Fast and slow dynamics of the cytoskeleton

Stress and strain in the contractile and cytoskeletal filaments of airway smooth muscle

Stress and strain are omnipresent in the lung due to constant lung volume fluctuation associated with respiration, and they modulate the phenotype and function of all cells residing in the airways including the airway smooth muscle (ASM) cell. There is ample evidence that the ASM cell is very sensitive to its physical environment, and can alter its structure and/or function accordingly, resulting in either desired or undesired consequences. The forces that are either conferred to the ASM cell due to external stretching or generated inside the cell must be borne and transmitted inside the cytoskeleton (CSK). Thus, maintaining appropriate levels of stress and strain within the CSK is essential for maintaining normal function. Despite the importance, the mechanisms regulating/dysregulating ASM cytoskeletal filaments in response to stress and strain remained poorly understood until only recently. For example, it is now understood that ASM length and force are dynamically regulated, and both can adapt over a wide range of length, rendering ASM one of the most malleable living tissues. The malleability reflects the CSK's dynamic mechanical properties and plasticity, both of which strongly interact with the loading on the CSK, and all together ultimately determines airway narrowing in pathology. Here we review the latest advances in our understanding of stress and strain in ASM cells, including the organization of contractile and cytoskeletal filaments, range and adaptation of functional length, structural and functional changes of the cell in response to mechanical perturbation, ASM tone as a mediator of strain-induced responses, and the novel glassy dynamic behaviors of the CSK in relation to asthma pathophysiology.

Electromechanical coupling in the membranes of Shaker-transfected HEK cells

Membranes flex with changes in transmembrane potential as a result of changes in interfacial tension, the Lippman effect. We studied the membrane electromotility of Shaker K(+)-transfected HEK-293 cells in real time by using combined patch-clamp atomic force microscopy. In the voltage range where the channels were closed, Shaker expression had little effect on electromotility relative to wild-type cells. Depolarization between -120 and -40 mV resulted in a linear upward cantilever deflection equivalent to an increase in membrane tension. However, when depolarized sufficiently for channel opening, the electromotility saturated and only recovered over 10 s of milliseconds. This remarkable loss of motility was associated with channel opening, not ionic flux or movement of the voltage sensors. The IL mutant of Shaker, in which the voltage dependence of channel opening but not sensor movement is shifted to more positive potentials, caused the loss of electromotility saturation also to shift to more positive potentials. The temporary loss of electromotility associated with channel opening is probably caused by local buckling of the bilayer as the inner half of the channel expands as expected from X-ray structural data.

Plectin contributes to mechanical properties of living cells

Plectin is a 500-kDa cross-linking protein that plays important roles in a number of cell functions including migration and wound healing. We set out to characterize the role of plectin in mechanical properties of living cells. Plectin(-/-) cells were less stiff than plectin(+/+) cells, but the slopes of the two power laws in response to loading frequencies (0.002-1,000 Hz) were similar. Plectin(-/-) cells lost the capacity to propagate mechanical stresses to long distances in the cytoplasm; traction forces in plectin(-/-) cells were only half of those in plectin(+/+) cells, suggesting that plectin deficiency compromised prestress generation, which, in turn, resulted in the inhibition of long distance stress propagation. Both plectin(+/+) and plectin(-/-) cells exhibited nonlinear stress-strain relationships. However, plectin(+/+) cells, but not plectin(-/-) cells, further stiffened in response to lysophosphatidic acid (LPA). Dynamic fluorescence resonance energy transfer analysis revealed that RhoA GTPase proteins were activated in plectin(+/+) cells but not in plectin(-/-) cells after treatment with LPA. Expression in plectin(-/-) cells of constitutively active RhoA (RhoA-V14) but not a dominant negative mutant of RhoA (RhoA-N19) or an empty vector restored the long distance force propagation behavior, suggesting that plectin is important in normal functions of RhoA. Our findings underscore the importance of plectin for mechanical properties, stress propagation, and prestress of living cells, thereby influencing their biological functions.

Cell stiffness, contractile stress and the role of extracellular matrix

Here we have assessed the effects of extracellular matrix (ECM) composition and rigidity on mechanical properties of the human airway smooth muscle (ASM) cell. Cell stiffness and contractile stress showed appreciable changes from the most relaxed state to the most contracted state: we refer to the maximal range of these changes as the cell contractile scope. The contractile scope was least when the cell was adherent upon collagen V, followed by collagen IV, laminin, and collagen I, and greatest for fibronectin. Regardless of ECM composition, upon adherence to increasingly rigid substrates, the ASM cell positively regulated expression of antioxidant genes in the glutathione pathway and heme oxygenase, and disruption of a redox-sensitive transcription factor, nuclear erythroid 2 p45-related factor (Nrf2), culminated in greater contractile scope. These findings provide biophysical evidence that ECM differentially modulates muscle contractility and, for the first time, demonstrate a link between muscle contractility and Nrf2-directed responses.

The number distribution of complex shear modulus of single cells measured by atomic force microscopy

The viscoelastic properties of a large number of mouse fibroblast NIH3T3 cells (n approximately 130) were investigated by combining atomic force microscopy (AFM) with a microarray technique. In the experiments, the cells were arranged and cultured in the wells of a microarray substrate, and a force modulation mode experiment was used to measure the complex shear modulus, G*, of individual cells in a frequency range 0.5-200Hz. The frequency dependence of G* of the cells exhibited a power-law behavior and similar frequency dependencies have been observed in several cell types cultured on flat substrates. This indicated that the NIH3T3 cells cultured in the wells of a microarray have analogous structural organization to those cells cultured on flat substrates. The number distribution of both the storage and loss moduli of G* fitted well to a log-normal distribution function, whereas the power-law exponent estimated by a power-law structural damping model showed a normal distribution function. These results showed that combining AFM with a microarray technique was a suitable approach for investigating the statistics of rheological properties of living cells without the requirement of cell surface modification.

