Local measurements of viscoelastic moduli of entangled actin networks using an oscillating magnetic bead micro-rheometer

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.

Modelling the rheology of living cell cytoplasm: poroviscoelasticity and fluid-to-solid transition

Eukaryotic cell rheology has important consequences for vital processes such as adhesion, migration, and differentiation. Experiments indicate that cell cytoplasm can exhibit both elastic and viscous characteristics in different regimes, while the transport of fluid (cytosol) through the cross-linked filamentous scaffold (cytoskeleton) is reminiscent of mass transfer by diffusion through a porous medium. To gain insights into this complex rheological behaviour, we construct a computational model for the cell cytoplasm as a poroviscoelastic material formulated on the principles of nonlinear continuum mechanics, where we model the cytoplasm as a porous viscoelastic scaffold with an embedded viscous fluid flowing between the pores to model the cytosol. Baseline simulations (neglecting the viscosity of the cytosol) indicate that the system exhibits seven different regimes across the parameter space spanned by the viscoelastic relaxation timescale of the cytoskeleton and the poroelastic diffusion timescale; these regimes agree qualitatively with experimental measurements. Furthermore, the theoretical model also allows us to elucidate the additional role of pore fluid viscosity, which enters the system as a distinct viscous timescale. We show that increasing this viscous timescale hinders the passage of the pore fluid (reducing the poroelastic diffusion) and makes the cytoplasm rheology increasingly incompressible, shifting the phase boundaries between the regimes.

Extreme heterogeneity in the microrheology of lamellar surfactant gels analyzed with neural networks

The heterogeneity of the viscoelasticity of a lamellar gel network based on cetyl-trimethylammonium chloride and cetostearyl alcohol was studied using particle-tracking microrheology. A recurrent neural network (RNN) architecture was used for estimating the Hurst exponent, H, on small sections of tracks of probe spheres moving with fractional Brownian motion. Thus, dynamic segmentation of tracks via neural networks was used in microrheology and it is significantly more accurate than using mean square displacements (MSDs). An ensemble of 414 particles produces a MSD that is subdiffusive in time, t, with a power law of the form t^{0.74±0.02}, indicating power law viscoelasticity. RNN analysis of the probability distributions of H, combined with detailed analysis of the time-averaged MSDs of individual tracks, revealed diverse diffusion processes belied by the simple scaling of the ensemble MSD, such as caging phenomena, which give rise to the complex viscoelasticity of lamellar gels.

Peroxidase-mediated mucin cross-linking drives pathologic mucus gel formation in IL-13-stimulated airway epithelial cells

Mucus plugs occlude airways to obstruct airflow in asthma. Studies in patients and in mouse models show that mucus plugs occur in the context of type 2 inflammation, and studies in human airway epithelial cells (HAECs) show that IL-13-activated cells generate pathologic mucus independently of immune cells. To determine how HAECs autonomously generate pathologic mucus, we used a magnetic microwire rheometer to characterize the viscoelastic properties of mucus secreted under varying conditions. We found that normal HAEC mucus exhibited viscoelastic liquid behavior and that mucus secreted by IL-13-activated HAECs exhibited solid-like behavior caused by mucin cross-linking. In addition, IL-13-activated HAECs shows increased peroxidase activity in apical secretions, and an overlaid thiolated polymer (thiomer) solution shows an increase in solid behavior that was prevented by peroxidase inhibition. Furthermore, gene expression for thyroid peroxidase (TPO), but not lactoperoxidase (LPO), was increased in IL-13-activated HAECs and both TPO and LPO catalyze the formation of oxidant acids that cross-link thiomer solutions. Finally, gene expression for TPO in airway epithelial brushings was increased in patients with asthma with high airway mucus plug scores. Together, our results show that IL-13-activated HAECs autonomously generated pathologic mucus via peroxidase-mediated cross-linking of mucin polymers.

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.

Indentation induces instantaneous nuclear stiffening and unfolding of nuclear envelope wrinkles

The nuclear envelope (NE) separates genomic DNA from the cytoplasm and regulates transport between the cytosol and the nucleus in eukaryotes. Nuclear stiffening enables the cell nucleus to protect itself from extensive deformation, loss of NE integrity, and genome instability. It is known that the reorganization of actin, lamin, and chromatin can contribute to nuclear stiffening. In this work, we show that structural alteration of NE also contributes to instantaneous nuclear stiffening under indentation. In situ mechanical characterization of cell nuclei in intact cells shows that nuclear stiffening and unfolding of NE wrinkles occur simultaneously at the indentation site. A positive correlation between the initial state of NE wrinkles, the unfolding of NE wrinkles, and the stiffening ratio (stiffness fold-change) is found. Additionally, NE wrinkles unfold throughout the nucleus outside the indentation site. Finite element simulation, which involves the purely passive process of structural unfolding, shows that unfolding of NE wrinkles alone can lead to an increase in nuclear stiffness and a reduction in stress and strain levels. Together, these results provide a perspective on how cell nucleus adapts to mechanical stimuli through structural alteration of the NE.

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.

Determining Thermodynamic and Material Properties of Biomolecular Condensates by Confocal Microscopy and Optical Tweezers

While the roles of biomolecular condensates in health and disease are being intensely studied, it is equally important that their physical properties are characterized in order to achieve mechanistic understanding. Here we share some of the protocols developed in our lab for measuring thermodynamic and materials properties of condensates. These include a simple method for determining the droplet-phase concentrations of condensate components on a confocal microscope, and a method for determining the viscoelasticity of condensates by optical tweezers. These protocols are either generally applicable to biomolecular condensates or are unique for their characterization.

