Active Microrheology Research Articles

Non-monotonic dynamic correlation explored via active microrheology

Abstract In the study of local and heterogeneous structures in supercooled liquids, microrheology plays a crucial role, offering a closer examination of the mechanical properties at a local level. We concentrate on active microrheology, where an external force drives a probe particle. This technique is employed in the study of a Kob–Andersen mixture, using extensive molecular dynamics simulations. Through active microrheology, we analyze the positional dependence of viscosity, observing how probe particles respond to activation velocity. Utilizing advanced stochastic analysis, we disentangle the deterministic and stochastic components of the local viscosity time series, characterizing its nonlinear and intermittent properties, which indicate heterogeneity. We construct a Langevin equation to model the dynamics of local viscosity and derive its drift and diffusion coefficients from simulation data. Additionally, we investigate the temperature-dependent variations of viscosity dynamics, unveiling their multiplicative and nonlinear nature. We elaborate on how the existence of multiplicative dynamics in viscosity results in the characteristic emergence of heterogeneity within viscosity dynamics. We derive a dynamic correlation length from local viscosity. Moreover, this correlation length shows a non-monotonic dependence on temperature with a maximum at about the Kauzmann temperature.

Direct computations of viscoelastic moduli of biomolecular condensates.

Biomolecular condensates are viscoelastic materials defined by time-dependent, sequence-specific complex shear moduli. Here, we show that viscoelastic moduli can be computed directly using a generalization of the Rouse model that leverages information regarding intra- and inter-chain contacts, which we extract from equilibrium configurations of lattice-based Metropolis Monte Carlo (MMC) simulations of phase separation. The key ingredient of the generalized Rouse model is a graph Laplacian that we compute from equilibrium MMC simulations. We compute two flavors of graph Laplacians, one based on a single-chain graph that accounts only for intra-chain contacts, and the other referred to as a collective graph that accounts for inter-chain interactions. Calculations based on the single-chain graph systematically overestimate the storage and loss moduli, whereas calculations based on the collective graph reproduce the measured moduli with greater fidelity. However, in the long time, low-frequency domain, a mixture of the two graphs proves to be most accurate. In line with the theory of Rouse and contrary to recent assertions, we find that a continuous distribution of relaxation times exists in condensates. The single crossover frequency between dominantly elastic vs dominantly viscous behaviors does not imply a single relaxation time. Instead, it is influenced by the totality of the relaxation modes. Hence, our analysis affirms that viscoelastic fluid-like condensates are best described as generalized Maxwell fluids. Finally, we show that the complex shear moduli can be used to solve an inverse problem to obtain the relaxation time spectra that underlie the dynamics within condensates. This is of practical importance given advancements in passive and active microrheology measurements of condensate viscoelasticity.

Viscoelasticity of diverse biological samples quantified by Acoustic Force Microrheology (AFMR)

In the context of soft matter and cellular mechanics, microrheology - the use of micron-sized particles to probe the frequency-dependent viscoelastic response of materials – is widely used to shed light onto the mechanics and dynamics of molecular structures. Here we present the implementation of active microrheology in an Acoustic Force Spectroscopy setup (AFMR), which combines multiplexing with the possibility of probing a wide range of forces ( ~ pN to ~nN) and frequencies (0.01–100 Hz). To demonstrate the potential of this approach, we perform active microrheology on biological samples of increasing complexity and stiffness: collagen gels, red blood cells (RBCs), and human fibroblasts, spanning a viscoelastic modulus range of five orders of magnitude. We show that AFMR can successfully quantify viscoelastic properties by probing many beads with high single-particle precision and reproducibility. Finally, we demonstrate that AFMR to map local sample heterogeneities as well as detect cellular responses to drugs.

Active microrheology of fluids with orientational order

We study the dynamics of a driven spherical colloidal particle moving in a fluid with a broken rotational symmetry. Using a nematic liquid crystal as a model, we demonstrate that when the applied force is not aligned along or perpendicular to the orientational order, the colloidal velocity does not align with the force, but forms an angle with respect to the pulling direction. This leads to blue an anisotropic hydrodynamic drag tensor which depends on the material parameters. In the case of nematic liquid crystal, we give an analytical expression and discuss the resulting implications for active microrheology experiments on fluids with broken rotational symmetry.