Biomechanics: cell research and applications for the next decade

With the recent revolution in Molecular Biology and the deciphering of the Human Genome, understanding of the building blocks that comprise living systems has advanced rapidly. We have yet to understand, however, how the physical forces that animate life affect the synthesis, folding, assembly, and function of these molecular building blocks. We are equally uncertain as to how these building blocks interact dynamically to create coupled regulatory networks from which integrative biological behaviors emerge. Here we review recent advances in the field of biomechanics at the cellular and molecular levels, and set forth challenges confronting the field. Living systems work and move as multi-molecular collectives, and in order to understand key aspects of health and disease we must first be able to explain how physical forces and mechanical structures contribute to the active material properties of living cells and tissues, as well as how these forces impact information processing and cellular decision making. Such insights will no doubt inform basic biology and rational engineering of effective new approaches to clinical therapy.

Continuum modeling of forces in growing viscoelastic cytoskeletal networks

Mechanical properties of the living cell are important in cell movement, cell division, cancer development and cell signaling. There is considerable interest in measuring local mechanical properties of living materials and the living cytoskeleton using micromechanical techniques. However, living materials are constantly undergoing internal dynamics such as growth and remodeling. A modeling framework that combines mechanical deformations with cytoskeletal growth dynamics is necessary to describe cellular shape changes. The present paper develops a general finite deformation modeling approach that can treat the viscoelastic cytoskeleton. Given the growth dynamics in the cytoskeletal network and the relationship between deformation and stress, the shape of the network is computed in an incremental fashion. The growth dynamics of the cytoskeleton can be modeled as stress dependent. The result is a consistent treatment of overall cell deformation. The framework is applied to a growing 1-d bundle of actin filaments against an elastic cantilever, and a 2-d cell undergoing wave-like protrusion dynamics. In the latter example, mechanical forces on the cell adhesion are examined as a function of the protrusion dynamics.

The mechanical transduction of physiological strength electric fields

In this article it is proposed that electric fields of physiological strength (approximately 100 V/m) are transduced by the mechanical torque they exert on glycoproteins. The resulting mechanical signal is then transmitted to the cytoskeleton and propagated throughout the cell interior. This mechanical coupling is analyzed for transmembrane glycoproteins, such as integrins and the glycocalyx, and for glycoproteins in the extracellular matrix of cartilage. The applied torque is opposed by viscous fluid drag and restoring forces exerted by adjacent molecules in the membrane or cartilage. The resulting system represents a damped, driven harmonic oscillator. The amplitude of oscillation is constant at low frequencies, but falls off rapidly in the range 1-1000 Hz. The transition frequency depends on parameters such as the viscosity of the surrounding fluid and the restoring force exerted by the surrounding structure. The amplitude increases as the fourth power of the length of the transmembrane glycoproteins and as the square of the applied field. This process may operate in concert with other transduction mechanisms, such as the opening of voltage-gated channels and electrodiffusion/osmosis for DC fields.

Contribution of actin filaments and microtubules to quasi-in situ tensile properties and internal force balance of cultured smooth muscle cells on a substrate

The effects of actin filaments (AFs) and microtubules (MTs) on quasi-in situ tensile properties and intracellular force balance were studied in cultured rat aortic smooth muscle cells (SMCs). A SMC cultured on substrates was held using a pair of micropipettes, gradually detached from the substrate while maintaining in situ cell shape and cytoskeletal integrity, and then stretched up to approximately 15% and unloaded three times at the rate of 1 mum every 5 s. Cell stiffness was approximately 20 nN per percent strain in the untreated case and decreased by approximately 65% and approximately 30% following AF and MT disruption, respectively. MT augmentation did not affect cell stiffness significantly. The roles of AFs and MTs in resisting cell stretching and shortening were assessed using the area retraction of the cell upon noninvasive detachment from thermoresponsive gelatin-coated dishes. The retraction was approximately 40% in untreated cells, while in AF-disrupted cells it was <20%. The retraction increased by approximately 50% and decreased by approximately 30% following MT disruption and augmentation, respectively, suggesting that MTs resist intercellular tension generated by AFs. Three-dimensional measurements of cell morphology using confocal microscopy revealed that the cell volume remained unchanged following drug treatment. A concomitant increase in cell height and decrease in cell area was observed following AF disruption and MT augmentation. In contrast, MT disruption significantly reduced the cell height. These results indicate that both AFs and MTs play crucial roles in maintaining whole cell mechanical properties of SMCs, and that while AFs act as an internal tension generator, MTs act as a tension reducer, and these contribute to intracellular force balance three dimensionally.

Is cell rheology governed by nonequilibrium-to-equilibrium transition of noncovalent bonds?

A living cell deforms or flows in response to mechanical stresses. A recent report shows that dynamic mechanics of living cells depends on the timescale of mechanical loading, in contrast to the prevailing view of some authors that cell rheology is timescale-free. Yet the molecular basis that governs this timescale-dependent behavior is elusive. Using molecular dynamics simulations of protein-protein noncovalent interactions, we show that multipower laws originate from a nonequilibrium-to-equilibrium transition: when the loading rate is faster than the transition rate, the power-law exponent alpha(1) is weak; when the loading rate is slower than the transition rate, the exponent alpha(2) is strong. The model predictions are confirmed in both embryonic stem cells and differentiated cells. Embryonic stem cells are less stiff, more fluidlike, and exhibit greater alpha(1) than their differentiated counterparts. By introducing a near-equilibrium frequency f(eq), we show that all data collapse into two power laws separated by f/f(eq), which is unity. These findings suggest that the timescale-dependent rheology in living cells originates from the nonequilibrium-to-equilibrium transition of the dynamic response of distinct, force-driven molecular processes.

Exciting cytoskeleton-membrane waves

Propagating waves on the surface of cells, over many micrometers, involve active forces. We investigate here the mechanical excitation of such waves when the membrane is perturbed by an external oscillatory force. The external perturbation may trigger the propagation of such waves away from the force application. This scheme is then suggested as a method to probe the properties of the excitable medium of the cell, and learn about the mechanisms that drive the wave propagation. We then apply these ideas to a specific model of active cellular membrane waves, demonstrating how the response of the system to the external perturbation depends on the properties of the model. The most outstanding feature that we find is that the excited waves exhibit a resonance phenomenon at the frequency corresponding to the tendency of the system to develop a linear instability. Mechanical excitation of membrane waves in cells at different frequencies can therefore be used to characterize the properties of the mechanism underlying the existence of these waves.

