The role of prestress and architecture of the cytoskeleton and deformability of cytoskeletal filaments in mechanics of adherent cells: a quantitative analysis

Prestrain-induced contraction in one-dimensional random elastic chains

Prestrained elastic networks arise in a number of biological and technological systems ranging from the cytoskeleton of cells to tensegrity structures. Motivated by this observation, we here consider a minimal model in one dimension to set the stage for understanding the response of such networks as a function of the prestrain. To this end we consider a chain [one-dimensional (1D) network] of elastic springs upon which a random, zero mean, finite variance prestrain is imposed. Numerical simulations and analytical predictions quantify the magnitude of the contraction as a function of the variance of the prestrain, and show that the chain always shrinks. To test these predictions, we vary the topology of the chain, consider more complex connectivity and show that our results are relatively robust to these changes.

Impact of physiological loads of arterial wall on nucleus deformation in endothelial cells: A computational study

INTRODUCTION

Computational modeling can enhance the understanding of cell mechanics. To achieve this, finite element models of endothelial cells were proposed with shapes mimicking their natural state inside the endothelium within the cardiovascular system. Implementing the recently proposed bendo-tensegrity concept, these models consider flexural (buckling) as well as tensional/compressional behavior of microtubules and also incorporate the waviness of intermediate filaments.

MATERIALS AND METHODS

Four different models were created (flat and domed hexagons, both regular and elongated in the direction of blood flow) and loaded by biaxial deformation, blood pressure, and shear load from blood flow - natural physiological conditions of the arterial endothelium - aiming to investigate the "in situ" mechanical response of the cell.

RESULTS

The impact of individual components of loads on the nucleus deformation (more specifically on the first principal strain) potentially influencing mechanotransduction was investigated and the role of the cytoskeleton and its constituents in the mechanical response of the endothelial cell was assessed. The results show (i) the impact of pulsating blood pressure on cyclic deformations of the nucleus, which increase substantially with decreasing axial pre-stretch of the cell, (ii) the importance of relatively low shear stresses in the cell response and nucleus deformation.

CONCLUSION

Not only the pulsatile blood pressure but also the wall shear stress may induce significant deformation of the nucleus and thus trigger remodelation processes in endothelial cells.

Biomechanics of cells and subcellular components: A comprehensive review of computational models and applications

Cells are a fundamental structural, functional and biological unit for all living organisms. Up till now, considerable efforts have been made to study the responses of single cells and subcellular components to an external load, and understand the biophysics underlying cell rheology, mechanotransduction and cell functions using experimental and in silico approaches. In the last decade, computational simulation has become increasingly attractive due to its critical role in interpreting experimental data, analysing complex cellular/subcellular structures, facilitating diagnostic designs and therapeutic techniques, and developing biomimetic materials. Despite the significant progress, developing comprehensive and accurate models of living cells remains a grand challenge in the 21st century. To understand current state of the art, this review summarises and classifies the vast array of computational biomechanical models for cells. The article covers the cellular components at multi-spatial levels, that is, protein polymers, subcellular components, whole cells and the systems with scale beyond a cell. In addition to the comprehensive review of the topic, this article also provides new insights into the future prospects of developing integrated, active and high-fidelity cell models that are multiscale, multi-physics and multi-disciplinary in nature. This review will be beneficial for the researchers in modelling the biomechanics of subcellular components, cells and multiple cell systems and understanding the cell functions and biological processes from the perspective of cell mechanics.

A Finite Element Bendo-Tensegrity Model of Eukaryotic Cell

Mechanical interaction of cell with extracellular environment affects its function. The mechanisms by which mechanical stimuli are sensed and transduced into biochemical responses are still not well understood. Considering this, two finite element (FE) bendo-tensegrity models of a cell in different states are proposed with the aim to characterize cell deformation under different mechanical loading conditions: a suspended cell model elucidating the global response of cell in tensile test simulation and an adherent cell model explicating its local response in atomic force microscopy (AFM) indentation simulation. The force-elongation curve obtained from tensile test simulation lies within the range of experimentally obtained characteristics of smooth muscle cells (SMCs) and illustrates a nonlinear increase in reaction force with cell stretching. The force-indentation curves obtained from indentation simulations lie within the range of experimentally obtained curves of embryonic stem cells (ESCs) and exhibit the influence of indentation site on the overall reaction force of cell. Simulation results have demonstrated that actin filaments (AFs) and microtubules (MTs) play a crucial role in the cell stiffness during stretching, whereas actin cortex (AC) along with actin bundles (ABs) and MTs are essential for the cell rigidity during indentation. The proposed models quantify the mechanical contribution of individual cytoskeletal components to cell mechanics and the deformation of nucleus under different mechanical loading conditions. These results can aid in better understanding of structure-function relationships in living cells.

