Determining Microscopic Viscoelasticity in Flexible and Semiflexible Polymer Networks from Thermal Fluctuations

Non-Markovian Modeling of Nonequilibrium Fluctuations and Dissipation in Active Viscoelastic Biomatter

Based on a Hamiltonian that incorporates the elastic coupling between a tracer particle and the embedding active viscoelastic biomatter, we derive a generalized non-Markovian Langevin model for the nonequilibrium mechanical tracer response. Our analytical expressions for the frequency-dependent tracer response function and the tracer positional autocorrelation function agree quantitatively with experimental data for red blood cells and actomyosin networks with and without adenosine triphosphate over the entire frequency range and in particular reproduce the low-frequency violation of the fluctuation-dissipation theorem. The viscoelastic power laws, the elastic constants and effective friction coefficients extracted from the experimental data allow straightforward physical interpretation.

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.

Measuring fluctuating dynamics of sparsely crosslinked actin gels with dual-feedback nonlinear microrheology

We investigate the fluctuating dynamics of colloidal particles in weakly crosslinked F-actin networks with optical-trap-based microrheology. Using the dual-feedback technology, embedded colloidal particles were stably forced beyond the linear regime in a manner that does not suppress spontaneous fluctuations of particles. Upon forcing, a particle that was stably confined in a cage made of the network's crosslinks started to intermittently jump to the next caging microenvironments. By investigating the statistics of the jump dynamics, we discuss how heterogeneous relaxations observed in equilibrium systems became homogeneous when similar jumps were activated under constant forcing beyond the linear regime.

Fabrication and mechanical characterization of hydrogel-based 3D cell-like structures

In this article, we demonstrate the fabrication of 3D cell-like structures using a femtosecond laser-based two-photon polymerization technique. By employing poly(ethylene glycol) diacrylate monomers as a precursor solution, we fabricate 3D hemispheres that resemble morphological and biomechanical characteristics of natural cells. We employ an optical tweezers-based microrheology technique to measure the viscoelastic properties of the precursor solutions inside and outside the structures. In addition, we demonstrate the interchangeability of the precursor solution within fabricated structures without impairing the microstructures. The combination of two-photon polymerization and microrheological measurements by optical tweezers demonstrated here represents a powerful toolbox for future investigations into cell mimic and artificial cell studies.

Microrheology near jamming

The jamming transition is a nonequilibrium critical phenomenon, which governs characteristic mechanical properties of jammed soft materials, such as pastes, emulsions, and granular matters. Both experiments and theory of jammed soft materials have revealed that the complex modulus measured by conventional macrorheology exhibits a characteristic frequency dependence. Microrheology is a new type of method to obtain the complex modulus, which transforms the microscopic motion of probes to the complex modulus through the generalized Stokes relation (GSR). Although microrheology has been applied to jammed soft materials, its theoretical understanding is limited. In particular, the validity of the GSR near the jamming transition is far from obvious since there is a diverging length scale lc, which characterizes the heterogeneous response of jammed particles. Here, we study the microrheology of jammed particles by theory and numerical simulation. First, we develop a linear response formalism to calculate the response function of the probe particle, which is transformed to the complex modulus via the GSR. Then, we apply our formalism to a numerical model of jammed particles and find that the storage and loss modulus follow characteristic scaling laws near the jamming transition. Importantly, the observed scaling law coincides with that in macrorheology, which indicates that the GSR holds even near the jamming transition. We rationalize this equivalence by asymptotic analysis of the obtained formalism and numerical analysis on the displacement field of jammed particles under a local perturbation.

Microrheology and structural quantification of hypercoagulable clots

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

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.

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.

Mechanical analogue for cities

Motivated from the increasing need to develop a science-based, predictive understanding of the dynamics and response of cities when subjected to natural hazards, in this paper, we apply concepts from statistical mechanics and microrheology to develop mechanical analogues for cities with predictive capabilities. We envision a city to be a matrix where cell-phone users are driven by the city's economy and other incentives while using the collection of its infrastructure networks in a similar way that thermally driven Brownian particles are moving within a complex viscoelastic material. Mean-square displacements of thousands of cell-phone users are computed from GPS location data to establish the creep compliance and the resulting impulse response function of a city. The derivation of these time-response functions allows the synthesis of simple mechanical analogues that model satisfactorily the city's behaviour under normal conditions. Our study concentrates on predicting the response of cities to acute shocks (natural hazards) that are approximated with a rectangular pulse; and we show that the derived solid-like mechanical networks predict that cities revert immediately to their pre-event response suggesting an inherent resilience. Our findings are in remarkable good agreement with the recorded response of the Dallas metroplex following the February 2021 North American winter storm.