Power-law creep behavior of a semiflexible chain

Rheological properties of adherent cells are essential for their physiological functions, and microrheological measurements on living cells have shown that their viscoelastic responses follow a weak power law over a wide range of time scales. This power law is also influenced by mechanical prestress borne by the cytoskeleton, suggesting that cytoskeletal prestress determines the cell's viscoelasticity, but the biophysical origins of this behavior are largely unknown. We have recently developed a stochastic two-dimensional model of an elastically joined chain that links the power-law rheology to the prestress. Here we use a similar approach to study the creep response of a prestressed three-dimensional elastically jointed chain as a viscoelastic model of semiflexible polymers that comprise the prestressed cytoskeletal lattice. Using a Monte Carlo based algorithm, we show that numerical simulations of the chain's creep behavior closely correspond to the behavior observed experimentally in living cells. The power-law creep behavior results from a finite-speed propagation of free energy from the chain's end points toward the center of the chain in response to an externally applied stretching force. The property that links the power law to the prestress is the chain's stiffening with increasing prestress, which originates from entropic and enthalpic contributions. These results indicate that the essential features of cellular rheology can be explained by the viscoelastic behaviors of individual semiflexible polymers of the cytoskeleton.

Transient binding and dissipation in cross-linked actin networks

In contrast with entangled actin solutions, transiently cross-linked actin networks can provide highly elastic properties while still allowing for local rearrangements in the microstructure-on biological relevant time scales. Here, we show that thermal unbinding of transient cross-links entails local stress relaxation and energy dissipation in an intermediate elasticity dominated frequency regime. We quantify the viscoelastic response of an isotropically cross-linked actin network by experimentally tuning the off rate of the transiently cross-linking molecules, their density, and the solvent viscosity. We reproduce the measured frequency response by a semiphenomenological model that is predicated on microscopic unbinding events.

Dynamical theory of active cellular response to external stress

We present a comprehensive, theoretical treatment of the orientational response to external stress of active, contractile cells embedded in a gel-like elastic medium. The theory includes both the forces that arise from the deformation of the matrix as well as forces due to the internal regulation of the stress fibers and focal adhesions of the cell. We calculate the time-dependent response of both the magnitude and the direction of the elastic dipole that characterizes the active forces exerted by the cell, for various situations. For static or quasistatic external stress, cells orient parallel to the stress while for high frequency dynamic external stress, cells orient nearly perpendicular. Both numerical and analytical calculations of these effects are presented. In addition we predict the relaxation time for the cellular response for both slowly and rapidly varying external stresses; several characteristic scaling regimes for the relaxation time as a function of applied frequency are predicted. We also treat the case of cells for which the regulation of the stress fibers and focal adhesions is controlled by strain (instead of stress) and show that the predicted dependence of the cellular orientation on the Poisson ratio of the matrix can differentiate strain vs stress regulation of cellular response.

Adaptation of airway smooth muscle to basal tone: relevance to airway hyperresponsiveness

Lung inflammation and airway hyperresponsiveness (AHR) are hallmarks of asthma, but their interrelationship is unclear. Excessive shortening of airway smooth muscle (ASM) in response to bronchoconstrictors is likely an important determinant of AHR. Hypercontractility of ASM could stem from a change in the intrinsic properties of the muscle, or it could be due to extrinsic factors such as chronic exposure of the muscle to inflammatory mediators in the airways. The latter could be the link between lung inflammation and AHR. The present study was designed to examine the influence of chronic exposure to a contractile agonist on the force-generating capacity of ASM. Force generation in response to electric field stimulation (EFS) was measured in ovine trachealis with or without a basal tone induced by acetylcholine (ACh). While the tone was maintained, the EFS-induced force decreased transiently but increased over time to reach a plateau in approximately 50 minutes. The total force (ACh tone + EFS force) increased monotonically and in proportion to ACh concentration. The results indicate that the muscle adapted to the basal tone and regained its contractile ability in response to a second stimulus (EFS) over time. Analysis suggests that this is due to a cytoskeletal transformation that allows the cytoskeleton to bear force, thus freeing up actomyosin crossbridges to generate more force. Force adaptation in ASM as a consequence of prolonged exposure to the many spasmogens found in asthmatic airways could be a mechanism contributing to AHR seen in asthma.

Fast fluorescence laser tracking microrheometry, II: quantitative studies of cytoskeletal mechanotransduction

Fluorescence laser tracking microrheometry (FLTM) is what we believe to be a novel method able to assess the local, frequency-dependent mechanical properties of living cells with nanometer spatial sensitivity at speeds up to 50 kHz. In an earlier article, we described the design, development, and optimization phases of the FLTM before reporting its performances in a variety of viscoelastic materials. In the work presented here, we demonstrate the suitability of FLTM to study local cellular rheology and obtain values for the storage and loss moduli G'(omega) and G''(omega) of fibroblasts consistent with past literature. We further establish that chemically induced cytoskeletal disruption is accompanied by reduced cellular stiffness and viscosity. Next, we provide a systematic study of some experimental variables that may critically influence microrheology measurements. First, we interrogate and justify the relevance of bead endocytosis as a method of cellular internalization of 1-microm probes in FLTM. Second, we show that as sample temperature increases, FLTM findings are elevated toward higher frequencies. Third, we confirm that relevant bead sizes (1 and 2 microm) have no effect on FLTM measurements. Fourth, we report the lack of influence of bead coatings (antiintegrin, antitransferrin, antidystroglycan, or uncoated tracers were surveyed) on their rheological readouts. Finally, we demonstrate the potential of FLTM in studying how substratum rigidity regulates cellular rheological properties. Interestingly, multiple, coupled strain relaxation mechanisms can be observed separated by two plateau moduli. Although these observations can be partly explained by rheological theories describing entangled actin filaments, there is a clear need to extend existing microrheology models to the cytoskeleton, including potentially important factors such as network geometry and remodeling.