Modelling Cell Origami via a Tensegrity Model of the Cytoskeleton in Adherent Cells

Cell origami has been widely used in the field of three-dimensional (3D) cell-populated microstructures due to their multiple advantages, including high biocompatibility, the lack of special requirements for substrate materials, and the lack of damage to cells. A 3D finite element method (FEM) model of an adherent cell based on the tensegrity structure is constructed to describe cell origami by using the principle of the origami folding technique and cell traction forces. Adherent cell models contain a cytoskeleton (CSK), which is primarily composed of microtubules (MTs), microfilaments (MFs), intermediate filaments (IFs), and a nucleoskeleton (NSK), which is mainly made up of the nuclear lamina and chromatin. The microplate is assumed to be an isotropic linear-elastic solid material with a flexible joint that is connected to the cell tensegrity structure model by spring elements representing focal adhesion complexes (FACs). To investigate the effects of the degree of complexity of the tensegrity structure and NSK on the folding angle of the microplate, four models are established in the study. The results demonstrate that the inclusion of the NSK can increase the folding angle of the microplate, indicating that the cell is closer to its physiological environment, while increased complexity can reduce the folding angle of the microplate since the folding angle is depended on the cell types. The proposed adherent cell FEM models are validated by comparisons with reported results. These findings can provide theoretical guidance for the application of biotechnology and the analysis of 3D structures of cells and have profound implications for the self-assembly of cell-based microscale medical devices.

Radiosensitization and a Less Aggressive Phenotype of Human Malignant Glioma Cells Expressing Isocitrate Dehydrogenase 1 (IDH1) Mutant Protein: Dissecting the Mechanisms

The presence of an isocitrate dehydrogenase 1 (IDH1) mutation is associated with a less aggressive phenotype, increased sensitivity to radiation, and increased overall survival in patients with diffuse glioma. Based on in vitro experimentations in malignant glioma cell lines, the consequences on cellular processes of IDH1^R132H expression were analyzed. The results revealed that IDH1^R132H expression enhanced the radiation induced accumulation of residual γH2AX foci and decreased the amount of glutathione (GSH) independent of the oxygen status. In addition, expression of the mutant IDH1 caused a significant increase of cell stiffness and induced an altered organization of the cytoskeleton, which has been shown to reinforce cell stiffness. Furthermore, IDH1^R132H expression decreased the expression of vimentin, an important component of the cytoskeleton and regulator of the cell stiffness. The results emphasize the important role of mutant IDH1 in treatment of patients with diffuse gliomas especially in response to radiation. Hence, detection of the genetic status of IDH1 before therapy massively expands the utility of immunohistochemistry to accurately distinguish patients with a less aggressive and radiosensitive IDH1-mutant diffuse glioma suitable for radiotherapy from those with a more aggressive IDH1-wildtype diffuse glioma who might benefit from an individually intensified therapy comprising radiotherapy and alternative medical treatments.

Key developments that impacted the field of mechanobiology and mechanotransduction

Advances in mechanobiology have evolved through insights from multiple disciplines including structural engineering, biomechanics, vascular biology, and orthopaedics. In this paper, we reviewed the impact of key reports related to the study of applied loads on tissues and cells and the resulting signal transduction pathways. We addressed how technology has helped advance the burgeoning field of mechanobiology (over 33,600 publications from 1970 to 2016). We analyzed the impact of critical ideas and then determined how these concepts influenced the mechanobiology field by looking at the citation frequency of these reports as well as tracking how the overall number of citations within the field changed over time. These data allowed us to understand how a key publication, idea, or technology guided or enabled the field. Initial observations of how forces acted on bone and soft tissues stimulated the development of computational solutions defining how forces affect tissue modeling and remodeling. Enabling technologies, such as cell and tissue stretching, compression, and shear stress devices, allowed more researchers to explore how deformation and fluid flow affect cells. Observation of the cell as a tensegrity structure and advanced methods to study genetic regulation in cells further advanced knowledge of specific mechanisms of mechanotransduction. The future of the field will involve developing gene and drug therapies to simulate or augment beneficial load regimens in patients and in mechanically conditioning organs for implantation. Here, we addressed a history of the field, but we limited our discussions to advances in musculoskeletal mechanobiology, primarily in bone, tendon, and ligament tissues. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 36:605-619, 2018.