Extracting, quantifying, and comparing dynamical and biomechanical properties of living matter through single particle tracking

A panoply of new tools for tracking single particles and molecules has led to an explosion of experimental data, leading to novel insights into physical properties of living matter governing cellular development and function, health and disease. In this Perspective, we present tools to investigate the dynamics and mechanics of living systems from the molecular to cellular scale via single-particle techniques. In particular, we focus on methods to measure, interpret, and analyse complex data sets that are associated with forces, materials properties, transport, and emergent organisation phenomena within biological and soft-matter systems. Current approaches, challenges, and existing solutions in the associated fields are outlined in order to support the growing community of researchers at the interface of physics and the life sciences. Each section focuses not only on the general physical principles and the potential for understanding living matter, but also on details of practical data extraction and analysis, discussing limitations, interpretation, and comparison across different experimental realisations and theoretical frameworks. Particularly relevant results are introduced as examples. While this Perspective describes living matter from a physical perspective, highlighting experimental and theoretical physics techniques relevant for such systems, it is also meant to serve as a solid starting point for researchers in the life sciences interested in the implementation of biophysical methods.

Foregut organ progenitors and their niche display distinct viscoelastic properties in vivo during early morphogenesis stages

Material properties of living matter play an important role for biological function and development. Yet, quantification of material properties of internal organs in vivo, without causing physiological damage, remains challenging. Here, we present a non-invasive approach based on modified optical tweezers for quantifying sub-cellular material properties deep inside living zebrafish embryos. Material properties of cells within the foregut region are quantified as deep as 150 µm into the biological tissue through measurements of the positions of an inert tracer. This yields an exponent, α, which characterizes the scaling behavior of the positional power spectra and the complex shear moduli. The measurements demonstrate differential mechanical properties: at the time when the developing organs undergo substantial displacements during morphogenesis, gut progenitors are more elastic (α = 0.57 ± 0.07) than the neighboring yolk (α = 0.73 ± 0.08), liver (α = 0.66 ± 0.06) and two mesodermal (α = 0.68 ± 0.06, α = 0.64 ± 0.06) progenitor cell populations. The higher elasticity of gut progenitors correlates with an increased cellular concentration of microtubules. The results infer a role of material properties during morphogenesis and the approach paves the way for quantitative material investigations in vivo of embryos, explants, or organoids.

Here, the authors present a method based on optical tweezers to measure mechanical properties of cells inside living zebrafish embryos. The measurement reveals spatiotemporally distinct mechanical properties, linking cell mechanics and morphogenesis.

Oscillatory active microrheology of active suspensions

Using the method of Brownian dynamics, we investigate the dynamic properties of a 2d suspension of active disks at high Péclet numbers using active microrheology. In our simulations the tracer particle is driven either by a constant or an oscillatory external force. In the first case, we find that the mobility of the tracer initially appreciably decreases with the external force and then becomes approximately constant for larger forces. For an oscillatory driving force we find that the dynamic mobility shows a quite complex behavior-it displays a highly nonlinear behavior on both the amplitude and frequency of the driving force. In the range of forces studied, we do not observe a linear regime. This result is important because it reveals that a phenomenological description of tracer motion in active media in terms of a simple linear stochastic equation even with a memory-mobility kernel is not appropriate, in the general case.

Changes in Cell Morphology and Actin Organization in Embryonic Stem Cells Cultured under Different Conditions

The cellular cytoskeleton provides the cell with a mechanical rigidity that allows mechanical interaction between cells and the extracellular environment. The actin structure plays a key role in mechanical events such as motility or the establishment of cell polarity. From the earliest stages of development, as represented by the ex vivo expansion of naïve embryonic stem cells (ESCs), the critical mechanical role of the actin structure is becoming recognized as a vital cue for correct segregation and lineage control of cells and as a regulatory structure that controls several transcription factors. Naïve ESCs have a characteristic morphology, and the ultrastructure that underlies this condition remains to be further investigated. Here, we investigate the 3D actin cytoskeleton of naïve mouse ESCs using super-resolution optical reconstruction microscopy (STORM). We investigate the morphological, cytoskeletal, and mechanical changes in cells cultured in 2i or Serum/LIF media reflecting, respectively, a homogeneous preimplantation cell state and a state that is closer to embarking on differentiation. STORM imaging showed that the peripheral actin structure undergoes a dramatic change between the two culturing conditions. We also detected micro-rheological differences in the cell periphery between the cells cultured in these two media correlating well with the observed nano-architecture of the ESCs in the two different culture conditions. These results pave the way for linking physical properties and cytoskeletal architecture to cell morphology during early development.

Effects of Vimentin Intermediate Filaments on the Structure and Dynamics of In Vitro Multicomponent Interpenetrating Cytoskeletal Networks

We investigate the rheological properties of interpenetrating networks reconstituted from the main cytoskeletal components: filamentous actin, microtubules, and vimentin intermediate filaments. The elastic modulus is determined largely by actin, with little contribution from either microtubules or vimentin. However, vimentin dramatically impacts the relaxation, with even small amounts significantly increasing the relaxation time of the interpenetrating network. This highly unusual decoupling between dissipation and elasticity may reflect weak attractive interactions between vimentin and actin networks.

