Invited review: engineering approaches to cytoskeletal mechanics

Valve interstitial cells under impact load, a mechanobiology study

Understanding the relationship between mechanobiology and the biosynthetic activities of the valve interstitial cells (VICs) in health and disease under severe dynamic loading conditions is of particular interest. The purpose of this study is to further understand the mechanobiology of heart valve leaflet tissue and the VICs under impact forces. Two novel computational and experimental platforms were developed to study the effect of impact load on the VICs to monitor for apoptosis. The first objective was to design and develop an apparatus to experimentally study viability (apoptosis) of the porcine heart valve leaflet tissue VICs in the aortic position under controlled impact forces. Apoptosis was assessed based on terminal transferase dUTP nick end-labelling (TUNEL) assay. The second objective was to develop a computational platform to estimate the stress and strain fields in the vicinity of VICs when the tissue experiences impact forces. A nonlinear finite element (FE) model with an anisotropic, hyperelastic and heterogeneous material model for the matrix and cells was developed. Preliminary results confirm that interstitial cells are successfully resistant to impact loads up to 30 times more than normal physiological conditions. Additionally, the structure and composition of heart valve leaflet tissue provides a mechanical shield for VICs protecting them from excessive mechanical forces such as impact loads. Although, the entire tissue may experience excessive stresses, which may lead to structural damage, the stresses around and near VICs remain consistency low. Results of this study may be used for heart valve leaflet tissue-engineering, as well as further understanding the mechanobiology of the VICs in health and disease.

Viscoelasticity, Like Forces, Plays a Role in Mechanotransduction

Viscoelasticity and its alteration in time and space has turned out to act as a key element in fundamental biological processes in living systems, such as morphogenesis and motility. Based on experimental and theoretical findings it can be proposed that viscoelasticity of cells, spheroids and tissues seems to be a collective characteristic that demands macromolecular, intracellular component and intercellular interactions. A major challenge is to couple the alterations in the macroscopic structural or material characteristics of cells, spheroids and tissues, such as cell and tissue phase transitions, to the microscopic interferences of their elements. Therefore, the biophysical technologies need to be improved, advanced and connected to classical biological assays. In this review, the viscoelastic nature of cytoskeletal, extracellular and cellular networks is presented and discussed. Viscoelasticity is conceptualized as a major contributor to cell migration and invasion and it is discussed whether it can serve as a biomarker for the cells' migratory capacity in several biological contexts. It can be hypothesized that the statistical mechanics of intra- and extracellular networks may be applied in the future as a powerful tool to explore quantitatively the biomechanical foundation of viscoelasticity over a broad range of time and length scales. Finally, the importance of the cellular viscoelasticity is illustrated in identifying and characterizing multiple disorders, such as cancer, tissue injuries, acute or chronic inflammations or fibrotic diseases.

Quantification of the mesh structure of bundled actin filaments

Biopolymer networks are essential for a wide variety of cellular functions. The biopolymer actin is known to self-assemble into a variety of spatial structures in response to physiological and physical mechanisms. So far, the mechanics of networks of single actin filaments and bundles has previously been described. However, the spatial structure of actin bundles remains poorly understood. Here, we investigate this question by bundling actin filaments with systematically varied concentrations of known physical bundling agents (MgCl2 and PEG) and physiological bundling agents (α-actinin and fascin). We image bundled actin networks with confocal microscopy and perform analysis to describe their mesh size and the nearest-distance distribution, which we call "mesh structure". We find that the mesh size ξ scales universally with actin concentration as ξ ∼ [actin]-1/2. However, the dependence of ξ on the concentration of the bundling agent depends on the agent used. Finally, we find that nearest-distance distributions are best fit by Weibull and Gamma distributions. A complete understanding of the mesh structure of biopolymer networks leads to a more mechanistic understanding of the structure of the cytoskeleton, and can be exploited to design filters with variable porosity for microfluidic devices.

Finite Element Simulations of Mechanical Behaviour of Endothelial Cells

Biomechanical models based on the finite element method have already shown their potential in the simulation of the mechanical behaviour of cells. For instance, development of atherosclerosis is accelerated by damage of the endothelium, a monolayer of endothelial cells on the inner surface of arteries. Finite element models enable us to investigate mechanical factors not only at the level of the arterial wall but also at the level of individual cells. To achieve this, several finite element models of endothelial cells with different shapes are presented in this paper. Implementing the recently proposed bendotensegrity concept, these models consider the flexural behaviour of microtubules and incorporate also waviness of intermediate filaments. The suspended and adherent cell models are validated by comparison of their simulated force-deformation curves with experiments from the literature. The flat and dome cell models, mimicking natural cell shapes inside the endothelial layer, are then used to simulate their response in compression and shear which represent typical loads in a vascular wall. The models enable us to analyse the role of individual cytoskeletal components in the mechanical responses, as well as to quantify the nucleus deformation which is hypothesized to be the quantity decisive for mechanotransduction.

Adjustable viscoelasticity allows for efficient collective cell migration

Cell migration is essential for a wide range of biological processes such as embryo morphogenesis, wound healing, regeneration, and also in pathological conditions, such as cancer. In such contexts, cells are required to migrate as individual entities or as highly coordinated collectives, both of which requiring cells to respond to molecular and mechanical cues from their environment. However, whilst the function of chemical cues in cell migration is comparatively well understood, the role of tissue mechanics on cell migration is just starting to be studied. Recent studies suggest that the dynamic tuning of the viscoelasticity within a migratory cluster of cells, and the adequate elastic properties of its surrounding tissues, are essential to allow efficient collective cell migration in vivo. In this review we focus on the role of viscoelasticity in the control of collective cell migration in various cellular systems, mentioning briefly some aspects of single cell migration. We aim to provide details on how viscoelasticity of collectively migrating groups of cells and their surroundings is adjusted to ensure correct morphogenesis, wound healing, and metastasis. Finally, we attempt to show that environmental viscoelasticity triggers molecular changes within migrating clusters and that these new molecular setups modify clusters' viscoelasticity, ultimately allowing them to migrate across the challenging geometries of their microenvironment.

Quantitative cell-based model predicts mechanical stress response of growing tumor spheroids over various growth conditions and cell lines

Model simulations indicate that the response of growing cell populations on mechanical stress follows the same functional relationship and is predictable over different cell lines and growth conditions despite experimental response curves look largely different. We develop a hybrid model strategy in which cells are represented by coarse-grained individual units calibrated with a high resolution cell model and parameterized by measurable biophysical and cell-biological parameters. Cell cycle progression in our model is controlled by volumetric strain, the latter being derived from a bio-mechanical relation between applied pressure and cell compressibility. After parameter calibration from experiments with mouse colon carcinoma cells growing against the resistance of an elastic alginate capsule, the model adequately predicts the growth curve in i) soft and rigid capsules, ii) in different experimental conditions where the mechanical stress is generated by osmosis via a high molecular weight dextran solution, and iii) for other cell types with different growth kinetics from the growth kinetics in absence of external stress. Our model simulation results suggest a generic, even quantitatively same, growth response of cell populations upon externally applied mechanical stress, as it can be quantitatively predicted using the same growth progression function.