Mechanics and Buckling of Biopolymeric Shells and Cell Nuclei

We study a Brownian dynamics simulation model of a biopolymeric shell deformed by axial forces exerted at opposing poles. The model exhibits two distinct, linear force-extension regimes, with the response to small tensions governed by linear elasticity and the response to large tensions governed by an effective spring constant that scales with radius as R^-0.25. When extended beyond the initial linear elastic regime, the shell undergoes a hysteretic, temperature-dependent buckling transition. We experimentally observe this buckling transition by stretching and imaging the lamina of isolated cell nuclei. Furthermore, the interior contents of the shell can alter mechanical response and buckling, which we show by simulating a model for the nucleus that quantitatively agrees with our micromanipulation experiments stretching individual nuclei.

Theoretical modeling of mechanical homeostasis of a mammalian cell under gravity-directed vector

Translocation of dense nucleus along gravity vector initiates mechanical remodeling of a eukaryotic cell. In our previous experiments, we quantified the impact of gravity vector on cell remodeling by placing an MC3T3-E1 cell onto upward (U)-, downward (D)-, or edge-on (E)- orientated substrate. Our experimental data demonstrate that orientation dependence of nucleus longitudinal translocation is positively correlated with cytoskeletal (CSK) remodeling of their expressions and structures and also is associated with rearrangement of focal adhesion complex (FAC). However, the underlying mechanism how CSK network and FACs are reorganized in a mammalian cell remains unclear. In this paper, we developed a theoretical biomechanical model to integrate the mechanosensing of nucleus translocation with CSK remodeling and FAC reorganization induced by a gravity vector. The cell was simplified as a nucleated tensegrity structure in the model. The cell and CSK filaments were considered to be symmetrical. All elements of CSK filaments and cytomembrane that support the nucleus were simplified as springs. FACs were simplified as an adhesion cluster of parallel bonds with shared force. Our model proposed that gravity vector-directed translocation of the cell nucleus is mechanically balanced by CSK remodeling and FAC reorganization induced by a gravitational force. Under gravity, dense nucleus tends to translocate and exert additional compressive or stretching force on the cytoskeleton. Finally, changes of the tension force acting on talin by microfilament alter the size of FACs. Results from our model are in qualitative agreement with those from experiments.

Mechanisms of Cdc42-mediated rat MSC differentiation on micro/nano-textured topography

Micro/nano-textured titanium surface topography promotes osteoblast differentiation and the Wnt/β-catenin signaling pathway. However, the response of rat bone mesenchymal stem cells (MSCs) to micro/nano-textured topography, and the underlying mechanisms of its effects, are not well understood. We hypothesized that cell division cycle 42 protein (Cdc42), a key member of the Rho GTPases family, may regulate rat MSCs morphology and osteogenic differentiation by micro/nano-textured topography, and that crosstalk between Cdc42 and Wnt/β-catenin is the underlying mechanism. To confirm the hypothesis, we first tested rat MSCs' morphology, cytoskeleton, and osteogenic differentiation on micro/nano-textured topography. We then examined the cells' Wnt pathway and Cdc42 signaling activity. The results show that micro/nano-textured topography enhances MSCs' osteogenic differentiation. In addition, the cells' morphology and cytoskeletal reorganization were dramatically different on smooth surfaces and micropitted/nanotubular topography. Ligands of the canonical Wnt pathway, as well as accumulation of β-catenin in the nucleus, were up-regulated by micro/nano-textured topography. Cdc42 protein expression was markedly increased under these conditions; conversely, Cdc42 silencing significantly depressed the enhancement of MSCs osteogenic differentiation by micro/nano-textured topography. Moreover, Cdc42si attenuated p-GSK3β activation and resulted in β-catenin cytoplasmic degradation on the micro/nano-textured topography. Our results indicate that Cdc42 is a key modulator of rat MSCs morphology and cytoskeletal reorganization, and that crosstalk between Cdc42 and Wnt/β-catenin signaling though GSK3β regulates MSCs osteogenic differentiation by implant topographical cues.

