamics simulations to elucidate the unique viscoelastic properties of custom-engineered blends of entangled flexible DNA molecules and semiflexible actin filaments. We show that composites exhibit enhanced stress stiffening and prolonged mechanomemory compared to systems of actin or DNA alone, and that these nonlinear features display a surprising nonmonotonic dependence on the fraction of actin in the composite. Simulations reveal that these counterintuitive results arise from synergistic microscale interactions between the two biopolymers. Namely, DNA entropically drives actin filaments to form bundles that stiffen the network but reduce the entanglement density, while a uniform well-connected actin network is required to reinforce the DNA network against yielding and flow. The competition between bundling and connectivity triggers an unexpected stress response that leads equal mass DNA-actin composites to exhibit the most pronounced stress stiffening and the most long-lived entanglements.

Comment on "A symmetrical method to obtain shear moduli from microrheology" by K. Nishi, M. L. Kilfoil, C. F. Schmidt, and F. C. MacKintosh, Soft Matter, 2018, 14, 3716

Nishi et al. have presented a new analytical method for transforming the time-dependent materials' compliance into their frequency-dependent complex shear modulus, without the need of a preconceived fitting function nor the use of Kramers-Kronig transformations. They claim that their method significantly improves the accuracy of the outcomes, especially at high frequencies, up to "almost" the Nyquist frequency. Here, I corroborate that their method is actually able to provide a close estimation of the materials' complex shear modulus over the 'entire' range of explored frequencies (i.e. beyond the Nyquist frequency), as long as the compliance values are linearly spaced in the time-domain and its value at time zero is included as the first data point in the input file. Moreover, as a means of comparison, I employ the analytical method introduced by Tassieri et al. [New J. Phys., 2012, 14, 115032] for performing the Fourier transform of any generic time-dependent function that vanishes for negative times, is sampled at a finite rate, need not be equally spaced and extends over a finite time window. This existing method does not need preconceived fitting functions nor the use of Kramers-Kronig transformations; yet it shows a higher degree of accuracy compared to the one proposed by Nishi et al.

Free and confined Brownian motion in viscoelastic Stokes-Oldroyd B fluids

We linearize the Stokes-Oldroyd B model for small perturbations and instantaneous hydrodynamic friction to simulate the environment for a free and confined Brownian particle. We use the standard Green's function approach to determine the viscoelasticity, and show that the expression obtained for the frequency dependent viscosity is similar to that given by the Jeffrey's model, though the latter describes viscoelasticity by the bulk storage and loss moduli that is represented by a complex elastic modulus [Formula: see text] of the fluid concerned. In contrast, we consider the characteristics of the polymer chains and the Newtonian solvent of the complex fluid individually, and determine an expression for frequency-dependent viscosity that would be useful for microrheology performed from Brownian trajectories measured in experiments. Finally, we evaluate the trajectory of a free Brownian particle in a viscoelastic environment using our formalism, and calculate various important parameters quantifying Brownian dynamics, which we then extend to the particle confined in a harmonic potential as provided by optical tweezers.

Two-point active microrheology in a viscous medium exploiting a motional resonance excited in dual-trap optical tweezers

Two-point microrheology measurements from widely separated colloidal particles approach the bulk viscosity of the host medium more reliably than corresponding single-point measurements. In addition, active microrheology offers the advantage of enhanced signal to noise over passive techniques. Recently, we reported the observation of a motional resonance induced in a probe particle in dual-trap optical tweezers when the control particle was driven externally [Paul et al., Phys. Rev. E 96, 050102(R) (2017)2470-004510.1103/PhysRevE.96.050102]. We now demonstrate that the amplitude and phase characteristics of the motional resonance can be used as a sensitive tool for active two-point microrheology to measure the viscosity of a viscous fluid. Thus, we measure the viscosity of viscous liquids from both the amplitude and phase response of the resonance, and demonstrate that the zero crossing of the phase response of the probe particle with respect to the external drive is superior compared to the amplitude response in measuring viscosity at large particle separations. We compare our viscosity measurements with those using a commercial rheometer and obtain an agreement ∼1%. The method can be extended to viscoelastic material where the frequency dependence of the resonance may provide further accuracy for active microrheological measurements.