Curvature-Induced Spatial Ordering of Composition in Lipid Membranes

Phase segregation of membranal components, such as proteins, lipids, and cholesterols, leads to the formation of aggregates or domains that are rich in specific constituents. This process is important in the interaction of the cell with its surroundings and in determining the cell's behavior and fate. Motivated by published experiments on curvature-modulated phase separation in lipid membranes, we formulate a mathematical model aiming at studying the spatial ordering of composition in a two-component biomembrane that is subjected to a prescribed (imposed) geometry. Based on this model, we identified key nondimensional quantities that govern the biomembrane response and performed numerical simulations to quantitatively explore their influence. We reproduce published experimental observations and extend them to surfaces with geometric features (imposed geometry) and lipid phases beyond those used in the experiments. In addition, we demonstrate the possibility for curvature-modulated phase separation above the critical temperature and propose a systematic procedure to determine which mechanism, the difference in bending stiffness or difference in spontaneous curvatures of the two phases, dominates the coupling between shape and composition.

Nano- and microstructured materials for in vitro studies of the physiology of vascular cells

The extracellular environment of vascular cells in vivo is complex in its chemical composition, physical properties, and architecture. Consequently, it has been a great challenge to study vascular cell responses in vitro, either to understand their interaction with their native environment or to investigate their interaction with artificial structures such as implant surfaces. New procedures and techniques from materials science to fabricate bio-scaffolds and surfaces have enabled novel studies of vascular cell responses under well-defined, controllable culture conditions. These advancements are paving the way for a deeper understanding of vascular cell biology and materials-cell interaction. Here, we review previous work focusing on the interaction of vascular smooth muscle cells (SMCs) and endothelial cells (ECs) with materials having micro- and nanostructured surfaces. We summarize fabrication techniques for surface topographies, materials, geometries, biochemical functionalization, and mechanical properties of such materials. Furthermore, various studies on vascular cell behavior and their biological responses to micro- and nanostructured surfaces are reviewed. Emphasis is given to studies of cell morphology and motility, cell proliferation, the cytoskeleton and cell-matrix adhesions, and signal transduction pathways of vascular cells. We finalize with a short outlook on potential interesting future studies.

A novel function for the MAP kinase SMA-5 in intestinal tube stability

In vivo evidence links SMA-5 to the maintenance of the apical domain in the Caenorhabditis elegans intestine. sma-5 mutations induce morphological and biochemical changes of the intermediate filament system, demonstrating the close relationship between posttranslational modification and structural integrity of the evolutionarily conserved intestinal cytoskeleton.

Intermediate filaments are major cytoskeletal components whose assembly into complex networks and isotype-specific functions are still largely unknown. Caenorhabditis elegans provides an excellent model system to study intermediate filament organization and function in vivo. Its intestinal intermediate filaments localize exclusively to the endotube, a circumferential sheet just below the actin-based terminal web. A genetic screen for defects in the organization of intermediate filaments identified a mutation in the catalytic domain of the MAP kinase 7 orthologue sma-5(kc1). In sma-5(kc1) mutants, pockets of lumen penetrate the cytoplasm of the intestinal cells. These membrane hernias increase over time without affecting epithelial integrity and polarity. A more pronounced phenotype was observed in the deletion allele sma-5(n678) and in intestine-specific sma-5(RNAi). Besides reduced body length, an increased time of development, reduced brood size, and reduced life span were observed in the mutants, indicating compromised food uptake. Ultrastructural analyses revealed that the luminal pockets include the subapical cytoskeleton and coincide with local thinning and gaps in the endotube that are often enlarged in other regions. Increased intermediate filament phosphorylation was detected by two-dimensional immunoblotting, suggesting that loss of SMA-5 function leads to reduced intestinal tube stability due to altered intermediate filament network phosphorylation.

Epithelial Intermediate Filaments: Guardians against Microbial Infection?

Intermediate filaments are abundant cytoskeletal components of epithelial tissues. They have been implicated in overall stress protection. A hitherto poorly investigated area of research is the function of intermediate filaments as a barrier to microbial infection. This review summarizes the accumulating knowledge about this interaction. It first emphasizes the unique spatial organization of the keratin intermediate filament cytoskeleton in different epithelial tissues to protect the organism against microbial insults. We then present examples of direct interaction between viral, bacterial, and parasitic proteins and the intermediate filament system and describe how this affects the microbe-host interaction by modulating the epithelial cytoskeleton, the progression of infection, and host response. These observations not only provide novel insights into the dynamics and function of intermediate filaments but also indicate future avenues to combat microbial infection.

Low-Intensity Pulsed Ultrasound Affects Chondrocyte Extracellular Matrix Production via an Integrin-Mediated p38 MAPK Signaling Pathway

Although low-intensity pulsed ultrasound (LIPUS) regulates p38 mitogen-activated protein kinase (MAPK) and promotes cartilage repair in osteoarthritis, the role of integrin-mediated p38 MAPK in the effect of LIPUS on extracellular matrix (ECM) production of normal and OA chondrocytes remains unknown. The aim of this study was to investigate whether LIPUS affects ECM production in normal and OA rabbit chondrocytes through an integrin-p38 signaling pathway. A rabbit model of OA was established by anterior cruciate ligament transection, and chondrocytes were isolated from normal or OA cartilage and cultured in vitro. Chondrocytes were treated with LIPUS and then pre-incubated with the integrin inhibitor GRGDSP or the p38 inhibitor SB203580. Expression of type II collagen, MMP-13, integrin β1, p38 and phosphorylated p38 was assessed by Western blot analysis. We found that type II collagen and integrin β1 were upregulated (p < 0.05), whereas MMP-13 was downregulated (p < 0.05) in normal and OA chondrocytes. Furthermore, phosphorylated p38 was upregulated (p < 0.05) in normal chondrocytes, but downregulated (p < 0.05) in OA chondrocytes after LIPUS stimulation. Pre-incubation of chondrocytes with the integrin inhibitor disrupted the effects of LIPUS on normal and OA chondrocytes. Pre-incubation of chrondocytes with the p38 inhibitor reduced the effects of LIPUS on normal chondrocytes, but had no impact on OA chondrocytes. Our findings suggest that the integrin-p38 MAPK signaling pathway plays an important role in LIPUS-mediated ECM production in chondrocytes.