Technological perspectives on laser speckle micro-rheology for cancer mechanobiology research

SIGNIFICANCE

The ability to measure the micro-mechanical properties of biological tissues and biomaterials is crucial for numerous fields of cancer research, including tumor mechanobiology, tumor-targeting drug delivery, and therapeutic development.

AIM

Our goal is to provide a renewed perspective on the mainstream techniques used for micro-mechanical evaluation of biological tissues and biomimetic scaffoldings. We specifically focus on portraying the outlook of laser speckle micro-rheology (LSM), a technology that quantifies the mechanical properties of biomaterials and tissues in a rapid, non-contact manner.

APPROACH

First, we briefly explain the motivation and significance of evaluating the tissue micro-mechanics in various fields of basic and translational cancer research and introduce the key concepts and quantitative metrics used to explain the mechanical properties of tissue. This is followed by reviewing the general active and passive themes of measuring micro-mechanics. Next, we focus on LSM and elaborate on the theoretical grounds and working principles of this technique. Then, the perspective for measuring the micro-mechanical properties via LSM is outlined. Finally, we draw an overview picture of LSM in cancer mechanobiology research.

RESULTS

With the continued emergence of new approaches for measuring the mechanical attributes of biological tissues, the field of micro-mechanical imaging is at its boom. As one of these competent innovations, LSM presents a tremendous potential for both technical maturation and prospective applications in cancer biomechanics and mechanobiology research.

CONCLUSION

By elaborating the current viewpoint of LSM, we expect to accelerate the expansion of this approach to new territories in both technological domains and applied fields. This renewed perspective on LSM may also serve as a road map for other micro-mechanical measurement concepts to be applied for answering mechanobiological questions.

Multi-frequency passive and active microrheology with optical tweezers

Optical tweezers have attracted significant attention for microrheological applications, due to the possibility of investigating viscoelastic properties in vivo which are strongly related to the health status and development of biological specimens. In order to use optical tweezers as a microrheological tool, an exact force calibration in the complex system under investigation is required. One of the most promising techniques for optical tweezers calibration in a viscoelastic medium is the so-called active–passive calibration, which allows determining both the trap stiffness and microrheological properties of the medium with the least a-priori knowledge in comparison to the other methods. In this manuscript, we develop an optimization of the active–passive calibration technique performed with a sample stage driving, whose implementation is more straightforward with respect to standard laser driving where two different laser beams are required. We performed microrheological measurements over a broad frequency range in a few seconds implementing an accurate multi-frequency driving of the sample stage. The optical tweezers-based microrheometer was first validated by measuring water, and then exemplarily applied to more viscous medium and subsequently to a viscoelastic solution of methylcellulose in water. The described method paves the way to microrheological precision metrology in biological samples with high temporal- and spatial-resolution allowing for investigation of even short time-scale phenomena.

Impulse response function for Brownian motion

Motivated from the central role of the mean-square displacement and its second time-derivative - that is the velocity autocorrelation function in the description of Brownian motion and its implications to microrheology, we revisit the physical meaning of the first time-derivative of the mean-square displacement of Brownian particles. By employing a rheological analogue for Brownian motion, we show that the time-derivative of the mean-square displacement of Brownian microspheres with mass m and radius R immersed in any linear, isotropic viscoelastic material is identical to , where h(t) is the impulse response function (strain history γ(t), due to an impulse stress τ(t) = δ(t - 0)) of a rheological network that is a parallel connection of the linear viscoelastic material with an inerter with distributed inertance . The impulse response function of the viscoelastic material-inerter parallel connection derived in this paper at the stress-strain level of the rheological analogue is essentially the response function of the Brownian particles expressed at the force-displacement level by Nishi et al. after making use of the fluctuation-dissipation theorem. By employing the viscoelastic material-inerter rheological analogue we derive the mean-square displacement and its time-derivatives of Brownian particles immersed in a viscoelastic material described with a Maxwell element connected in parallel with a dashpot and we show that for Brownian motion of microparticles immersed in such fluid-like materials, the impulse response function h(t) maintains a finite constant value in the long term.

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.

Spatial distribution of mechanical properties in Pseudomonas aeruginosa biofilms, and their potential impacts on biofilm deformation

The mechanical properties of biofilms can be used to predict biofilm deformation under external forces, for example, under fluid flow. We used magnetic tweezers to spatially map the compliance of Pseudomonas aeruginosa biofilms at the microscale, then applied modeling to assess its effects on biofilm deformation. Biofilms were grown in capillary flow cells with Reynolds numbers (Re) ranging from 0.28 to 13.9, bulk dissolved oxygen (DO) concentrations from 1 mg/L to 8 mg/L, and bulk calcium ion (Ca²⁺ ) concentrations of 0 and 100 mg CaCl₂ /L. Higher Re numbers resulted in more uniform biofilm morphologies. The biofilm was stiffer at the center of the flow cell than near the walls. Lower bulk DO led to more stratified biofilms. Higher Ca²⁺ concentrations led to increased stiffness and more uniform mechanical properties. Using the experimental mechanical properties, fluid-structure interaction models predicted up to 64% greater deformation for heterogeneous biofilms, compared with a homogeneous biofilms with the same average properties. However, the deviation depended on the biofilm morphology and flow regime. Our results show significant spatial mechanical variability exists at the microscale, and that this variability can potentially affect biofilm deformation. The average biofilm mechanical properties, provided in many studies, should be used with caution when predicting biofilm deformation.