Active microrheology determines scale-dependent material properties of Chaetopterus mucus

We characterize the lengthscale-dependent rheological properties of mucus from the ubiquitous Chaetopterus marine worm. We use optically trapped probes (2-10 μm) to induce microscopic strains and measure the stress response as a function of oscillation amplitude. Our results show that viscoelastic properties are highly dependent on strain scale (l), indicating three distinct lengthscale-dependent regimes at l1 ≤4 μm, l2≈4-10 μm, and l3≥10 μm. While mucus response is similar to water for l1, suggesting that probes rarely contact the mucus mesh, the response for l2 is distinctly more viscous and independent of probe size, indicative of continuum mechanics. Only for l3 does the response match the macroscopic elasticity, likely due to additional stiffer constraints that strongly resist probe displacement. Our results suggest that, rather than a single lengthscale governing crossover from viscous to elastic, mucus responds as a hierarchical network with a loose biopolymer mesh coupled to a larger scaffold responsible for macroscopic gel-like mechanics.

Active rotational and translational microrheology beyond the linear spring regime

Active particle tracking microrheometers have the potential to perform accurate broadband measurements of viscoelasticity within microscopic systems. Generally, their largest possible precision is limited by Brownian motion and low frequency changes to the system. The signal to noise ratio is usually improved by increasing the size of the driven motion compared to the Brownian as well as averaging over repeated measurements. New theory is presented here whereby error in measurements of the complex shear modulus can be significantly reduced by analyzing the motion of a spherical particle driven by nonlinear forces. In some scenarios error can be further reduced by applying a variable transformation which linearizes the equation of motion. This enables normalization that eliminates error introduced by low frequency drift in the particle's equilibrium position. Our measurements indicate that this can further resolve an additional decade of viscoelasticity at high frequencies. Using this method will easily increase the signal strength enough to significantly reduce the measurement time for the same error. Thus the method is more conducive to measuring viscoelasticity in slowly changing microscopic systems, such as a living cell.

Integrated Optofluidic Chip for Low-Volume Fluid Viscosity Measurement

In the present work, an integrated optofluidic chip for fluid viscosity measurements in the range from 1 mPa·s to 100 mPa·s is proposed. The device allows the use of small sample volumes (<1 µL) and the measurement of viscosity as a function of temperature. Thanks to the precise control of the force exerted on dielectric spheres by optical beams, the viscosity of fluids is assessed by comparing the experimentally observed movement of dielectric beads produced by the optical forces with that expected by numerical calculations. The chip and the developed technique are validated by analyzing several fluids, such as Milli-Q water, ethanol and water–glycerol mixtures. The results show a good agreement between the experimental values and those reported in the literature. The extremely reduced volume of the sample required and the high flexibility of this technique make it a good candidate for measuring a wide range of viscosity values as well as for the analysis of nonlinear viscosity in complex fluids.

In situ calibration of position detection in an optical trap for active microrheology in viscous materials

In optical trapping, accurate determination of forces requires calibration of the position sensitivity relating displacements to the detector readout via the V-nm conversion factor (β). Inaccuracies in measured trap stiffness (k) and dependent calculations of forces and material properties occur if β is assumed to be constant in optically heterogeneous materials such as tissue, necessitating calibration at each probe. For solid-like samples in which probes are securely positioned, calibration can be achieved by moving the sample with a nanopositioning stage and stepping the probe through the detection beam. However, this method may be applied to samples only under select circumstances. Here, we introduce a simple method to find β in any material by steering the detection laser beam while the probe is trapped. We demonstrate the approach in the yolk of living Danio rerio (zebrafish) embryos and measure the viscoelastic properties over an order of magnitude of stress-strain amplitude.

Relevance of interfacial viscoelasticity in stability and conformation of biomolecular organizates at air/fluid interface

Soft materials are complex macromolecular systems often exhibiting perplexing non-Newtonian viscoelastic properties, especially when the macromolecules are entangled, crowded or cross-linked. These materials are ubiquitous in the biology, food and pharma industry and have several applications in biotechnology and in the field of biosensors. Based on the length scales, topologies, flexibility and concentration, the systems behave both as liquids (viscous) and solids (elastic). Particularly, for proteins and protein-lipid systems, viscoelasticity is an important parameter because it often relates directly to stability and thermodynamic interactions of the pure biological components as well as their mixtures. Despite the large body of work that is available in solution macro-rheometry, there are still a number of issues that need to be addressed in dealing with proteins at air/fluid interfaces and with protein-polymer or protein-lipid interfaces that often exhibit very low interfacial viscosity values. Considering the important applications that they have in biopharmaceutical, biotechnological and nutraceutical industries, there is a need for developing methods that meet the following three specific issues: small volume, large dynamic range of shear rates and interfacial properties of different biomolecules. Further, the techniques that are developed should include Newtonian, shear thinning and yielding properties, which are representative of the different solution behaviors typically encountered. The review presented here is a comprehensive account of the rheological properties of different biomolecules at air/fluid and solid/fluid interfaces. It addresses the usefulness of 'viscoelasticity' of the systems at the interfaces analyzed at the molecular level that can be correlated with the microscopic material properties and touches upon some recent techniques in microrheology that are being used to measure the unusually low viscosity values sensitively.