Temporal responses of human endothelial and smooth muscle cells exposed to uniaxial cyclic tensile strain

The physiology of vascular cells depends on stimulating mechanical forces caused by pulsatile flow. Thus, mechano-transduction processes and responses of primary human endothelial cells (ECs) and smooth muscle cells (SMCs) have been studied to reveal cell-type specific differences which may contribute to vascular tissue integrity. Here, we investigate the dynamic reorientation response of ECs and SMCs cultured on elastic membranes over a range of stretch frequencies from 0.01 to 1 Hz. ECs and SMCs show different cell shape adaptation responses (reorientation) dependent on the frequency. ECs reveal a specific threshold frequency (0.01 Hz) below which no responses is detectable while the threshold frequency for SMCs could not be determined and is speculated to be above 1 Hz. Interestingly, the reorganization of the actin cytoskeleton and focal adhesions system, as well as changes in the focal adhesion area, can be observed for both cell types and is dependent on the frequency. RhoA and Rac1 activities are increased for ECs but not for SMCs upon application of a uniaxial cyclic tensile strain. Analysis of membrane protrusions revealed that the spatial protrusion activity of ECs and SMCs is independent of the application of a uniaxial cyclic tensile strain of 1 Hz while the total number of protrusions is increased for ECs only. Our study indicates differences in the reorientation response and the reaction times of the two cell types in dependence of the stretching frequency, with matching data for actin cytoskeleton, focal adhesion realignment, RhoA/Rac1 activities, and membrane protrusion activity. These are promising results which may allow cell-type specific activation of vascular cells by frequency-selective mechanical stretching. This specific activation of different vascular cell types might be helpful in improving strategies in regenerative medicine.

Effects of low-intensity pulsed ultrasound on integrin-FAK-PI3K/Akt mechanochemical transduction in rabbit osteoarthritis chondrocytes

The effect of low-intensity pulsed ultrasound (LIPUS) on extracellular matrix (ECM) production via modulation of the integrin/focal adhesion kinase (FAK)/phosphatidylinositol 3-kinase (PI3K)/Akt pathway has been investigated in previous studies in normal chondrocytes, but not in osteoarthritis (OA). Therefore, we investigated the LIPUS-induced integrin β1/FAK/PI3K/Akt mechanochemical transduction pathway in a single study in rabbit OA chondrocytes. Normal and OA chondrocytes were exposed to LIPUS, and mRNA and protein expression of cartilage, metalloproteinases and integrin-FAK-PI3K/Akt signal pathway-related genes was determined by quantitative reverse transcription polymerase chain reaction and Western blotting, respectively. Compared with levels in normal chondrocytes, expression levels of ECM-related genes were significantly lower in OA chondrocytes and those of metalloproteinase-related genes were significantly higher. In addition, integrin β1 gene expression and the phosphorylation of FAK, PI3K and Akt were significantly higher in OA chondrocytes. The expression of all tested genes was significantly increased except for that of metalloproteinase, which was significantly decreased in the LIPUS-treated OA group compared to the untreated OA group. LIPUS may affect the integrin-FAK-PI3K/Akt mechanochemical transduction pathway and alter ECM production by OA chondrocytes. Our findings will aid the future development of a treatment or even cure for OA.

Tensegrity, cellular biophysics, and the mechanics of living systems

The recent convergence between physics and biology has led many physicists to enter the fields of cell and developmental biology. One of the most exciting areas of interest has been the emerging field of mechanobiology that centers on how cells control their mechanical properties, and how physical forces regulate cellular biochemical responses, a process that is known as mechanotransduction. In this article, we review the central role that tensegrity (tensional integrity) architecture, which depends on tensile prestress for its mechanical stability, plays in biology. We describe how tensional prestress is a critical governor of cell mechanics and function, and how use of tensegrity by cells contributes to mechanotransduction. Theoretical tensegrity models are also described that predict both quantitative and qualitative behaviors of living cells, and these theoretical descriptions are placed in context of other physical models of the cell. In addition, we describe how tensegrity is used at multiple size scales in the hierarchy of life—from individual molecules to whole living organisms—to both stabilize three-dimensional form and to channel forces from the macroscale to the nanoscale, thereby facilitating mechanochemical conversion at the molecular level.

Evaluation of a collagen-chitosan hydrogel for potential use as a pro-angiogenic site for islet transplantation

Islet transplantation to treat type 1 diabetes (T1D) has shown varied long-term success, due in part to insufficient blood supply to maintain the islets. In the current study, collagen and collagen:chitosan (10:1) hydrogels, +/- circulating angiogenic cells (CACs), were compared for their ability to produce a pro-angiogenic environment in a streptozotocin-induced mouse model of T1D. Initial characterization showed that collagen-chitosan gels were mechanically stronger than the collagen gels (0.7 kPa vs. 0.4 kPa elastic modulus, respectively), had more cross-links (9.2 vs. 7.4/µm(2)), and were degraded more slowly by collagenase. After gelation with CACs, live/dead staining showed greater CAC viability in the collagen-chitosan gels after 18 h compared to collagen (79% vs. 69%). In vivo, collagen-chitosan gels, subcutaneously implanted for up to 6 weeks in a T1D mouse, showed increased levels of pro-angiogenic cytokines over time. By 6 weeks, anti-islet cytokine levels were decreased in all matrix formulations ± CACs. The 6-week implants demonstrated increased expression of VCAM-1 in collagen-chitosan implants. Despite this, infiltrating vWF(+) and CXCR4(+) angiogenic cell numbers were not different between the implant types, which may be due to a delayed and reduced cytokine response in a T1D versus non-diabetic setting. The mechanical, degradation and cytokine data all suggest that the collagen-chitosan gel may be a suitable candidate for use as a pro-angiogenic ectopic islet transplant site.

Effect of mechanical instability of polymer scaffolds on cell adhesion

The adhesion of fibroblast on polymer bilayers composed of a glassy polystyrene (PS) prepared on top of a rubbery polyisoprene (PI) was studied. Since the top PS layer is not build on a glassy, or firm, foundation, the system becomes mechanically unstable with decreasing thickness of the PS layer. When the PS film was thinner than 25 nm, the number of cells adhered to the surface decreased and the cells could not spread well. On a parallel experiment, the same cell adhesion behavior was observed on plasma-treated PS/PI bilayer films, where in this case, the surface was more hydrophilic than that of the intact films. In addition, the fluorescence microscopic observations revealed that the formation of F-actin filaments in fibroblasts attached to the thicker PS/PI bilayer films was greater than those using the thinner PS/PI bilayer films. On the other hand, the thickness dependence of the cell adhesion behavior was not observed for the PS monolayer films. Taking into account that the amount of adsorbed protein molecules evaluated by a quartz crystal microbalance method was independent of the PS layer thickness of the bilayer films, our results indicate that cells, unlike protein molecules, could sense a mechanical instability of the scaffold.