STATEMENT OF SIGNIFICANCE

Topographical modification at micro- and nanoscale is widely applied to enhance the tissue integration properties of biomaterials. However, the response of bone mesenchymal stem cells (MSCs) to the micro/nano-textured topography and the underlying mechanisms are not well understood. This study shows that the micropitted/nanotubular hierarchical topography produced by etching and anodic oxidation treatment drives fusiform cell morphology, cytoskeletal reorganization as well as better MSCs osteogenic differentiation. The cross-talk between Cdc42 pathway and Wnt/β-catenin pathway though GSK3β modulates the osteoinductive effect of the micro/nano-textured topography on MSCs. This finding sheds light on a novel mechanism involved in micro/nano-textured surface-mediated MSCs osteogenic differentiation and is a major step in the development of new surface modifications aiming to accelerate and enhance the process of osseointegration.

Stiffness of pancreatic cancer cells is associated with increased invasive potential

Metastasis is a fundamentally physical process in which cells are required to deform through narrow gaps as they invade surrounding tissues and transit to distant sites. In many cancers, more invasive cells are more deformable than less invasive cells, but the extent to which mechanical phenotype, or mechanotype, can predict disease aggressiveness in pancreatic ductal adenocarcinoma (PDAC) remains unclear. Here we investigate the invasive potential and mechanical properties of immortalized PDAC cell lines derived from primary tumors and a secondary metastatic site, as well as noncancerous pancreatic ductal cells. To investigate how invasive behavior is associated with cell mechanotype, we flow cells through micron-scale pores using parallel microfiltration and microfluidic deformability cytometry; these results show that the ability of PDAC cells to passively transit through pores is only weakly correlated with their invasive potential. We also measure the Young's modulus of pancreatic ductal cells using atomic force microscopy, which reveals that there is a strong association between cell stiffness and invasive potential in PDAC cells. To determine the molecular origins of the variability in mechanotype across our PDAC cell lines, we analyze RNAseq data for genes that are known to regulate cell mechanotype. Our results show that vimentin, actin, and lamin A are among the most differentially expressed mechanoregulating genes across our panel of PDAC cell lines, as well as a cohort of 38 additional PDAC cell lines. We confirm levels of these proteins across our cell panel using immunoblotting, and find that levels of lamin A increase with both invasive potential and Young's modulus. Taken together, we find that stiffer PDAC cells are more invasive than more compliant cells, which challenges the paradigm that decreased cell stiffness is a hallmark of metastatic potential.

Atomic Force Microscopy Mechanical Mapping of Micropatterned Cells Shows Adhesion Geometry-Dependent Mechanical Response on Local and Global Scales

In multicellular organisms, cell shape and organization are dictated by cell-cell or cell-extracellular matrix adhesion interactions. Adhesion complexes crosstalk with the cytoskeleton enabling cells to sense their mechanical environment. Unfortunately, most of cell biology studies, and cell mechanics studies in particular, are conducted on cultured cells adhering to a hard, homogeneous, and unconstrained substrate with nonspecific adhesion sites, thus far from physiological and reproducible conditions. Here, we grew cells on three different fibronectin patterns with identical overall dimensions but different geometries (▽, T, and Y), and investigated their topography and mechanics by atomic force microscopy (AFM). The obtained mechanical maps were reproducible for cells grown on patterns of the same geometry, revealing pattern-specific subcellular differences. We found that local Young's moduli variations are related to the cell adhesion geometry. Additionally, we detected local changes of cell mechanical properties induced by cytoskeletal drugs. We thus provide a method to quantitatively and systematically investigate cell mechanics and their variations, and present further evidence for a tight relation between cell adhesion and mechanics.

RhoA controls Wnt upregulation on microstructured titanium surfaces

Rough topography enhances the activation of Wnt canonical signaling in vitro, and this mediates its effects on cell differentiation. However, the molecular mechanisms underlying topography-dependent control of Wnt signaling are still poorly understood. As the small GTPase RhoA controls cytoskeletal reorganization and actomyosin-induced tensional forces, we hypothesized that RhoA could affect the activation of Wnt signaling in cells on micropatterned titanium surfaces. G-LISA assay revealed that RhoA activation was higher in C2C12 cells on rough (SLA) surfaces under basal conditions than on smooth (Polished) titanium. Transfection with dominant negative RhoA decreased Wnt activation by normalized TCF-Luc activity on SLA, whilst transfection with constitutively active RhoA increased TCF-Luc activation on Polished titanium. One mM Myosin II inhibitor Blebbistatin increased RhoA activation but decreased Wnt activation on SLA surfaces, indicating that tension-generating structures are required for canonical Wnt modulation on titanium surfaces. Actin inhibitor Cytochalasin markedly enhanced RhoA and TCF-Luc activation on both surfaces and increased the expression of differentiation markers in murine osteoblastic MC3T3 cells. Taken together, these data show that RhoA is upregulated in cells on rough surfaces and it affects the activation of Wnt canonical signaling through Myosin II modulation.