Screening of hydrodynamic interactions in Brownian rod suspensions

We present the details and results of a simulation study addressing the dynamics and rheology of rod suspensions over a wide regime of concentrations ranging from dilute to concentrated systems. Our study compares the results of two complementary simulation methods. The first method adapts a recently proposed explicit solvent simulation strategy and incorporates both hydrodynamical effects and steric interactions between the rod units. We compare the results of such a method with those obtained from a Brownian dynamics simulation approach which retains the steric interactions but neglects the effects of hydrodynamic interactions. Overall, our results in the context of the translational and rotational diffusivities are in agreement with the hydrodynamical predictions in the dilute regime and the corresponding results of the tube model and its extensions thereof in the semidilute regimes. The latter results suggest that effects of hydrodynamic interactions on the translational and rotational diffusivities are secondary relative to the steric interactions and at best lead only to a small correction to the results of the classical tube model. Our results in the context of linear viscoelasticity also broadly confirms the predictions of the tube model for the storage and loss moduli and allows us to extract for the first time the independent hydrodynamic and Brownian contributions to the zero shear viscosity. While the relative magnitudes of these contributions are consistent with the theoretical predictions, the quantitative magnitudes are quite different from the theoretical predictions. Overall, these results confirm the validity of the hydrodynamic "screening" hypothesis and ratify the neglect of hydrodynamical stresses in quantifying the linear rheology of Brownian rod suspensions.

A mechanics model of microtubule buckling in living cells

As the most rigid cytoskeletal filaments, microtubules bear compressive forces in living cells, balancing the tensile forces within the cytoskeleton to maintain the cell shape. It is often observed that, in living cells, microtubules under compression severely buckle into short wavelengths. By contrast, when compressed, isolated microtubules in vitro buckle into single long-wavelength arcs. The critical buckling force of the microtubules in vitro is two orders of magnitude lower than that of the microtubules in living cells. To explain this discrepancy, we describe a mechanics model of microtubule buckling in living cells. The model investigates the effect of the surrounding filament network and the cytosol on the microtubule buckling. The results show that, while the buckling wavelength is set by the interplay between the microtubules and the elastic surrounding filament network, the buckling growth rate is set by the viscous cytosol. By considering the nonlinear deformation of the buckled microtubule, the buckling amplitude can be determined at the kinetically constrained equilibrium. The model quantitatively correlates the microtubule bending rigidity, the surrounding filament network elasticity, and the cytosol viscosity with the buckling wavelength, the buckling growth rate, and the buckling amplitude of the microtubules. Such results shed light on designing a unified experimental protocol to measure various critical mechanical properties of subcellular structures in living cells.

On the cytoskeleton and soft glassy rheology

The cytoskeleton is a complex structure within the cellular corpus that is responsible for the main structural properties and motilities of cells. A wide range of models have been utilized to understand cytoskeletal rheology and mechanics (see e.g. [Mofrad, M., Kamm, R., 2006. Cytoskeletal Mechanics: Models and Measurements. Cambridge University Press, Cambridge]). From this large collection of proposed models, the soft glassy rheological model (originally developed for inert soft glassy materials) has gained a certain traction in the literature due to the close resemblance of its predictions to certain mechanical data measured on cell cultures [Fabry, B., Maksym, G., Butler, J., Glogauer, M., Navajas, D., Fredberg, J., 2001. Scaling the microrheology of living cells. Physical Review Letters 87, 14102]. We first review classical linear rheological theory in a concise fashion followed by an examination of the soft glassy rheological theory. With this background we discuss the observed behavior of the cytoskeleton and the inherent limitations of classical rheological models for the cytoskeleton. This then leads into a discussion of the advantages and disadvantages presented to us by the soft glassy rheological model. We close with some comments of caution and recommendations on future avenues of exploration.

Imaging red blood cell dynamics by quantitative phase microscopy

Red blood cells (RBCs) play a crucial role in health and disease, and structural and mechanical abnormalities of these cells have been associated with important disorders such as Sickle cell disease and hereditary cytoskeletal abnormalities. Although several experimental methods exist for analysis of RBC mechanical properties, optical methods stand out as they enable collecting mechanical and dynamic data from live cells without physical contact and without the need for exogenous contrast agents. In this report, we present quantitative phase microscopy techniques that enable imaging RBC membrane fluctuations with nanometer sensitivity at arbitrary time scales from milliseconds to hours. We further provide a theoretical framework for extraction of membrane mechanical and dynamical properties using time series of quantitative phase images. Finally, we present an experimental approach to extend quantitative phase imaging to 3-dimensional space using tomographic methods. By providing non-invasive methods for imaging mechanics of live cells, these novel techniques provide an opportunity for high-throughput analysis and study of RBC mechanical properties in health and disease.

Cytoskeletal mechanics in airway smooth muscle cells

Mechanical properties and contractility of airway smooth muscle tissue are largely responsible for airway narrowing and airway hyperresponsiveness in asthma. To explain these pathological phenomena, investigators have studied the mechanical behaviour of airway smooth muscle cells and its relationship to the underlying cellular biophysical and biochemical mechanisms. During the past decade, a growing body of evidence has indicated that a deformable intracellular polymer network, known as the cytoskeleton, plays a major role in transmitting and distributing mechanical forces within the cell and in their conversion into biochemical responses. We review here evidence suggesting that the tensed and crosslinked cytoskeletal lattice, the contractile apparatus, and the cytoskeleton-extracellular matrix interactions are key determinants of mechanical properties and mechanosensing of airway smooth muscle cells, with the mechanical distending stress of the cytoskeleton playing the central role.

Different effects of deep inspirations on central and peripheral airways in healthy and allergen-challenged mice

BACKGROUND

Deep inspirations (DI) have bronchodilatory and bronchoprotective effects in healthy human subjects, but these effects appear to be absent in asthmatic lungs. We have characterized the effects of DI on lung mechanics during mechanical ventilation in healthy mice and in a murine model of acute and chronic airway inflammation.

