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Linear and Nonlinear Rheology of Living Cells
Abstract
Living cells are an active soft material with fascinating mechanical properties. Under mechanical loading, cells exhibit creep and stress relaxation behavior that follows a power-law response rather than a classical exponential response. Such a response puts cells in the context of soft colloidal glasses and other disordered metastable materials that share the same properties. In cells, however, both the power-law exponent and stiffness are related to the contractile prestress in the cytoskeleton. In addition, cells are made of a highly nonlinear material that stiffens and fluidizes under mechanical stress. They show active and adaptive mechanical behavior such as contraction and remodeling that sets them apart from any other nonliving material. Strikingly, all these observations can be linked by simple relationships with the power-law exponent as the only organizing parameter. Current theoretical models capture specific facets of cell mechanical behavior, but a comprehensive understanding is still emerging.
... As a result, we employ power-law rheology to describe the variations in cell strain (ε) during the creeping stage (t creep ). The relationship between ε and t creep . is described by Eq. (2) 16,22,23 , which is as follows: ...
... where ΔP ¼ 1=t creep R 4p t ð Þdt represents the mean pressure difference in the microconstriction; E cell is the Young's Modulus of cells; β is the power-law exponent, and the value is 0.1~0.5 of cell 22 . Since t 0 is the timescale, which can be arbitrarily set to 1 s, Eq. (2) can be transformed into Eq. ...
... To establish a quantitative parameter for measuring cell stiffness, multiple parameters related to cell morphology and motility during deformation should be obtained and applied to fit the mechanical model based on power-law rheology 16,22 . Here, individual cells were identified and tracked using Yolov5-based object detection in combination with cell tracking. ...
Cellular deformability is a promising biomarker for evaluating the physiological state of cells in medical applications. Microfluidics has emerged as a powerful technique for measuring cellular deformability. However, existing microfluidic-based assays for measuring cellular deformability rely heavily on image analysis, which can limit their scalability for high-throughput applications. Here, we develop a parallel constriction-based microfluidic flow cytometry device and an integrated computational framework (ATMQcD). The ATMQcD framework includes automatic training set generation, multiple object tracking, segmentation, and cellular deformability quantification. The system was validated using cancer cell lines of varying metastatic potential, achieving a classification accuracy of 92.4% for invasiveness assessment and stratifying cancer cells before and after hypoxia treatment. The ATMQcD system also demonstrated excellent performance in distinguishing cancer cells from leukocytes (accuracy = 89.5%). We developed a mechanical model based on power-law rheology to quantify stiffness, which was fitted with measured data directly. The model evaluated metastatic potentials for multiple cancer types and mixed cell populations, even under real-world clinical conditions. Our study presents a highly robust and transferable computational framework for multiobject tracking and deformation measurement tasks in microfluidics. We believe that this platform has the potential to pave the way for high-throughput analysis in clinical applications, providing a powerful tool for evaluating cellular deformability and assessing the physiological state of cells.
... where G' and G" represent the storage and loss moduli of the cell, respectively, and AFM data were analyzed using Igor Pro software (WaveMetrics, Portland, OR, USA). For each cell, G' and G" as a function of f were fitted to the power-law structural damping model with additional Newtonian viscosity [16,17,[23][24][25][27][28][29] given by ...
... We performed statistical analyses on rheological properties such as G 0 , α, and μ between three individuals in RCM and healthy CFs with unpaired t-test. As a result, the G 0 , which is related to cell stiffness [21], was significantly higher in RCM CFs than that in healthy CFs (P = 0.0153 ; Fig 2A), indicating that intracellular structures such as the cytoskeleton of RCM CFs were stiffer compared to those of healthy CFs [11,21,25,[27][28][29]. In addition, we found that α was significantly decreased in RCM CFs compared to those in healthy CFs (P = 0.0237; Fig 2B). ...
... In addition, we found that α was significantly decreased in RCM CFs compared to those in healthy CFs (P = 0.0237; Fig 2B). According to the soft glassy rheology [27][28][29], α corresponds to the probability that a system evolves in a complex energy landscape with a high number of traps. Thus, the results shown in Fig 2B suggest that the intracellular structures in RCM were more stable than those in healthy CFs. ...
Restrictive cardiomyopathy (RCM) is a rare disease characterized by increased ventricular stiffness and preserved ventricular contraction. Various sarcomere gene variants are known to cause RCM; however, more than a half of patients do not harbor such pathogenic variants. We recently demonstrated that cardiac fibroblasts (CFs) play important roles in inhibiting the diastolic function of cardiomyocytes via humoral factors and direct cell–cell contact regardless of sarcomere gene mutations. However, the mechanical properties of CFs that are crucial for intercellular communication and the cardiomyocyte microenvironment remain less understood. In this study, we evaluated the rheological properties of CFs derived from pediatric patients with RCM and healthy control CFs via atomic force microscopy. Then, we estimated the cellular modulus scale factor related to the cell stiffness, fluidity, and Newtonian viscosity of single cells based on the single power-law rheology model and analyzed the comprehensive gene expression profiles via RNA-sequencing. RCM-derived CFs showed significantly higher stiffness and viscosity and lower fluidity compared to healthy control CFs. Furthermore, RNA-sequencing revealed that the signaling pathways associated with cytoskeleton elements were affected in RCM CFs; specifically, cytoskeletal actin-associated genes ( ACTN1 , ACTA2 , and PALLD ) were highly expressed in RCM CFs, whereas several tubulin genes ( TUBB3 , TUBB , TUBA1C , and TUBA1B ) were down-regulated. These results implies that the signaling pathways associated with cytoskeletal elements alter the rheological properties of RCM CFs, particularly those related to CF–cardiomyocyte interactions, thereby leading to diastolic cardiac dysfunction in RCM.
... Intermediate filaments contribute significantly to the mechanical response of the cells at large cell deformation when they are stretched [5]. Compared to those, microtubules are stiff [6] and play a vital role in mitosis [7]. ...
... For the general understanding of cells, significant efforts have been put into studying the mechanical cell behavior. During the last decades, different techniques, like optical and magnetic tweezers, atomic force microscopy, magnetic twisting cytometry, micropipette aspiration, cell poking, particle tracking micro-rheology, optical stretching, and high-throughput microfluidic techniques have been employed to measure the viscoelastic behavior of single cells [2,6,[24][25][26][27][28]. Frequency-dependent changes in the viscoelastic properties of single cells have been studied extensively. ...
... Over a wide frequency range, cells show a power-law rheology, like soft glassy materials. The exponents typically range between 0.1 and 0.5, being smaller for stiffer cells [6]. Yet, quantitative data on the absolute value of the cell stiffness or the storage and loss moduli can differ depending on the method employed [12]. ...
The viscoelastic properties of a cell cytoskeleton contain abundant information about the state of a cell. Cells show a response to a specific environment or an administered drug through changes in their viscoelastic properties. Studies of single cells have shown that chemical agents that interact with the cytoskeleton can alter mechanical cell properties and suppress mitosis. This envisions using rheological measurements as a non-specific tool for drug development, the pharmacological screening of new drug agents, and to optimize dosage. Although there exists a number of sophisticated methods for studying mechanical properties of single cells, studying concentration dependencies is difficult and cumbersome with these methods: large cell-to-cell variations demand high repetition rates to obtain statistically significant data. Furthermore, method-induced changes in the cell mechanics cannot be excluded when working in a nonlinear viscoelastic range. To address these issues, we not only compared narrow-gap rheometry with commonly used single cell techniques, such as atomic force microscopy and microfluidic-based approaches, but we also compared existing cell monolayer studies used to estimate cell mechanical properties. This review provides insight for whether and how narrow-gap rheometer could be used as an efficient drug screening tool, which could further improve our current understanding of the mechanical issues present in the treatment of human diseases.
... As an active complex material, cells and tissues exhibit both solidelastic and fluid-viscous properties [9,10]. Amazingly, a variety of living cells have been shown that they exhibit a universal power-law rheological response as J t [11][12][13], where the power-law exponent follows in a range from 0.1 to 0.5. Moreover, the cell exhibits the power-law response not only in the elastic stage but also in its plastic stage [14,15]. ...
... To date, there are two main types of cell mechanical models [13]. One is the top-down macroscopic model, such as the linear viscoelastic model [19][20][21][22][23], tensegrity [24,25], and soft glassy rheology (SGR) [12,23], which treats the cell as a whole. ...
... One is the top-down macroscopic model, such as the linear viscoelastic model [19][20][21][22][23], tensegrity [24,25], and soft glassy rheology (SGR) [12,23], which treats the cell as a whole. In contrast, the second type is the bottom-up microscopic model, which explores the mechanical response of cells at the molecular level [13]. However, both two-type models are neither easy to be extended to tissue-scale nor to study the static and dynamic mechanics of tissues. ...
Epithelial monolayers act as a vital player in a variety of physiological activities, such as wound healing and embryonic development. The mechanical behavior of epithelial monolayers has been increasingly studied with the recent rapid development of techniques. Under dynamic loadings, the creep response of epithelial monolayers shows a power-law dependence on the time with an exponent larger than that of a single cell. Under static loadings, the elastic modulus of epithelial monolayers is nearly two orders of magnitude higher than that of a single cell. To date, there is a lack of a mechanical model that can describe both the dynamic and static mechanical responses of epithelial monolayers. Here, based on the structural features of cells, we establish a multi-scale structural model of cell monolayers. It is found that the proposed model can naturally capture the dynamic and static mechanical properties of cell monolayers. Further, we explore the effects of the cytoskeleton and the membrane moduli on the dynamical power-law rheological responses and static stress-strain relations of a single cell and cell monolayers, respectively. Our work lays the foundation for subsequent studies of the mechanical behavior of more complex epithelial tissues.
... Single-cell rheology is known to follow a power law behavior, such that the relaxation modulus (time-dependent Young's modulus) E(t) is E(t) = E1(t/t1) -α , where E1 is the modulus at time t1 and α is the power-law exponent, indicating that cells have no characteristic relaxation modes (Fabry et al., 2001). The single-cell rheology is described by the soft glass rheology (SGR) model, which is expressed as an energy landscape with many energy minima and the conformations being trapped by the potential minima (Sollich, 1998;Kollmannsberger and Fabry, 2011) (Fig. 4a). In the power-law rheology (PLR), α has a value between the elastic state (α = 0), which is trapped by the minima and cannot escape, and the viscous state (α = 1), which is not trapped by the minima (Kollmannsberger and Fabry, 2011). ...
... The single-cell rheology is described by the soft glass rheology (SGR) model, which is expressed as an energy landscape with many energy minima and the conformations being trapped by the potential minima (Sollich, 1998;Kollmannsberger and Fabry, 2011) (Fig. 4a). In the power-law rheology (PLR), α has a value between the elastic state (α = 0), which is trapped by the minima and cannot escape, and the viscous state (α = 1), which is not trapped by the minima (Kollmannsberger and Fabry, 2011). The concept of the SGR model is essentially different from the linear viscoelastic model consisting of a spring and a dashpot, but it is known that the power-law behavior can be described using the infinite number of elastic and viscous elements (Balland et al., 2006) (Fig. 4b). ...
Atomic force microscopy (AFM) has been extensively used to measure the mechanical properties of single cells and tissues with a high force sensitivity. AFM has been established to quantify mechanical differences between cells, e.g., between normal and disease cells, and between untreated (controlled) and treated cells. However, since these biological samples are intrinsically heterogeneous and hierarchical materials, AFM often suffers from the quantification of cell and tissue mechanics due to the high spatial resolution of AFM from the nanoscale to the microscale, comparable to the spatial variation and fluctuation of living systems. Thus, it is still challenging to elucidate universal nano- and micro-mechanical features of living systems using AFM data. This review addresses how AFM can quantify the heterogeneities and hierarchies of cell systems. For single-cell mechanical analysis, AFM has been combined with micropatterned substrate to control cell shape and precisely define the AFM measurement within cells, allowing us to analyze the cell-to-cell mechanical variation. For tissue mechanical analysis, we introduce AFM with a wide-scan range to map multicellular samples from a few hundred to millimeter scales, depending on the type of scanner, allowing us to quantify the spatial mechanical variation in multicellular systems. The reliability and the possibility of AFM to apply mechanics studies on cells and tissues with a range of Pascal (Pa) to MPa are addressed.
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... The past studies have shown that the cell mechanics can change in various physiological and pathological processes, including aging, stem cell differentiation, and cancer progression [6,19,44,46,61]. The cell mechanics is closely linked to the cytoskeleton structure, mainly that of F-actin, and the contractile state of the cell, for which the effect on the viscoelastic parameters was shown in the experiments with selective cytoskeleton modifications [25,28,40,54]. While several methods are available for the cell mechanical measurements, atomic force microscopy (AFM) remains one of the most popular techniques with wide analytical possibilities, despite its relatively low throughput [32,56,63]. ...