Tidal stretches differently regulate the contractile and cytoskeletal elements in intact airways

Recent reports suggest that tidal stretches do not cause significant and sustainable dilation of constricted intact airways ex vivo. To better understand the underlying mechanisms, we aimed to map the physiological stretch-induced molecular changes related to cytoskeletal (CSK) structure and contractile force generation through integrin receptors. Using ultrasound, we measured airway constriction in isolated intact airways during 90 minutes of static transmural pressure (Ptm) of 7.5 cmH2O or dynamic variations between Ptm of 5 and 10 cmH20 mimicking breathing. Integrin and focal adhesion kinase activity increased during Ptm oscillations which was further amplified during constriction. While Ptm oscillations reduced β-actin and F-actin formation implying lower CSK stiffness, it did not affect tubulin. However, constriction was amplified when the microtubule structure was disassembled. Without constriction, α-smooth muscle actin (ASMA) level was higher and smooth muscle myosin heavy chain 2 was lower during Ptm oscillations. Alternatively, during constriction, overall molecular motor activity was enhanced by Ptm oscillations, but ASMA level became lower. Thus, ASMA and motor protein levels change in opposite directions due to stretch and contraction maintaining similar airway constriction levels during static and dynamic Ptm. We conclude that physiological Ptm variations affect cellular processes in intact airways with constriction determined by the balance among contractile and CSK molecules and structure.

Tensegrity, cellular biophysics, and the mechanics of living systems

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

Biotensegrity: a unifying theory of biological architecture with applications to osteopathic practice, education, and research--a review and analysis

Since its inception, osteopathic medicine has sought to identify the mechanical causes of disease and to understand the body's structure-function relationship. Research conducted during the past 25 years has demonstrated that the architectural principles of tensegrity can be applied to biological organisms (termed biotensegrity) and that these principles can demonstrate the mechanical structure-function relationship at all size scales in the human body. Further, biotensegrity at the cellular level allows the cell to mechanically sense its environment and convert mechanical signals into biochemical changes. When applied to the principles of osteopathic medicine, biotensegrity provides a conceptual understanding of the hierarchical organization of the human body and explains the body's ability to adapt to change. Further, biotensegrity explains how mechanical forces applied during osteopathic manipulative treatment could lead to effects at the cellular level, providing a platform for future research on the mechanisms of action of osteopathic manipulative treatment.

Effect of membrane stiffness and cytoskeletal element density on mechanical stimuli within cells: an analysis of the consequences of ageing in cells

A finite element model of a single cell was created and used to compute the biophysical stimuli generated within a cell under mechanical loading. Major cellular components were incorporated in the model: the membrane, cytoplasm, nucleus, microtubules, actin filaments, intermediate filaments, nuclear lamina and chromatin. The model used multiple sets of tensegrity structures. Viscoelastic properties were assigned to the continuum components. To corroborate the model, a simulation of atomic force microscopy indentation was performed and results showed a force/indentation simulation with the range of experimental results. A parametric analysis of both increasing membrane stiffness (thereby modelling membrane peroxidation with age) and decreasing density of cytoskeletal elements (thereby modelling reduced actin density with age) was performed. Comparing normal and aged cells under indentation predicts that aged cells have a lower membrane area subjected to high strain as compared with young cells, but the difference, surprisingly, is very small and may not be measurable experimentally. Ageing is predicted to have a more significant effect on strain deep in the nucleus. These results show that computation of biophysical stimuli within cells are achievable with single-cell computational models; correspondence between computed and measured force/displacement behaviours provides a high-level validation of the model. Regarding the effect of ageing, the models suggest only small, although possibly physiologically significant, differences in internal biophysical stimuli between normal and aged cells.