Activity-dependent glassy cell mechanics II: Nonthermal fluctuations under metabolic activity

The glassy cytoplasm, crowded with bio-macromolecules, is fluidized in living cells by mechanical energy derived from metabolism. Characterizing the living cytoplasm as a nonequilibrium system is crucial in elucidating the intricate mechanism that relates cell mechanics to metabolic activities. In this study, we conducted active and passive microrheology in eukaryotic cells, and quantified nonthermal fluctuations by examining the violation of the fluctuation-dissipation theorem. The power spectral density of active force generation was estimated following the Langevin theory extended to nonequilibrium systems. However, experiments performed while regulating cellular metabolic activity showed that the nonthermal displacement fluctuation, rather than the active nonthermal force, is linked to metabolism. We discuss that mechano-enzymes in living cells do not act as microscopic objects. Instead, they generate meso-scale collective fluctuations with displacements controlled by enzymatic activity. The activity induces structural relaxations in glassy cytoplasm. Even though the autocorrelation of nonthermal fluctuations is lost at long timescales due to the structural relaxations, the nonthermal displacement fluctuation remains regulated by metabolic reactions. Our results therefore demonstrate that nonthermal fluctuations serve as a valuable indicator of a cell’s metabolic activities, regardless of the presence or absence of structural relaxations.

Active and passive microrheology with large tracers in hard colloids.

The dynamics of a tracer particle in a bath of quasi-hard colloidal spheres is studied by Langevin dynamics simulations and mode coupling theory (MCT); the tracer radius is varied from equal to up to seven times larger than the bath particles radius. In the simulations, two cases are considered: freely diffusing tracer (passive microrheology) and tracer pulled with a constant force (active microrheology). Both cases are connected by linear response theory for all tracer sizes. It links both the stationary and transient regimes of the pulled tracer (for low forces) with the equilibrium correlation functions; the velocity of the pulled tracer and its displacement are obtained from the velocity auto-correlation function and the mean squared displacement, respectively. The MCT calculations give insight into the physical mechanisms: At short times, the tracer rattles in its cage of neighbours, with the frequency increasing linearly with the tracer radius asymptotically. The long-time tracer diffusion coefficient from passive microrheology, which agrees with the inverse friction coefficient from the active case, arises from the transport of transverse momentum around the tracer. It can be described with the Brinkman equation for the transverse flow field obtained in extension of MCT, but cannot be recovered from the MCT kernel coupling to densities only. The dynamics of the bath particles is also studied; for the unforced tracer the dynamics is unaffected. When the tracer is pulled, the velocity field in the bath follows the prediction of the Brinkman model, but different from the case of a Newtonian fluid.

Memory-induced oscillations of a driven particle in a dissipative correlated medium

The overdamped dynamics of a particle is in general affected by its interaction with the surrounding medium, especially out of equilibrium, and when the latter develops spatial and temporal correlations. Here we consider the case in which the medium is modeled by a scalar Gaussian field with relaxational dynamics, and the particle is dragged at constant velocity through the medium by a moving harmonic trap. This mimics the setting of an active microrheology experiment conducted in a near-critical medium. When the particle is displaced from its average position in the nonequilibrium steady state, its subsequent relaxation is shown to feature damped oscillations. This is similar to what has been recently predicted and observed in viscoelastic fluids, but differs from what happens in the absence of driving or for an overdamped Markovian dynamics, in which cases oscillations cannot occur. We characterize these oscillating modes in terms of the parameters of the underlying mesoscopic model for the particle and the medium, confirming our analytical predictions via numerical simulations.

Insight into the Viscoelasticity of Self-Assembling Smectic Liquid Crystals of Colloidal Rods from Active Microrheology Simulations.