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.

Frontiers in single cell analysis: multimodal technologies and their clinical perspectives

Single cell multimodal analysis is at the frontier of single cell research: it defines the roles and functions of distinct cell types through simultaneous analysis to provide unprecedented insight into cellular processes. Current single cell approaches are rapidly moving toward multimodal characterizations. It replaces one-dimensional single cell analysis, for example by allowing for simultaneous measurement of transcription and post-transcriptional regulation, epigenetic modifications and/or surface protein expression. By providing deeper insights into single cell processes, multimodal single cell analyses paves the way to new understandings in various cellular processes such as cell fate decisions, physiological heterogeneity or genotype-phenotype linkages. At the forefront of this, microfluidics is key for high-throughput single cell analysis. Here, we present an overview of the recent multimodal microfluidic platforms having a potential in biomedical research, with a specific focus on their potential clinical applications.

Cellular Microbiaxial Stretching Assay for Measurement and Characterization of the Anisotropic Mechanical Properties of Micropatterned Cells

Characterizing the mechanical properties of single cells is important for developing descriptive models of tissue mechanics and improving the understanding of mechanically driven cell processes. Standard methods for measuring single-cell mechanical properties typically provide isotropic mechanical descriptions. However, many cells exhibit specialized geometries in vivo, with anisotropic cytoskeletal architectures reflective of their function, and are exposed to dynamic multiaxial loads, raising the need for more complete descriptions of their anisotropic mechanical properties under complex deformations. Here, we describe the cellular microbiaxial stretching (CμBS) assay in which controlled deformations are applied to micropatterned cells while simultaneously measuring cell stress. CμBS utilizes a set of linear actuators to apply tensile or compressive, short- or long-term deformations to cells micropatterned on a fluorescent bead-doped polyacrylamide gel. Using traction force microscopy principles and the known geometry of the cell and the mechanical properties of the underlying gel, we calculate the stress within the cell to formulate stress-strain curves that can be further used to create mechanical descriptions of the cells, such as strain energy density functions. © 2022 Wiley Periodicals LLC. Basic Protocol 1: Assembly of CμBS stretching constructs Basic Protocol 2: Polymerization of micropatterned, bead-doped polyacrylamide gel on an elastomer membrane Support Protocol: Cell culture and seeding onto CμBS constructs Basic Protocol 3: Implementing CμBS stretching protocols and traction force microscopy Basic Protocol 4: Data analysis and cell stress measurements.

Biophysical Approaches for Applying and Measuring Biological Forces

Over the past decades, increasing evidence has indicated that mechanical loads can regulate the morphogenesis, proliferation, migration, and apoptosis of living cells. Investigations of how cells sense mechanical stimuli or the mechanotransduction mechanism is an active field of biomaterials and biophysics. Gaining a further understanding of mechanical regulation and depicting the mechanotransduction network inside cells require advanced experimental techniques and new theories. In this review, the fundamental principles of various experimental approaches that have been developed to characterize various types and magnitudes of forces experienced at the cellular and subcellular levels are summarized. The broad applications of these techniques are introduced with an emphasis on the difficulties in implementing these techniques in special biological systems. The advantages and disadvantages of each technique are discussed, which can guide readers to choose the most suitable technique for their questions. A perspective on future directions in this field is also provided. It is anticipated that technical advancement can be a driving force for the development of mechanobiology.

Simulations of dynamically cross-linked actin networks: Morphology, rheology, and hydrodynamic interactions

Cross-linked actin networks are the primary component of the cell cytoskeleton and have been the subject of numerous experimental and modeling studies. While these studies have demonstrated that the networks are viscoelastic materials, evolving from elastic solids on short timescales to viscous fluids on long ones, questions remain about the duration of each asymptotic regime, the role of the surrounding fluid, and the behavior of the networks on intermediate timescales. Here we perform detailed simulations of passively cross-linked non-Brownian actin networks to quantify the principal timescales involved in the elastoviscous behavior, study the role of nonlocal hydrodynamic interactions, and parameterize continuum models from discrete stochastic simulations. To do this, we extend our recent computational framework for semiflexible filament suspensions, which is based on nonlocal slender body theory, to actin networks with dynamic cross linkers and finite filament lifetime. We introduce a model where the cross linkers are elastic springs with sticky ends stochastically binding to and unbinding from the elastic filaments, which randomly turn over at a characteristic rate. We show that, depending on the parameters, the network evolves to a steady state morphology that is either an isotropic actin mesh or a mesh with embedded actin bundles. For different degrees of bundling, we numerically apply small-amplitude oscillatory shear deformation to extract three timescales from networks of hundreds of filaments and cross linkers. We analyze the dependence of these timescales, which range from the order of hundredths of a second to the actin turnover time of several seconds, on the dynamic nature of the links, solvent viscosity, and filament bending stiffness. We show that the network is mostly elastic on the short time scale, with the elasticity coming mainly from the cross links, and viscous on the long time scale, with the effective viscosity originating primarily from stretching and breaking of the cross links. We show that the influence of nonlocal hydrodynamic interactions depends on the network morphology: for homogeneous meshworks, nonlocal hydrodynamics gives only a small correction to the viscous behavior, but for bundled networks it both hinders the formation of bundles and significantly lowers the resistance to shear once bundles are formed. We use our results to construct three-timescale generalized Maxwell models of the networks.