... From the previous numerical analysis, the combination of such changes leads to an even more pronounced decrease in the apparent Young's modulus E Hertz , which depends on both parameters [12]. Indeed, a decrease in the apparent Young's modulus was statistically significant for all the performed treatments [16,25,26]. These viscoelastic changes agree with the previously described master curve, predicting interdependent changes in the two viscoelastic parameters: an increase in the stiffness together with a more solid-like behavior, and vice versa, a decrease in the stiffness together with a more fluid-like behavior. ...
Cytotoxicity assays are essential tests in studies on the safety and biocompatibility of various substances and on the efficiency of anticancer drugs. The most frequently used assays commonly require application of externally added labels and read only collective response of cells. Recent studies show that the internal biophysical parameters of cells can be associated with the cellular damage. Therefore, using atomic force microscopy, we assessed the changes in the viscoelastic parameters of cells treated with eight different common cytotoxic agents to gain a more systematic view of the occurring mechanical changes. With the robust statistical analysis to account for both the cell-level variability and the experimental reproducibility, we have found that cell softening is a common response after each treatment. More precisely, the combined changes in the viscoelastic parameters of power-law rheology model led to a significant decrease of the apparent elastic modulus. The comparison with the morphological parameters (cytoskeleton and cell shape) demonstrated a higher sensitivity of the mechanical parameters versus the morphological ones. The obtained results support the idea of cell mechanics-based cytotoxicity tests and suggest a common way of a cell responding to damaging actions by softening.
... To retrieve a value for c, for force-clamps conducted at high forces (e.g. 500-700 pN), a power-law can be fitted to the data (see Note 7) [20]. In case of vimentin filaments, we found c ¼ 0.2 [9,21], indicative for viscoelastic materials and typical for cells [20]. ...
... 500-700 pN), a power-law can be fitted to the data (see Note 7) [20]. In case of vimentin filaments, we found c ¼ 0.2 [9,21], indicative for viscoelastic materials and typical for cells [20]. At lower clamping forces, individual steps in the strain-time data are resolved and can be further analyzed. ...
The eukaryotic cytoskeleton consists of three different types of biopolymers - microtubules, actin filaments, and intermediate filaments - and provides cells with versatile mechanical properties, combining stability and flexibility. The unique molecular structure of intermediate filaments leads to high extensibility and stability under load. With high laser power dual optical tweezers, the mechanical properties of intermediate filaments may be investigated, while monitoring the extension with fluorescence microscopy. Here, we provide detailed protocols for the preparation of single vimentin intermediate filaments and general measurement protocols for (i) stretching experiments, (ii) repeated loading and relaxation cycles, and (iii) force-clamp experiments. We describe methods for the analysis of the experimental data in combination with computational modeling approaches.Key wordsCytoskeletal filamentsIntermediate filamentsOptical tweezersSingle-molecule force spectroscopyForce-strain-relationshipLoading-relaxation cycleForce-clampConfocal microscopyMicrofluidics
... In a purely thermal homogeneous system, an MSD that scales linearly with time indicates diffusive motion through a viscous fluid, with the prefactor establishing the particle diffusivity. An MSD that scales subdiffusively (∼t α , α < 1) can instead indicate a viscoelastic medium with characteristic power-law scaling α [15], as well as other possible mechanisms [16,17]. This analysis has been employed in a number of cellular systems, establishing diffusive behavior in the case of some protein-sized particles [18][19][20], and subdiffusive dynamics for vesicles and similar-sized exogenous probes in the cytoplasm [12,15,21,22]. ...
... An MSD that scales subdiffusively (∼t α , α < 1) can instead indicate a viscoelastic medium with characteristic power-law scaling α [15], as well as other possible mechanisms [16,17]. This analysis has been employed in a number of cellular systems, establishing diffusive behavior in the case of some protein-sized particles [18][19][20], and subdiffusive dynamics for vesicles and similar-sized exogenous probes in the cytoplasm [12,15,21,22]. An alternate recent approach focuses instead on the velocity autocorrelation function, with negative correlations that decay as a power law in time taken to be a sign of viscoelastic rheology [16,23,24]. ...
The analysis of single-particle trajectories plays an important role in elucidating dynamics within complex environments such as those found in living cells. However, the characterization of intracellular particle motion is often confounded by confinement of the particles within nontrivial subcellular geometries. Here we focus specifically on the case of particles undergoing Brownian motion within a network of narrow tubules, as found in some cellular organelles. A computational unraveling algorithm is developed to uncouple particle motion from the confining network structure, allowing for an accurate extraction of the underlying one-dimensional diffusion coefficient, as well as differentiating between Brownian and fractional Langevin motion. We validate the algorithm with simulated trajectories and then highlight its application to an example system: analyzing the motion of membrane proteins confined in the tubules of the peripheral endoplasmic reticulum in mammalian cells. We show that these proteins undergo diffusive motion and provide a quantitative estimate of their diffusion coefficient. Our algorithm provides a generally applicable approach for disentangling geometric morphology and particle dynamics in networked architectures.
... From the point of view of a material scientist, cells are viscoelastic material [31]. This means that cells undergoing deformation dissipate mechanical energy and store it at the same time [32]. ...
... This means that cells undergoing deformation dissipate mechanical energy and store it at the same time [32]. On short time scales, cells behave as elastic materials, after a relaxation time of seconds to minutes they show liquid behaviour [31]. Empiric models to study the viscoelasticity of cells are combinations of springs and dashpots or powerlaw models. ...
Epithelial tissues line out all inner and outer cavities of the body, and serve as a barrier between the organism and the external world, or between different organs and their compartments. Epithelia have important sensory and signalling roles, while responding to changes in external conditions. The epithelial cell layers are constantly exposed to deformations, exerted on the level of the moving and developing organism, as well as due to internal flows and stresses that act on the cellular level. Nevertheless, the tissue has to maintain its shape and architecture over all scales – from the internal structure of comprising cells, to the shapes of the cells themselves, their connectivity, and ultimately, the shape and macroscopic structure of the tissue. Compromised morphology of the tissue is associated with numerous pathological conditions although it is not clear if the disease is the cause or the result of the altered morphology. The reason for this ambiguity is that the coupling between tissue architecture, the response to stress and the tissue function is still not understood. This relation is investigated in this thesis using epithelial model tissues. The first part of the thesis focuses on the effect of uniaxial stretch and shear deformations on the maintenance of the tissue structure. To this end, MDCK II tissues are grown on elastic substrates, while the deformation is imposed using mechanical manipulators developed with collaborators. In agreement with previous reports in literature, our experiments show a linear elastic behaviour on short time scales, and on length scales of several cells. This linear response can be understood from the observations that on short time scales very little topological restructuring occurs, and the proliferation rate is decreased. However, if the deformation is maintained for more than 30 minutes, the active response sets in targeting the reconstitution of tissue architecture. Cell proliferation increases significantly and, concomitantly, changes of the cell neighbourhood become more common. Depending on the amplitude of the deformation, the tissue needs 48 to 72 hours to restore its initial structure, with most of the recovery taking place in the first 6 hours. On these long time scales, small stretching amplitudes were found to speed up the overall tissue growth, compared to the control, while fast changes of area of more than 30% slow down the development, presumably due to damage on the cellular level. Consequently, the second part of the thesis focuses on the maintenance of the intracellular structure, in particular on the positioning of the nucleus. Namely, it was recently discovered that the shapes of the cells in the epithelium strongly correlate with the position and the shape of the nuclei, with the common assumption that it is the cytoskeleton that regulates the latter. However, mechanistic understanding of this process is not yet available. To get more insights, different components of the cytoskeleton were systematically manipulated to establish their role in the nuclear mechanics. Intermediate filaments were found to play only a little role in this process. Actin filaments push the nuclei towards the centre, while microtubules are responsible for pulling the nuclei out of the centre, in a myosin II-independent manner. The presented results deepen our understanding of the organisation of epithelial tissue and its maintenance. While in this thesis the focus lies on physical aspects of the response to mechanical stimuli, in the future, the coupling to biochemical signalling will be a relevant mechanism to be studied over all the time and length scales involved, in order to achieve full understanding of the maintenance of cell and tissue shape. The here elucidated biophysical response is an important step forward towards this goal.
... Cells exhibit creep and stress relaxation behavior under mechanical loading, commonly described using powerlaw responses [102]. Raj et al. [103] developed a theoretical model to predict Young's modulus of various cells, revealing a linear relationship with velocity and a nonlinear relationship with cell deformation (strain rate). ...
Single‐cell biophysical properties play a crucial role in regulating cellular physiological states and functions, demonstrating significant potential in the fields of life sciences and clinical diagnostics. Therefore, over the last few decades, researchers have developed various detection tools to explore the relationship between the biophysical changes of biological cells and human diseases. With the rapid advancement of modern microfabrication technology, microfluidic devices have quickly emerged as a promising platform for single‐cell analysis offering advantages including high‐throughput, exceptional precision, and ease of manipulation. Consequently, this paper provides an overview of the recent advances in microfluidic analysis and detection systems for single‐cell biophysical properties and their applications in the field of cancer. The working principles and latest research progress of single‐cell biophysical property detection are first analyzed, highlighting the significance of electrical and mechanical properties. The development of data acquisition and processing methods for real‐time, high‐throughput, and practical applications are then discussed. Furthermore, the differences in biophysical properties between tumor and normal cells are outlined, illustrating the potential for utilizing single‐cell biophysical properties for tumor cell identification, classification, and drug response assessment. Lastly, we summarize the limitations of existing microfluidic analysis and detection systems in single‐cell biophysical properties, while also pointing out the prospects and future directions of their applications in cancer diagnosis and treatment.
... Since tissue rheology has been studied extensively, there are good estimates of the properties of the cytosol [96], the cortex (including cortical tension) [97,98], and the effects of perturbations of actomyosin activity [99]. This level of detail in the model is necessary for several reasons. ...
Simple Summary
Control of tissue growth is an important component of cancer treatment, but understanding how to do this effectively is still in the early stages. Tissue growth typically involves both complex interacting signal transduction networks as well as mechanical interactions within and between cells, and how they interact to control growth is an open problem. Herein we begin the process of how to understand the interactions by focusing on tissue growth in the fruit fly Drosophila melanogaster. A model of the Hippo pathway, which is one of the primary growth-control pathways, is integrated with a description of the mechanical behavior of cells in wing-disc tissue to predict how mechanics and signaling interact, and a number of significant insights and predictions have emerged from the analysis of the model.
Abstract
Drosophila melanogaster has emerged as an ideal system for studying the networks that control tissue development and homeostasis and, given the similarity of the pathways involved, controlled and uncontrolled growth in mammalian systems. The signaling pathways used in patterning the Drosophila wing disc are well known and result in the emergence of interaction of these pathways with the Hippo signaling pathway, which plays a central role in controlling cell proliferation and apoptosis. Mechanical effects are another major factor in the control of growth, but far less is known about how they exert their control. Herein, we develop a mathematical model that integrates the mechanical interactions between cells, which occur via adherens and tight junctions, with the intracellular actin network and the Hippo pathway so as to better understand cell-autonomous and non-autonomous control of growth in response to mechanical forces.
... At short time scales, correlating to high frequencies, 20,28 single cell's rheological behavior is thought to be governed by internal fluid redistribution throughout the cytoplasm 30 and the dynamics of a single cytoskeleton filament. 28,31 For the liver tissue where there is a high proportion of liver cells (∼80% of liver mass is hepatocytes), 32 the intercellular and extracellular fluid phases are compressed and flow through the porous meshwork of the cytoplasm and ECM, respectively, during the instantaneous stress. 30 Hence, we detected significant creep deformation with large power-law exponents at the initial subsecond time scale. ...
Understanding liver tissue mechanics, particularly in the context of liver pathologies like fibrosis, cirrhosis, and carcinoma, holds pivotal significance for assessing disease severity and prognosis. Although the static mechanical properties of livers have been gradually studied, the intricacies of their dynamic mechanics remain enigmatic. Here, we characterize the dynamic creep responses of healthy, fibrotic, and mesenchymal stem cells (MSCs)-treated fibrotic lives. Strikingly, we unearth a ubiquitous two-stage power-law rheology of livers across different time scales with the exponents and their distribution profiles highly correlated to liver status. Moreover, our self-similar hierarchical theory effectively captures the delicate changes in the dynamical mechanics of livers. Notably, the viscoelastic multiscale mechanical indexes (i.e., power-law exponents and elastic stiffnesses of different hierarchies) and their distribution characteristics prominently vary with liver fibrosis and MSCs therapy. This study unveils the viscoelastic characteristics of livers and underscores the potential of proposed mechanical criteria for assessing disease evolution and prognosis.
... Liquid drop models and solid models can interpret the experimental data by applying a number of springs and dashpots as their elastic and viscous elements that are coupled either in series or in parallel, resulting in exponential decay functions with a finite number of relaxation times [10]. The power-law damping models describe the mechanical behavior of adherent cells and fit experimental relaxation data over much longer time scales than spring-dashpot models, but they do not have any characteristic relaxation time [11,12]. Using a power-law damping model, Land et al. [13] presented the passive and viscoelastic properties of isolated myocytes which are mainly derived from the molecule titin. ...