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.

Anomalous diffusion of active Brownian particles cross-linked to a networked polymer: Langevin dynamics simulation and theory

Quantitatively understanding the dynamics of an active Brownian particle (ABP) interacting with a viscoelastic polymer environment is a scientific challenge. It is intimately related to several interdisciplinary topics such as the microrheology of active colloids in a polymer matrix and the athermal dynamics of the in vivo chromosomes or cytoskeletal networks. Based on Langevin dynamics simulation and analytic theory, here we explore such a viscoelastic active system in depth using a star polymer of functionality f with the center cross-linker particle being ABP. We observe that the ABP cross-linker, despite its self-propelled movement, attains an active subdiffusion with the scaling ΔR2(t) ∼ tα with α ≤ 1/2, through the viscoelastic feedback from the polymer. Counter-intuitively, the apparent anomaly exponent α becomes smaller as the ABP is driven by a larger propulsion velocity, but is independent of functionality f or the boundary conditions of the polymer. We set forth an exact theory and show that the motion of the active cross-linker is a Gaussian non-Markovian process characterized by two distinct power-law displacement correlations. At a moderate Péclet number, it seemingly behaves as fractional Brownian motion with a Hurst exponent H = α/2, whereas, at a high Péclet number, the self-propelled noise in the polymer environment leads to a logarithmic growth of the mean squared displacement (∼ln t) and a velocity autocorrelation decaying as -t-2. We demonstrate that the anomalous diffusion of the active cross-linker is precisely described by a fractional Langevin equation with two distinct random noises.

Physical limits to sensing material properties

All materials respond heterogeneously at small scales, which limits what a sensor can learn. Although previous studies have characterized measurement noise arising from thermal fluctuations, the limits imposed by structural heterogeneity have remained unclear. In this paper, we find that the least fractional uncertainty with which a sensor can determine a material constant λ0 of an elastic medium is approximately [Formula: see text] for a ≫ d ≫ ξ, [Formula: see text], and D > 1, where a is the size of the sensor, d is its spatial resolution, ξ is the correlation length of fluctuations in λ0, Δλ is the local variability of λ0, and D is the dimension of the medium. Our results reveal how one can construct devices capable of sensing near these limits, e.g. for medical diagnostics. We use our theoretical framework to estimate the limits of mechanosensing in a biopolymer network, a sensory process involved in cellular behavior, medical diagnostics, and material fabrication.

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.

Viscous-viscoelastic correspondence principle for Brownian motion

Motivated by the classical expressions of the mean-square displacement and the velocity autocorrelation function of Brownian particles either suspended in a Newtonian viscous fluid or trapped in a harmonic potential, we show that for all timescales the mean-square displacement of Brownian microspheres with mass m and radius R suspended in any linear, isotropic viscoelastic material is identical to the creep compliance of a linear mechanical network that is a parallel connection of the linear viscoelastic material with an inerter with distributed inertance m_{R}=m/6πR. The synthesis of this mechanical network leads to the statement of a viscous-viscoelastic correspondence principle for Brownian motion which simplifies appreciably the calculations of the mean-square displacement and the velocity autocorrelation function of Brownian particles suspended in viscoelastic materials where inertia effects are non-negligible at longer timescales. The viscous-viscoelastic correspondence principle established in this paper by introducing the concept of the inerter is equivalent to the viscous-viscoelastic analogy adopted by Mason and Weitz [T. G. Mason and D. A. Weitz, Phys. Rev. Lett. 74, 1250 (1995)10.1103/PhysRevLett.74.1250].