Mathematical modeling of the impact of actin and keratin filaments on keratinocyte cell spreading

Keratin intermediate filaments (IFs) form cross-linked arrays to fulfill their structural support function in epithelial cells and tissues subjected to external stress. How the cross-linking of keratin IFs impacts the morphology and differentiation of keratinocytes in the epidermis and related surface epithelia remains an open question. Experimental measurements have established that keratinocyte spreading area is inversely correlated to the extent of keratin IF bundling in two-dimensional culture. In an effort to quantitatively explain this relationship, we developed a mathematical model in which isotropic cell spreading is considered as a first approximation. Relevant physical properties such as actin protrusion, adhesion events, and the corresponding response of lamellum formation at the cell periphery are included in this model. Through optimization with experimental data that relate time-dependent changes in keratinocyte surface area during spreading, our simulation results confirm the notion that the organization and mechanical properties of cross-linked keratin filaments affect cell spreading; in addition, our results provide details of the kinetics of this effect. These in silico findings provide further support for the notion that differentiation-related changes in the density and intracellular organization of keratin IFs affect tissue architecture in epidermis and related stratified epithelia.

Computational aspects in mechanical modeling of the articular cartilage tissue

This review focuses on the modeling of articular cartilage (at the tissue level), chondrocyte mechanobiology (at the cell level) and a combination of both in a multiscale computation scheme. The primary objective is to evaluate the advantages and disadvantages of conventional models implemented to study the mechanics of the articular cartilage tissue and chondrocytes. From monophasic material models as the simplest form to more complicated multiscale theories, these approaches have been frequently used to model articular cartilage and have contributed significantly to modeling joint mechanics, addressing and resolving numerous issues regarding cartilage mechanics and function. It should be noted that attentiveness is important when using different modeling approaches, as the choice of the model limits the applications available. In this review, we discuss the conventional models applicable to some of the mechanical aspects of articular cartilage such as lubrication, swelling pressure and chondrocyte mechanics and address some of the issues associated with the current modeling approaches. We then suggest future pathways for a more realistic modeling strategy as applied for the simulation of the mechanics of the cartilage tissue using multiscale and parallelized finite element method.

Response of an actin filament network model under cyclic stretching through a coarse grained Monte Carlo approach

Cells are complex, dynamic systems that actively adapt to various stimuli including mechanical alterations. Central to understanding cellular response to mechanical stimulation is the organization of the cytoskeleton and its actin filament network. In this manuscript, we present a minimalistic network Monte Carlo based approach to model actin filament organization under cyclic stretching. Utilizing a coarse-grained model, a filament network is prescribed within a two-dimensional circular space through nodal connections. When cyclically stretched, the model demonstrates that a perpendicular alignment of the filaments to the direction of stretch emerges in response to nodal repositioning to minimize net nodal forces from filament stress states. In addition, the filaments in the network rearrange and redistribute themselves to reduce the overall stress by decreasing their individual stresses. In parallel, we cyclically stretch NIH 3T3 fibroblasts and find a similar cytoskeletal response. With this work, we test the hypothesis that a first-principles mechanical model of filament assembly in a confined space is by itself capable of yielding the remodeling behavior observed experimentally. Identifying minimal mechanisms sufficient to reproduce mechanical influences on cellular structure has important implications in a diversity of fields, including biology, physics, medicine, computer science, and engineering.

Stress transmission within the cell

An outstanding problem in cell biology is how cells sense mechanical forces and how those forces affect cellular functions. During past decades, it has become evident that the deformable cytoskeleton (CSK), an intracellular network of various filamentous biopolymers, provides a physical basis for transducing mechanical signals into biochemical responses. To understand how mechanical forces regulate cellular functions, it is necessary to first understand how the CSK develops mechanical stresses in response to applied forces, and how those stresses are propagated through the CSK where various signaling molecules are immobilized. New experimental techniques have been developed to quantify cytoskeletal mechanics, which together with new computational approaches have given rise to new theories and models for describing mechanics of living cells. In this article, we discuss current understanding of cell biomechanics by focusing on the biophysical mechanisms that are responsible for the development and transmission of mechanical stresses in the cell and their effect on cellular functions. We compare and contrast various theories and models of cytoskeletal mechanics, emphasizing common mechanisms that those theories are built upon, while not ignoring irreconcilable differences. We highlight most recent advances in the understanding of mechanotransduction in the cytoplasm of living cells and the central role of the cytoskeletal prestress in propagating mechanical forces along the cytoskeletal filaments to activate cytoplasmic enzymes. It is anticipated that advances in cell mechanics will help developing novel therapeutics to treat pulmonary diseases like asthma, pulmonary fibrosis, and chronic obstructive pulmonary disease.

Frictional Behavior of Individual Vascular Smooth Muscle Cells Assessed By Lateral Force Microscopy

With the advancement of the field of biotribology, considerable interest has arisen in the study of cell and tissue frictional properties. From the perspective of medical device development, the frictional properties between a rigid surface and underlying cells and tissues are of a particular clinical interest. As with many bearing surfaces, it is likely that contact asperities exist at the size scale of single cells and below. Thus, a technique to measure cellular frictional properties directly would be beneficial from both a clinical and a basic science perspective. In the current study, an atomic force microscope (AFM) with a 5 μm diameter borosilicate spherical probe simulating endovascular metallic stent asperities was used to characterize the surface frictional properties of vascular smooth muscle cells (VSMCs) in contact with a metallic endovascular stent. Various treatments were used to alter cell structure, in order to better understand the cellular components and mechanisms responsible for governing frictional properties. The frictional coefficient of the probe on VSMCs was found to be approximately 0.06. This frictional coefficient was significantly affected by cellular crosslinking and cytoskeletal depolymerization agents. These results demonstrate that AFM-based lateral force microscopy is a valuable technique to assess the friction properties of individual single cells on the micro-scale.