Shear relaxation governs fusion dynamics of biomolecular condensates

Phase-separated biomolecular condensates must respond agilely to biochemical and environmental cues in performing their wide-ranging cellular functions, but our understanding of condensate dynamics is lagging. Ample evidence now indicates biomolecular condensates as viscoelastic fluids, where shear stress relaxes at a finite rate, not instantaneously as in viscous liquids. Yet the fusion dynamics of condensate droplets has only been modeled based on viscous liquids, with fusion time given by the viscocapillary ratio (viscosity over interfacial tension). Here we used optically trapped polystyrene beads to measure the viscous and elastic moduli and the interfacial tensions of four types of droplets. Our results challenge the viscocapillary model, and reveal that the relaxation of shear stress governs fusion dynamics. These findings likely have implications for other dynamic processes such as multiphase organization, assembly and disassembly, and aging.

Multi-oscillation microrheology via acoustic force spectroscopy enables frequency-dependent measurements on endothelial cells at high-throughput

Active microrheology is one of the main methods to determine the mechanical properties of cells and tissue, and the modelling of these viscoelastic properties is under heavy debate with many competing approaches. Most experimental methods of active microrheology such as optical tweezers or atomic force microscopy based approaches rely on single cell measurements, and thus suffer from a low throughput. Here, we present a novel method for frequency-dependent microrheology on cells using acoustic forces which allows multiplexed measurements of several cells in parallel. Acoustic force spectroscopy (AFS) is used to generate multi-oscillatory forces in the range of pN-nN on particles attached to primary human umbilical vein endothelial cells (HUVEC) cultivated inside a microfluidic chip. While the AFS was introduced as a single-molecule technique to measure mechanochemical properties of biomolecules, we exploit the AFS to measure the dynamic viscoelastic properties of cells exposed to different conditions, such as flow shear stresses or drug injections. By controlling the force and measuring the position of the particle, the complex shear modulus G*(ω) can be measured continuously over several hours. The resulting power-law shear moduli are consistent with fractional viscoelastic models. In our experiments we confirm a decrease in shear modulus after perturbing the actin cytoskeleton via cytochalasin B. This effect was reversible after washing out the drug. Additionally, we include critical information for the usage of the new method AFS as a measurement tool showing its capabilities and limitations and we find that for performing viscoelastic measurements with the AFS, a thorough calibration and careful data analysis is crucial, for which we provide protocols and guidelines.

Measuring the elastic modulus of soft culture surfaces and three-dimensional hydrogels using atomic force microscopy

Growing interest in exploring mechanically mediated biological phenomena has resulted in cell culture substrates and 3D matrices with variable stiffnesses becoming standard tools in biology labs. However, correlating stiffness with biological outcomes and comparing results between research groups is hampered by variability in the methods used to determine Young's (elastic) modulus, E, and by the inaccessibility of relevant mechanical engineering protocols to most biology labs. Here, we describe a protocol for measuring E of soft 2D surfaces and 3D hydrogels using atomic force microscopy (AFM) force spectroscopy. We provide instructions for preparing hydrogels with and without encapsulated live cells, and provide a method for mounting samples within the AFM. We also provide details on how to calibrate the instrument, and give step-by-step instructions for collecting force-displacement curves in both manual and automatic modes (stiffness mapping). We then provide details on how to apply either the Hertz or the Oliver-Pharr model to calculate E, and give additional instructions to aid the user in plotting data distributions and carrying out statistical analyses. We also provide instructions for inferring differential matrix remodeling activity in hydrogels containing encapsulated single cells or organoids. Our protocol is suitable for probing a range of synthetic and naturally derived polymeric hydrogels such as polyethylene glycol, polyacrylamide, hyaluronic acid, collagen, or Matrigel. Although sample preparation timings will vary, a user with introductory training to AFM will be able to use this protocol to characterize the mechanical properties of two to six soft surfaces or 3D hydrogels in a single day.

An Acoustic Platform for Single-Cell, High-Throughput Measurements of the Viscoelastic Properties of Cells

Cellular processes including adhesion, migration, and differentiation are governed by the distinct mechanical properties of each cell. Importantly, the mechanical properties of individual cells can vary depending on local physical and biochemical cues in a time-dependent manner resulting in significant inter-cell heterogeneity. While several different methods have been developed to interrogate the mechanical properties of single cells, throughput to capture this heterogeneity remains an issue. Here, single-cell, high-throughput characterization of adherent cells is demonstrated using acoustic force spectroscopy (AFS). AFS works by simultaneously, acoustically driving tens to hundreds of silica beads attached to cells away from the cell surface, allowing the user to measure the stiffness of adherent cells under multiple experimental conditions. It is shown that cells undergo marked changes in viscoelasticity as a function of temperature, by altering the temperature within the AFS microfluidic circuit between 21 and 37 °C. In addition, quantitative differences in cells exposed to different pharmacological treatments specifically targeting the membrane-cytoskeleton interface are shown. Further, the high-throughput format of the AFS is utilized to rapidly probe, in excess of 1000 cells, three different cell lines expressing different levels of a mechanosensitive protein, Piezo1, demonstrating the ability to differentiate between cells based on protein expression levels.

Rapid local compression in active gels is caused by nonlinear network response

The actin cytoskeleton in living cells generates forces in conjunction with myosin motor proteins to directly and indirectly drive essential cellular processes. The semiflexible filaments of the cytoskeleton can respond nonlinearly to the collective action of motors. We here investigate mechanics and force generation in a model actin cytoskeleton, reconstituted in vitro, by observing the response and fluctuations of embedded micron-scale probe particles. Myosin mini-filaments can be modeled as force dipoles and give rise to deformations in the surrounding network of cross-linked actin. Anomalously correlated probe fluctuations indicate the presence of rapid local compression or draining of the network that emerges in addition to the ordinary linear shear elastic (incompressible) response to force dipoles. The anomalous propagation of compression can be attributed to the nonlinear response of actin filaments to the microscopic forces, and is quantitatively consistent with motor-generated large-scale stiffening of the gels.