Multiple particle tracking analysis in isolated nuclei reveals the mechanical phenotype of leukemia cells

The nucleus is fundamentally composed by lamina and nuclear membranes that enclose the chromatin, nucleoskeletal components and suspending nucleoplasm. The functional connections of this network integrate external stimuli into cell signals, including physical forces to mechanical responses of the nucleus. Canonically, the morphological characteristics of the nucleus, as shape and size, have served for pathologists to stratify and diagnose cancer patients; however, novel biophysical techniques must exploit physical parameters to improve cancer diagnosis. By using multiple particle tracking (MPT) technique on chromatin granules, we designed a SURF (Speeded Up Robust Features)-based algorithm to study the mechanical properties of isolated nuclei and in living cells. We have determined the apparent shear stiffness, viscosity and optical density of the nucleus, and how the chromatin structure influences on these biophysical values. Moreover, we used our MPT-SURF analysis to study the apparent mechanical properties of isolated nuclei from patients of acute lymphoblastic leukemia. We found that leukemia cells exhibited mechanical differences compared to normal lymphocytes. Interestingly, isolated nuclei from high-risk leukemia cells showed increased viscosity than their counterparts from normal lymphocytes, whilst nuclei from relapsed-patient's cells presented higher density than those from normal lymphocytes or standard- and high-risk leukemia cells. Taken together, here we presented how MPT-SURF analysis of nuclear chromatin granules defines nuclear mechanical phenotypic features, which might be clinically relevant.

Complex modulus and compliance for airway smooth muscle cells

A cell can be described as a complex viscoelastic material with structural relaxations that is modulated by thermal and chemically nonequilibrium processes. Tissue morphology and function rely upon cells' physical responses to mechanical force. We measured the frequency-dependent mechanical relaxation response of adherent human airway smooth muscle cells under adenosine triphosphate (ATP) depletion and normal ATP conditions. The frequency dependence of the complex compliance J^{*} and modulus G^{*} was measured over the frequencies 10^{-1}<f<10^{3} Hz at selected temperatures between 4<T<54^{∘}C. Our results show characteristic relaxation features which can be interpreted by the mode-coupling theory (MCT) of viscoelastic liquids. We analyze the shape of the spectra in terms of a so-called A_{4} scenario with logarithmic scaling laws. Characteristic timescales τ_{β} and τ_{α} appear with corresponding energy barriers E_{β}≈(10-20)k_{B}T and E_{α}≈(20-30)k_{B}T. We demonstrate that cells are close to a glass transition. We find that the cell becomes softer around physiological temperatures, where its surface structure is more liquid-like with a plateau modulus around 0.1-0.8 kPa compared with the more solid-like interior cytoskeletal structures with a plateau modulus 1-15 kPa. Corresponding values for the viscosity are 10^{2}-10^{3} Pa s for the surface structures closer to the membrane and 10^{4}-10^{6} Pa s for the core cytoskeletal structures.

Equilibrium fluctuations of a semiflexible filament cross linked into a network

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

Spectroscopic photonic force optical coherence elastography

We demonstrate spectroscopic photonic force optical coherence elastography (PF-OCE). Oscillations of microparticles embedded in viscoelastic hydrogels were induced by harmonically modulated optical radiation pressure and measured by phase-sensitive spectral-domain optical coherence tomography. PF-OCE can detect microparticle displacements with pico- to nano-meter sensitivity and millimeter-scale volumetric coverage. With spectroscopic PF-OCE, we quantified viscoelasticity over a broad frequency range from 1 Hz to 7 kHz, revealing rich microstructural dynamics of polymer networks across multiple microrheological regimes. Reconstructed frequency-dependent loss moduli of polyacrylamide hydrogels were observed to follow a general power scaling law G''∼ω0.75, consistent with that of semiflexible polymer networks. Spectroscopic PF-OCE provides an all-optical approach to microrheological studies with high sensitivity and high spatiotemporal resolution, and could be especially beneficial for time-lapse and volumetric mechanical characterization of viscoelastic materials.

Microrheological quantification of viscoelastic properties with photonic force optical coherence elastography

Photonic force optical coherence elastography (PF-OCE) is a new approach for volumetric characterization of microscopic mechanical properties of three-dimensional viscoelastic medium. It is based on measurements of the complex mechanical response of embedded micro-beads to harmonically modulated radiation-pressure force from a weakly-focused beam. Here, we utilize the Generalized Stokes-Einstein relation to reconstruct local complex shear modulus in polyacrylamide gels by combining PF-OCE measurements of bead mechanical responses and experimentally measured depth-resolved radiation-pressure force profile of our forcing beam. Data exclusion criteria for quantitative PF-OCE based on three noise-related parameters were identified from the analysis of measurement noise at key processing steps. Shear storage modulus measured by quantitative PF-OCE was found to be in good agreement with standard shear rheometry, whereas shear loss modulus was in agreement with previously published atomic force microscopy results. The analysis and results presented here may serve to inform practical, application-specific implementations of PF-OCE, and establish the technique as a viable tool for quantitative mechanical microscopy.