Knowing the mechanical properties of cardiac myofibrils isolated from human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) can provide valuable insight into the structure and function of the heart muscle. Previous studies focused mostly on studying myofibrillar stiffness using simplified elastic models. In this study, the mechanical properties of myofibrils isolated from hiPSC-CMs were measured using atomic force microscopy (AFM). The quasi-linear viscoelastic (QLV) model was used to interpret the elastic and viscous properties of myofibrils. Since there have been no previous studies on the viscoelastic properties of myofibrils extracted from hiPSC-CMs, myofibrils extracted from porcine left-ventricular (LV) tissue were used to compare and verify experimental processes and QLV model parameters. The elastic modulus of myofibrils extracted from porcine LV tissue was determined to be 8.82 ± 6.09 kPa which is consistent with previous studies which reported that porcine LV tissue is less stiff on average than mouse and rat cardiac myofibrils. The elastic modulus of myofibrils extracted from hiPSC-CMs was found to be 9.78 ± 5.80 kPa, which is consistent with the range of 5–20 kPa reported for myofibrils extracted from the adult human heart. We found that myofibrils isolated from hiPSC-CMs relax slower than myofibrils extracted from porcine LV tissue, particularly in the first 0.25 s after the peak stress in the stress relaxation test. These findings provide important insights into the mechanical behavior of hiPSC-CMs and have implications for the development of treatments for heart diseases.
... doi: bioRxiv preprint material's internal structure. Cytoskeleton, which consists of many disordered elements and are held together by weak attractive forces, may represent such a structure in cells 59 . Rheological behavior of cells is mediated by changes in the level of internal disorder and the effective temperature associated with cytoskeleton remodeling as suggested by SGR theory 60 freely moving actin elements are expected to be more liquid-like compared to cells in which actin is present in the same amount but whose movement is restricted. ...
Protein aggregation is a common underlying feature of neurodegenerative disorders. Cells expressing neurodegeneration associated mutant proteins show altered uptake of ligands, suggestive of impaired endocytosis, in a manner as yet unknown. Using live cell imaging, we show that clathrin mediated endocytosis (CME) is affected due to altered actin cytoskeletal organization in the presence of Huntingtin aggregates. Additionally, we find that cells containing Huntingtin aggregates are stiffer and less viscous than their wild type counterparts due to altered actin conformation, and not merely due to the physical presence of aggregate(s). We further demonstrate that CME and cellular viscosity can be rescued by overexpressing Hip1, Arp2/3 or transient LatrunculinA treatment. Examination of other pathogenic aggregates revealed that only a subset of these display defective CME, along with altered actin organization and increased stiffness. Together, our results point to an intimate connection between functional CME, actin organization and cellular stiffness in the context of neurodegeneration.
... It has been shown that even after optimizing biological and chemical conditions [14], such hydrodynamic stresses remain a crucial source of cell damage and death [15][16][17][18][19][20][21][22][23][24][25]. Understanding these mechanical stress response processes is notoriously difficult as they result from an interplay between the complex rheology of the bioink, which is typically shear thinning [26][27][28][29], and the even more complex viscoelastic response of the cell itself [30][31][32][33][34][35][36][37][38][39][40]. Despite these difficulties, certain progress towards reliable theoretical estimates of the cell stress inside printing needles has been achieved [15,18,41]. ...
Bioprinting of living cells can cause major shape deformations, which may severely affect cell survival and functionality. While the shear stresses occurring during cell flow through the printer nozzle have been quantified to some extent, the extensional stresses occurring as cells leave the nozzle into the free printing strand have been mostly ignored. Here we use lattice Boltzmann simulations together with a finite-element based cell model to study cell deformation inside the nozzle and at its exit. Our simulation results are in good qualitative agreement with experimental microscopy images. We show that, for cells flowing in the center of the nozzle, extensional stresses can be significant while, for cells flowing off-center, their deformation is dominated by the shear flow inside the nozzle. From the results of these simulations, we develop two simple methods that only require the printing parameters (nozzle diameter, flow rate, bioink rheology) to (i) accurately predict the maximum cell stress occurring during the three-dimensional bioprinting process and (ii) approximately predict the cell strains caused by the elongational flow at the nozzle exit.
... Living soft matter, ranging from cytoskeletal assemblies to multicellular tissue, is typically considered as a viscoelastic gel which resists shear deformations [11], while being internally driven by molecular motor-generated mechanical forces [12][13][14]. While at long time scales they can self-organize through active flows [15,16], at short time scales relative to the cytoskeletal remodeling such materials behave as active solids with a well-defined reference state about which elastic deformations can occur [17][18][19][20] . ...
Morphogenesis involves the transformation of initially simple shapes, such as multicellular spheroids, into more complex $3D$ shapes. These shape changes are governed by mechanical forces including molecular motor-generated forces as well as hydrostatic fluid pressure, both of which are actively regulated in living matter through mechano-chemical feedback. Inspired by autonomous, biophysical shape change, such as occurring in the model organism hydra, we introduce a minimal, active, elastic model featuring a network of springs in a globe-like spherical shell geometry. In this model there is coupling between activity and the shape of the shell: if the local curvature of a filament represented by a spring falls below a critical value, its elastic constant is actively changed. This results in deformation of the springs that changes the shape of the shell. By combining excitation of springs and pressure regulation, we show that the shell undergoes a transition from spheroidal to either elongated ellipsoidal or a different spheroidal shape, depending on pressure. There exists a critical pressure at which there is an abrupt change from ellipsoids to spheroids, showing that pressure is potentially a sensitive switch for material shape. More complex shapes, involving loss of cylindrical symmetry, can arise when springs are excited both above (spring constants increase) and below (spring constants decrease) the curvature threshold. We thus offer biologically inspired design principles for autonomous shape transitions in active elastic shells.
... Various techniques are available for single cell studies such as atomic force microscopy, micropipette aspiration, microplate rheometer, magnetic bead cytometry, and particle tracking microrheology [3,4]. Cells show stiffness variation by an order of magnitude based on stages of cell cycle, shape, structure, and protein expression [5,6]. ...
The method of cell monolayer rheology enables quantifying average rheological properties of cell in a single experimental run of few millions cells together in a single layer. Here we describe step-by-step procedure as to how to employ a modified commercial rotational rheometer to run rheological measurement and detect average viscoelastic properties of cells while maintaining the necessary precision level at the same time.Key wordsCell rheologyLinear viscoelasticityNarrow-gap rheometryCell monolayer
... This parameter leans on Hooke's law, which assumes a linear stress/strain relation. Real samples like cells are non-linear; however, at small stress/strain they exhibit linear response.29 Hereby, we selected small indentations for our analysis in an attempt to remain in the cell linear regime. ...
We have measured the elastic properties of live cells by Atomic Force Microscope (AFM) using different tip geometries commonly used in AFM studies. Soft 4-sided pyramidal probes (spring constant = 12 mN/m and 30 mN/m, radius 20 nm), 3-sided pyramidal probes (spring constant = 100 mN/m, radius of curvature 65-75 nm), flat (circular) probes (spring constant = 63 mN/m, radius 290 nm) and spherical probes (spring constant = 43 mN/m, radius 5 μm) have been used. Cells (3T3 fibroblasts) having elastic moduli around 0.5 kPa were investigated. We found that cell measured stiffness shows a systematic dependence on tip geometry: the sharper the tip, the higher the average modulus values. We hypothesize that the blunter the tip, the larger the contact area over which the mechanical response is measured or averaged. If there are small-scale stiffer areas (like actin bundles) they will be easier to pick up by a sharp probe. This effect can be seen in the wider distribution of the histograms of the measured elastic moduli on cells. Furthermore, non-linear responses of cells may be present due to the high average pressures applied by sharp probes, which would lead to an overestimation of the Young's modulus. Pressure versus contact radius simulations for the different tip geometries for a 0.5 kPa sample suggested similar average pressure for Bio-MLCTs, PFQNM and cut tips, except spherical tips that showed much lower average pressure at the same 400 nm indentation. However, real data of the cells suggested different results. Using the same indentation depth (400 nm) PFQNM and Bio-MLCTs showed similar average pressure and it decreased for cut and spherical tips. The calculated contact area at 400 nm cell indentation, using the obtained apparent Young's modulus for each tip geometry, showed the following distribution: Bio-MLCTs < PFQNM < cut << spherical. In summary, tip geometry as well as average pressure and tip-sample contact area are important parameters to take into account when measuring mechanical properties of soft samples. The larger the tip radius, the larger the contact area that will lead to a more evenly distribution of the applied pressure.
... At time scales too short for cytoskeletal remodeling to occur, the cytoskeleton behaves as an elastic material that can sustain and transmit mechanical stresses [20]. The disordered cytoskeleton can therefore be modeled as a network of elastic fibers that resist both stretching and bending with elastic moduli, µ and κ, respectively [21][22][23]. ...
Mechanical forces generated by myosin II molecular motors drive diverse cellular processes, most notably shape change, division and locomotion. These forces may be transmitted over long range through the cytoskeletal medium - a disordered, viscoelastic network of biopolymers. The resulting cell size scale force chains can in principle mediate mechanical interactions between distant actomyosin units, leading to self-organized structural order in the cell cytoskeleton. To investigate this process, we model the actin cytoskeleton on a percolated fiber lattice network, where fibers are modeled as linear elastic elements that can both bend and stretch, whereas myosin motors exert contractile force dipoles. We quantify the range and heterogeneity of force transmission in these networks in response to a force dipole, showing how these depend on varying bond dilution and fiber bending-to-stretching stiffness ratio. By analyzing clusters of nodes connected to highly strained bonds, as well as the decay rate of strain energy with distance from the force dipole, we show that long-range force transmission is screened out by fiber bending in diluted networks. We further characterize the difference in the propagation of tensile and compressive forces. This leads to a dependence of the mechanical interaction between a pair of force dipoles on their mutual separation and orientation. In more homogeneous networks, the interaction between force dipoles recapitulates the power law dependence on separation distance predicted by continuum elasticity theory, while in diluted networks, the interactions are short-ranged and fluctuate strongly with local network configurations. Altogether, our work suggests that elastic interactions between force dipoles in disordered, fibrous media can act as an organizing principle in biological materials.
... As well as possessing a stiffness, the cell cortex is a viscoelastic material, whose mechanical properties exhibit a dependence on time and frequency. Extensive studies of live cells using microrheology have established that the cortical stiffness follows a power law dependency [37]. This is a common feature of soft structured materials and indicates a disordered and metastable material. ...
The interaction between the actin cytoskeleton and the plasma membrane in eukaryotic cells is integral to a large number of functions such as shape change, mechanical reinforcement and contraction. These phenomena are driven by the architectural regulation of a thin actin network, directly beneath the membrane through interactions with a variety of binding proteins, membrane anchoring proteins and molecular motors. An increasingly common approach to understanding the mechanisms that drive these processes is to build model systems from reconstituted lipids, actin filaments and associated actin-binding proteins. Here we review recent progress in this field, with a particular emphasis on how the actin cytoskeleton provides mechanical reinforcement, drives shape change and induces contraction. Finally, we discuss potential future developments in the field, which would allow the extension of these techniques to more complex cellular processes.
... The mechanical properties of eukaryotic cells are mainly governed by the cytoskeleton. It is a complex protein structure, covering the entire cell and supporting cell shape [4]. Main components of the cytoskeleton responsible for the mechanical behaviour are actin filaments and microtubules [5]. ...
The rheological properties of cells have vital functional implications. Depending, for instance, on the life cycle, cells show large cell-to-cell variations making it cumbersome to quantify average viscoelastic properties of cells by single-cell techniques. Microfluidic devices, typically working in the nonlinear viscoelastic range, allow fast analysis of single-cell deformation. Averaging over a large number of cells can also be achieved by studying them in a monolayer between rheometer discs. This technique allows applying well-established rheological standard procedures to cell rheology. It offers further advantages like studying cells in the linear viscoelastic range while quantifying cell vitality. Here, we study the applicability of the technique to rather adverse conditions, like for microtubule-active anti-cancer drugs and for a cell line with large size variation. We found a strong impact of the gap width and of normal forces on the moduli and obtained high vitality levels during the rheological study. To enable studying the impact of microtubule-active drugs on vital cells at concentrations several orders of magnitude beyond the half maximal effective concentration for cytotoxicity, we arrested the cell cycle with hydroxyurea. Irrespective of the high concentrations, we observed no clear impact of the microtubule-active drugs.