Cancer cells display increased migration and deformability in pace with metastatic progression

In this study, we explored the relation between metastatic states vs the capacity of confined migration, amoeboid transition, and cellular stiffness. We compared across an isogenic panel of human breast cancer cells derived from MDA-MB-231 cells. It was observed that cells after lung metastasis have the fastest migration and lowest stiffness, with a significantly higher capacity to transition into an amoeboid mode. Our findings illustrate that metastasis is a selective process favoring motile and softer cells. Moreover, the observation that circulating tumor cells resemble the parental cell line, but not lung-metastatic cells, suggests that cells with higher deformability and motility are likely selected during extravasation and colonization.

Helical nanobots as mechanical probes of intra- and extracellular environments

A rheological probe that can measure mechanical properties of biological milieu at well-defined locations with high spatial resolution, on a time scale faster than most biological processes, can further improve our understanding of how living systems operate and behave. Here, we demonstrate nanorobots actively driven in realistic ex vivo biological systems for fast mechanical measurements with high spatial accuracy. In the various demonstrations of magnetic nanobots as mechanical probes, we report the first direct observation of the internalization of probes by a living cell, the accurate measurement of the 'fluid phase' cytoplasmic viscosity of ~200 cP for a HeLa cell, demonstration of intracellular measurements in cells derived from human patients; all of which establish the strength of this novel technique for measurements in both intra- and extracellular environments.

Double power-law viscoelastic relaxation of living cells encodes motility trends

Living cells are constantly exchanging momentum with their surroundings. So far, there is no consensus regarding how cells respond to such external stimuli, although it reveals much about their internal structures, motility as well as the emergence of disorders. Here, we report that twelve cell lines, ranging from healthy fibroblasts to cancer cells, hold a ubiquitous double power-law viscoelastic relaxation compatible with the fractional Kelvin-Voigt viscoelastic model. Atomic Force Microscopy measurements in time domain were employed to determine the mechanical parameters, namely, the fast and slow relaxation exponents, the crossover timescale between power law regimes, and the cell stiffness. These cell-dependent quantities show strong correlation with their collective migration and invasiveness properties. Beyond that, the crossover timescale sets the fastest timescale for cells to perform their biological functions.

Determination of rheology and surface tension of airway surface liquid: a review of clinical relevance and measurement techniques

By airway surface liquid, we mean a thin fluid continuum consisting of the airway lining layer and the alveolar lining layer, which not only serves as a protective barrier against foreign particles but also contributes to maintaining normal respiratory mechanics. In recent years, measurements of the rheological properties of airway surface liquid have attracted considerable clinical attention due to new advances in microrheology instruments and methods. This article reviews the clinical relevance of measurements of airway surface liquid viscoelasticity and surface tension from four main aspects: maintaining the stability of the airways and alveoli, preventing ventilator-induced lung injury, optimizing surfactant replacement therapy for respiratory syndrome distress, and characterizing the barrier properties of airway mucus to improve drug and gene delivery. Primary measuring techniques and methods suitable for determining the viscoelasticity and surface tension of airway surface liquid are then introduced with respect to principles, advantages and limitations. Cone and plate viscometers and particle tracking microrheometers are the most commonly used instruments for measuring the bulk viscosity and microviscosity of airway surface liquid, respectively, and pendant drop methods are particularly suitable for the measurement of airway surface liquid surface tension in vitro. Currently, in vivo and in situ measurements of the viscoelasticity and surface tension of the airway surface liquid in humans still presents many challenges.

Role of a Kinesin Motor in Cancer Cell Mechanics

Molecular motors play important roles in force generation, migration, and intracellular trafficking. Changes in specific motor activities are altered in numerous diseases. KIF20A, a motor protein of the kinesin-6 family, is overexpressed in bladder cancer, and KIF20A levels correlate negatively with clinical outcomes. We report here a new role for the KIF20A kinesin motor protein in intracellular mechanics. Using optical tweezers to probe intracellular mechanics and surface AFM to probe cortical mechanics, we first confirm that bladder urothelial cells soften with an increasing cancer grade. We then show that inhibiting KIF20A makes the intracellular environment softer for both high- and low-grade bladder cancer cells. Upon inhibition of KIF20A, cortical stiffness also decreases in lower grade cells, while it surprisingly increases in higher grade malignant cells. Changes in cortical stiffness correlate with the interaction of KIF20A with myosin IIA. Moreover, KIF20A inhibition negatively regulates bladder cancer cell motility irrespective of the underlying substrate stiffness. Our results reveal a central role for a microtubule motor in cell mechanics and migration in the context of bladder cancer.