Collagen networks determine viscoelastic properties of connective tissues yet do not hinder diffusion of the aqueous solvent

Collagen accounts for the major extracellular matrix (ECM) component in many tissues and provides mechanical support for cells. Magnetic Resonance (MR) Imaging, MR based diffusion measurements and MR Elastography (MRE) are considered sensitive to the microstructure of tissues including collagen networks of the ECM. However, little is known whether water diffusion interacts with viscoelastic properties of tissues. This study combines highfield MR based diffusion measurements, novel compact tabletop MRE and confocal microscopy in collagen networks of different cross-linking states (untreated collagen gels versus additional treatment with glutaraldehyde). The consistency of bulk rheology and MRE within a wide dynamic range is demonstrated in heparin gels, a viscoelastic standard for MRE. Additional crosslinking of collagen led to an 8-fold increased storage modulus, a 4-fold increased loss modulus and a significantly decreased power law exponent, describing multi-relaxational behavior, corresponding to a pronounced transition from viscous-soft to elastic-rigid properties. Collagen network changes were not detectable by MR based diffusion measurements and microscopy which are sensitive to the micrometer scale. The MRE-measured shear modulus is sensitive to collagen fiber interactions which take place on the intrafiber level such as fiber stiffness. The insensitivity of MR based diffusion measurements to collagen hydrogels of different cross-linking states alludes that congeneric collagen structures in connective tissues do not hinder extracellular diffusive water transport. Furthermore, the glutaraldehyde induced rigorous changes in viscoelastic properties indicate that intrafibrillar dissipation is the dominant mode of viscous dissipation in collagen-dominated connective tissue.

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.

Generalized Langevin dynamics: construction and numerical integration of non-Markovian particle-based models

We propose a generalized Langevin dynamics (GLD) technique to construct non-Markovian particle-based coarse-grained models from fine-grained reference simulations and to efficiently integrate them. The proposed GLD model has the form of a discretized generalized Langevin equation with distance-dependent two-particle contributions to the self- and pair-memory kernels. The memory kernels are iteratively reconstructed from the dynamical correlation functions of an underlying fine-grained system. We develop a simulation algorithm for this class of non-Markovian models that scales linearly with the number of coarse-grained particles. Our GLD method is suitable for coarse-grained studies of systems with incomplete time scale separation, as is often encountered, e.g., in soft matter systems. We apply the method to a suspension of nanocolloids with frequency-dependent hydrodynamic interactions. We show that the results from GLD simulations perfectly reproduce the dynamics of the underlying fine-grained system. The effective speedup of these simulations amounts to a factor of about 104. Additionally, the transferability of the coarse-grained model with respect to changes of the nanocolloid density is investigated. The results indicate that the model is transferable to systems with nanocolloid densities that differ by up to one order of magnitude from the density of the reference system.

Acute effects of combined exercise and oscillatory positive expiratory pressure therapy on sputum properties and lung diffusing capacity in cystic fibrosis: a randomized, controlled, crossover trial

Background

Regular airway clearance by chest physiotherapy and/or exercise is critical to lung health in cystic fibrosis (CF). Combination of cycling exercise and chest physiotherapy using the Flutter® device on sputum properties has not yet been investigated.

Methods

This prospective, randomized crossover study compared a single bout of continuous cycling exercise at moderate intensity (experiment A, control condition) vs a combination of interval cycling exercise plus Flutter® (experiment B). Sputum properties (viscoelasticity, yield stress, solids content, spinnability, and ease of sputum expectoration), pulmonary diffusing capacity for nitric oxide (DLNO) and carbon monoxide (DLCO) were assessed at rest, directly and 45 min post-exercise (recovery) at 2 consecutive visits. Primary outcome was change in sputum viscoelasticity (G’, storage modulus; G”, loss modulus) over a broad frequency range (0.1–100 rad.s^− 1).

Results

15 adults with CF (FEV₁range 24–94% predicted) completed all experiments. No consistent differences between experiments were observed for G’ and G” and other sputum properties, except for ease of sputum expectoration during recovery favoring experiment A. DLNO, DLCO, alveolar volume (V_A) and pulmonary capillary blood volume (V_cap) increased during experiment A, while DLCO and V_cap increased during experiment B (all P < 0.05). We found no differences in absolute changes in pulmonary diffusing capacity and its components between experiments, except a higher V_A immediately post-exercise favoring experiment A (P = 0.032).

Conclusions

The additional use of the Flutter® to moderate intensity interval cycling exercise has no measurable effect on the viscoelastic properties of sputum compared to moderate intensity continuous cycling alone. Elevations in diffusing capacity represent an acute exercise-induced effect not sustained post-exercise.

Trial registration

ClinicalTrials.gov; No.: NCT02750722; URL: clinical.trials.gov; Registration date: April 25th, 2016.

Electronic supplementary material

The online version of this article (10.1186/s12890-018-0661-1) contains supplementary material, which is available to authorized users.

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.