The rheology of colloidal suspensions is of utmost importance in a wide variety of interdisciplinary applications in formulation technology, determining equally interesting questions in fundamental science. This is especially intriguing when colloids exhibit a degree of long-range positional or orientational ordering, as in liquid crystals (LCs) of elongated particles. Along with standard methods, microrheology (MR) has emerged in recent years as a tool to assess the mechanical properties of materials at the microscopic level. In particular, by active MR one can infer the viscoelastic response of a soft material from the dynamics of a tracer particle being dragged through it by external forces. Although considerable efforts have been made to study the diffusion of guest particles in LCs, little is known about the combined effect of tracer size and directionality of the dragging force on the system's viscoelastic response. By dynamic Monte Carlo simulations, we apply active MR to investigate the viscoelasticity of self-assembling smectic (Sm) LCs consisting of rodlike particles. In particular, we track the motion of a spherical tracer whose size is varied within a range of values matching the system's characteristic length scales and being dragged by constant forces that are parallel, perpendicular, or at 45° to the nematic director. Our results reveal a uniform value of the effective friction coefficient as probed by the tracer at small and large forces, whereas a nonlinear, force-thinning regime is observed at intermediate forces. However, at relatively weak forces the effective friction is strongly determined by correlations between the tracer size and the structure of the host fluid. Moreover, we also show that external forces forming an angle with the nematic director provide additional details that cannot be simply inferred from the mere analysis of parallel and perpendicular forces. Our results highlight the fundamental interplay between tracer size and force direction in assessing the MR of Sm LC fluids.

Activity-dependent glassy cell mechanics Ⅰ: Mechanical properties measured with active microrheology

Active microrheology was conducted in living cells by applying an optical-trapping force to vigorously fluctuating tracer beads with feedback-tracking technology. The complex shear modulus G(ω)=G′(ω)−iG″(ω) was measured in HeLa cells in an epithelial-like confluent monolayer. We found that G(ω)∝(−iω)1/2 over a wide range of frequencies (1 Hz < ω/2π < 10 kHz). Actin disruption and cell-cycle progression from G1 to S and G2 phases only had a limited effect on G(ω) in living cells. On the other hand, G(ω) was found to be dependent on cell metabolism; ATP-depleted cells showed an increased elastic modulus G′(ω) at low frequencies, giving rise to a constant plateau such that G(ω)=G0+A(−iω)1/2. Both the plateau and the additional frequency dependency ∝(−iω)1/2 of ATP-depleted cells are consistent with a rheological response typical of colloidal jamming. On the other hand, the plateau G0 disappeared in ordinary metabolically active cells, implying that living cells fluidize their internal states such that they approach the critical jamming point.

Experimental Realization of a Colloidal Ratchet Effect in a non-Newtonian Fluid

The transport of matter via a ratchet effect represents a convenient way to extract useful work from a thermodynamic system, and can have direct applications in several microscale fluid-based technologies. Most realizations so far have been centered on using Newtonian fluids. This study shows how to achieve directed transport of magnetic microparticles in a non-Newtonian shear-thinning fluid under a square-wave magnetic force. This technique could be used in active microrheology, to infer the nonlinear properties of viscoelastic media.

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.

Adiabatic limit collapse and local interaction effects in non-linear active microrheology molecular simulations of two-dimensional fluids.

Nonlinear active microrheology molecular dynamics simulations of high-density two-dimensional fluids show that the presence of strong confining forces and an external pulling force induces a correlation between the velocity and position dynamics of the tracer particle. This correlation manifests in the form of an effective temperature and an effective mobility of the tracer particle, which is responsible for the breaking of the equilibrium fluctuation-dissipation theorem. This fact is shown by measuring the tracer particle's temperature and mobility directly from the first two moments of the velocity distribution of a tracer particle and by formulating a diffusion theory in which effective thermal and transport properties are decoupled from the velocity dynamics. Furthermore, the flexibility of the attractive and repulsive forces in the tested interaction potentials allowed us to relate the temperature and mobility behaviors to the nature of the interactions and the structure of the surrounding fluid as a function of the pulling force. These results provide a refreshing physical interpretation of the phenomena observed in non-linear active microrheology.