Microfluidic Cytometry for High-Throughput Characterization of Single Cell Cytoplasmic Viscosity Using Crossing Constriction Channels

This article presents an approach of microfluidic flow cytometry capable of continuously characterizing cytoplasmic viscosities of single cells. The microfluidic system consists of a major constriction channel and a side constriction channel perpendicularly crossing each other. Cells are forced to rapidly travel through the major channel and are partially aspirated into the side channel when passing the channel junction. Numerical simulations were conducted to model the time dependence of the aspiration length into the side channel, which enables the measurement of cytoplasmic viscosity by fitting the model results to experimental data. As a demonstration for high-throughput measurement, the cytoplasmic viscosities of HL-60 cells that were native or treated by N-Formylmethionine-leucyl-phenylalanine (fMLP) were quantified with sample sizes as large as thousands of cells. Both the average and median cytoplasmic viscosities of native HL-60 cells were found to be about 10% smaller than those of fMLP-treated HL-60 cells, consistent with previous observations that fMLP treatment can increase the rigidity of white blood cells. Furthermore, the microfluidic system was used to process granulocytes from three donors (sample size >1,000 cells for each donor). The results revealed that the cytoplasmic viscosity of granulocytes from one donor was significantly higher than the other two, which may result from the fact that this donor just recovered from an inflammation. In summary, the developed microfluidic system can collect cytoplasmic viscosities from thousands of cells and may function as an enabling tool in the field of single-cell analysis. © 2019 International Society for Advancement of Cytometry.

From isolated structures to continuous networks: A categorization of cytoskeleton-based motile engineered biological microstructures

As technology at the small scale is advancing, motile engineered microstructures are becoming useful in drug delivery, biomedicine, and lab-on-a-chip devices. However, traditional engineering methods and materials can be inefficient or functionally inadequate for small-scale applications. Increasingly, researchers are turning to the biology of the cytoskeleton, including microtubules, actin filaments, kinesins, dyneins, myosins, and associated proteins, for both inspiration and solutions. They are engineering structures with components that range from being entirely biological to being entirely synthetic mimics of biology and on scales that range from isotropic continuous networks to single isolated structures. Motile biological microstructures trace their origins from the development of assays used to study the cytoskeleton to the array of structures currently available today. We define 12 types of motile biological microstructures, based on four categories: entirely biological, modular, hybrid, and synthetic, and three scales: networks, clusters, and isolated structures. We highlight some key examples, the unique functionalities, and the potential applications of each microstructure type, and we summarize the quantitative models that enable engineering them. By categorizing the diversity of motile biological microstructures in this way, we aim to establish a framework to classify these structures, define the gaps in current research, and spur ideas to fill those gaps. This article is categorized under: Nanotechnology Approaches to Biology > Nanoscale Systems in Biology Nanotechnology Approaches to Biology > Cells at the Nanoscale Biology-Inspired Nanomaterials > Protein and Virus-Based Structures Therapeutic Approaches and Drug Discovery > Emerging Technologies.

Hierarchy of Hybrid Materials-The Place of Inorganics-in-Organics in it, Their Composition and Applications

Hybrid materials, or hybrids incorporating both organic and inorganic constituents, are emerging as a very potent and promising class of materials due to the diverse, but complementary nature of the properties inherent of these different classes of materials. The complementarity leads to a perfect synergy of properties of desired material and eventually an end-product. The diversity of resultant properties and materials used in the construction of hybrids, leads to a very broad range of application areas generated by engaging very different research communities. We provide here a general classification of hybrid materials, wherein organics-in-inorganics (inorganic materials modified by organic moieties) are distinguished from inorganics-in-organics (organic materials or matrices modified by inorganic constituents). In the former area, the surface functionalization of colloids is distinguished as a stand-alone sub-area. The latter area-functionalization of organic materials by inorganic additives-is the focus of the current review. Inorganic constituents, often in the form of small particles or structures, are made of minerals, clays, semiconductors, metals, carbons, and ceramics. They are shown to be incorporated into organic matrices, which can be distinguished as two classes: chemical and biological. Chemical organic matrices include coatings, vehicles and capsules assembled into: hydrogels, layer-by-layer assembly, polymer brushes, block co-polymers and other assemblies. Biological organic matrices encompass bio-molecules (lipids, polysaccharides, proteins and enzymes, and nucleic acids) as well as higher level organisms: cells, bacteria, and microorganisms. In addition to providing details of the above classification and analysis of the composition of hybrids, we also highlight some antagonistic yin-&-yang properties of organic and inorganic materials, review applications and provide an outlook to emerging trends.

A mesoscale study of creep in a microgel using the acoustic radiation force

We study the motion of a sphere of diameter 330 μm embedded in a Carbopol microgel under the effect of the acoustic radiation pressure exerted by a focused ultrasonic field. The sphere motion within the microgel is tracked using videomicroscopy and compared to conventional creep and recovery measurements performed with a rheometer. We find that under moderate ultrasonic intensities, the sphere creeps as a power law of time with an exponent α ≃ 0.2 that is significantly smaller than the one inferred from global creep measurements below the yield stress of the microgel (α ≃ 0.4). Moreover, the sphere relaxation motion after creep and the global recovery are respectively consistent with these two different exponents. By allowing a rheological characterization at the scale of the sphere with forces of the order of micronewtons, the present experiments pave the way for acoustic "mesorheology" which probes volumes and forces an intermediate between standard macroscopic rheology and classical microrheology. They also open new questions about the effects of the geometry of the deformation field and of the sphere size and surface properties on the creep behaviour of soft materials.