METHODS

Balb/c mice were sensitized to ovalbumin (OVA) and exposed to nebulized OVA for 1 week or 12 weeks. Control mice were challenged with PBS. Mice were randomly selected to receive DI, which were given twice during the minute before assessment of lung mechanics.

RESULTS

DI protected against bronchoconstriction of central airways in healthy mice and in mice with acute airway inflammation, but not when OVA-induced chronic inflammation was present. DI reduced lung resistance induced by methacholine from 3.8 +/- 0.3 to 2.8 +/- 0.1 cmH2O.s.mL-1 in healthy mice and 5.1 +/- 0.3 to 3.5 +/- 0.3 cmH2O.s.mL-1 in acute airway inflammation (both P < 0.001). In healthy mice, DI reduced the maximum decrease in lung compliance from 15.9 +/- 1.5% to 5.6 +/- 0.6% (P < 0.0001). This protective effect was even more pronounced in mice with chronic inflammation where DI attenuated maximum decrease in compliance from 44.1 +/- 6.6% to 14.3 +/- 1.3% (P < 0.001). DI largely prevented increased peripheral tissue damping (G) and tissue elastance (H) in both healthy (G and H both P < 0.0001) and chronic allergen-treated animals (G and H both P < 0.0001).

CONCLUSION

We have tested a mouse model of potential value for defining mechanisms and sites of action of DI in healthy and asthmatic human subjects. Our current results point to potent protective effects of DI on peripheral parts of chronically inflamed murine lungs and that the presence of DI may blunt airway hyperreactivity.

Cell and biomolecular mechanics in silico

Recent developments in computational cell and biomolecular mechanics have provided valuable insights into the mechanical properties of cells, subcellular components and biomolecules, while simultaneously complementing new experimental techniques used for deciphering the structure-function paradigm in living cells. These computational approaches have direct implications in understanding the state of human health and the progress of disease and can therefore aid immensely in the diagnosis and treatment of diseases. We provide an overview of the computational approaches that are currently used in understanding various aspects of cell and bimolecular mechanics. Our emphasis is on state-of-the-art techniques and the progress made in addressing key challenges in biomechanics.

Strange dynamics of a dynamic cytoskeleton

A novel physical perspective of molecular interactions within the cytoskeleton of the airway smooth muscle cell may help to explain why the most efficacious of all known bronchodilatory agencies-a simple deep inspiration-becomes abrogated during the spontaneous asthma attack and leads thereby to excessive airway narrowing. This perspective invites us to think of airway smooth muscle not only biochemically as a nidus of traditional cell signaling and immune modulation or mechanically as a motor for generation of active forces but also physically as a phase of soft condensed matter that can restrict airway stretch and dilation. This is perhaps a risky path and is surely an unconventional one, but it is where the trail of evidence leads. This line of investigation is unlikely by itself to provide an asthma cure but will lead to a new conceptual framework without which novel pathways, unsuspected phase transitions, and unanticipated mechanisms of action of target molecules would almost surely remain hidden. Glassy dynamics of the cytoskeleton are likely to be important in a wide range of biological functions and disease processes, but had it not been for their preeminent role in bronchospasm, they might never have been discovered.

Glass transition and rheological redundancy in F-actin solutions

The unique mechanical performance of animal cells and tissues is attributed mostly to their internal biopolymer meshworks. Its perplexing universality and robustness against structural modifications by drugs and mutations is an enigma in cell biology and provides formidable challenges to materials science. Recent investigations could pinpoint highly universal patterns in the soft glassy rheology and nonlinear elasticity of cells and reconstituted networks. Here, we report observations of a glass transition in semidilute F-actin solutions, which could hold the key to a unified explanation of these phenomena. Combining suitable rheological protocols with high-precision dynamic light scattering, we can establish a remarkable rheological redundancy and trace it back to a highly universal exponential stretching of the single-polymer relaxation spectrum of a "glassy wormlike chain." By exploiting the ensuing generalized time-temperature superposition principle, the time domain accessible to microrheometry can be extended by several orders of magnitude, thus opening promising new metrological opportunities.

Biophysical basis for airway hyperresponsiveness

Airway hyperresponsiveness is the excessive narrowing of the airway lumen caused by stimuli that would cause little or no narrowing in the normal individual. It is one of the cardinal features of asthma, but its mechanisms remain unexplained. In asthma, the key end-effector of acute airway narrowing is contraction of the airway smooth muscle cell that is driven by myosin motors exerting their mechanical effects within an integrated cytoskeletal scaffolding. In just the past few years, however, our understanding of the rules that govern muscle biophysics has dramatically changed, as has their classical relationship to airway mechanics. It has become well established, for example, that muscle length is equilibrated dynamically rather than statically, and that in a dynamic setting nonclassical features of muscle biophysics come to the forefront, including unanticipated interactions between the muscle and its time-varying load, as well as the ability of the muscle cell to adapt (remodel) its internal microstructure rapidly in response to its ever-changing mechanical environment. Here, we consider some of these emerging concepts and, in particular, focus on structural remodeling of the airway smooth muscle cell as it relates to excessive airway narrowing in asthma.

Cytoskeletal bundle mechanics

The mechanical properties of cytoskeletal actin bundles play an essential role in numerous physiological processes, including hearing, fertilization, cell migration, and growth. Cells employ a multitude of actin-binding proteins to actively regulate bundle dimensions and cross-linking properties to suit biological function. The mechanical properties of actin bundles vary by orders of magnitude depending on diameter and length, cross-linking protein type and concentration, and constituent filament properties. Despite their importance to cell function, the molecular design principles responsible for this mechanical behavior remain unknown. Here, we examine the mechanics of cytoskeletal bundles using a molecular-based model that accounts for the discrete nature of constituent actin filaments and their distinct cross-linking proteins. A generic competition between filament stretching and cross-link shearing determines three markedly different regimes of mechanical response that are delineated by the relative values of two simple design parameters, revealing the universal nature of bundle-bending mechanics. In each regime, bundle-bending stiffness displays distinct scaling behavior with respect to bundle dimensions and molecular composition, as observed in reconstituted actin bundles in vitro. This mechanical behavior has direct implications on the physiological bending, buckling, and entropic stretching behavior of cytoskeletal processes, as well as reconstituted actin systems. Results are used to predict the bending regimes of various in vivo cytoskeletal bundles that are not easily accessible to experiment and to generate hypotheses regarding implications of the isolated behavior on in vivo bundle function.