Two dominant timescales of cytoskeletal crosslinking in the viscoelastic response of the cytoplasm

Cells precisely regulate their frequency-dependent viscoelastic properties in response to chemical and mechanical cues. We use optical trap-based active microrheology using intracellular probes to measure the cytoplasmic mechanical response of fibroblast and macrophage cells over a broad frequency range ($\ensuremath{\sim}0.02--350$ Hz). Both cell types show similar frequency-dependent behavior, suggesting that the mechanisms that control the cell's mechanical response are general to many cell types. At frequencies above 1 Hz, the cytoplasmic mechanical behavior shows a broad distribution of relaxation timescales consistent with power-law mechanics. At low frequencies ($&lt;1$ Hz), cells exhibit fluidlike behavior with distinct relaxation timescales, similar to that observed in reconstituted networks of transiently crosslinked actin filaments. The response across all frequencies can be captured by a mathematical model combining a power-law term with two crosslinker-unbinding terms. The two unbinding rates required to describe the low-frequency response suggest that the viscoelastic relaxation of the cytoplasm is governed either by multiple dominant crosslinkers or by a single crosslinker with multiple states.

Microrheological properties and local structure of ι-carrageenan gels probed by using optical tweezers

Iota carrageenan (IC) is one of the most important gelling carrageenans in food and biotechnological applications; however, some of its potential applications have been constrained by its weak gelation ability. In order to better understand the origin of the weak mechanical response of IC gels, the hierarchical network structure based on meso- and microrheological properties of IC gels at 20 °C were probed via passive and active microrheology both performed by using optical tweezers (OT). Passive microrheology captures a wide spectral content of IC viscoelastic properties, revealing a rubbery plateau of the elastic modulus at relatively high frequencies for all IC concentrations; thus, uncovering the dynamics of the network. Moreover, different microstructures of IC gels were inferred by analyzing the concentration-dependent stress response when applying large deformation to the network. At low IC concentration, yielding was observed as indicated by the stress-independent response vs. strain, implying the structural rearrangement and disentanglement. As the IC concentration increased, the yielding diminished with increasing strain rate due to increased entanglement density, which limits the rearrangement of clusters. Therefore, this study presents novel insights into the meso- and microscale properties of IC gels that otherwise would not be accessible by conventional bulk rheology and submicroscopic probe diffusion measurements.

Local Yield and Compliance in Active Cell Monolayers.

The rheology of biological tissue plays an important role in many processes, from organ formation to cancer invasion. Here, we use a multiphase field model of motile cells to simulate active microrheology within a tissue monolayer. When unperturbed, the tissue exhibits a transition between a solidlike state and a fluidlike state tuned by cell motility and deformability-the ratio of the energetic costs of steric cell-cell repulsion and cell-edge tension. When perturbed, solid tissues exhibit local yield-stress behavior, with a threshold force for the onset of motion of a probe particle that vanishes upon approaching the solid-to-liquid transition. This onset of motion is qualitatively different in the low and high deformability regimes. At high deformability, the tissue is amorphous when solid, it responds compliantly to deformations, and the probe transition to motion is smooth. At low deformability, the monolayer is more ordered translationally and stiffer, and the onset of motion appears discontinuous. Our results suggest that cellular or nanoparticle transport in different types of tissues can be fundamentally different and point to ways in which it can be controlled.

Active microrheology of colloidal suspensions of hard cuboids.

By performing dynamic Monte Carlo simulations, we investigate the microrheology of isotropic suspensions of hard-core colloidal cuboids. In particular, we infer the local viscoelastic behavior of these fluids by studying the dynamics of a probe spherical particle that is incorporated in the host phase and is dragged by an external force. This technique, known as active microrheology, allows one to characterize the microscopic response of soft materials upon application of a constant force, whose intensity spans here three orders of magnitude. By tuning the geometry of cuboids from oblate to prolate as well as the system density, we observe different responses that are quantified by measuring the effective friction perceived by the probe particle. The resulting friction coefficient exhibits a linear regime at forces that are much weaker and larger than the thermal forces, whereas a nonlinear, force-thinning regime is observed at intermediate force intensities.

A compact rotary magnetic tweezers device for dynamic material analysis.