A symmetrical method to obtain shear moduli from microrheology

Passive microrheology typically deduces shear elastic loss and storage moduli from displacement time series or mean-squared displacements (MSD) of thermally fluctuating probe particles in equilibrium materials. Common data analysis methods use either Kramers-Kronig (KK) transformation or functional fitting to calculate frequency-dependent loss and storage moduli. We propose a new analysis method for passive microrheology that avoids the limitations of both of these approaches. In this method, we determine both real and imaginary components of the complex, frequency-dependent response function χ(ω) = χ'(ω) + iχ''(ω) as direct integral transforms of the MSD of thermal particle motion. This procedure significantly improves the high-frequency fidelity of χ(ω) relative to the use of KK transformation, which has been shown to lead to artifacts in χ'(ω). We test our method on both model and experimental data. Experiments were performed on solutions of worm-like micelles and dilute collagen solutions. While the present method agrees well with established KK-based methods at low frequencies, we demonstrate significant improvement at high frequencies using our symmetric analysis method, up to almost the fundamental Nyquist limit.

Technological strategies to estimate and control diffusive passage times through the mucus barrier in mucosal drug delivery

In mucosal drug delivery, two design goals are desirable: 1) insure drug passage through the mucosal barrier to the epithelium prior to drug removal from the respective organ via mucus clearance; and 2) design carrier particles to achieve a prescribed arrival time and drug uptake schedule at the epithelium. Both goals are achievable if one can control "one-sided" diffusive passage times of drug carrier particles: from deposition at the mucus interface, through the mucosal barrier, to the epithelium. The passage time distribution must be, with high confidence, shorter than the timescales of mucus clearance to maximize drug uptake. For 100nm and smaller drug-loaded nanoparticulates, as well as pure drug powders or drug solutions, diffusion is normal (i.e., Brownian) and rapid, easily passing through the mucosal barrier prior to clearance. Major challenges in quantitative control over mucosal drug delivery lie with larger drug-loaded nanoparticulates that are comparable to or larger than the pores within the mucus gel network, for which diffusion is not simple Brownian motion and typically much less rapid; in these scenarios, a timescale competition ensues between particle passage through the mucus barrier and mucus clearance from the organ. In the lung, as a primary example, coordinated cilia and air drag continuously transport mucus toward the trachea, where mucus and trapped cargo are swallowed into the digestive tract. Mucus clearance times in lung airways range from minutes to hours or significantly longer depending on deposition in the upper, middle, lower airways and on lung health, giving a wide time window for drug-loaded particle design to achieve controlled delivery to the epithelium. We review the physical and chemical factors (of both particles and mucus) that dictate particle diffusion in mucus, and the technological strategies (theoretical and experimental) required to achieve the design goals. First we describe an idealized scenario - a homogeneous viscous fluid of uniform depth with a particle undergoing passive normal diffusion - where the theory of Brownian motion affords the ability to rigorously specify particle size distributions to meet a prescribed, one-sided, diffusive passage time distribution. Furthermore, we describe how the theory of Brownian motion provides the scaling of one-sided diffusive passage times with respect to mucus viscosity and layer depth, and under reasonable caveats, one can also prescribe passage time scaling due to heterogeneity in viscosity and layer depth. Small-molecule drugs and muco-inert, drug-loaded carrier particles 100nm and smaller fall into this class of rigorously controllable passage times for drug delivery. Second we describe the prevalent scenarios in which drug-loaded carrier particles in mucus violate simple Brownian motion, instead exhibiting anomalous sub-diffusion, for which all theoretical control over diffusive passage times is lost, and experiments are prohibitive if not impossible to measure one-sided passage times. We then discuss strategies to overcome these roadblocks, requiring new particle-tracking experiments and emerging advances in theory and computation of anomalous, sub-diffusive processes that are necessary to predict and control one-sided particle passage times from deposition at the mucosal interface to epithelial uptake. We highlight progress to date, remaining hurdles, and prospects for achieving the two design goals for 200nm and larger, drug-loaded, non-dissolving, nanoparticulates.

Dynamics of Nanoparticles in Entangled Polymer Solutions

The mean square displacement ⟨r²⟩ of nanoparticle probes dispersed in simple isotropic liquids and in polymer solutions is interrogated using fluorescence correlation spectroscopy and single-particle tracking (SPT) experiments. Probe dynamics in different regimes of particle diameter (d), relative to characteristic polymer length scales, including the correlation length (ξ), the entanglement mesh size (a), and the radius of gyration (R_g), are investigated. In simple fluids and for polymer solutions in which d ≫ R_g, long-time particle dynamics obey random-walk statistics ⟨r²⟩:t, with the bulk zero-shear viscosity of the polymer solution determining the frictional resistance to particle motion. In contrast, in polymer solutions with d < R_g, polymer molecules in solution exert noncontinuum resistances to particle motion and nanoparticle probes appear to interact hydrodynamically only with a local fluid medium with effective drag comparable to that of a solution of polymer chain segments with sizes similar to those of the nanoparticle probes. Under these conditions, the nanoparticles exhibit orders of magnitude faster dynamics than those expected from continuum predictions based on the Stokes-Einstein relation. SPT measurements further show that when d > a, nanoparticle dynamics transition from diffusive to subdiffusive on long timescales, reminiscent of particle transport in a field with obstructions. This last finding is in stark contrast to the nanoparticle dynamics observed in entangled polymer melts, where X-ray photon correlation spectroscopy measurements reveal faster but hyperdiffusive dynamics. We analyze these results with the help of the hopping model for particle dynamics in polymers proposed by Cai et al. and, on that basis, discuss the physical origins of the local drag experienced by the nanoparticles in entangled polymer solutions.