Actin cytoskeleton controls activation of Wnt/β-catenin signaling in mesenchymal cells on implant surfaces with different topographies

Surface topography affects cell function and differentiation. It has been previously shown that rough surfaces can enhance the activation of canonical Wnt signaling, an important pathway for osteoblast differentiation and bone maintenance, but the underlying mechanisms are still poorly understood. The present paper investigates whether cytoskeletal organization contributes to regulating this pathway. Rho-associated protein kinase (ROCK), an important controller of actin microfilaments, was inhibited with 2mM specific antagonist Y-27632 in mesenchymal and osteoblastic cells growing on titanium discs with a polished or acid-etched, sand-blasted (SLA) surface. Y-27632 subverted the morphology of the cytoskeleton on polished and, to a lesser extent, on SLA surfaces, as evidenced by fluorescence microscopy. Although ROCK inhibition did not affect cell viability, it increased activation of Wnt signaling in uncommitted C2C12 mesenchymal cells on polished surfaces but not on SLA discs upon reporter assay. Consistently with this, real-time polymerase chain reaction analysis showed that MC3T3 cells on polished surfaces expressed higher mRNA levels for β-catenin and alkaline phosphatase, a known Wnt target gene, and for the osteoblastic differentiation marker osteocalcin after ROCK inhibition. Taken together, these data demonstrate that cytoskeletal organization mediates activation of Wnt canonical signaling in cells on titanium surfaces with different topographies.

Mechanobiology of tumor invasion: engineering meets oncology

The physical sciences and engineering have introduced novel perspectives into the study of cancer through model systems, tools, and metrics that enable integration of basic science observations with clinical data. These methods have contributed to the identification of several overarching mechanisms that drive processes during cancer progression including tumor growth, angiogenesis, and metastasis. During tumor cell invasion - the first clinically observable step of metastasis - cells demonstrate diverse and evolving physical phenotypes that cannot typically be defined by any single molecular mechanism, and mechanobiology has been used to study the physical cell behaviors that comprise the "invasive phenotype". In this review, we discuss the continually evolving pathological characterization and in vitro mechanobiological characterization of tumor invasion, with emphasis on emerging physical biology and mechanobiology strategies that have contributed to a more robust mechanistic understanding of tumor cell invasion. These physical approaches may ultimately help to better predict and identify tumor metastasis.

Comparing mechano-transduction in fibroblasts deficient of focal adhesion proteins

Mechano-transduction was studied in wildtype and focal adhesion (FA) protein-deficient mouse embryonic fibroblasts (MEFs). Using a cell stretcher, we determined the effect of stretch on cell morphology, apoptosis, and phosphorylation of ERK(1/2). After 20% cyclic, uniaxial stretch, FA-deficient MEFs showed morphological changes and levels of apoptosis of the order: focal adhesion kinase>p130Cas>vinculin compared to wildtype cells. ERK(1/2) phosphorylation peaked in wildtype cells at around 10 min, and in all FA-deficient cells at around 5 min. The relative change in strain energy of FA-deficient cells compared to wildtype cells was of the order: vinculin>FAK>p130Cas. Taken together, FAK and p130Cas are more important in the stretch-mediated downstream signaling and cell survival pathway, while vinculin is more critical in maintaining cell contractility.

Mechanical stiffness grades metastatic potential in patient tumor cells and in cancer cell lines

Cancer cells are defined by their ability to invade through the basement membrane, a critical step during metastasis. While increased secretion of proteases, which facilitates degradation of the basement membrane, and alterations in the cytoskeletal architecture of cancer cells have been previously studied, the contribution of the mechanical properties of cells in invasion is unclear. Here, we applied a magnetic tweezer system to establish that stiffness of patient tumor cells and cancer cell lines inversely correlates with migration and invasion through three-dimensional basement membranes, a correlation known as a power law. We found that cancer cells with the highest migratory and invasive potential are five times less stiff than cells with the lowest migration and invasion potential. Moreover, decreasing cell stiffness by pharmacologic inhibition of myosin II increases invasiveness, whereas increasing cell stiffness by restoring expression of the metastasis suppressor TβRIII/betaglycan decreases invasiveness. These findings are the first demonstration of the power-law relation between the stiffness and the invasiveness of cancer cells and show that mechanical phenotypes can be used to grade the metastatic potential of cell populations with the potential for single cell grading. The measurement of a mechanical phenotype, taking minutes rather than hours needed for invasion assays, is promising as a quantitative diagnostic method and as a discovery tool for therapeutics. By showing that altering stiffness predictably alters invasiveness, our results indicate that pathways regulating these mechanical phenotypes are novel targets for molecular therapy of cancer.