Advances in the microrheology of complex fluids

New developments in the microrheology of complex fluids are considered. Firstly the requirements for a simple modern particle tracking microrheology experiment are introduced, the error analysis methods associated with it and the mathematical techniques required to calculate the linear viscoelasticity. Progress in microrheology instrumentation is then described with respect to detectors, light sources, colloidal probes, magnetic tweezers, optical tweezers, diffusing wave spectroscopy, optical coherence tomography, fluorescence correlation spectroscopy, elastic- and quasi-elastic scattering techniques, 3D tracking, single molecule methods, modern microscopy methods and microfluidics. New theoretical techniques are also reviewed such as Bayesian analysis, oversampling, inversion techniques, alternative statistical tools for tracks (angular correlations, first passage probabilities, the kurtosis, motor protein step segmentation etc), issues in micro/macro rheological agreement and two particle methodologies. Applications where microrheology has begun to make some impact are also considered including semi-flexible polymers, gels, microorganism biofilms, intracellular methods, high frequency viscoelasticity, comb polymers, active motile fluids, blood clots, colloids, granular materials, polymers, liquid crystals and foods. Two large emergent areas of microrheology, non-linear microrheology and surface microrheology are also discussed.

Simple method to measure and analyze the fluctuations of a small particle in biopolymer solutions

We developed a simple method to investigate the motion of a small particle in biopolymer solutions. Using optical tweezers with low stiffness, a trapped probe particle fluctuates widely for a long time along the light axis, which reflects the rheological properties of the surrounding environment. We present a convenient technique for three-dimensional position tracking and the analysis focused on the distribution of particle positions and its variance in a given time interval. It allows us to obtain useful information about the dynamics of a small particle in a wide range from a free diffusive motion to a constrained motion with statistical significance. We applied this method to investigate the dynamics in collagen and DNA solutions; it was found that a collagen solution behaves as a simple viscous liquid and a DNA solution has apparent elasticity due to the slow relaxation of the configuration of molecules.

Linear microrheology with optical tweezers of living cells 'is not an option'!

Optical tweezers have been successfully adopted as exceptionally sensitive transducers for microrheology studies of complex fluids. Despite the general trend, in this article I explain why a similar approach should not be adopted for microrheology studies of living cells. This conclusion is acheived on the basis of statistical mechanics principles that indicate the unsuitability of optical tweezers for such purpose.

Microrheology with optical tweezers: measuring the relative viscosity of solutions 'at a glance'

We present a straightforward method for measuring the relative viscosity of fluids via a simple graphical analysis of the normalised position autocorrelation function of an optically trapped bead, without the need of embarking on laborious calculations. The advantages of the proposed microrheology method are evident when it is adopted for measurements of materials whose availability is limited, such as those involved in biological studies. The method has been validated by direct comparison with conventional bulk rheology methods, and has been applied both to characterise synthetic linear polyelectrolytes solutions and to study biomedical samples.

Nonlinear microrheology reveals entanglement-driven molecular-level viscoelasticity of concentrated DNA

We optically drive a trapped microscale probe through entangled DNA at rates up to 100× the disentanglement rate (Wi≈100), then remove the trap and track subsequent probe recoil motion. We identify a unique crossover to the nonlinear regime at Wi≈20. Recoil dynamics display rate-dependent dilation and complex power-law healing of the reptation tube. The force response during strain exhibits key nonlinear features such as shear thinning and yielding with power-law rate dependence. Our results, distinctly nonclassical and in accord with recent theoretical predictions, reveal molecular dynamics governed by individual stress-dependent entanglements rather than chain stretching.

Using optical tweezers for the characterization of polyelectrolyte solutions with very low viscoelasticity

Recently, optical tweezing has been used to provide a method for microrheology addressed to measure the rheological properties of small volumes of samples. In this work, we corroborate this emerging field of microrheology by using these optical methods for the characterization of polyelectrolyte solutions with very low viscoelasticity. The influence of polyelectrolyte (i.e., polyacrylamide, PAM) concentration, specifically its aging, of the salt concentration is shown. The close agreement of the technique with classical bulk rheological measurements is demonstrated, illustrating the advantages of the technique.