Simple peptide coacervates adapted for rapid pressure-sensitive wet adhesion

We report here that a dense liquid formed by spontaneous condensation, also known as simple coacervation, of a single mussel foot protein-3S-mimicking peptide exhibits properties critical for underwater adhesion. A structurally homogeneous coacervate is deposited on underwater surfaces as micrometer-thick layers, and, after compression, displays orders of magnitude higher underwater adhesion at 2 N m^-1 than that reported from thin films of the most adhesive mussel-foot-derived peptides or their synthetic mimics. The increase in adhesion efficiency does not require nor rely on post-deposition curing or chemical processing, but rather represents an intrinsic physical property of the single-component coacervate. Its wet adhesive and rheological properties correlate with significant dehydration, tight peptide packing and restriction in peptide mobility. We suggest that such dense coacervate liquids represent an essential adaptation for the initial priming stages of mussel adhesive deposition, and provide a hitherto untapped design principle for synthetic underwater adhesives.

Effects of finite and discrete sampling and blur on microrheology experiments

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

Universal glass-forming behavior of in vitro and living cytoplasm

Physiological processes in cells are performed efficiently without getting jammed although cytoplasm is highly crowded with various macromolecules. Elucidating the physical machinery is challenging because the interior of a cell is so complex and driven far from equilibrium by metabolic activities. Here, we studied the mechanics of in vitro and living cytoplasm using the particle-tracking and manipulation technique. The molecular crowding effect on cytoplasmic mechanics was selectively studied by preparing simple in vitro models of cytoplasm from which both the metabolism and cytoskeletons were removed. We obtained direct evidence of the cytoplasmic glass transition; a dramatic increase in viscosity upon crowding quantitatively conformed to the super-Arrhenius formula, which is typical for fragile colloidal suspensions close to jamming. Furthermore, the glass-forming behaviors were found to be universally conserved in all the cytoplasm samples that originated from different species and developmental stages; they showed the same tendency for diverging at the macromolecule concentrations relevant for living cells. Notably, such fragile behavior disappeared in metabolically active living cells whose viscosity showed a genuine Arrhenius increase as in typical strong glass formers. Being actively driven by metabolism, the living cytoplasm forms glass that is fundamentally different from that of its non-living counterpart.

Feedback-tracking microrheology in living cells

Living cells are composed of active materials, in which forces are generated by the energy derived from metabolism. Forces and structures self-organize to shape the cell and drive its dynamic functions. Understanding the out-of-equilibrium mechanics is challenging because constituent materials, the cytoskeleton and the cytosol, are extraordinarily heterogeneous, and their physical properties are strongly affected by the internally generated forces. We have analyzed dynamics inside two types of eukaryotic cells, fibroblasts and epithelial-like HeLa cells, with simultaneous active and passive microrheology using laser interferometry and optical trapping technology. We developed a method to track microscopic probes stably in cells in the presence of vigorous cytoplasmic fluctuations, by using smooth three-dimensional (3D) feedback of a piezo-actuated sample stage. To interpret the data, we present a theory that adapts the fluctuation-dissipation theorem (FDT) to out-of-equilibrium systems that are subjected to positional feedback, which introduces an additional nonequilibrium effect. We discuss the interplay between material properties and nonthermal force fluctuations in the living cells that we quantify through the violations of the FDT. In adherent fibroblasts, we observed a well-known polymer network viscoelastic response where the complex shear modulus scales as G* ∝ (-iω)3/4. In the more 3D confluent epithelial cells, we found glassy mechanics with G* ∝ (-iω)1/2 that we attribute to glassy dynamics in the cytosol. The glassy state in living cells shows characteristics that appear distinct from classical glasses and unique to nonequilibrium materials that are activated by molecular motors.

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.

High-frequency microrheology reveals cytoskeleton dynamics in living cells

Living cells are viscoelastic materials, with the elastic response dominating at long timescales (≳1 ms)1. At shorter timescales, the dynamics of individual cytoskeleton filaments are expected to emerge, but active microrheology measurements on cells accessing this regime are scarce2. Here, we develop high-frequency microrheology (HF-MR) to probe the viscoelastic response of living cells from 1Hz to 100 kHz. We report the viscoelasticity of different cell types and upon cytoskeletal drug treatments. At previously inaccessible short timescales, cells exhibit rich viscoelastic responses that depend on the state of the cytoskeleton. Benign and malignant cancer cells revealed remarkably different scaling laws at high frequency, providing a univocal mechanical fingerprint. Microrheology over a wide dynamic range up to the frequency of action of the molecular components provides a mechanistic understanding of cell mechanics.