Effects of cyclic stretch waveform on endothelial cell morphology using fractal analysis

Endothelial cells are remodeled when subjected to cyclic loading. Previous in vitro studies have indicated that frequency, strain amplitude, and duration are determinants of endothelial cell morphology, when cells are subjected to cyclic strain. In addition to those parameters, the current study investigated the effects of strain waveform on morphology of cultured endothelial cells quantified by fractal and topological analyses. Cultured endothelial cells were subjected to cyclic stretch by a designed device, and cellular images before and after tests were obtained. Fractal and topological parameters were calculated by development of an image-processing code. Tests were performed for different load waveforms. Results indicated cellular alignment by application of cyclic stretch. By alteration of load waveform, statistically significant differences between cell morphology of test groups were observed. Such differences are more prominent when load cycles are elevated. The endothelial cell remodeling was optimized when the applied cyclic load waveform was similar to blood pressure waveform. Effects of load waveform on cell morphology are influenced by alterations in load amplitude and frequency. It is concluded that load waveform is a determinant of endothelial morphology in addition to amplitude and frequency, and such effect is elevated by increase of load cycles. Due to high correlation between fractal and topological analyses, it is recommended that fractal analysis can be used as a proper method for evaluation of alteration in cell morphology and tissue structure caused by application of external stimuli such as mechanical loading.

Magnetic Biotransport: Analysis and Applications

Magnetic particles are finding increasing use in bioapplications, especially as carrier particles to transport biomaterials such as proteins, enzymes, nucleic acids and whole cells etc. Magnetic particles can be prepared with biofunctional coatings to target and label a specific biomaterial, and they enable controlled manipulation of a labeled biomaterial using an external magnetic field. In this review, we discuss the use of magnetic nanoparticles as transport agents in various bioapplications. We provide an overview of the properties of magnetic nanoparticles and their functionalization for bioapplications. We discuss the basic physics and equations governing the transport of magnetic particles at the micro- and nanoscale. We present two different transport models: a classical Newtonian model for predicting the motion of individual particles, and a drift-diffusion model for predicting the behavior of a concentration of nanoparticles that takes into account Brownian motion. We review specific magnetic biotransport applications including bioseparation, drug delivery and magnetofection. We demonstrate the transport models via application to these processes.

Theoretical concepts and models of cellular mechanosensing

Recent discoveries have established that mechanical properties of the cellular environment such as its rigidity, geometry, and external stresses play an important role in determining the cellular function and fate. Mechanical properties have been shown to influence cell shape and orientation, regulate cell proliferation and differentiation, and even govern the development and organization of tissues. In recent years, many theoretical and experimental investigations have been carried out to elucidate the mechanisms and consequences of the mechanosensitivity of cells. In this review, we discuss recent theoretical concepts and approaches that explain and predict cell mechanosensitivity. We focus on the interplay of active and passive processes that govern cell-cell and cell-matrix interactions and discuss the role of this interplay in the processes of cell adhesion, regulation of cytoskeleton mechanics and the response of cells to applied mechanical stresses.

Brushes, cables, and anchors: recent insights into multiscale assembly and mechanics of cellular structural networks

The remarkable ability of living cells to sense, process, and respond to mechanical stimuli in their environment depends on the rapid and efficient interconversion of mechanical and chemical energy at specific times and places within the cell. For example, application of force to cells leads to conformational changes in specific mechanosensitive molecules which then trigger cellular signaling cascades that may alter cellular structure, mechanics, and migration and profoundly influence gene expression. Similarly, the sensitivity of cells to mechanical stresses is governed by the composition, architecture, and mechanics of the cellular cytoskeleton and extracellular matrix (ECM), which are in turn driven by molecular-scale forces between the constituent biopolymers. Understanding how these mechanochemical systems coordinate over multiple length and time scales to produce orchestrated cell behaviors represents a fundamental challenge in cell biology. Here, we review recent advances in our understanding of these complex processes in three experimental systems: the assembly of axonal neurofilaments, generation of tensile forces by actomyosin stress fiber bundles, and mechanical control of adhesion assembly.

Cell morphology and migration linked to substrate rigidity

A mathematical model, based on thermodynamics, was developed to demonstrate how substrate rigidity influences cell morphology and migration. The mechanisms by which substrate rigidity are translated into cell-morphological changes and cell movement are described. The model takes into account the competition between the elastic energies in the cell-substrate system and work of adhesion at the cell periphery. The cell morphology and migration are dictated by the minimum of the total free energy of the cell-substrate system. By using this model, reported experimental observations on cell morphological changes and migration can be better understood with a theoretical basis. In addition, these observations can be more accurately correlated with the variation of substrate rigidity. This study indicates that the activity of the adherent cell is dependent not only on the substrate rigidity but also is correlated with the relative rigidity between the cell and substrate. Moreover, the study suggests that the cell stiffness can be estimated based on the substrate stiffness corresponding to the change of trend in morphological stability.

Modulation of cellular mechanics during osteogenic differentiation of human mesenchymal stem cells

Recognition of the growing role of human mesenchymal stem cells (hMSC) in tissue engineering and regenerative medicine requires a thorough understanding of intracellular biochemical and biophysical processes that may direct the cell's commitment to a particular lineage. In this study, we characterized the distinct biomechanical properties of hMSCs, including the average Young's modulus determined by atomic force microscopy (3.2 +/- 1.4 kPa for hMSC vs. 1.7 +/- 1.0 kPa for fully differentiated osteoblasts), and the average membrane tether length measured with laser optical tweezers (10.6 +/- 1.1 microm for stem cells, and 4.0 +/- 1.1 microm for osteoblasts). These differences in cell elasticity and membrane mechanics result primarily from differential actin cytoskeleton organization in these two cell types, whereas microtubules did not appear to affect the cellular mechanics. The membrane-cytoskeleton linker proteins may contribute to a stronger interaction of the plasma membrane with F-actins and shorter membrane tether length in osteoblasts than in stem cells. Actin depolymerization or ATP depletion caused a two- to threefold increase in the membrane tether length in osteoblasts, but had essentially no effect on the stem-cell membrane tethers. Actin remodeling in the course of a 10-day osteogenic differentiation of hMSC mediates the temporally correlated dynamical changes in cell elasticity and membrane mechanics. For example, after a 10-day culture in osteogenic medium, hMSC mechanical characteristics were comparable to those of mature bone cells. Based on quantitative characterization of the actin cytoskeleton remodeling during osteodifferentiation, we postulate that the actin cytoskeleton plays a pivotal role in determining the hMSC mechanical properties and modulation of cellular mechanics at the early stage of stem-cell osteodifferentiation.

Cell dynamic adhesion and elastic properties probed with cylindrical atomic force microscopy cantilever tips

Cell adhesion is required for essential biological functions such as migration, tissue formation and wound healing, and it is mediated by individual molecules that bind specifically to ligands on other cells or on the extracellular matrix. Atomic force microscopy (AFM) has been successfully used to measure cell adhesion at both single molecule and whole cell levels. However, the measurement of inherent cell adhesion properties requires a constant cell-probe contact area during indentation, a requirement which is not fulfilled in common pyramidal or spherical AFM tips. We developed a procedure using focused ion beam (FIB) technology by which we modified silicon pyramidal AFM cantilever tips to obtain flat-ended cylindrical tips with a constant and known area of contact. The tips were validated on elastic gels and living cells. Cylindrical tips showed a fairly linear force-indentation behaviour on both gels and cells for indentations >200 nm. Cylindrical tips coated with ligands were used to quantify inherent dynamic cell adhesion and elastic properties. Force, work of adhesion and elasticity showed a marked dynamic response. In contrast, the deformation applied to the cells before rupture was fairly constant within the probed dynamic range. Taken together, these results suggest that the dynamic adhesion strength is counterbalanced by the dynamic elastic response to keep a constant cell deformation regardless of the applied pulling rate.