Optical trapping at gigapascal pressures

Diamond anvil cells allow the behavior of materials to be studied at pressures up to hundreds of gigapascals in a small and convenient instrument. However, physical access to the sample is impossible once it is pressurized. We show that optical tweezers can be used to hold and manipulate particles in such a cell, confining micron-sized transparent beads in the focus of a laser beam. Here, we use a modified optical tweezers geometry, allowing us to trap through an objective lens with a higher working distance, overcoming the constraints imposed by the limited angular acceptance of the anvil cell. We demonstrate the effectiveness of the technique by measuring water's viscosity at pressures of up to 1.3 GPa. In contrast to previous viscosity measurements in anvil cells, our technique measures absolute viscosity and does not require scaling to the accepted value at atmospheric pressure. This method could also measure the frequency dependence of viscosity as well as being sensitive to anisotropy in the medium's viscosity.

Optical trapping and binding

The phenomenon of light's momentum was first observed in the laboratory at the beginning of the twentieth century, and its potential for manipulating microscopic particles was demonstrated by Ashkin some 70 years later. Since that initial demonstration, and the seminal 1986 paper where a single-beam gradient-force trap was realized, optical trapping has been exploited as both a rich example of physical phenomena and a powerful tool for sensitive measurement. This review outlines the underlying theory of optical traps, and explores many of the physical observations that have been made in such systems. These phenomena include 'optical binding', where trapped objects interact with one another through the trapping light field. We also discuss a number of the applications of 'optical tweezers' across the physical and life sciences, as well as covering some of the issues involved in constructing and using such a tool.

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.

Rheological responses of cardiac fibroblasts to mechanical stretch

Rheological characterization of cells using passive particle tracking techniques can yield substantial information regarding local cellular material properties. However, limited work has been done to establish the changes in material properties of mechanically-responsive cells that experience external stimuli. In this study, cardiac fibroblasts plated on either fibronectin or collagen were treated with cytochalasin, mechanically stretched, or both, and their trajectories and complex moduli were extracted. Results demonstrate that both solid and fluid components were altered by such treatments in a receptor-dependent manner, and that, interestingly, cells treated with cytochalasin were still capable of stiffening in response to mechanical stimuli despite gross stress fiber disruption. These results suggest that the material properties of cells are dependent on a variety of environmental cues and can provide insight into physiological and disease processes.

Acousto-optically generated potential energy landscapes: potential mapping using colloids under flow

Optical potential energy landscapes created using acousto-optical deflectors are characterized via solvent-driven colloidal particles. The full potential energy of both single optical traps and complex landscapes composed of multiple overlapping traps are determined using a simple force balance argument. The potential of a single trap is shown to be well described by a Gaussian trap with stiffness found to be consistent with those obtained by a thermal equilibrium method. We also obtain directly the depth of the well, which (as with stiffness) varies with laser power. Finally, various complex systems ranging from double-well potentials to random landscapes are generated from individually controlled optical traps. Predictions of these landscapes as a sum of single Gaussian wells are shown to be a good description of experimental results, offering the potential for fully controlled design of optical landscapes, constructed from single optical traps.

Splinelike interpolation in particle tracking microrheology

Converting time dependent creep compliance to frequency dependent complex shear modulus is an important step in analyzing the results of particle tracking microrheology. Fitting a function to the whole time range and transforming it to calculate the shear modulus is one way of solving this problem. However, the creep compliance of many samples, such as gels of biopolymers, shows different trends under different time regimes. Fitting in these regimes segmentwise results in a function which usually cannot be transformed in a closed analytical form. In general, unlike for beta and cubic splines, also the continuity of the first derivative cannot be ensured. In this paper, we present a method for using segmentwise fitting and numerical conversion, discussing interpolation for improving the transition between the fitted ranges, and propose a dynamic sampling technique to control the accuracy of the resultant complex shear modulus.

Optical shield: measuring viscosity of turbid fluids using optical tweezers

The viscosity of a fluid can be measured by tracking the motion of a suspended micron-sized particle trapped by optical tweezers. However, when the particle density is high, additional particles entering the trap compromise the tracking procedure and degrade the accuracy of the measurement. In this work we introduce an additional Laguerre-Gaussian, i.e. annular, beam surrounding the trap, acting as an optical shield to exclude contaminating particles.

Holographic optical tweezers and their relevance to lab on chip devices

During the last decade, optical tweezers have been transformed by the combined availability of spatial light modulators and the speed of low-cost computing to drive them. Holographic optical tweezers can trap and move many objects simultaneously and their compatibility with other optical techniques, particularly microscopy, means that they are highly appropriate to lab-on-chip systems to enable optical manipulation, actuation and sensing.