... It has been shown that even after optimizing biological and chemical conditions [14], such hydrodynamic stresses remain a crucial source of cell damage and death [15][16][17][18][19][20][21][22][23][24][25]. Understanding these mechanical stress response processes is notoriously difficult as they result from an interplay between the complex rheology of the bioink, which is typically shear thinning [26][27][28][29], and the even more complex viscoelastic response of the cell itself [30][31][32][33][34][35][36][37][38][39]. Despite these difficulties, certain progress towards reliable theoretical estimates of the cell stress inside printing needles has been achieved [15,18,40]. ...
Bioprinting of living cells can cause major shape deformations, which may severely affect cell survival and functionality. While the shear stresses occurring during cell flow through the printer nozzle have been quantified to some extent, the extensional stresses occurring as cells leave the nozzle into the free printing strand have been mostly ignored. Here we use Lattice-Boltzmann simulations together with a finite-element based cell model to study cell deformation at the nozzle exit. Our simulation results are in good qualitative agreement with experimental microscopy images. We show that for cells flowing in the center of the nozzle extensional stresses can be significant, while for cells flowing off-center their deformation is dominated by the shear flow inside the nozzle. From the results of these simulations, we develop two simple methods that only require the printing parameters (nozzle diameter, flow rate, bioink rheology) to (i) accurately predict the maximum cell stress occurring during the 3D bioprinting process and (ii) approximately predict the cell strains caused by the elongational flow at the nozzle exit.
... It has been shown that even after optimizing biological and chemical conditions [14], such hydrodynamic stresses remain a crucial source of cell damage and death [15][16][17][18][19][20][21][22][23][24][25]. Understanding these mechanical stress response processes is notoriously difficult as they result from an interplay between the complex rheology of the bioink, which is typically shear thinning [26][27][28][29], and the even more complex viscoelastic response of the cell itself [30][31][32][33][34][35][36][37][38][39]. Despite these difficulties, certain progress towards reliable theoretical estimates of the cell stress inside printing needles has been achieved [15,18,40]. ...
Bioprinting of living cells can cause major shape deformations, which may severely affect cell survival and functionality. While the shear stresses occurring during cell flow through the printer nozzle have been quantified to some extent, the extensional stresses occurring as cells leave the nozzle into the free printing strand have been mostly ignored. Here we use Lattice-Boltzmann simulations together with a finite-element based cell model to study cell deformation at the nozzle exit. Our simulation results are in good qualitative agreement with experimental microscopy images. We show that for cells flowing in the center of the nozzle extensional stresses can be significant, while for cells flowing off-center their deformation is dominated by the shear flow inside the nozzle. From the results of these simulations, we develop two simple methods that only require the printing parameters (nozzle diameter, flow rate, bioink rheology) to (i) accurately predict the maximum cell stress occurring during the 3D bioprinting process and (ii) approximately predict the cell strains caused by the elongational flow at the nozzle exit.
... The ensemble-averaged mean squared displacement (MSD) was graphed versus lag time, tau ( τ ), to quantify the power-law behavior using Eq. (2 ) [39] . ...
Cells are continuously exposed to dynamic environmental cues that influence their behavior. Mechanical cues can influence cellular and genomic architecture, gene expression, and intranuclear mechanics, providing evidence of mechanosensing by the nucleus, and a mechanoreciprocity between the nucleus and environment. Force disruption at the tissue level through aging, disease, or trauma, propagates to the nucleus and can have lasting consequences on proper functioning of the cell and nucleus. While the influence of mechanical cues leading to axonal damage has been well studied in neuronal cells, the mechanics of the nucleus following high impulse loading is still largely unexplored. Using an in vitro model of traumatic neural injury, we show a dynamic nuclear behavioral response to impulse stretch (up to 170% strain per second) through quantitative measures of nuclear movement, including tracking of rotation and internal motion. Differences in nuclear movement were observed between low and high strain magnitudes. Increased exposure to impulse stretch exaggerated the decrease in internal motion, assessed by particle tracking microrheology, and in intranuclear displacements, assessed through high-resolution deformable image registration. An increase in F-actin puncta surrounding nuclei exposed to impulse stretch additionally demonstrated a corresponding disruption of the cytoskeletal network. Our results show direct biophysical nuclear responsiveness in neuronal cells through force propagation from the substrate to the nucleus. Understanding how mechanical forces perturb the morphological and behavioral response can lead to a greater understanding of how mechanical strain drives changes within the cell and nucleus, and may inform fundamental nuclear behavior after traumatic axonal injury.
Statement of Significance
: The nucleus of the cell has been implicated as a mechano-sensitive organelle, courting molecular sensors and transmitting physical cues in order to maintain cellular and tissue homeostasis. Disruption of this network due to disease or high velocity forces (e.g., trauma) can not only result in orchestrated biochemical cascades, but also biophysical perturbations. Using an in vitro model of traumatic neural injury, we aimed to provide insight into the neuronal nuclear mechanics and biophysical responses at a continuum of strain magnitudes and after repetitive loads. Our image-based methods demonstrate mechanically-induced changes in cellular and nuclear behavior after high intensity loading and have the potential to further defined mechanical thresholds of neuronal cell injury.
... Importantly, the measured relaxation times scale with the experimental time. It should therefore be considered with great care and the experimental time must be reported (Kollmannsberger & Fabry, 2011 Recently, the continuous relaxation spectrum was described using fractional viscoelastic models. In the simplest case, a power law model (such as used here) can be defined by a springpot element. ...
Cells are complex, viscoelastic bodies. Their mechanical properties are defined by the arrangement of semiflexible cytoskeletal fibers, their crosslinking, and the active remodeling of the cytoskeletal network. Atomic force microscopy (AFM) is an often‐used technique for the study of cell mechanics, enabling time‐ and frequency‐dependent measurements with nanometer resolution. Cells exhibit time‐dependent deformation when stress is applied. In this work, we have investigated the stress relaxation of HeLa cells when subjected to a constant strain. We have varied the applied force (1, 2, 4, and 8 nN) and pause time (1, 10, and 60 s) to check for common assumptions for the use of models of linear viscoelasticity. Then, we have applied three models (standard linear solid, five element Maxwell, power law rheology) to study their suitability to fit the datasets. We show that the five element Maxwell model captures the stress relaxation response the best while still retaining a low number of free variables. This work serves as an introduction and guide when performing stress relaxation experiments on soft matter using AFM.
Research Highlights
Cells exhibit linear viscoelastic properties when subjected to stress relaxation measurements at the studied different forces and times.
The stress relaxation is best described by a five element Maxwell model.
All three used models capture a softening and fluidization of cells when disrupting actin filaments.
Morphogenesis involves the transformation of initially simple shapes, such as multicellular spheroids, into more complex 3D shapes. These shape changes are governed by mechanical forces including molecular motor-generated forces as well as hydrostatic fluid pressure, both of which are actively regulated in living matter through mechano-chemical feedback. Inspired by autonomous, biophysical shape change, such as occurring in the model organism hydra, we introduce a minimal, active, elastic model featuring a network of springs in a globe-like spherical shell geometry. In this model there is coupling between activity and the shape of the shell: if the local curvature of a filament represented by a spring falls below a critical value, its elastic constant is actively changed. This results in deformation of the springs that changes the shape of the shell. By combining excitation of springs and pressure regulation, we show that the shell undergoes a transition from spheroidal to either elongated ellipsoidal or a different spheroidal shape, depending on pressure. There exists a critical pressure at which there is an abrupt change from ellipsoids to spheroids, showing that pressure is potentially a sensitive switch for material shape. We thus offer biologically inspired design principles for autonomous shape transitions in active elastic shells.
In order to provide context and help for newcomers in the area of biological physics, the goal of this chapter is to develop a feeling for the physics of cell membranes. Our aim is to present our interpretation of EMB in a language familiar to physicists. In practice, most of the attention will be focused at the cellular level, focusing on the electrical and mechanical properties of membranes. Thus, we begin with a brief overview of the basic morphological characteristics of the membrane enveloping living cells which separates the cytoplasmic medium (cytosol) from the extracellular medium. Since we are interested in the ED and EP mechanisms we first place an emphasis on the electrical properties of membranes. We outline the interpretation of typical cell membrane electrical measurements and show how this allows a basic introduction into the mechanisms underlying ED and EP. Since perturbations to the mechanical environment can affect cell behavior and its normal physiology, we next briefly review the current understanding of how the mechanical characteristics of cell relate to underlying architectural changes and describe how these changes evolve with membrane deformability in response to an applied stress. The chapter closes with a discussion of possible generalizations to cell assemblies and simple models of biological tissues.
The mechanical properties of soft tissues can often be strongly correlated with the progression of various diseases, such as myocardial infarction (MI). However, the dynamic mechanical properties of cardiac tissues during MI progression remain poorly understood. Herein, we investigate the rheological responses of cardiac tissues at different stages of MI (i.e., early-stage, mid-stage, and late-stage) with atomic force microscopy-based microrheology. Surprisingly, we discover that all cardiac tissues exhibit a universal two-stage power-law rheological behavior at different time scales. The experimentally found power-law exponents can capture an inconspicuous initial rheological change, making them particularly suitable as markers for early-stage MI diagnosis. We further develop a self-similar hierarchical model to characterize the progressive mechanical changes from subcellular to tissue scales. The theoretically calculated mechanical indexes are found to markedly vary among different stages of MI. These new mechanical markers are applicable for tracking the subtle changes of cardiac tissues during MI progression.
Shear stress plays a crucial role in many physiological processes, such as atherosclerosis, angiogenesis, and metastasis. However, how cells respond to static and dynamical shear stresses remains poorly understood. Here, we propose a structure-based cellular model, consisting of cell membrane, cytoplasm, and cytoskeleton, to explore the shear rheology of cells. By simulating the mechanical responses of a single cell under shear stress, we find that this model can reproduce both the universal power-law rheology at small deformations and stress stiffening at large deformations. Besides, the loss moduli of cells at high frequencies exhibit a stronger frequency dependence than the storage moduli. Moreover, we present two master relations: one is between the power-law exponent and cell stiffness; the other is between cell stiffness and external forces. Our results are in broad agreement with experiments. The self-similar hierarchical theory offers a physical explanation of the power-law responses of cells under shear stress. In addition, we consider the geometrical nonlinearity of single filaments to account for the stress stiffening of cells. The present model can be used to examine the effects of shear flow on living cells in physiological environments.
Mechanical forces generated by myosin II molecular motors drive diverse cellular processes, most notably shape change, division and locomotion. These forces may be transmitted over long range through the cytoskeletal...
Background
Dilated cardiomyopathy (DCM) is a major cause of heart failure in children. Despite intensive genetic analyses, pathogenic gene variants have not been identified in most patients with DCM, which suggests that cardiomyocytes are not solely responsible for DCM. Cardiac fibroblasts (CFs) are the most abundant cell type in the heart. They have several roles in maintaining cardiac function; however, the pathological role of CFs in DCM remains unknown.
Methods and Results
Four primary cultured CF cell lines were established from pediatric patients with DCM and compared with 3 CF lines from healthy controls. There were no significant differences in cellular proliferation, adhesion, migration, apoptosis, or myofibroblast activation between DCM CFs compared with healthy CFs. Atomic force microscopy revealed that cellular stiffness, fluidity, and viscosity were not significantly changed in DCM CFs. However, when DCM CFs were cocultured with healthy cardiomyocytes, they deteriorated the contractile and diastolic functions of cardiomyocytes. RNA sequencing revealed markedly different comprehensive gene expression profiles in DCM CFs compared with healthy CFs. Several humoral factors and the extracellular matrix were significantly upregulated or downregulated in DCM CFs. The pathway analysis revealed that extracellular matrix receptor interactions, focal adhesion signaling, Hippo signaling, and transforming growth factor‐β signaling pathways were significantly affected in DCM CFs. In contrast, single‐cell RNA sequencing revealed that there was no specific subpopulation in the DCM CFs that contributed to the alterations in gene expression.
Conclusions
Although cellular physiological behavior was not altered in DCM CFs, they deteriorated the contractile and diastolic functions of healthy cardiomyocytes through humoral factors and direct cell–cell contact.
The mechanical response and relaxation behavior of hydrogels are crucial to their diverse functions and applications. However, understanding how stress relaxation depends on the material properties of hydrogels and accurately modeling relaxation behavior at multiple time scales remains a challenge for soft matter mechanics and soft material design. While a crossover phenomenon in stress relaxation has been observed in hydrogels, living cells, and tissues, little is known about how the crossover behavior and characteristic crossover time depend on material properties. In this study, we conducted systematic atomic-force-microscopy (AFM) measurements of stress relaxation in agarose hydrogels with varying types, indentation depths, and concentrations. Our findings show that the stress relaxation of these hydrogels features a crossover from short-time poroelastic relaxation to long-time power-law viscoelastic relaxation at the micron scale. The crossover time for a poroelastic-dominant hydrogel is determined by the length scale of the contact and diffusion coefficient of the solvent inside the gel network. In contrast, for a viscoelastic-dominant hydrogel, the crossover time is closely related to the shortest relaxation time of the disordered network. We also compared the stress relaxation and crossover behavior of hydrogels with those of living cells and tissues. Our experimental results provide insights into the dependence of crossover time on poroelastic and viscoelastic properties and demonstrate that hydrogels can serve as model systems for studying a wide range of mechanical behaviors and emergent properties in biomaterials, living cells, and tissues.