Contributions of the active and passive components of the cytoskeletal prestress to stiffening of airway smooth muscle cells

Airway smooth muscle cells exhibit stiffening during contractile activation. This stiffening may be interpreted as a result of the stabilizing influence of the mechanical prestress stored within the cytoskeleton (CSK). However, in vivo, airway smooth muscle cells contract while simultaneously experiencing breathing-induced stretching. Excessive stretching of cells could cause actin-myosin crosslinks, and possibly other cytoskeletal filaments, to break, thereby leading to dissipation of the prestress and inhibition of further cell stiffening. The aim of this study is to investigate the stiffening behavior of individual human airway smooth muscle (HASM) cells exposed to a combination of substrate stretching, contractile activation and relaxation. We treated cultured HASM cells with either contractile (histamine) or relaxing (DBcAMP) pharmacological agonists and used magnetic cytometry technique to investigate the stiffening behavior of these cells during uniform substrate stretching (0-30%). Cells that were not treated, as well as those treated with histamine, exhibited increasing stiffening during stretching up to 20% of substrate strain, with additional stiffening becoming inhibited for substrate strains of 20-30%. In contrast, in cells treated with DBcAMP, stretching produced moderate but continuous stiffening with increasing substrate strain. These results indicate that both active and passive components of the prestress contribute to cell stiffening. We also observed that cells permeabilized with saponin exhibited stiffening at low levels (<10%) of substrate stretching, similar to non-permeabilized cells, but not at high levels (10-30%) of stretching, where stiffening was inhibited. These data suggest that at low levels of substrate strains the relative contributions of ion channel activation as well as actin and focal adhesion remodeling are less important for stiffening than passive distension of the CSK. Taken together, our results suggest that both the active and passive components of the cytoskeletal prestress contribute to the stiffening behavior of HASM cells under physiological conditions, but that at high levels of cellular distensions there is a possible tradeoff between these two components with the contribution from the passive component becoming increasingly more important.

Cell nanosurgery using ultrashort (femtosecond) laser pulses: applications to membrane surgery and cell isolation

Membrane surgery and nanosurgical cell isolation using high-intensity femtosecond laser pulses is reported. We demonstrate the applicability of using ultrashort (femtosecond) laser pulses for performing surgery on live mammalian cells. When sub-10 femtosecond pulses were focused onto the cell, precise sub-micron surgical cuts were made on the biological membrane. Traversing the cells relative to the focused laser spot, we report on localized nanosurgical ablation of focal adhesion adjoining epithelial cells. In each study, the surgery was conducted without morphologically compromising the cells.

Effect of stretch on structural integrity and micromechanics of human alveolar epithelial cell monolayers exposed to thrombin

Alveolar epithelial cells in patients with acute lung injury subjected to mechanical ventilation are exposed to increased procoagulant activity and mechanical strain. Thrombin induces epithelial cell stiffening, contraction, and cytoskeletal remodeling, potentially compromising the balance of forces at the alveolar epithelium during cell stretching. This balance can be further compromised by the loss of integrity of cell-cell junctions in the injured epithelium. The aim of this work was to study the effect of stretch on the structural integrity and micromechanics of human alveolar epithelial cell monolayers exposed to thrombin. Confluent and subconfluent cells (A549) were cultured on collagen-coated elastic substrates. After exposure to thrombin (0.5 U/ml), a stepwise cell stretch (20%) was applied with a vacuum-driven system mounted on an inverted microscope. The structural integrity of the cell monolayers was assessed by comparing intercellular and intracellular strains within the monolayer. Strain was measured by tracking beads tightly bound to the cell surface. Simultaneously, cell viscoelasticity was measured using optical magnetic twisting cytometry. In confluent cells, thrombin did not induce significant changes in transmission of strain from the substrate to overlying cells. By contrast, thrombin dramatically impaired the ability of subconfluent cells to follow imposed substrate deformation. Upon substrate unstretching, thrombin-treated subconfluent cells exhibited compressive strain (9%). Stretch increased stiffness (56-62%) and decreased cell hysteresivity (13-22%) of vehicle cells. By contrast, stretch did not increase stiffness of thrombin-treated cells, suggesting disruption of cytoskeletal structures. Our findings suggest that thrombin could exacerbate epithelial barrier dysfunction in injured lungs subjected to mechanical ventilation.

Cellular stress failure in ventilator-injured lungs

The clinical and experimental literature has unequivocally established that mechanical ventilation with large tidal volumes is injurious to the lung. However, uncertainty about the micromechanics of injured lungs and the numerous degrees of freedom in ventilator settings leave many unanswered questions about the biophysical determinants of lung injury. In this review we focus on experimental evidence for lung cells as injury targets and the relevance of these studies for human ventilator-associated lung injury. In vitro, the stress-induced mechanical interactions between matrix and adherent cells are important for cellular remodeling as a means for preventing compromise of cell structure and ultimately cell injury or death. In vivo, these same principles apply. Large tidal volume mechanical ventilation results in physical breaks in alveolar epithelial and endothelial plasma membrane integrity and subsequent triggering of proinflammatory signaling cascades resulting in the cytokine milieu and pathologic and physiologic findings of ventilator-associated lung injury. Importantly, though, alveolar cells possess cellular repair and remodeling mechanisms that in addition to protecting the stressed cell provide potential molecular targets for the prevention and treatment of ventilator-associated lung injury in the future.

Effects of cytoskeletal prestress on cell rheological behavior

Normal tissue development requires that cells alter their mechanical behavior in different microenvironments to carry out their diverse functions. During cell spreading, migration, invasion and mitosis, cells exhibit a high degree of deformability, exhibiting almost a fluid-like behavior, whereas within quiescent differentiated tissues, cells must behave like an elastic solid to maintain their structural integrity in the face of an applied mechanical stress. A growing body of experimental evidence suggests that rheological properties of adherent cells depend on pre-existing tensional stress ("prestress") borne by the cytoskeleton. This prestress results from the action of tensional forces borne by actin microfilaments, transmitted over intermediate filaments and resisted by both extracellular matrix adhesions and internal microtubules. Observations that the prestress influences mechanical properties of the cell are intimately related to the cellular tensegrity model. This model depicts the cytoskeleton as an interconnected network of cables that carry pre-existing tension that is balanced by compression-bearing struts and by anchoring forces of the substrate. This paper offers a brief survey of the basic concept of cellular tensegrity model, comparison of model predictions with experimental data obtained from rheological measurements on living cells, and comparison with other models that have been used in studies of rheology of cells.