Bone cell elasticity and morphology changes during the cell cycle

The mechanical properties of cells are reported to be regulated by a range of factors including interactions with the extracellular environment and other cells, differentiation status, the onset of pathological states, as well as the intracellular factors, for example, the cytoskeleton. The cell cycle is considered to be a well-ordered sequence of biochemical events. A number of processes reported to occur during its progression are inherently mechanical and, as such, require mechanical regulation. In spite of this, few attempts have been made to investigate the putative regulatory role of the cell cycle in mechanobiology. In the present study, Atomic Force Microscopy (AFM) was employed to investigate the elastic modulus of synchronised osteoblasts. The data obtained confirm that osteoblast elasticity is regulated by cell cycle phase; specifically, cells in S phase were found to have a modulus approximately 1.7 times that of G1 phase cells. Confocal microscopy studies revealed that aspects of osteoblast morphology, namely F-actin expression, were also modulated by the cell cycle, and tended to increase with phase progression from G0 onwards. The data obtained in this study are likely to have implications for the fields of tissue- and bio-engineering, where prior knowledge of cell mechanobiology is essential for the effective replacement and repair of tissue. Furthermore, studies focused on biomechanics and the biophysical properties of cells are important in the understanding of the onset and progression of disease states, for example cancer at the cellular level. Our study demonstrates the importance of the combined use of traditional and relatively novel microscopy techniques in understanding mechanical regulation by crucial cellular processes, such as the cell cycle.

Stress transmission within the cell

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

Complexity of the tensegrity structure for dynamic energy and force distribution of cytoskeleton during cell spreading

Cytoskeleton plays important roles in intracellular force equilibrium and extracellular force transmission from/to attaching substrate through focal adhesions (FAs). Numerical simulations of intracellular force distribution to describe dynamic cell behaviors are still limited. The tensegrity structure comprises tension-supporting cables and compression-supporting struts that represent the actin filament and microtubule respectively, and has many features consistent with living cells. To simulate the dynamics of intracellular force distribution and total stored energy during cell spreading, the present study employed different complexities of the tensegrity structures by using octahedron tensegrity (OT) and cuboctahedron tensegrity (COT). The spreading was simulated by assigning specific connection nodes for radial displacement and attachment to substrate to form FAs. The traction force on each FA was estimated by summarizing the force carried in sounding cytoskeletal elements. The OT structure consisted of 24 cables and 6 struts and had limitations soon after the beginning of spreading by declining energy stored in struts indicating the abolishment of compression in microtubules. The COT structure, double the amount of cables and struts than the OT structure, provided sufficient spreading area and expressed similar features with documented cell behaviors. The traction force pointed inward on peripheral FAs in the spread out COT structure. The complex structure in COT provided further investigation of various FA number during different spreading stages. Before the middle phase of spreading (half of maximum spreading area), cell attachment with 8 FAs obtained minimized cytoskeletal energy. The maximum number of 12 FAs in the COT structure was required to achieve further spreading. The stored energy in actin filaments increased as cells spread out, while the energy stored in microtubules increased at initial spreading, peaked in middle phase, and then declined as cells reached maximum spreading. The dynamic flows of energy in struts imply that microtubules contribute to structure stabilization.

Biophysical properties of Saccharomyces cerevisiae and their relationship with HOG pathway activation

Parameterized models of biophysical and mechanical cell properties are important for predictive mathematical modeling of cellular processes. The concepts of turgor, cell wall elasticity, osmotically active volume, and intracellular osmolarity have been investigated for decades, but a consistent rigorous parameterization of these concepts is lacking. Here, we subjected several data sets of minimum volume measurements in yeast obtained after hyper-osmotic shock to a thermodynamic modeling framework. We estimated parameters for several relevant biophysical cell properties and tested alternative hypotheses about these concepts using a model discrimination approach. In accordance with previous reports, we estimated an average initial turgor of 0.6 ± 0.2 MPa and found that turgor becomes negligible at a relative volume of 93.3 ± 6.3% corresponding to an osmotic shock of 0.4 ± 0.2 Osm/l. At high stress levels (4 Osm/l), plasmolysis may occur. We found that the volumetric elastic modulus, a measure of cell wall elasticity, is 14.3 ± 10.4 MPa. Our model discrimination analysis suggests that other thermodynamic quantities affecting the intracellular water potential, for example the matrix potential, can be neglected under physiological conditions. The parameterized turgor models showed that activation of the osmosensing high osmolarity glycerol (HOG) signaling pathway correlates with turgor loss in a 1:1 relationship. This finding suggests that mechanical properties of the membrane trigger HOG pathway activation, which can be represented and quantitatively modeled by turgor.