The advent of atomic force microscopy, along with optical tweezers, ushered in a new field of single molecule force spectroscopy, wherein the response of a single protein or a macromolecule to external mechanical perturbations is measured. Controlled forces ranging from pN to nN are applied to measure the unfolding force distribution of a single protein domain. In a clamp type experiment, the folded protein is subjected to a constant force to measure the unfolding time distribution. Simultaneously, there were efforts to measure the elastic and viscous response of a single domain by applying sinusoidal forces and measuring the resulting deformations produced in a bid to quantify its viscoelasticity. The deformation's phase lag with respect to the applied force provides the elastic and viscous response of the protein, akin to oscillatory rheology. Despite numerous technical advances in AFM, an artefact-free measurement of a folded protein's viscoelasticity largely remains a challenge. In this perspective, we review efforts to measure the viscoelasticity of proteins using dynamic AFM, identifying pitfalls that make these measurements elusive. Finally, we discuss a new promising method, which reported viscoelasticity of a folded protein and its implications for our understanding of protein dynamics and structural flexibility.
In preparation for leveraging extracellular vesicles (EVs) for disease diagnostics and therapeutics, fundamental research is being done to understand EV biological, chemical, and physical properties. Most published studies have investigated nanoscale EVs and focused on EV biochemical content. There is much less understanding of large microscale EV characteristics and EV mechanical properties. Recently a non‐contact microfluidic technique that measures the stiffness of large EVs (>1 µm diameter) is introduced. This pilot study probes the robustness of the microfluidic technique to distinguish between EV populations by comparing stiffness distributions of large EVs derived from glioblastoma cell lines. EVs derived from cells expressing the IDH1 mutation, a common glioblastoma mutation known to disrupt lipid metabolism, are stiffer than those expressed from wild‐type cells in a statistical comparison of sample medians. A supporting lipidomics analysis showed that the IDH1 mutation increased the number of saturated lipids in EVs. Taken together, these data encourage further investigation into the potential of high‐throughput microfluidics to distinguish between large EV populations that differ in biomolecular composition. These findings contribute to the understanding of EV biomechanics, in particular for the less studied microscale EVs. A non‐contact microfluidic technique detects changes in membrane composition by measuring the effective stiffness of large extracellular vesicles. Microscale extracellular vesicles derived from glioblastoma cells are stiffer with the IDH1 mutation, which is consistent with the increase in saturated lipids. Microfluidics is a promising mechanical measurement approach for large extracellular vesicles to complement nanoscale atomic force microscopy measurements.
Every cell in the human body, regardless of its type, is exposed to mechanical stimuli. These mechanical stimuli can take many forms: Muscle contractions cause stretch in the surrounding tissue, blood flow causes shear stress on cells at the surface of blood vessels, and the mechanical stiffness of tissue has fundamental effects on the proper functioning of cells within that tissue. Cells can directly sense mechanical stresses, deformations, and the stiffness of their environment. Cellular mechanosensors are for example integrins, which are transmembrane proteins that form physical links with the surrounding matrix, and stretch-activated ion channels in the cell membrane. Through complex intracellular mechanochemical signal transduction pathways, mechanical stimuli are transmitted and processed by the cell, leading to a large range of responses at the cellular or tissue level. These responses can be rapid, short-term, and physiological, such as in the form of altered cell shape or migration. However, in the case of longterm abnormal mechanical stimuli, cellular adaptation can also lead to pathological consequences. For example, increased fluid shear stress in blood vessels can lead to tissue inflammation and arteriosclerosis. Numerous seemingly unrelated diseases can be attributed to altered or impaired cellular mechanotransduction, including various muscular dystrophies, polycystic kidney disease, and some forms of hearing loss. Often, these diseases can be attributed to genetic mutations of individual structural components of mechanotransduction, such as intermediate filaments of the cellular cytoskeleton (for example, mutations of the protein desmin in muscle tissue), or in proteins that connect the cytoskeleton to the nucleus (for example, mutations in lamins in the nuclear lamina). It is therefore not surprising that mechanical properties and mechanotransduction of cells have increasingly become a focus in basic and clinical research. The study of cellular mechanotransduction requires appropriate in vitro cell culture methods. Classically, two-dimensional cell cultures, e.g. in Petri dishes, are used for this purpose, which allow for controlled laboratory conditions with relatively high experimental throughput, but only reflect to a limited extent the complex geometric environment to which cells are exposed in vivo. A current research trend is therefore to use three-dimensional cell culture, whereby cells grow in a native or synthetic extracellular matrix. For this, methods and devices are needed to apply mechanical stimuli on cells. A simple approach here is to seed cells on substrates with controlled stiffness in order to mimic varied tissue mechanics. This can be easily achieved, for example, with polydimethylsiloxane, a biocompatible silicone-like gel with adaptable Young's modulus. Mechanical strain, on the other hand, can be applied by cell stretchers, which are devices that can deform flexible cell substrates in a controlled manner in one or more directions. Finally, methods and devices are needed to characterize the mechanical properties of cells. For this purpose, there are contact-based methods, such as indenters, which are used to investigate the relationship between applied stress and resulting cell strain (or the other way around), as well as contactless methods, such as optical or magnetic tweezers, in which the application of deformation (or force) is achieved by electromagnetic field gradients. In order to interpret the results obtained by such methods, models are needed that explain the mechanical, in particular the viscoelastic, properties of cells dominated by the cytoskeleton. In the following cumulative dissertation, I will first provide an overview of the current state of research regarding mechanical stimuli on cells, the cellular mechanosensors and mechanisms of cellular mechanotransduction, their impairment in disease, as well as the mechanical properties of cells. I will then focus on the methods and devices that can be used to investigate the resulting questions in a laboratory context. During my review I will give concrete examples which are mostly taken from a series of reports that I published during the time of my doctorate. A selection of five of my first-author papers are attached in full to this dissertation.
A thorough understanding of the changes in mechanical property behind intracellular biophysical and biochemical processes during differentiation of human mesenchymal stem cells (hMSCs) is helpful to direct and enhance the commitment of cells to a particular lineage. In this study, displacement creep of the mesenchymal cell lineages (osteogenic, chondrogenic and adipogenic hMSCs) were determined by using atomic force microscopy, which was then used to determine their mechanical properties. We found that at any stages of differentiation, the mesenchymal cell lineages are linear viscoelastic materials and well matched with a simple power-law creep compliance. In addition, the viscoelasticity of mesenchymal cell lineages showed different trends during differentiation. The adipogenic hMSCs showed continuous softening at all stages. The osteogenic and chondrogenic hMSCs only continuously soften and become more fluid-like in the early stage of differentiation, and get stiffened and less fluid-like in the later stage. These findings will help more accurately imitate cellular biomechanics in the microenvironment, and provided an important reference in the biophysics biomimetic design of stem cell differentiation.
The mechanical properties of biological soft tissues are inextricably linked to the field of health care, and their mechanical properties can be important indicators for diagnosing and detecting diseases; they can also be used to analyze the causes of organ diseases from a pathological point of view and thus guide the deployment of medical solutions. As an effective method to characterize the mechanical properties of materials, mechanical loading experiments have been successfully applied to the mechanical properties of materials, including tension, compression, pure shear, and so on. Under quasi-static loading, when the material is a biological soft tissue material between a solid and an ideal fluid, its viscoelastic properties strongly respond to the force stimulus, and the stress-strain-time in the elastic phase will have obvious disturbance characteristics. Therefore, the existing statistical methods are often difficult to quantitatively describe the mechanical properties of materials. Therefore, this study proposes an Interval Capture Point based on the principle of integration. The experimental data based on this method can characterize its nonlinear mechanical properties well, especially when the loading speed is extremely low and the soft materials show strong disturbance characteristics. The proposed method can still accurately characterize the hyperelastic and viscoelastic properties of the mechanical properties of biological soft tissues under quasi-static loading.
The mechanical properties of single cells have been recognized as biomarkers for identifying individual cells and diagnosing human diseases. Microfluidic devices based on the flow cytometry principle, which are not limited by the vision field of a microscope and can achieve a very high throughput, have been extensively adopted to measure the mechanical properties of single cells. However, these kinds of microfluidic devices usually required pressure-driven pumps with a very low flow rate and high precision. In this study, we developed a high-throughput microfluidic device inspired by the Wheatstone bridge principle for characterizing the mechanical properties of single cells. The microfluidic analogue of the Wheatstone bridge not only took advantage of flow cytometry, but also allowed precise control of a very low flow rate through the constricted channel with a higher input flow rate generated by a commercially available pressure-driven pump. Under different input flow rates of the pump, the apparent elastic moduli and the fluidity of osteosarcoma (U-2OS) cells and cervical carcinoma (HeLa) cells were measured by monitoring their dynamic deformations passing through the bridge-channel with different sizes of rectangular constrictions. The results showed that the input flow rate had little effect on measuring the mechanical properties of the cells, while the ratio of cell radius to effective constriction radius was different, i.e., for U-2OS cells it was 1.20 and for HeLa cells it was 1.09. Under this condition compared with predecessors, our statistic results of cell mechanical properties exhibited minimal errors. Furthermore, the cell viability after measurements was kept above 90% that demonstrated the non-destructive property of our proposed method.
Living cells are known to exhibit universal power-law rheological behaviors, but their underlying biomechanical principles are still not fully understood. Here, we present a network dynamics picture to decipher the nonlinear power-law relaxation of cortical cytoskeleton. Under step strains, we present a scaling relation between instantaneous differential stiffness and external stress as a result of chain reorientation. Then, during the relaxation, we show how the scaling law theoretically originates from an exponential form of cortical disorder, with the scaling exponent decreased by the imposed strain or crosslinker density in the nonlinear regime. We attribute this exponent variation to the molecular realignment along the stretch direction or the transition of network structure from in-series to in-parallel modes, both solidifying the network towards our one-dimensional theoretical limit. In addition, the rebinding of crosslinkers is found to be crucial for moderating the relaxation speed under small strains. Together with the disorder nature, we demonstrate that the structural effects of networks provide a unified interpretation for the nonlinear power-law relaxation of cell cortex, and may help to understand cell mechanics from the molecular scale.
Although short bamboo nodes function in mechanical support and fluid exchange for bamboo survival, their structures are not fully understood compared to unidirectional fibrous internodes. Here, we identify the spatial heterostructure of the bamboo node via multiscale imaging strategies and investigate its mechanical properties by multimodal mechanical tests. We find three kinds of hierarchical fiber reinforcement schemes origined from the bamboo node, including spatially tightened interlocking, triaxial interconnected scaffolding, and isotropic intertwining. These reinforcement schemes built on porous vascular bundles, microfibers, and more-refined twist-aligned nanofibers govern the structural stability of the bamboo via hierarchical toughening. In addition, the spatial liquid transport associated with these multiscale fibers within the bamboo node is experimentally verified, which gives perceptible evidence for the life-indispensable multidirectional fluid exchange. The functional integration of mechanical reinforcement and liquid transport reflects the bamboo node's wisdom of elaborate structural optimization rather than ingredient richness. This study would advance our understanding of biological materials and provide insights into the design of fiber-reinforced structures and biomass utilization.
Cell stiffness is an important characteristic of cells and their response to external stimuli. In this review, we survey methods used to measure cell stiffness, summarize stimuli that alter cell stiffness, and discuss signaling pathways and mechanisms that control cell stiffness. Several pathological states are characterized by changes in cell stiffness, suggesting this property can serve as a potential diagnostic marker or therapeutic target. Therefore, we consider the effect of cell stiffness on signaling and growth processes required for homeostasis and dysfunction in healthy and pathological states. Specifically, the composition and structure of the cell membrane and cytoskeleton are major determinants of cell stiffness, and studies have identified signaling pathways that affect cytoskeletal dynamics both directly and by altered gene expression. We present the results of studies interrogating the effects of biophysical and biochemical stimuli on the cytoskeleton and other cellular components and how these factors determine the stiffness of both individual cells and multicellular structures. Overall, these studies represent an intersection of the fields of polymer physics, protein biochemistry, and mechanics, and identify specific mechanisms involved in mediating cell stiffness that can serve as therapeutic targets.