MICROFILAMENTS ARE INVOLVED IN RENAL CELL RESPONSES TO SUSTAINED HYDROSTATIC PRESSURE

PURPOSE

Increased pressures within renal interstitial fluid, as associated with a number of renal pathologies, could affect cell function and gene expression. The long-term objective of this research is to elucidate kidney cell responses to pathological hydrostatic pressures.

MATERIALS AND METHODS

In vitro studies were performed in 2 kidney cell lines (cortical tubular and medullary) to determine changes in cell numbers and cytoskeletal (specifically microfilament, microtubule and intermediate filament) arrangement following exposure to pathological (60 cm H2O) pressures. A novel pressure system was used to apply pressure to renal cells for up to 7 days. Cell counts and fluorescent staining were performed to determine alterations in response to pressure.

RESULTS

Exposure to pressures of 60 cm H2O resulted in increased renal cell numbers and rearrangement in individual microfilament structures after 7 days.

CONCLUSIONS

These results prove that hydrostatic pressure alters the function of renal cells. In the future such knowledge of renal cell responses to pressure along with an understanding of the mechanisms involved will aid in the design of novel, targeted drug therapies for treating kidney pathologies.

Rheology of airway smooth muscle cells is associated with cytoskeletal contractile stress

Recently reported data from mechanical measurements of cultured airway smooth muscle cells show that stiffness of the cytoskeletal matrix is determined by the extent of static contractile stress borne by the cytoskeleton (Wang N, Tolić-Nørrelykke IM, Chen J, Mijailovich SM, Butler JP, Fredberg JJ, and Stamenović D. Am J Physiol Cell Physiol 282, C606-C616, 2002). On the other hand, rheological measurements on these cells show that cytoskeletal stiffness changes with frequency of imposed mechanical loading according to a power law (Fabry B, Maksym GN, Butler JP, Glogauer M, Navajas DF, and Fredberg JJ. Phys Rev Lett 87: 148102, 2001). In this study, we examine the possibility that these two empirical observations might be interrelated. We combine previously reported data for contractile stress of human airway smooth muscle cells with new data describing rheological properties of these cells and derive quantitative, mathematically tractable, and experimentally verifiable empirical relationships between contractile stress and indexes of cell rheology. These findings reveal an intriguing role of the contractile stress: although it maintains structural stability of the cell under applied mechanical loads, it may also regulate rheological properties of the cytoskeleton, which are essential for other cell functions.

Physical law not natural selection as the major determinant of biological complexity in the subcellular realm: new support for the pre-Darwinian conception of evolution by natural law

Before Darwin many biologists considered organic forms to be immutable natural forms or types which like inorganic forms such as atoms or crystals are part of a changeless world order and determined by physical law. Adaptations were viewed as secondary modifications of these 'crystal like' abstract afunctional 'givens of physics.' We argue here that much of the emerging picture of biological order in the subcellular realm resembles closely the pre-Darwinian conception of nature. We point out that in the subcellular realm, between nano and micrometers, physical law necessarily plays a far more significant role in organizing matter than in the familiar 'Darwinian world' between millimeters and meters (where matter can be arranged into almost any contingent artifactual arrangement we choose, as witness Lego toys, watches or jumbo jets). Consequently, when deploying matter into complex structures in the subcellular realm the cell must necessarily make extensive use of natural forms-such as the protein and RNA folds, microtubular forms and tensegrity structures-which like atoms or crystals self-organize under the direction of physical law into what are essentially 'pre-Darwinian' afunctional abstract molecular architectures in which adaptations are trivial secondary modifications of what are evidently primary givens of physics.

Microrheology of human lung epithelial cells measured by atomic force microscopy

Lung epithelial cells are subjected to large cyclic forces from breathing. However, their response to dynamic stresses is poorly defined. We measured the complex shear modulus (G(*)(omega)) of human alveolar (A549) and bronchial (BEAS-2B) epithelial cells over three frequency decades (0.1-100 Hz) and at different loading forces (0.1-0.9 nN) with atomic force microscopy. G(*)(omega) was computed by correcting force-indentation oscillatory data for the tip-cell contact geometry and for the hydrodynamic viscous drag. Both cell types displayed similar viscoelastic properties. The storage modulus G'(omega) increased with frequency following a power law with exponent approximately 0.2. The loss modulus G"(omega) was approximately 2/3 lower and increased similarly to G'(omega) up to approximately 10 Hz, but exhibited a steeper rise at higher frequencies. The cells showed a weak force dependence of G'(omega) and G"(omega). G(*)(omega) conformed to the power-law model with a structural damping coefficient of approximately 0.3, indicating a coupling of elastic and dissipative processes within the cell. Power-law behavior implies a continuum distribution of stress relaxation time constants. This complex dynamics is consistent with the rheology of soft glassy materials close to a glass transition, thereby suggesting that structural disorder and metastability may be fundamental features of cell architecture.

A prestressed cable network model of the adherent cell cytoskeleton

A prestressed cable network is used to model the deformability of the adherent cell actin cytoskeleton. The overall and microstructural model geometries and cable mechanical properties were assigned values based on observations from living cells and mechanical measurements on isolated actin filaments, respectively. The models were deformed to mimic cell poking (CP), magnetic twisting cytometry (MTC) and magnetic bead microrheometry (MBM) measurements on living adherent cells. The models qualitatively and quantitatively captured the fibroblast cell response to the deformation imposed by CP while exhibiting only some qualitative features of the cell response to MTC and MBM. The model for CP revealed that the tensed peripheral actin filaments provide the key resistance to indentation. The actin filament tension that provides mechanical integrity to the network was estimated at approximately 158 pN, and the nonlinear mechanical response during CP originates from filament kinematics. The MTC and MBM simulations revealed that the model is incomplete, however, these simulations show cable tension as a key determinant of the model response.

Is tensegrity a unifying concept of protein folds?

We suggest that the three-dimensional architecture of globular proteins can be described in terms of tensegrets, i.e. structural elements that are held together through attractive and repulsive forces. Hard elements of tensegrets are represented by secondary structure elements, i.e. alpha-helices and beta-strands, while the role of elastic elements is played by attractive and repulsive atomic forces. Characteristics of tensegrets is that they can auto-assemble and that they respond to changes of tension in some part of the entire object through a deformation in another part, thus partially preserving their structure, despite their deformation. This latter property well explains both the folding process and the behavior of globular proteins under mild denaturing conditions, as revealed by the molten globule state.