Fragility and mechanosensing in a thermalized cytoskeleton model with forced protein unfolding

We describe a model of cytoskeletal mechanics based on the force-induced conformational change of protein cross-links in a stressed polymer network. Slow deformation of simulated networks containing cross-links that undergo repeated, serial domain unfolding leads to an unusual state-with many cross-links accumulating near the critical force for further unfolding. This state is robust to thermalization and does not occur in similar protein unbinding based simulations. Moreover, we note that the unusual configuration of near-critical protein cross-links in the fragile state provides a physical mechanism for the chemical transduction of cell-level mechanical strain and extra-cellular matrix stiffness.

Cell mechanics: integrating cell responses to mechanical stimuli

Forces are increasingly recognized as major regulators of cell structure and function, and the mechanical properties of cells are essential to the mechanisms by which cells sense forces, transmit them to the cell interior or to other cells, and transduce them into chemical signals that impact a spectrum of cellular responses. Comparison of the mechanical properties of intact cells with those of the purified cytoskeletal biopolymers that are thought to dominate their elasticity reveal the extent to which the studies of purified systems can account for the mechanical properties of the much more heterogeneous and complex cell. This review summarizes selected aspects of current work on cell mechanics with an emphasis on the structures that are activated in cell-cell contacts, that regulate ion flow across the plasma membrane, and that may sense fluid flow that produces low levels of shear stress.

Out-of-equilibrium dynamics in the cytoskeleton of the living cell

We report here measurements of rheological properties of the human airway smooth muscle cell using forced nanoscale motions of Arg-Gly-Asp RGD-coated microbeads tightly bound to the cytoskeleton. With changes of forcing amplitude, the storage modulus showed small but systematic nonlinearities, especially after treatment with a contractile agonist. In a dose-dependent manner, a large oscillatory shear applied from a few seconds up to 400 s caused the cytoskeleton matrix to soften, a behavior comparable to physical rejuvenation observed in certain inert soft materials; the stiffness remained constant for as long as the large oscillatory shear was maintained, but suddenly fell with shear cessation. Stiffness then followed a slow scale-free recovery, a phenomenon comparable to physical aging. However, acetylated low-density lipoprotein acLDL-coated microbeads, which connect mainly to scavenger receptors, did not show similar out-of-equilibrium behaviors. Taken together, these data demonstrate in the cytoskeleton of the living cell behaviors with all the same signatures as that of soft inert condensed systems. This unexpected intersection of condensed matter physics and cytoskeletal biology suggests that trapping, intermittency, and approach to kinetic arrest represent central mesoscale features linking underlying molecular events to integrative cellular functions.

Physical integrity of smooth muscle myosin filaments is enhanced by phosphorylation of the regulatory myosin light chain

BACKGROUND AND AIMS

Smooth muscle myosin monomers self-assemble in solution to form filaments. Phosphorylation of the 20-kD regulatory myosin light chain (MLC20) enhances filament formation. It is not known whether the phosphorylated and non-phosphorylated filaments possess the same structural integrity.

METHODS

We purified myosin from bovine trachealis to form filaments, in ATP-containing zero-calcium solution during a slow dialysis that gradually reduced the ionic strength. Sufficient myosin light chain kinase and phosphatase, as well as calmodulin, were retained after the myosin purification and this enabled phosphorylation of MLC20 within 20-40s after addition of calcium to the filament suspension. The phosphorylated and non-phosphorylated filaments were then partially disassembled by ultrasonification. The extent of filament disintegration was visualized and quantified by atomic force microscopy.

RESULTS

MLC20 phosphorylation reduced the diameter of the filaments and rendered the filaments more resistant to ultrasonic agitation. Electron microscopy revealed a similar reduction in filament diameter in intact smooth muscle when the cells were activated.

CONCLUSION

Modification of the structural and physical properties of myosin filaments by MLC20 phosphorylation may be a key regulation step in smooth muscle where formation and dissolution of the filaments are required in the cells' adaptation to different cell length.

Coherence properties of red blood cell membrane motions

We use a highly sensitive, noncontact, optical interferometric technique to quantify the red blood cell membrane fluctuations at the nanometer and millisecond scales. The results reveal significant properties of both temporal and spatial coherence associated with the membrane dynamics. We show that these correlations can be accounted for by the viscoelastic properties of the cell membrane. From this measurement, we extract the loss and storage moduli associated with the membrane and find a crossover frequency at which the buffer viscosity seems to become dominant.

Rheological behavior of living cells is timescale-dependent

The dynamic mechanical behavior of living cells has been proposed to result from timescale-invariant processes governed by the soft glass rheology theory derived from soft matter physics. But this theory is based on experimental measurements over timescales that are shorter than those most relevant for cell growth and function. Here we report results measured over a wider range of timescales which demonstrate that rheological behaviors of living cells are not timescale-invariant. These findings demonstrate that although soft glass rheology appears to accurately predict certain cell mechanical behaviors, it is not a unified model of cell rheology under biologically relevant conditions and thus, alternative mechanisms need to be considered.

Mechanics of single cells: rheology, time dependence, and fluctuations

The results of mechanical measurements on single cultured epithelial cells using both magnetic twisting cytometry (MTC) and laser tracking microrheology (LTM) are described. Our unique approach uses laser deflection for high-performance tracking of cell-adhered magnetic beads either in response to an oscillatory magnetic torque (MTC) or due to random Brownian or ATP-dependent forces (LTM). This approach is well suited for accurately determining the rheology of single cells, the study of temporal and cell-to-cell variations in the MTC signal amplitude, and assessing the statistical character of the tracers' random motion in detail. The temporal variation of the MTC rocking amplitude is surprisingly large and manifests as a frequency-independent multiplicative factor having a 1/f spectrum in living cells, which disappears upon ATP depletion. In the epithelial cells we study, random bead position fluctuations are Gaussian to the limits of detection both in the Brownian and ATP-dependent cases, unlike earlier studies on other cell types.