The rheological characterization of any biopolymer solution is crucial for evaluating the overall printability or injectability of the hydrogel. However, the effect of cells in the cell-laden hydrogel's rheological profile is often ignored. As a result, there is a significant difference in the predicted and experimental outcome in the structural stability of the construct as well as on the cell viability, proliferation, and differentiation potential of the embedded cells. Our present study has addressed the effect of different cell densities (0.1 million cells/ml, 0.5 million cells/ml, 1 million cells/ml and 2 million cells/ml) of TVA-BMSCs on the flow property, modulus behaviour, gelation kinetics and printability of our proprietary silk fibroin-gelatin (5SF-6G) bioink. The cell-laden hydrogels demonstrated a characteristic shear thinning behaviour (low initial viscosity), low storage modulus and increased gelation time when compared to the acellular 5SF-6G hydrogel. The printability analysis also portrayed a square pore geometry with low spreading ratio in 1 million cells/ml encapsulated 5SF-6G hydrogel comparable to the acellular hydrogel. We postulated that incorporation of cells in the bioink interfered with the gelation mechanism of the mushroom tyrosinase in the 5SF-6G bioink by masking the active sites. Additionally, the mechanistic crosstalk between the cell-surface integrins with the cell-attachment motifs of the biomaterial alters the cellular biomechanics of the cell that in-turn profoundly impacts the rheological properties of the polymer blend. Therefore, cell density of 1 million cells/ml was considered the best fit for extrusion-based 3D bioprinting owing to its optimum rheological traits and printability index akin the acellular hydrogel.
Granular hydrogels have evolved an innovative technology in biomedicine. Unlike conventional hydrogels, granular hydrogels display dynamic properties like injectability and porosity, making them feasible for applications in 3D bioprinting and tissue engineering. High-energy electron irradiation combines sterilization and tuning of hydrogel properties without adding potentially cytotoxic chemicals. In this study, granular agarose/alginate hydrogels are prepared by electrospraying. Utilizing 10 MeV electron irradiation, the granular hydrogels are treated in a dose range of 0 kGy–30 kGy relevant for sterilization. Herein, a size reduction of the microparticles is observed. Mechanical properties of individual agarose/alginate beads are examined using AFM measurements revealing a gel softening attributed to radiation degradation. Shear-thinning and self-healing characteristics of the entire granular hydrogel are studied employing rheology. Although viscoelasticity changes under irradiation, shear-thinning and self-healing maintains. These dynamic properties enable injection, which is demonstrated for 27 G needles. This study presents a mechanical characterization of high-energy electron irradiated granular agarose/alginate hydrogels that extends the diversity of available injectable hydrogels and provides a basis for biomedical applications of this scaffold.
Many glassy and amorphous materials, like martensites, show characteristic behaviours during constraintinduced fractures. These fractures are avalanche processes whose statistics is known to follow in most cases a power-law distribution, reminding of collective behaviour and self-organised criticality. Avalanches of fractures are observed as well in living systems which, if we do not consider active remodelling, can be seen as a glassy network, with a frozen structure.The actin cytoskeleton (CSK) forms microfilaments organisedinto higher-order structures by a dynamic assembly-disassembly mechanism with cross-linkers.Experiments revealed that cells respond to external constraints bya cascade of random and abrupt ruptures of their CSK, suggesting that they behaveas a quasi-rigid random network of intertwined filaments. We analyse experimental data on CD34+ cells, isolated from healthy andleukemic bone marrows, however these behaviours have been reproduced on other cells.Surprisingly, the distribution of thestrength, the size and the energy of these rupture events do not follow the power-law statistics typical of critical phenomena and of avalanche size distributions in amorphous materials. In fact, the avalanche size turns out to be log-normal, suggesting that the mechanics of living systems in catastrophic events would not fitinto self-organised critical systems (power-laws).In order to give an interpretation of this peculiar behaviour we first proposea minimal (1D) stochastic model. This model gives an interpretation of the energy released along the rupture events, in terms of the sum (being energy additive) of a multiplicative cascade process relaxing with time. We distinguish 2 types of rupture events, brittle failures likely corresponding toirreversible ruptures in a stiff and highly cross-linked CSK and ductile failures resulting from dynamiccross-linker unbindings during plastic deformation without loss of CSK integrity. Our model provides somemathematical and mechanistic understanding of the robustness of the log-normal statistics observedin both brittle and ductile situations. We also show that brittle failures are relatively more prominentin leukemic than in healthy cells, suggesting their greater fragility and their different CSK architecture, stiffer and more reticulated.This minimal model motivates the more general question of what are the resulting distributions of a sum of correlated random variables coming from a multiplicative process. Therefore, we analyse the distribution of the sum of a generalised branching process evolving with a continuous random reproduction (growth) rate. The process depends only on 2 parameters: the first 2 central moments of the reproduction rate distribution.We then create a phase diagram showing 3 different regions: 1) a region where the final distribution has all central moments finite and is approximately log-normal. 2) A region where the asymptotic distribution is a power-law, with a decay exponent belonging to the interval [1;3], whose value is uniquely determined by the model parameters. 3) Finally, we found an exact log-normal size, non-stationary, distribution region. In all cases correlations are fundamental.Increasing the level of complexity for avalanche modelling, we propose then a random Erdös-Rényi network to model a cell CSK, identifying the networknodes as the actin filaments, and its links as actin cross-linkers. On this structure wesimulate avalanches of ruptures.Our simulations show that we can reproduce the log-normal statistics with two simple ingredients: a random network without characteristic length scale, and a breaking rule capturingthe observed visco-elasticity of living cells. This work paves the way for future applications to many phenomena in living systems that include large populations of individual, non-linear, elements(brain, heart, epidemics) where similar log-normal statistics have also been observed.
Living cells are a complex soft material with fascinating mechanical properties. Confusingly, experiments have shown that cells exhibit stiffening and more solid-like behaviors under uniaxial stretches or shear, while they present softening and more fluid-like behaviors under biaxial stretches. For both of these seemingly paradoxical stiffening and softening rheological behaviors, cells often exhibit a robust power-law rheological characteristic. Here, based on the structural features, we propose a cellular structural model to investigate these rheological behaviors of cells under different loading conditions. It is found that this structural model can naturally capture the stiffening and softening behaviors in the power-law rheological responses of cells, depending on the loading conditions. Both stiffening and softening of cells originate from changes in the configuration of the discrete cytoskeleton: stiffening from the rotation of the microtubules to the loading direction and softening from the elastic buckling of individual microtubules. Moreover, for both stiffening and softening in the rheological behaviors of cells, there exists a unified relationship that the power-law exponent decreases linearly with the cellular stiffness in a semi-logarithmic coordination. We further present that a self-similar hierarchical model can be used to analyze this unified relationship. This study not only provides a discrete cellular structural model to capture the essential mechanisms of cellular rheology, but also suggests that the scaling rheological exponent may be treated as a mechanical marker for monitoring cellular healthy states.
Viscoelastic properties of epithelial cells subject to shape changes were monitored by indentation-retraction/relaxation experiments. MDCK II cells cultured on extensible polydimethylsiloxane substrates were laterally stretched and, in response, displayed increased cortex contractility and loss of excess surface area. Thereby, the cells preserve their fluidity but inevitably become stiffer. We found similar behavior in demixed cell monolayers of ZO-1/2 double knock down (dKD) cells, cells exposed to different temperatures and after removal of cholesterol from the plasma membrane. Conversely, the mechanical response of single cells adhered onto differently sized patches displays no visible rheological change. Sacrificing excess surface area allows the cells to respond to mechanical challenges without losing their ability to flow. They gain a new degree of freedom that permits resolving the interdependence of fluidity β on stiffness KA0. We also propose a model that permits to tell apart contributions from excess membrane area and excess cell surface area. The viscoelastic properties of cells subjected to external strain are assessed, showing that cells become stiffer but preserve fluidity by sacrificing their excess surface area.
Knowledge of physical properties of cells is vital for many research areas in biology and medicine. Atomic force microscopy (AFM) and scanning ion conductance microscopy (SICM) are two techniques to assess the three-dimensional topography and mechanical properties of cells. This chapter introduces the basic working principles and imaging modes of AFM and SICM and then focuses on their similarities and differences. Strengths and limitations in terms of image resolution, imaging speed, and biomechanical applications are discussed. Also, combined applications of SICM and AFM are highlighted. This chapter shows that SICM has emerged as a major addition to the field of biophysics.
Interactions between microtubules and actin are a basic phenomenon that underlies many fundamental processes in which dynamic cellular asymmetries need to be established and maintained. These are processes as diverse as cell motility, neuronal pathfinding, cellular wound healing, cell division and cortical flow. Microtubules and actin exhibit two mechanistic classes of interactions — regulatory and structural. These interactions comprise at least three conserved 'mechanochemical activity modules' that perform similar roles in these diverse cell functions.
The mechanical stability and integrity of biological cells is provided by the cytoskeleton, a semidilute meshwork of biopolymers. Recent research has underscored its role as a dynamic, multifunctional muscle, whose passive and active mechanical performance is highly heterogeneous in space and time and intimately linked to many biological functions, such that it may serve as a sensitive indicator for the health or developmental state of the cell. In vitro reconstitution of 'functional modules' of the cytoskeleton is now seen as a way of balancing the mutually conflicting demands for simplicity, which is required for systematic and quantitative studies, and for a sufficient degree of complexity that allows a faithful representation of biological functions. This bottom-up strategy, aimed at unravelling biological complexity from its physical basis, builds on the latest advances in technology, experimental design and theoretical modelling, which are reviewed in this progress report.
Cell mechanical properties are fundamental to the organism but remain poorly understood. We report a comprehensive phenomenological framework for the complex rheology of single fibroblast cells: a superposition of elastic stiffening and viscoplastic kinematic hardening. Despite the complexity of the living cell, its mechanical properties can be cast into simple, well-defined rules. Our results reveal the key role of crosslink slippage in determining mechanical cell strength and robustness.
We propose a physical model for the nonlinear inelastic mechanics of sticky
biopolymer networks with potential applications to inelastic cell mechanics. It
consists in a minimal extension of the glassy wormlike chain (GWLC) model,
which has recently been highly successful as a quantitative mathematical
description of the viscoelastic properties of biopolymer networks and cells. To
extend its scope to nonequilibrium situations, where the thermodynamic state
variables may evolve dynamically, the GWLC is furnished with an explicit
representation of the kinetics of breaking and reforming sticky bonds. In spite
of its simplicity the model exhibits many experimentally established
non-trivial features such as power-law rheology, stress stiffening,
fluidization, and cyclic softening effects.
The dynamics of semi-flexible polymers and membranes is discussed. The effect of thermal undulations on both the transversal and longitudinal Mean Square Displacement (MSD) of a tagged “monomer” is studied in free polymers and membranes. The two MSDs are found to be proportional to one another, and behave as $\sim t^{3/4}$ for polymers and $\sim t^{2/3}$ for membranes on the short time scale. The longitudinal motion is shown to be linked to the dynamics of fluctuations of the projected length (area) of the polymer (membrane). We demonstrate how, at long times, these fluctuations lead to reptation motion of the polymer (membrane) in the longitudinal direction. We generalize this approach to investigate the motion of a membrane between two plates and a polymer in a tube. The latter problem is used as a model for polymer motion in semi-dilute solutions in which the persistence length is longer than the entanglement length. Such systems are not suitable for the classical reptation model of de-Gennes and of Doi and Edwards, which was designed for chains that are flexible on the entanglement distance. The reptation diffusion coefficient and relaxation times that we obtain have the same scaling with chain length $L$ as in the classical reptation model, but differ greatly in factors that are dependent on the ratio of persistence length to entanglement length. We also discuss the diffusion of a tagged “monomer” under imposed tension and liquid crystalline order.
We report a scaling law that governs both the elastic and frictional properties of a wide variety of living cell types, over a wide range of time scales and under a variety of biological interventions. This scaling identifies these cells as soft glassy materials existing close to a glass transition, and implies that cytoskeletal proteins may regulate cell mechanical properties mainly by modulating the effective noise temperature of the matrix. The practical implications are that the effective noise temperature is an easily quantified measure of the ability of the cytoskeleton to deform, flow, and reorganize.
Living cells sense the rigidity of their environment and adapt their activity to it. In particular, cells cultured on elastic substrates align their shape and their traction forces along the direction of highest stiffness and preferably migrate towards stiffer regions. Although numerous studies investigated the role of adhesion complexes in rigidity sensing, less is known about the specific contribution of acto-myosin based contractility. Here we used a custom-made single-cell technique to measure the traction force as well as the speed of shortening of isolated myoblasts deflecting microplates of variable stiffness. The rate of force generation increased with increasing stiffness and followed a Hill force-velocity relationship. Hence, cell response to stiffness was similar to muscle adaptation to load, reflecting the force-dependent kinetics of myosin binding to actin. These results reveal an unexpected mechanism of rigidity sensing, whereby the contractile acto-myosin units themselves can act as sensors. This mechanism may translate anisotropy in substrate rigidity into anisotropy in cytoskeletal tension, and could thus coordinate local activity of adhesion complexes and guide cell migration along rigidity gradients.