A cellular tensegrity model to analyse the structural viscoelasticity of the cytoskeleton

This study describes the viscoelastic properties of a refined cellular-tensegrity model composed of six rigid bars connected to a continuous network of 24 viscoelastic pre-stretched cables (Voigt bodies) in order to analyse the role of the cytoskeleton spatial rearrangement on the viscoelastic response of living adherent cells. This structural contribution was determined from the relationships between the global viscoelastic properties of the tensegrity model, i.e., normalized viscosity modulus (eta(*)), normalized elasticity modulus (E(*)), and the physical properties of the constitutive elements, i.e., their normalized length (L(*)) and normalized initial internal tension (T(*)). We used a numerical method to simulate the deformation of the structure in response to different types of loading, while varying by several orders of magnitude L(*) and T(*). The numerical results obtained reveal that eta(*) remains almost independent of changes in T(*) (eta(*) proportional, variant T(*+0.1)), whereas E(*) increases with approximately the square root of the internal tension T(*) (from E(*) proportional, variant T(*+0.3) to E(*) proportional, variant T(*+0.7)). Moreover, structural viscosity eta(*) and elasticity E(*) are both inversely proportional to the square of the size of the structure (eta(*) proportional, variant L(*-2) and E(*) proportional, variant L(*-2)). These structural properties appear consistent with cytoskeleton (CSK) mechanical properties measured experimentally by various methods which are specific to the CSK micromanipulation in living adherent cells. Present results suggest, for the first time, that the effect of structural rearrangement of CSK elements on global CSK behavior is characterized by a faster cellular mechanical response relatively to the CSK element response, which thus contributes to the solidification process observed in adherent cells. In extending to the viscoelastic properties the analysis of the mechanical response of the cellular 30-element tensegrity model, the present study contributes to the understanding of recent results on the cellular-dynamic response and allows to reunify the scattered data reported for the viscoelastic properties of living adherent cells.

Effect of the cytoskeletal prestress on the mechanical impedance of cultured airway smooth muscle cells

We investigated the effect of the cytoskeletal prestress (P) on the elastic and frictional properties of cultured human airway smooth muscle cells during oscillatory loading; P is preexisting tensile stress in the actin cytoskeleton generated by the cell contractile apparatus. We oscillated (0.1 Hz, 6 Pa peak to peak) small ferromagnetic beads bound to integrin receptors and computed the storage (elastic) modulus (G') and the loss (frictional) modulus (G") from the applied torque and the corresponding bead rotation. All measurements were done at baseline and after cells were treated with graded doses of either histamine (0.1, 1, 10 microM) or isoproterenol (0.01, 0.1, 1, 10 microM). Values for P for these concentrations were taken from a previous study (Wang et al., Am J Physiol Cell Physiol, in press). It was found that G' and G", as well as P, increased/decreased with increasing doses of histamine/isoproterenol. Both G' and G" exhibited linear dependences on P: G'(Pa) = 0.20P + 82 and G"(Pa) = 0.05P + 32. The dependence of G' on P is consistent with our previous findings and with the behavior of stress-supported structures. The dependence of G" on P is a novel finding. It could be attributed to a variety of mechanisms. Some of those mechanisms are discussed in detail. We concluded that, in addition to the central mechanisms by which stress-supported structures develop mechanical stresses, other mechanisms might need to be invoked to fully explain the observed dependence of the cell mechanical properties on the state of cell contractility.

Cell prestress. I. Stiffness and prestress are closely associated in adherent contractile cells

The tensegrity hypothesis holds that the cytoskeleton is a structure whose shape is stabilized predominantly by the tensile stresses borne by filamentous structures. Accordingly, cell stiffness must increase in proportion with the level of the tensile stress, which is called the prestress. Here we have tested that prediction in adherent human airway smooth muscle (HASM) cells. Traction microscopy was used to measure the distribution of contractile stresses arising at the interface between each cell and its substrate; this distribution is called the traction field. Because the traction field must be balanced by tensile stresses within the cell body, the prestress could be computed. Cell stiffness (G) was measured by oscillatory magnetic twisting cytometry. As the contractile state of the cell was modulated with graded concentrations of relaxing or contracting agonists (isoproterenol or histamine, respectively), the mean prestress ((t)) ranged from 350 to 1,900 Pa. Over that range, cell stiffness increased linearly with the prestress: G (Pa) = 0.18(t) + 92. While this association does not necessarily preclude other interpretations, it is the hallmark of systems that secure shape stability mainly through the prestress. Regardless of mechanism, these data establish a strong association between stiffness of HASM cells and the level of tensile stress within the cytoskeleton.

Measurement of cell microrheology by magnetic twisting cytometry with frequency domain demodulation

Magnetic twisting cytometry (MTC) (Wang N, Butler JP, and Ingber DE, Science 260: 1124-1127, 1993) is a useful technique for probing cell micromechanics. The technique is based on twisting ligand-coated magnetic microbeads bound to membrane receptors and measuring the resulting bead rotation with a magnetometer. Owing to the low signal-to-noise ratio, however, the magnetic signal must be modulated, which is accomplished by spinning the sample at approximately 10 Hz. Present demodulation approaches limit the MTC range to frequencies <0.5 Hz. We propose a novel demodulation algorithm to expand the frequency range of MTC measurements to higher frequencies. The algorithm is based on coherent demodulation in the frequency domain, and its frequency range is limited only by the dynamic response of the magnetometer. Using the new algorithm, we measured the complex modulus of elasticity (G*) of cultured human bronchial epithelial cells (BEAS-2B) from 0.03 to 16 Hz. Cells were cultured in supplemented RPMI medium, and ferromagnetic beads (approximately 5 microm) coated with an RGD peptide were bound to the cell membrane. Both the storage (G', real part of G*) and loss (G", imaginary part of G*) moduli increased with frequency as omega(alpha) (2 pi x frequency) with alpha approximately equal to 1/4. The ratio G"/G' was approximately 0.5 and varied little with frequency. Thus the cells exhibited a predominantly elastic behavior with a weak power law of frequency and a nearly constant proportion of elastic vs. frictional stresses, implying that the mechanical behavior conformed to the so-called structural damping (or constant-phase) law (Maksym GN, Fabry B, Butler JP, Navajas D, Tschumperlin DJ, LaPorte JD, and Fredberg JJ, J Appl Physiol 89: 1619-1632, 2000). We conclude that frequency domain demodulation dramatically increases the frequency range that can be probed with MTC and reveals that the mechanics of these cells conforms to constant-phase behavior over a range of frequencies approaching three decades.