Rheological properties of aging thermosensitive suspensions

Aging observed in soft glassy materials inherently affects the rheological properties of these systems and has been described by the soft glassy rheology (SGR) model [S. M. Fielding, J. Rheol. 44, 323 (2000)]. In this paper, we report the measured linear rheological behavior of thermosensitive microgel suspensions and compare it quantitatively with the predictions of the SGR model. The dynamic moduli [G'(omega,t) and G''(omega,t)] obtained from oscillatory measurements are in good agreement with the model. The model also predicts quantitatively the creep compliance J(t - t(w),t(w)), obtained from step stress experiments, for the short time regime [(t - t(w)) < t(w)]. The relative effective temperature X/X(g) obtained from both the oscillatory and the step stress experiments is indeed less than 1 (XX(g) < 1) in agreement with the definition of aging. Moreover, the elasticity of the compressed particles (G(p)) increases with increased compression, i.e., the degree of hindrance and consequently also the bulk elasticity (G' and 1/J) increases with the degree of compression.

Mechanism of partial adaptation in airway smooth muscle after a step change in length

The phenomenon of length adaptation in airway smooth muscle (ASM) is well documented; however, the underlying mechanism is less clear. Evidence to date suggests that the adaptation involves reassembly of contractile filaments, leading to reconfiguration of the actin filament lattice and polymerization or depolymerization of the myosin filaments within the lattice. The time courses for these events are unknown. To gain insights into the adaptation process, we examined ASM mechanical properties and ultrastructural changes during adaptation. Step changes in length were applied to isolated bundles of ASM cells; changes in force, shortening velocity, and myosin filament mass were then quantified. A greater decrease in force was found following an acute decrease in length, compared with that of an acute increase in length. A decrease in myosin filament mass was also found with an acute decrease in length. The shortening velocity measured immediately after the length change was the same as that measured after the muscle had fully adapted to the new length. These observations can be explained by a model in which partial adaptation of the muscle leads to an intermediate state in which reconfiguration of the myofilament lattice occurred rapidly, followed by a relatively slow process of polymerization of myosin filaments within the lattice. The partially adapted intermediate state is perhaps more physiologically relevant than the fully adapted state seen under static conditions, and it simulates a more realistic behavior for ASM in vivo.

Viscoelasticity of the human red blood cell

We report here the first measurements of the complex modulus of the isolated red blood cell (RBC). Because the RBC is often larger than capillary diameter, important determinants of microcirculatory function are RBC deformability and its changes with pathologies, such as sickle cell disease and malaria. A functionalized ferrimagnetic microbead was attached to the membrane of healthy RBC and then subjected to an oscillatory magnetic field. The resulting torque caused cell deformation. From the oscillatory forcing and resulting bead motions, which were tracked optically, we computed elastic and frictional moduli, g′ and g‴, respectively, from 0.1 to 100 Hz. The g′ was nearly frequency independent and dominated the response at all but the highest frequencies measured. Over three frequency decades, g‴ increased as a power law with an exponent of 0.64, a result not predicted by any simple model. These data suggest that RBC relaxation times that have been reported previously, and any models that rest upon them, are artifactual; the artifact, we suggest, arises from forcing to an exponential fit data of limited temporal duration. A linear range of response was observed, but, as forcing amplitude increased, nonlinearities became clearly apparent. A finite element model suggests that membrane bending was localized to the vicinity of the bead and dominated membrane shear. While the mechanisms accounting for these RBC dynamics remain unclear, methods described here establish new avenues for the exploration of connections among the mechanical, chemical, and biological characteristics of the RBC in health and disease.

Directional memory and caged dynamics in cytoskeletal remodelling

We report directional memory of spontaneous nanoscale displacements of an individual bead firmly anchored to the cytoskeleton of a living cell. A novel method of analysis shows that for shorter time intervals cytoskeletal displacements are antipersistent and thus provides direct evidence in a living cell of molecular trapping and caged dynamics. At longer time intervals displacements are persistent. The transition from antipersistence to persistence is indicative of a time-scale for cage rearrangements and is found to depend upon energy release due to ATP hydrolysis and proximity to a glass transition. Anomalous diffusion is known to imply memory, but we show here that memory is attributed to direction rather than step size. As such, these data are the first to provide a molecular-scale physical picture describing the cytoskeletal remodelling process and its rate of progression.

Ultrastructural basis of airway smooth muscle contractionThis article is one of a selection of papers published in the Special Issue on Recent Advances in Asthma Research

The sliding filament theory of contraction that was developed for striated muscle is generally believed to be also applicable to smooth muscle. However, the well-organized myofilament lattice (i.e., the sarcomeric structure) found in striated muscle has never been clearly delineated in smooth muscle. There is evidence that the myofilament lattice in some smooth muscles, such as airway smooth muscle, is malleable; it can be reshaped to fit a large range of cell dimensions while the maximal overlap between the contractile filaments is maintained. In this review, some early models of the structurally static contractile apparatus of smooth muscle are described. The focus of the review, however, is on the recent findings supporting a model of structurally dynamic contractile apparatus and cytoskeleton for airway smooth muscle. A list of unanswered questions regarding smooth muscle ultrastructure is also proposed in this review, in the hope that it will provide some guidance for future research.

Universal physical responses to stretch in the living cell

With every beat of the heart, inflation of the lung or peristalsis of the gut, cell types of diverse function are subjected to substantial stretch. Stretch is a potent stimulus for growth, differentiation, migration, remodelling and gene expression. Here, we report that in response to transient stretch the cytoskeleton fluidizes in such a way as to define a universal response class. This finding implicates mechanisms mediated not only by specific signalling intermediates, as is usually assumed, but also by non-specific actions of a slowly evolving network of physical forces. These results support the idea that the cell interior is at once a crowded chemical space and a fragile soft material in which the effects of biochemistry, molecular crowding and physical forces are complex and inseparable, yet conspire nonetheless to yield remarkably simple phenomenological laws. These laws seem to be both universal and primitive, and thus comprise a striking intersection between the worlds of cell biology and soft matter physics.