We describe an active polymer network in which processive molecular motors control network elasticity. This system consists of actin filaments cross-linked by filamin A (FLNa) and contracted by bipolar filaments of muscle myosin II. The myosin motors stiffen the network by more than two orders of magnitude by pulling on actin filaments anchored in the network by FLNa cross-links, thereby generating internal stress. The stiffening response closely mimics the effects of external stress applied by mechanical shear. Both internal and external stresses can drive the network into a highly nonlinear, stiffened regime. The active stress reaches values that are equivalent to an external stress of 14 Pa, consistent with a 1-pN force per myosin head. This active network mimics many mechanical properties of cells and suggests that adherent cells exert mechanical control by operating in a nonlinear regime where cell stiffness is sensitive to changes in motor activity. This design principle may be applicable to engineering novel biologically inspired, active materials that adjust their own stiffness by internal catalytic control.
Every adherent eukaryotic cell exerts appreciable traction forces upon its substrate. Moreover, every resident cell within the heart, great vessels, bladder, gut or lung routinely experiences large periodic stretches. As an acute response to such stretches the cytoskeleton can stiffen, increase traction forces and reinforce, as reported by some, or can soften and fluidize, as reported more recently by our laboratory, but in any given circumstance it remains unknown which response might prevail or why. Using a novel nanotechnology, we show here that in loading conditions expected in most physiological circumstances the localized reinforcement response fails to scale up to the level of homogeneous cell stretch; fluidization trumps reinforcement. Whereas the reinforcement response is known to be mediated by upstream mechanosensing and downstream signaling, results presented here show the fluidization response to be altogether novel: it is a direct physical effect of mechanical force acting upon a structural lattice that is soft and fragile. Cytoskeletal softness and fragility, we argue, is consistent with early evolutionary adaptations of the eukaryotic cell to material properties of a soft inert microenvironment.
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.
Rheological properties of living cells determine how cells interact with their mechanical microenvironment and influence their physiological functions. Numerous experimental studies have show that mechanical contractile stress borne by the cytoskeleton and weak power-law viscoelasticity are governing principles of cell rheology, and that the controlling physics is at the level of integrative cytoskeletal lattice properties. Based on these observations, two concepts have emerged as leading models of cytoskeletal mechanics. One is the tensegrity model, which explains the role of the contractile stress in cytoskeletal mechanics, and the other is the soft glass rheology model, which explains the weak power-law viscoelasticity of cells. While these two models are conceptually disparate, the phenomena that they describe are often closely associated in living cells for reasons that are largely unknown. In this review, we discuss current understanding of cell rheology by emphasizing the underlying biophysical mechanism and critically evaluating the existing rheological models.
The cytoplasm of vertebrate cells contains three distinct filamentous biopolymers, the microtubules, microfilaments, and intermediate filaments. The basic structural elements of these three filaments are linear polymers of the proteins tubulin, actin, and vimentin or another related intermediate filament protein, respectively. The viscoelastic properties of cytoplasmic filaments are likely to be relevant to their biologic function, because their extreme length and rodlike structure dominate the rheologic behavior of cytoplasm, and changes in their structure may cause gel-sol transitions observed when cells are activated or begin to move. This paper describes parallel measurements of the viscoelasticity of tubulin, actin, and vimentin polymers. The rheologic differences among the three types of cytoplasmic polymers suggest possible specialized roles for the different classes of filaments in vivo. Actin forms networks of highest rigidity that fluidize at high strains, consistent with a role in cell motility in which stable protrusions can deform rapidly in response to controlled filament rupture. Vimentin networks, which have not previously been studied by rheologic methods, exhibit some unusual viscoelastic properties not shared by actin or tubulin. They are less rigid (have lower shear moduli) at low strain but harden at high strains and resist breakage, suggesting they maintain cell integrity. The differences between F-actin and vimentin are optimal for the formation of a composite material with a range of properties that cannot be achieved by either polymer alone. Microtubules are unlikely to contribute significantly to interphase cell rheology alone, but may help stabilize the other networks.
We have used laser optical trapping and nanometer-level motion analysis to investigate the cytoskeletal associations and surface dynamics of beta 1 integrin, a cell-substrate adhesion molecule, on the dorsal surfaces of migrating fibroblast cells. A single-beam optical gradient trap (laser tweezers) was used to restrain polystyrene beads conjugated with anti-beta 1 integrin mAbs and place them at desired locations on the cell exterior. This technique was used to demonstrate a spatial difference in integrin-cytoskeleton interactions in migrating cells. We found a distinct increase in the stable attachment of beads, and subsequent rearward flow, on the lamellipodia of locomoting cells compared with the retracting portions. Complementary to the enhanced linkage of integrin at the cell lamellipodium, the membrane was more deformable at the rear versus the front of moving cells while nonmotile cells did not exhibit this asymmetry in membrane architecture. Video microscopy and nanometer-precision tracking routines were used to study the surface dynamics of integrin on the lamellipodia of migrating cells by monitoring the displacements of colloidal gold particles coated with anti-beta 1 integrin mAbs. Small gold aggregates were rapidly transported preferentially to the leading edge of the lamellipod where they resumed diffusion restricted along the edge. This fast transport was characterized by brief periods of directed movement ("jumps") having an instantaneous velocity of 37 +/- 15 microns/min (SD), separated by periods of diffusion. In contrast, larger aggregates of gold particles and the large latex beads underwent slow, steady rearward movement (0.85 +/- 0.44 micron/min) (SD) at a rate similar to that reported for other capping events and for migration of these cells. Cell lines containing mutated beta 1 integrins were used to show that the cytoplasmic domain is essential for an asymmetry in attachment of integrin to the underlying cytoskeletal network and is also necessary for rapid, intermittent transport. However, enhanced membrane deformability at the cell rear does not require integrin-cytoskeletal interactions. We also demonstrated that posttranslational modifications of integrin could potentially play a role in these phenomena. These results suggest a scheme for the role of dynamic integrin-mediated adhesive interactions in cell migration. Integrins are transported preferentially to the cell front where they form nascent adhesions. These adhesive structures grow in size and associate with the cytoskeleton that exerts a rearward force on them. Dorsal aggregates more rearward while those on the ventral side remain fixed to the substrate allowing the cell body to move forward. Detachment of the cell rear occurs by at least two modes: (a) weakened integrin-cytoskeleton interactions, potentially mediated by local modifications of linkage proteins, which lead to weakened cell-substratum interactions and (b) ripping of integrins and the highly deformable membrane from the cell body.
Physical forces play a fundamental role in the regulation of cell function in many tissues, but little is known about how cells are able to sense mechanical loads and realize signal transduction. Adhesion receptors like integrins are candidates for mechanotransducers. We used a magnetic drag force device to apply forces on integrin receptors in an osteoblastic cell line and studied the effect on tyrosine phosphorylation as a biochemical event in signal transduction. Mechanical stressing of both the beta1 and the alpha2 integrin subunit induced an enhanced tyrosine phosphorylation of proteins compared with integrin clustering. Application of cyclic forces with a frequency of 1 Hz was more effective than a continuous stress. Using Triton X-100 for cell extraction, we found that tyrosine-phosphorylated proteins became physically anchored to the cytoskeleton due to mechanical integrin loading. This cytoskeletal linkage was dependent on intracellular calcium. To see if mechanical integrin stressing induced further downstream signaling, we analyzed the activation of mitogen-activated protein (MAP) kinases and found an increased phosphorylation of MAP kinases due to mechanical stress. We conclude that integrins sense physical forces that control gene expression by activation of the MAP kinase pathway. The cytoskeleton may play a key role in the physical anchorage of activated signaling molecules, which enables the switch of physical forces to biochemical signaling events.
Loss of a vimentin network due to gene disruption created viable mice that did not differ overtly from wild-type littermates. Here, primary fibroblasts derived from vimentin-deficient (-/-) and wild-type (+/+) mouse embryos were cultured, and biological functions were studied in in vitro systems resembling stress situations. Stiffness of -/- fibroblasts was reduced by 40% in comparison to wild-type cells. Vimentin-deficient cells also displayed reduced mechanical stability, motility and directional migration towards different chemo-attractive stimuli. Reorganization of collagen fibrils and contraction of collagen lattices were severely impaired. The spatial organization of focal contact proteins, as well as actin microfilament organization was disturbed. Thus, absence of a vimentin filament network does not impair basic cellular functions needed for growth in culture, but cells are mechanically less stable, and we propose that therefore they are impaired in all functions depending upon mechanical stability.
We develop a model for gels and entangled solutions of semiflexible biopolymers such as F-actin. Such networks play a crucial structural role in the cytoskeleton of cells. We show that the rheologic properties of these networks can result from nonclassical rubber elasticity. This model can explain a number of elastic properties of such networks {\em in vitro}, including the concentration dependence of the storage modulus and yield strain. Comment: Uses RevTeX, full postscript with figures available at http://www.umich.edu/~fcm/preprints/agel/agel.html
It has been shown previously that intermediate filament (IF) gels in vitro exhibit stiffening at high-applied stress, and it was suggested that this stiffening property of IFs might be important for maintaining cell integrity at large deformations (Janmey PA, Evtenever V, Traub P, and Schliwa M, J Cell Biol 113: 155-160, 1991). In this study, the contribution of IFs to cell mechanical behavior was investigated by measuring cell stiffness in response to applied stress in adherent wild-type and vimentin-deficient fibroblasts using magnetic twisting cytometry. It was found that vimentin-deficient cells were less stiff and exhibited less stiffening than wild-type cells, except at the lowest applied stress (10 dyn/cm(2)) where the difference in the stiffness was not significant. Similar results were obtained from measurements on wild-type fibroblasts and endothelial cells after vimentin IFs were disrupted by acrylamide. If, however, cells were plated over an extended period of time (16 h), they exhibited a significantly greater stiffness before than after acrylamide, even at the lowest applied stress. A possible reason could be that the initially slack IFs became fully extended due to a high degree of cell spreading and thus contributed to the transmission of mechanical stress across the cell. Taken together, these findings were consistent with the notion that IFs play important roles in the mechanical properties of the cell during large deformation. The experimental data also showed that depleting or disrupting IFs reduced, but did not entirely abolish, cell stiffening. This residual stiffening might be attributed to the effect of geometrical realignment of cytoskeletal filaments in the direction of applied load. It was also found that vimentin-deficient cells exhibited a slower rate of proliferation and DNA synthesis than wild-type cells. This could be a direct consequence of the absence of the intracellular IFs that may be necessary for efficient mediation of mechanical signals within the cell. Taken together, results of this study suggest that IFs play important roles in the mechanical properties of cells and in cell growth.
We demonstrate a novel method for measuring the microrheology of soft viscoelastic media, based on cross correlating the thermal motion of pairs of embedded tracer particles. The method does not depend on the exact nature of the coupling between the tracers and the medium, and yields accurate rheological data for highly inhomogeneous materials. We demonstrate the accuracy of this method with a guar solution, for which other microscopic methods fail due to the polymer's mesoscopic inhomogeneity. Measurements in an F-actin solution suggest conventional microrheology measurements may not reflect the true bulk behavior.
A 2.91-billion base pair (bp) consensus sequence of the euchromatic portion of the human genome was generated by the whole-genome shotgun sequencing method. The 14.8-billion bp DNA sequence was generated over 9 months from 27,271,853 high-quality sequence reads (5.11-fold coverage of the genome) from both ends of plasmid clones made from the DNA of five individuals. Two assembly strategies-a whole-genome assembly and a regional chromosome assembly-were used, each combining sequence data from Celera and the publicly funded genome effort. The public data were shredded into 550-bp segments to create a 2.9-fold coverage of those genome regions that had been sequenced, without including biases inherent in the cloning and assembly procedure used by the publicly funded group. This brought the effective coverage in the assemblies to eightfold, reducing the number and size of gaps in the final assembly over what would be obtained with 5.11-fold coverage. The two assembly strategies yielded very similar results that largely agree with independent mapping data. The assemblies effectively cover the euchromatic regions of the human chromosomes. More than 90% of the genome is in scaffold assemblies of 100,000 bp or more, and 25% of the genome is in scaffolds of 10 million bp or larger. Analysis of the genome sequence revealed 26,588 protein-encoding transcripts for which there was strong corroborating evidence and an additional approximately 12,000 computationally derived genes with mouse matches or other weak supporting evidence. Although gene-dense clusters are obvious, almost half the genes are dispersed in low G+C sequence separated by large tracts of apparently noncoding sequence. Only 1.1% of the genome is spanned by exons, whereas 24% is in introns, with 75% of the genome being intergenic DNA. Duplications of segmental blocks, ranging in size up to chromosomal lengths, are abundant throughout the genome and reveal a complex evolutionary history. Comparative genomic analysis indicates vertebrate expansions of genes associated with neuronal function, with tissue-specific developmental regulation, and with the hemostasis and immune systems. DNA sequence comparisons between the consensus sequence and publicly funded genome data provided locations of 2.1 million single-nucleotide polymorphisms (SNPs). A random pair of human haploid genomes differed at a rate of 1 bp per 1250 on average, but there was marked heterogeneity in the level of polymorphism across the genome. Less than 1% of all SNPs resulted in variation in proteins, but the task of determining which SNPs have functional consequences remains an open challenge.