Triggered disassembly and reassembly of actin networks induces rigidity phase transitions

Non-equilibrium soft materials, such as networks of actin proteins, have been intensely investigated over the past decade due to their promise for designing smart materials and understanding cell mechanics. However, current methods are unable to measure the time-dependent mechanics of such systems or map mechanics to the corresponding dynamic macromolecular properties. Here, we present an experimental approach that combines time-resolved optical tweezers microrheology with diffusion-controlled microfluidics to measure the time-evolution of microscale mechanical properties of dynamic systems during triggered activity. We use these methods to measure the viscoelastic moduli of entangled and crosslinked actin networks during chemically-triggered depolymerization and repolymerization of actin filaments. During disassembly, we find that the moduli exhibit two distinct exponential decays, with experimental time constants of ∼169 min and ∼47 min. Conversely, during reassembly, measured moduli initially exhibit power-law increase with time, after which steady-state values are achieved. We develop toy mathematical models that couple the time-evolution of filament lengths with rigidity percolation theory to shed light onto the molecular mechanisms underlying the observed mechanical transitions. The models suggest that these two distinct behaviors both arise from phase transitions between a rigidly percolated network and a non-rigid regime. Our approach and collective results can inform the general principles underlying the mechanics of a large class of dynamic, non-equilibrium systems and materials of current interest.

Memory-based mediated interactions between rigid particulate inclusions in viscoelastic environments

Many practically relevant materials combine properties of viscous fluids and elastic solids to viscoelastic behavior. Our focus is on the induced dynamic behavior of damped finite-sized particulate inclusions in such substances. We explicitly describe history-dependent interactions that emerge between the embedded particles. These interactions are mediated by the viscoelastic surroundings. They result from the flows and distortions of the viscoelastic medium when induced by the rigid inclusions. Both viscoelastic environments of terminal fluidlike flow and of completely reversible damped elastic behavior are covered. For illustration and to highlight the role of the formalism in potential applications, we briefly address the relevant examples of dragging a rigid sphere through a viscoelastic environment together with subsequent relaxation dynamics, the switching dynamics of magnetic fillers in elastic gel matrices, and the swimming behavior of active microswimmers in viscoelastic solutions. The approach provides a basis for more quantitative and extended investigations of these and related systems in the future.

Near-surface microrheology reveals dynamics and viscoelasticity of soft matter

The development of experimental techniques able to probe the microscale viscoelastic properties of soft matter over a broad time scale is essential to uncover the physics that govern their behavior. Herein, we report the development of a microrheology technique that can determine the near-surface dynamics and viscoelastic behaviors of soft matter like polymer solution/gels and colloidal dispersions. Our approach combines a magnetic-field-induced stimulator with total internal reflection microscopy (TIRM) to apply mechanical loading (∼pN) to a micro-sized probe particle and capture its axial displacement near the surface with nano-scaled sensitivity. We demonstrate the use of this technique to measure the detachment of a colloid to a solid substrate and identify three quantitatively different regimes of mechanical coupling that differ in colloid-surface separation and interaction: exclusion, aging, and non-exclusion. We also apply it to study a physical gelation process of a volume-phase transition in thermosensitive microgels and a chemically cross-linked sol-gel transition of 4-arm star polymers by monitoring the evolution of complex modulus near solid surface with frequency, time, and separation distance. In contrast to passive microrheology techniques that rely on particle tracking, we can probe the viscoelastic behavior over five orders of magnitude in stiffness, from 10-3 to 102 Pa, providing excellent coverage for dynamics and heterogeneous samples. We expect this technique will stimulate the development of new experimental methods to explore the complex microscale rheology of macromolecular networks, soft materials, and living cytoplasm.

Biomechanical Characterization at the Cell Scale: Present and Prospects

The rapidly growing field of mechanobiology demands for robust and reproducible characterization of cell mechanical properties. Recent achievements in understanding the mechanical regulation of cell fate largely rely on technological platforms capable of probing the mechanical response of living cells and their physico–chemical interaction with the microenvironment. Besides the established family of atomic force microscopy (AFM) based methods, other approaches include optical, magnetic, and acoustic tweezers, as well as sensing substrates that take advantage of biomaterials chemistry and microfabrication techniques. In this review, we introduce the available methods with an emphasis on the most recent advances, and we discuss the challenges associated with their implementation.

Reversible magnetomechanical collapse: virtual touching and detachment of rigid inclusions in a soft elastic matrix

Soft elastic composite materials containing particulate rigid inclusions in a soft elastic matrix are candidates for developing soft actuators or tunable damping devices. The possibility to reversibly drive the rigid inclusions within such a composite together to a close-to-touching state by an external stimulus would offer important benefits. Then, a significant tuning of the mechanical properties could be achieved due to the resulting mechanical hardening. For a long time, it has been argued whether a virtual touching of the embedded magnetic particles with subsequent detachment can actually be observed in real materials, and if so, whether the process is reversible. Here, we present experimental results that demonstrate this phenomenon in reality. Our system consists of two paramagnetic nickel particles embedded at finite initial distance in a soft elastic polymeric gel matrix. Magnetization in an external magnetic field tunes the magnetic attraction between the particles and drives the process. We quantify our experimental results by different theoretical tools, i.e., explicit analytical calculations in the framework of linear elasticity theory, a projection onto simplified dipole-spring models, as well as detailed finite-element simulations. From these different approaches, we conclude that in our case the cycle of virtual touching and detachment shows hysteretic behavior due to the mutual magnetization between the paramagnetic particles. Our results are important for the design and construction of reversibly tunable mechanical damping devices. Moreover, our projection on dipole-spring models allows the formal connection of our description to various related systems, e.g., magnetosome filaments in magnetotactic bacteria.

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.

Gel-forming mucin interactome drives mucus viscoelasticity

Mucus is a hydrogel that constitutes the first innate defense in all mammals. The main organic component of mucus, gel-forming mucins, forms a complex network through both reversible and irreversible interactions that drive mucus gel formation. Significant advances in the understanding of irreversible gel-forming mucins assembly have been made using recombinant protein approaches. However, little is known about the reversible interactions that may finely modulate mucus viscoelasticity, which can be characterized using rheology. This approach can be used to investigate both the nature of gel-forming mucins interactions and factors that influence hydrogel formation. This knowledge is directly relevant to the development of new drugs to modulate mucus viscoelasticity and to restore normal mucus functions in diseases such as in cystic fibrosis. The aim of the present review is to summarize the current knowledge about the relationship between the mucus protein matrix and its functions, with emphasis on mucus viscoelasticity.