Fresnel particle tracing in three dimensions using diffraction phase microscopy

We have developed a novel experimental technique for tracking small particles in three dimensions with nanometer accuracy. The longitudinal positioning of a micrometer-sized particle is determined by using the Fresnel approximation to describe the transverse distribution of the wavefront that originated in the particle. The method utilizes the high-sensitivity quantitative phase imaging capability of diffraction phase microscopy recently developed in our laboratory. We demonstrate the principle of the technique with experiments on Brownian particles jittering in water both in bulk and in the vicinity of a boundary. The particles are localized in space within an error cube of 20 nm x 20 nm x 20 nm for a 33 Hz acquisition rate and 20s recording time.

Unfolding cross-linkers as rheology regulators in F-actin networks

We report on the nonlinear mechanical properties of a statistically homogeneous, isotropic semiflexible network cross-linked by polymers containing numerous small unfolding domains, such as the ubiquitous F-actin cross-linker filamin. We show that the inclusion of such proteins has a dramatic effect on the large strain behavior of the network. Beyond a strain threshold, which depends on network density, the unfolding of protein domains leads to bulk shear softening. Past this critical strain, the network spontaneously organizes itself so that an appreciable fraction of the filamin cross-linkers are at the threshold of domain unfolding. We discuss via a simple mean-field model the cause of this network organization and suggest that it may be the source of power-law relaxation observed in in vitro and in intracellular microrheology experiments. We present data which fully justify our model for a simplified network architecture.

Thermokinetic approach of single particles and clusters involving anomalous diffusion under viscoelastic response

We present a thermokinetic description of anomalous diffusion of single particles and clusters in a viscoelastic medium in terms of a non-Markovian diffusion equation involving memory functions. The scaling behavior of these functions is analyzed by considering hydrodynamics and cluster-size space random walk arguments. We explain experimental results on diffusion of Brownian particles in the cytoskeleton, in cluster-cluster aggregation, and in a suspension of micelles.

The cell as a material

To elucidate the dynamic and functional role of a cell within the tissue it belongs to, it is essential to understand its material properties. The cell is a viscoelastic material with highly unusual properties. Measurements of the mechanical behavior of cells are beginning to probe the contribution of constituent components to cell mechanics. Reconstituted cytoskeletal protein networks have been shown to mimic many aspects of the mechanical properties of cells, providing new insight into the origin of cellular behavior. These networks are highly nonlinear, with an elastic modulus that depends sensitively on applied stress. Theories can account for some of the measured properties, but a complete model remains elusive.

Multiple-particle tracking and two-point microrheology in cells

Mechanical stress and stiffness are increasingly recognized to play important roles in numerous cell biological processes, notably cell differentiation and tissue morphogenesis. Little definite is known, however, about how stress propagates through different cell structures or how it is converted to biochemical signals via mechanotransduction, due in large part to the difficulty of interpreting many cell mechanics experiments. A newly developed technique, two-point microrheology (TPM), can provide highly interpretable, quantitative measurements of cells' frequency-dependent shear moduli and spectra of their fluctuating intracellular stresses. TPM is a noninvasive method based on measuring the Brownian motion of large numbers of intracellular particles using multiple-particle tracking. While requiring only hardware available in many cell biology laboratories, a phase microscope and digital video camera, as a statistical technique, it also requires the automated analysis of many thousands of micrographs. Here we describe in detail the algorithms and software tools used for such large-scale multiple-particle tracking as well as common sources of error and the microscopy methods needed to minimize them. Moreover, we describe the physical principles behind TPM and other passive microrheological methods, their limitations, and typical results for cultured epithelial cells.

Active gels: dynamics of patterning and self-organization

The actin cytoskeleton is an active gel which constantly remodels during cellular processes such as motility and division. Myosin II molecular motors are involved in this active remodeling process and therefore control the dynamic self-organization of cytoskeletal structures. Due to the complexity of in vivo systems, it is hard to investigate the role of myosin II in the reorganization process which determines the resulting cytoskeletal structures. Here we use an in vitro model system to show that myosin II actively reorganizes actin into a variety of mesoscopic patterns, but only in the presence of bundling proteins. We find that the nature of the reorganization process is complex, exhibiting patterns and dynamical phenomena not predicted by current theoretical models and not observed in corresponding passive systems (excluding motors). This system generates active networks, asters and even rings depending on motor and bundling protein concentrations. Furthermore, the motors generate the formation of the patterns, but above a critical concentration they can also disassemble them and even totally prevent the polymerization and bundling of actin filaments. These results may suggest that tuning the assembly and disassembly of cytoskeletal structures can be obtained by tuning the local myosin II concentration/activity.

Dendritic spine viscoelasticity and soft-glassy nature: balancing dynamic remodeling with structural stability

Neuronal dendritic spines are a key component of brain circuitry, implicated in many mechanisms for plasticity and long-term stability of synaptic communication. They can undergo rapid actin-based activity-dependent shape fluctuations, an intriguing biophysical property that is believed to alter synaptic transmission. Yet, because of their small size (approximately 1 microm or less) and metastable behavior, spines are inaccessible to most physical measurement techniques. Here we employ atomic force microscopy elasticity mapping and novel dynamic indentation methods to probe the biomechanics of dendritic spines in living neurons. We find that spines exhibit 1), a wide range of rigidities, correlated with morphological characteristics, axonal association, and glutamatergic stimulation, 2), a uniquely large viscosity, four to five times that of other cell types, consistent with a high density of solubilized proteins, and 3), weak power-law rheology, described by the soft-glassy model for cellular mechanics. Our findings provide a new perspective on spine functionality and identify key mechanical properties that govern the ability of spines to rapidly remodel and regulate internal protein trafficking but also maintain structural stability.