The transition of cell-matrix adhesions from the initial punctate focal complexes into the mature elongated form, known as focal contacts, requires GTPase Rho activity. In particular, activation of myosin II-driven contractility by a Rho target known as Rho-associated kinase (ROCK) was shown to be essential for focal contact formation. To dissect the mechanism of Rho-dependent induction of focal contacts and to elucidate the role of cell contractility, we applied mechanical force to vinculin-containing dot-like adhesions at the cell edge using a micropipette. Local centripetal pulling led to local assembly and elongation of these structures and to their development into streak-like focal contacts, as revealed by the dynamics of green fluorescent protein-tagged vinculin or paxillin and interference reflection microscopy. Inhibition of Rho activity by C3 transferase suppressed this force-induced focal contact formation. However, constitutively active mutants of another Rho target, the formin homology protein mDia1 (Watanabe, N., T. Kato, A. Fujita, T. Ishizaki, and S. Narumiya. 1999. Nat. Cell Biol. 1:136-143), were sufficient to restore force-induced focal contact formation in C3 transferase-treated cells. Force-induced formation of the focal contacts still occurred in cells subjected to myosin II and ROCK inhibition. Thus, as long as mDia1 is active, external tension force bypasses the requirement for ROCK-mediated myosin II contractility in the induction of focal contacts. Our experiments show that integrin-containing focal complexes behave as individual mechanosensors exhibiting directional assembly in response to local force.
Alternative models of cell mechanics depict the living cell as a simple mechanical continuum, porous filament gel, tensed cortical membrane, or tensegrity network that maintains a stabilizing prestress through incorporation of discrete structural elements that bear compression. Real-time microscopic analysis of cells containing GFP-labeled microtubules and associated mitochondria revealed that living cells behave like discrete structures composed of an interconnected network of actin microfilaments and microtubules when mechanical stresses are applied to cell surface integrin receptors. Quantitation of cell tractional forces and cellular prestress by using traction force microscopy confirmed that microtubules bear compression and are responsible for a significant portion of the cytoskeletal prestress that determines cell shape stability under conditions in which myosin light chain phosphorylation and intracellular calcium remained unchanged. Quantitative measurements of both static and dynamic mechanical behaviors in cells also were consistent with specific a priori predictions of the tensegrity model. These findings suggest that tensegrity represents a unified model of cell mechanics that may help to explain how mechanical behaviors emerge through collective interactions among different cytoskeletal filaments and extracellular adhesions in living cells.
The tensegrity model hypothesizes that cytoskeleton-based microtubules (MTs) carry compression as they balance a portion of cell contractile stress. To test this hypothesis, we used traction force microscopy to measure traction at the interface of adhering human airway smooth muscle cells and a flexible polyacrylamide gel substrate. The prediction is that if MTs balance a portion of contractile stress, then, upon their disruption, the portion of stress balanced by MTs would shift to the substrate, thereby causing an increase in traction. Measurements were done first in maximally activated cells (10 microM histamine) and then again after MTs had been disrupted (1 microM colchicine). We found that after disruption of MTs, traction increased on average by approximately 13%. Because in activated cells colchicine induced neither an increase in intracellular Ca(2+) nor an increase in myosin light chain phosphorylation as shown previously, we concluded that the observed increase in traction was a result of load shift from MTs to the substrate. In addition, energy stored in the flexible substrate was calculated as work done by traction on the deformation of the substrate. This result was then utilized in an energetic analysis. We assumed that cytoskeleton-based MTs are slender elastic rods supported laterally by intermediate filaments and that MTs buckle as the cell contracts. Using the post-buckling equilibrium theory of Euler struts, we found that energy stored during buckling of MTs was quantitatively consistent with the measured increase in substrate energy after disruption of MTs. This is further evidence supporting the idea that MTs are intracellular compression-bearing elements.
The viscoelastic response of living cells to small external forces and deformations is characterized by a weak power law in time. The elastic modulus of cells and the power law exponent with which the elastic stresses decay depend on the active contractile prestress in the cytoskeleton. It is unknown whether this also holds in the physiologically relevant regime of large external forces and deformations. We used magnetic tweezers to apply stepwise increasing forces to magnetic beads bound to the cytoskeleton of different cell lines, and recorded the resulting cell deformation (creep response). The creep response followed a weak power law at all force levels. Stiffness and power law exponent increased with force in all cells, indicating simultaneous stress stiffening and fluidization of the cytoskeleton. The amount of stress stiffening and fluidization differed greatly between cell types but scaled with the contractile prestress as the only free parameter. Our results demonstrate that by modulating the internal mechanical tension, cells can actively control their mechanical properties over an exceedingly large range. This behavior is of fundamental importance for protection against damage caused by large external forces, and allows the cells to adapt to the highly variable and nonlinear mechanical properties of the extracellular matrix.
The mechanical properties of cells are dominated by the cytoskeleton, a crosslinked network of protein filaments. Unlike synthetic polymer networks, the cell cytoskeleton is a highly dynamical system due to the on-off kinetics of the crosslinking proteins and the polymerization depolymerization cycles of the filaments themselves. More remarkably, some of the crosslinkers are motor proteins, which are capable of generating forces and directional motion between the filaments by consuming chemical energy. Thus, the cell cytoskeleton is a highly complex and active polymer gel, which is responsible for the unique cell mechanical properties, which make it crawl, divide and assemble to higher functional units. This complexity of the cytoskeleton demands the development of novel experimental techniques as well as theoretical ideas. This review will deal with the recent technological, experimental and theoretical developments in the field of cell mechanics, and current trends. It will be shown that despite the cytoskeletal complexity, cells show some very general rheological properties.
The cytoskeleton (CSK) of the adherent living cell is arguably the most complex form of soft matter that exists in nature. It is constituted by hundreds of different proteins that interact with each other in a highly specific manner and, as a requirement for life, exists out of thermodynamic equilibrium and in a constant state of remodeling. While such structural and dynamical complexity may have conferred the cell with diverse and unpredictable mechanical properties, recent evidence indicates that the behavior of the CSK conforms to a limited set of empirical laws that appear to be simple and universal. While mechanistic understanding of such laws is still lacking, their very existence suggests that rather than being addressed solely in terms of molecular details and specific interactions, cell mechanics need to be addressed also from an integrative point of view.
We construct a model for the dynamic shear modulus G(omega) of entangled or crosslinked networks of semiflexible polymer that can account for the high-frequency scaling behavior, G(omega)~omega3/4, that has recently been observed in solutions of the biopolymer F-actin. As we argue, this behavior should not be unique to F-actin, but rather should be a clear characteristic of semiflexible polymers in general. We also report molecular dynamics simulations that support the single filament response that is the basis of our model for the network shear modulus.
Adherent cells show a wide range of complex mechanical behavior that traditionally has been accounted for by different mechanisms and models, each of which can explain a limited subset of cell behavior. Experimental evidence suggests that nearly all aspects of mechanical cell behavior are closely associated with the cell's contractile machinery of actin and myosin filaments. We propose that the molecular details of actin-myosin interactions can be combined in a unified active soft glassy model that considers the arrangement of stress fibers at the macro-scale, and the soft-glassy non-equilibrium interaction of myosin and actin filaments at the micro-scale.
The mechanical properties of some hollow organs are most conveniently described by a pressure-volume relationship. If the
material exhibits hysteresis, thep-v relation must include provision for time-dependent or path-dependent properties. Provided the amplitude of deformation is
fairly small and the hysteresis is primarily of the viscoelastic type, a linear description is possible. That this may take
the form of a simple transfer function in which material properties are implicit is illustrated for the case of a rubber balloon.
The transfer function was derived from the pressure transients which follow step changes in volume produced in a fluid-filled
plethysmograph. The applicability of the transfer function in predicting responses to other forcing functions was tested by
varying the balloon volume sinusoidally over a frequency range of 1000, at 4 different amplitudes. The good agreement between
the linear model and all types of data justifies the use of Laplace transform methods and the assumption that superposition
holds. When isolated cat lung is tested in the same manner, the transfer function quantitatively predicts the magnitude ratio
of sinusoidal responses but only about two-thirds of the phase angle. The additional energy loss per cycle is interpreted
as arising from static hysteresis. The analysis thus provides a simple means of estimating the relative contributions of viscoelastic
(dynamic) and static hysteretic processes to the total damping in a material.
In an attempt to understand the role of structural rearrangement onto the cell response during imposed cyclic stresses, we simulated numerically the frequency-dependent behaviour of a viscoelastic tensegrity structure (VTS model) made of 24 elastic cables and 6 rigid bars. The VTS computational model was based on the Non-Smooth Contact Dynamics (NSCD) method in which the constitutive elements of the tensegrity structure are considered as a set of material points that mutually interact. Low amplitude oscillatory loading conditions were applied and the frequency response of the overall structure was studied in terms of frequency-dependence of mechanical properties. The latter were normalised by the homogeneous properties of constitutive elements in order to capture the essential feature of spatial rearrangement. The results reveal a specific frequency-dependent contribution of elastic and viscous effects which is responsible for significant changes in the VTS model dynamical properties. The mechanism behind is related to the variable contribution of spatial rearrangement of VTS elements which is decreased from low to high frequency as dominant effects are transferred from mainly elastic to mainly viscous. More precisely, the elasticity modulus increases with frequency while the viscosity modulus decreases, each evolution corresponding to a specific power-law dependency. The satisfactorily agreement found between present numerical results and the literature data issued from in vitro cell experiments suggests that the frequency-dependent mechanism of spatial rearrangement presently described could play a significant and predictable role during oscillatory cell dynamics.
The cytoskeleton (CSK) of living cells is a crosslinked fiber network, subject to ongoing biochemical remodeling processes that can be visualized by tracking the spontaneous motion of CSK-bound microbeads. The bead motion is characterized by anomalous diffusion with a power-law time evolution of the mean square displacement (MSD), and can be described as a stochastic transport process with apparent diffusivity D and power-law exponent β: MSD ∼ D (t/t(0))(β). Here we studied whether D and β change with the time that has passed after the initial bead-cell contact, and whether they are sensitive to bead coating (fibronectin, integrin antibodies, poly-L-lysine, albumin) and bead size (0.5-4.5 µm). The measurements are interpreted in the framework of a simple model that describes the bead as an overdamped particle coupled to the fluctuating CSK network by an elastic spring. The viscous damping coefficient characterizes the degree of bead internalization into the cell, and the spring constant characterizes the strength of the binding of the bead to the CSK. The model predicts distinctive signatures of the MSD that change with time as the bead couples more tightly to the CSK and becomes internalized. Experimental data show that the transition from the unbound to the tightly bound state occurs in an all-or-nothing manner. The time point of this transition shows considerable variability between individual cells (2-30 min) and depends on the bead size and bead coating. On average, this transition occurs later for smaller beads and beads coated with ligands that trigger the formation of adhesion complexes (fibronectin, integrin antibodies). Once the bead is linked to the CSK, however, the ligand type and bead size have little effect on the MSD. On longer timescales of several hours after bead addition, smaller beads are internalized into the cell more readily, leading to characteristic changes in the MSD that are consistent with increased viscous damping by the cytoplasm and reduced binding strength.
Networks of the cytoskeletal biopolymer actin cross-linked by the compliant protein filamin form soft gels that stiffen dramatically under shear stress. We demonstrate that the elasticity of these networks shows a strong dependence on the mean length of the actin polymers, unlike networks with small, rigid cross-links. This behavior is in agreement with a model of rigid filaments connected by multiple flexible linkers.
Endothelial cell polarization and directional migration is required for angiogenesis. Polarization and motility requires not only local cytoskeletal remodeling but also the motion of intracellular organelles such as the nucleus. However, the physiological significance of nuclear positioning in the endothelial cell has remained largely unexplored. Here, we show that siRNA knockdown of nesprin-1, a protein present in the linker of nucleus to cytoskeleton complex, abolished the reorientation of endothelial cells in response to cyclic strain. Confocal imaging revealed that the nuclear height is substantially increased in nesprin-1 depleted cells, similar to myosin inhibited cells. Nesprin-1 depletion increased the number of focal adhesions and substrate traction while decreasing the speed of cell migration; however, there was no detectable change in nonmuscle myosin II activity in nesprin-1 deficient cells. Together, these results are consistent with a model in which the nucleus balances a portion of the actomyosin tension in the cell. In the absence of nesprin-1, actomyosin tension is balanced by the substrate, leading to abnormal adhesion, migration, and cyclic strain-induced reorientation.
Cell mechanical properties on a whole cell basis have been widely studied, whereas local intracellular variations have been less well characterized and are poorly understood. To fill this gap, here we provide detailed intracellular maps of regional cytoskeleton (CSK) stiffness, loss tangent, and rate of structural rearrangements, as well as their relationships to the u