Here we present a new, compact magnetic tweezers design that enables precise application of a wide range of dynamic forces to soft materials without the need to raise or lower the magnet height above the sample. This is achieved through the controlled rotation of the permanent magnet array with respect to the fixed symmetry axis defined by a custom-built iron yoke. These design improvements increase the portability of the device and can be implemented within existing microscope setups without the need for extensive modification of the sample holders or light path. This device is particularly well-suited to active microrheology measurements using either creep analysis, in which a step force is applied to a micron-sized magnetic particle that is embedded in a complex fluid, or oscillatory microrheology, in which the particle is driven with a periodic waveform of controlled amplitude and frequency. In both cases, the motions of the particle are measured and analyzed to determine the local dynamic mechanical properties of the material.

Cell mediated remodeling of stiffness matched collagen and fibrin scaffolds

Cells are known to continuously remodel their local extracellular matrix (ECM) and in a reciprocal way, they can also respond to mechanical and biochemical properties of their fibrous environment. In this study, we measured how stiffness around dermal fibroblasts (DFs) and human fibrosarcoma HT1080 cells differs with concentration of rat tail type 1 collagen (T1C) and type of ECM. Peri-cellular stiffness was probed in four directions using multi-axes optical tweezers active microrheology (AMR). First, we found that neither cell type significantly altered local stiffness landscape at different concentrations of T1C. Next, rat tail T1C, bovine skin T1C and fibrin cell-free hydrogels were polymerized at concentrations formulated to match median stiffness value. Each of these hydrogels exhibited distinct fiber architecture. Stiffness landscape and fibronectin secretion, but not nuclear/cytoplasmic YAP ratio differed with ECM type. Further, cell response to Y27632 or BB94 treatments, inhibiting cell contractility and activity of matrix metalloproteinases, respectively, was also dependent on ECM type. Given differential effect of tested ECMs on peri-cellular stiffness landscape, treatment effect and cell properties, this study underscores the need for peri-cellular and not bulk stiffness measurements in studies on cellular mechanotransduction.

Passive and Active Microrheology for Biomedical Systems.

Microrheology encompasses a range of methods to measure the mechanical properties of soft materials. By characterizing the motion of embedded microscopic particles, microrheology extends the probing length scale and frequency range of conventional bulk rheology. Microrheology can be characterized into either passive or active methods based on the driving force exerted on probe particles. Tracer particles are driven by thermal energy in passive methods, applying minimal deformation to the assessed medium. In active techniques, particles are manipulated by an external force, most commonly produced through optical and magnetic fields. Small-scale rheology holds significant advantages over conventional bulk rheology, such as eliminating the need for large sample sizes, the ability to probe fragile materials non-destructively, and a wider probing frequency range. More importantly, some microrheological techniques can obtain spatiotemporal information of local microenvironments and accurately describe the heterogeneity of structurally complex fluids. Recently, there has been significant growth in using these minimally invasive techniques to investigate a wide range of biomedical systems both in vitro and in vivo. Here, we review the latest applications and advancements of microrheology in mammalian cells, tissues, and biofluids and discuss the current challenges and potential future advances on the horizon.

Sol-gel transition induced by alumina nanoparticles in a model pulmonary surfactant

Inhaled airborne particles smaller than 100 nm entering the airways have been shown to deposit in significant amount in the alveolar region of the lungs. The interior of the alveoli is covered with a ~ 1 µm thick lining fluid, called pulmonary surfactant. Inhaled nanoparticles are susceptible to interact with the lung fluid and modify pulmonary functions. Here we evaluate the structural and rheological properties of the pulmonary surfactant substitute Curosurf® which is administered to premature babies for the treatment of respiratory distress syndrome. Curosurf® is considered a reliable model of endogenous pulmonary surfactant in terms of composition, structure and function. Using active microrheology based on magnetically actuated wires, we find that Curosurf® dispersions exhibit a Newtonian behavior at lipid concentration from 0 to 80 g L−1, and that the viscosity follows the Krieger-Dougherty law observed for a wide variety of colloids. Upon addition of 40 nm alumina nanoplatelets, a significant change of the Curosurf® rheology is noticed. The dispersions then enter a soft solid phase characterized by an infinite viscosity and a non-zero equilibrium elastic modulus. The sol-gel transition induced by the nanoparticles is interpreted as the result of the alumina/vesicle interaction, which are illustrated by transmission electron microscopy. It also suggests a potential toxicity associated with the modification of the lung fluid structural and dynamical properties.