Nonequilibrium dynamics of probe filaments in actin-myosin networks

Active dynamic processes of cells are largely driven by the cytoskeleton, a complex and adaptable semiflexible polymer network, motorized by mechanoenzymes. Small dimensions, confined geometries, and hierarchical structures make it challenging to probe dynamics and mechanical response of such networks. Embedded semiflexible probe polymers can serve as nonperturbing multiscale probes to detect force distributions in active polymer networks. We show here that motor-induced forces transmitted to the probe polymers are reflected in nonequilibrium bending dynamics, which we analyze in terms of spatial eigenmodes of an elastic beam under steady-state conditions. We demonstrate how these active forces induce correlations among the mode amplitudes, which furthermore break time-reversal symmetry. This leads to a breaking of detailed balance in this mode space. We derive analytical predictions for the magnitude of resulting probability currents in mode space in the white-noise limit of motor activity. We relate the structure of these currents to the spatial profile of motor-induced forces along the probe polymers and provide a general relation for observable currents on two-dimensional hyperplanes.

Magnetic particle translation as a surrogate measure for synovial fluid mechanics

The mechanics of synovial fluid vary with disease progression, but are difficult to quantify quickly in a clinical setting due to small sample volumes. In this study, a novel technique to measure synovial fluid mechanics using magnetic nanoparticles is introduced. Briefly, microspheres embedded with superparamagnetic iron oxide nanoparticles, termed magnetic particles, are distributed through a 100μL synovial fluid sample. Then, a permanent magnet inside a protective sheath is inserted into the synovial fluid sample. Magnetic particles translate toward the permanent magnet and the percentage of magnetic particles collected by the magnet in a given time can be related to synovial fluid viscosity. To validate this relationship, magnetic particle translation was demonstrated in three phases. First, magnetic particle translation was assessed in glycerol solutions with known viscosities, demonstrating that as fluid viscosity increased, magnetic particle translation decreased. Next, the relationship between magnetic particle translation and synovial fluid viscosity was assessed using bovine synovial fluid that was progressively degenerated via ultrasonication. Here, particle collection in a given amount of time increased as fluid degenerated, demonstrating that the relationship between particle collection and fluid mechanics holds in non-Newtonian synovial fluid. Finally, magnetic particle translation was used to assess differences between healthy and OA affected joints in equine synovial fluid. Here, particle collection in a given time was higher in OA joints relative to healthy horses (p<0.001). Combined, these data demonstrate potential viability of magnetic particle translation in a clinical setting to evaluate synovial fluid mechanics in limited volumes of synovial fluid sample.

Oscillating Ferrofluid Droplet Microrheology of Liquid-Immersed Sessile Droplets

The damped oscillations of liquid-immersed ferrofluid sessile droplets were studied with high-speed imaging experiments and analytical modeling to develop a novel microrheology technique. Droplet oscillations were induced with an external magnetic field, thereby avoiding transients in the resulting vibrational response of the droplet. By following the droplet relaxation with a high-speed camera, the frequency and relaxation time of the damped harmonic oscillations were measured. We extend upon existing analytical theories to describe our liquid-immersed sessile droplet system, and directly quantify the droplet relaxation with the viscosity of the internal and external fluid as well as the interfacial tension between these. The easily controllable magnetic droplets make our oscillating ferrofluid droplet technique a potential candidate for high-throughput microrheology and tensiometry in the future.

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.

Forces and torques on rigid inclusions in an elastic environment: Resulting matrix-mediated interactions, displacements, and rotations

Embedding rigid inclusions into elastic matrix materials is a procedure of high practical relevance, for instance, for the fabrication of elastic composite materials. We theoretically analyze the following situation. Rigid spherical inclusions are enclosed by a homogeneous elastic medium under stick boundary conditions. Forces and torques are directly imposed from outside onto the inclusions or are externally induced between them. The inclusions respond to these forces and torques by translations and rotations against the surrounding elastic matrix. This leads to elastic matrix deformations, and in turn results in mutual long-ranged matrix-mediated interactions between the inclusions. Adapting a well-known approach from low-Reynolds-number hydrodynamics, we explicitly calculate the displacements and rotations of the inclusions from the externally imposed or induced forces and torques. Analytical expressions are presented as a function of the inclusion configuration in terms of displaceability and rotateability matrices. The role of the elastic environment is implicitly included in these relations. That is, the resulting expressions allow a calculation of the induced displacements and rotations directly from the inclusion configuration, without having to explicitly determine the deformations of the elastic environment. In contrast to the hydrodynamic case, compressibility of the surrounding medium is readily taken into account. We present the complete derivation based on the underlying equations of linear elasticity theory. In the future, the method will, for example, be helpful to characterize the behavior of externally tunable elastic composite materials, to accelerate numerical approaches, as well as to improve the quantitative interpretation of microrheological results.

Dynamic cross-correlations between entangled biofilaments as they diffuse

Entanglement in polymer and biological physics involves a state in which linear interthreaded macromolecules in isotropic liquids diffuse in a spatially anisotropic manner beyond a characteristic mesoscopic time and length scale (tube diameter). The physical reason is that linear macromolecules become transiently localized in directions transverse to their backbone but diffuse with relative ease parallel to it. Within the resulting broad spectrum of relaxation times there is an extended period before the longest relaxation time when filaments occupy a time-averaged cylindrical space of near-constant density. Here we show its implication with experiments based on fluorescence tracking of dilutely labeled macromolecules. The entangled pairs of aqueous F-actin biofilaments diffuse with separation-dependent dynamic cross-correlations that exceed those expected from continuum hydrodynamics up to strikingly large spatial distances of ≈15 µm, which is more than 10⁴ times the size of the solvent water molecules in which they are dissolved, and is more than 50 times the dynamic tube diameter, but is almost equal to the filament length. Modeling this entangled system as a collection of rigid rods, we present a statistical mechanical theory that predicts these long-range dynamic correlations as an emergent consequence of an effective long-range interpolymer repulsion due to the de Gennes correlation hole, which is a combined consequence of chain connectivity and uncrossability. The key physical assumption needed to make theory and experiment agree is that solutions of entangled biofilaments localized in tubes that are effectively dynamically incompressible over the relevant intermediate time and length scales.

Forces on Rigid Inclusions in Elastic Media and Resulting Matrix-Mediated Interactions

To describe many-particle systems suspended in incompressible low-Reynolds-number fluids, effective hydrodynamic interactions can be introduced. Here, we consider particles embedded in elastic media. The effective elastic interactions between spherical particles are calculated analytically, inspired by the approach in the fluid case. Our experiments on interacting magnetic particles confirm the theory. In view of the huge success of the method in hydrodynamics, we similarly expect many future applications in the elastic case, e.g., for elastic composite materials.

Recent insights from in vitro single-molecule studies into nucleosome structure and dynamics

Eukaryotic DNA is tightly packed into a hierarchically ordered structure called chromatin in order to fit into the micron-scaled nucleus. The basic unit of chromatin is the nucleosome, which consists of a short piece of DNA wrapped around a core of eight histone proteins. In addition to their role in packaging DNA, nucleosomes impact the regulation of essential nuclear processes such as replication, transcription, and repair by controlling the accessibility of DNA. Thus, knowledge of this fundamental DNA-protein complex is crucial for understanding the mechanisms of gene control. While structural and biochemical studies over the past few decades have provided key insights into both the molecular composition and functional aspects of nucleosomes, these approaches necessarily average over large populations and times. In contrast, single-molecule methods are capable of revealing features of subpopulations and dynamic changes in the structure or function of biomolecules, rendering them a powerful complementary tool for probing mechanistic aspects of DNA-protein interactions. In this review, we highlight how these single-molecule approaches have recently yielded new insights into nucleosomal and subnucleosomal structures and dynamics.

Soft viscoelastic properties of nuclear actin age oocytes due to gravitational creep

The actin cytoskeleton helps maintain structural organization within living cells. In large X. laevis oocytes, gravity becomes a dominant force and is countered by a nuclear actin network that prevents liquid-like nuclear bodies from immediate sedimentation and coalescence. However, nuclear actin's mechanical properties, and how they facilitate the stabilization of nuclear bodies, remain unknown. Using active microrheology, we find that nuclear actin forms a weak viscoelastic network, with a modulus of roughly 0.1 Pa. Embedded probe particles subjected to a constant force exhibit continuous displacement, due to viscoelastic creep. Gravitational forces also cause creep displacement of nuclear bodies, resulting in their asymmetric nuclear distribution. Thus, nuclear actin does not indefinitely support the emulsion of nuclear bodies, but only kinetically stabilizes them by slowing down gravitational creep to ~2 months. This is similar to the viability time of large oocytes, suggesting gravitational creep ages oocytes, with fatal consequences on long timescales.

Frequency modulated microrheology

Coupling analog frequency modulation (FM) to the driving stimulus in active microrheology measurements conducted with optical tweezers effectively parallelizes numerous single-frequency experiments. Consequently, frequency modulated microrheology (FMMR) can efficiently characterize the dynamic stress response of complex fluids over several frequency decades in a single experiment. The time required to complete an FMMR measurement scales with the lowest frequency probed, improving throughput over the serial frequency sweep approach. The ease of implementation, straight-forward data analysis and rapidity of FMMR offer particular utility toward applications such as characterization of non-equilibrium materials, automated microrheology instrumentation, high-throughput screening of biomaterials and (bio) pharmaceutical formulations, and in situ monitoring of chemical and biochemical reaction processes.

Passive mechanical forces control cell-shape change during Drosophila ventral furrow formation

During Drosophila gastrulation, the ventral mesodermal cells constrict their apices, undergo a series of coordinated cell-shape changes to form a ventral furrow (VF) and are subsequently internalized. Although it has been well documented that apical constriction is necessary for VF formation, the mechanism by which apical constriction transmits forces throughout the bulk tissue of the cell remains poorly understood. In this work, we develop a computational vertex model to investigate the role of the passive mechanical properties of the cellular blastoderm during gastrulation. We introduce to our knowledge novel data that confirm that the volume of apically constricting cells is conserved throughout the entire course of invagination. We show that maintenance of this constant volume is sufficient to generate invagination as a passive response to apical constriction when it is combined with region-specific elasticities in the membranes surrounding individual cells. We find that the specific sequence of cell-shape changes during VF formation is critically controlled by the stiffness of the lateral and basal membrane surfaces. In particular, our model demonstrates that a transition in basal rigidity is sufficient to drive VF formation along the same sequence of cell-shape change that we observed in the actual embryo, with no active force generation required other than apical constriction.