Osteocytes and WNT: the Mechanical Control of Bone Formation

Mechanical loading is of pivotal importance in the maintenance of skeletal homeostasis, but the players involved in the transduction of mechanical stimuli to promote bone maintenance have long remained elusive. Osteocytes, the most abundant cells in bone, possess mechanosensing appendices stretching through a system of bone canaliculi. Mechanical stimulation plays an important role in osteocyte survival and hence in the preservation of bone mechanical properties, through the maintenance of bone hydratation. Osteocytes can also control the osteoblastic differentiation of mesenchymal precursors in response to mechanical loading by modulating WNT signaling pathways, essential regulators of cell fate and commitment, through the protein sclerostin. Mutations of Sost, the sclerostin-encoding gene, have dramatic effects on the skeleton, indicating that osteocytes may act as master regulators of bone formation and localized bone remodeling. Moreover, the development of sclerostin inhibitors is opening new possibilities for bone regeneration in orthopedics and the dental field.

Mapping the cytoskeletal prestress

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 underlying regional F-actin density and the local cytoskeletal prestress. In the human airway smooth muscle cell, we used micropatterning to minimize geometric variation. We measured the local cell stiffness and loss tangent with optical magnetic twisting cytometry and the local rate of CSK remodeling with spontaneous displacements of a CSK-bound bead. We also measured traction distributions with traction microscopy and cell geometry with atomic force microscopy. On the basis of these experimental observations, we used finite element methods to map for the first time the regional distribution of intracellular prestress. Compared with the cell center or edges, cell corners were systematically stiffer and more fluidlike and supported higher traction forces, and at the same time had slower remodeling dynamics. Local remodeling dynamics had a close inverse relationship with local cell stiffness. The principal finding, however, is that systematic regional variations of CSK stiffness correlated only poorly with regional F-actin density but strongly and linearly with the regional prestress. Taken together, these findings in the intact cell comprise the most comprehensive characterization to date of regional variations of cytoskeletal mechanical properties and their determinants.

Mechanical model of cytoskeleton structuration during cell adhesion and spreading

The biomechanical behavior of an adherent cell is intimately dependent on its cytoskeleton structure. Several models have been proposed to study this structure taking into account its existing internal forces. However, the structural and geometrical complexities of the cytoskeleton's filamentous networks lead to difficulties for determining a biologically realistic architecture. The objective of this paper is to present a mechanical model, combined with a numerical method, devoted to the form-finding of the cytoskeleton structure (shape and internal forces) when a cell adheres on a substrate. The cell is modeled as a granular medium, using rigid spheres (grains) corresponding to intracellular cross-linking proteins and distant mechanical interactions to reproduce the cytoskeleton filament internal forces. At the initial state (i.e., before adhesion), these interactions are tacit. The adhesion phenomenon is then simulated by considering microtubules growing from the centrosome towards transmembrane integrin-like receptors. The simulated cell shape changes in this process and results in a mechanically equilibrated structure with traction and compression forces, in interaction with the substrate reactions. This leads to a compressive microtubule network and a corresponding tensile actin-filament network. The results provide coherent shape and forces information for developing a mechanical model of the cytoskeleton structure, which can be exploitable in future biomechanical studies of adherent cells.

Tensegrity-based mechanosensing from macro to micro

This article is a summary of a lecture on cellular mechanotransduction that was presented at a symposium on "Cardiac Mechano-Electric Feedback and Arrhythmias" that convened at Oxford, England in April 2007. Although critical mechanosensitive molecules and cellular components, such as integrins, stretch-activated ion channels, and cytoskeletal filaments, have been shown to contribute to the response by which cells convert mechanical signals into a biochemical response, little is known about how they function in the structural context of living cells, tissues and organs to produce orchestrated changes in cell behavior in response to stress. Here, studies are reviewed that suggest our bodies use structural hierarchies (systems within systems) composed of interconnected extracellular matrix and cytoskeletal networks that span from the macroscale to the nanoscale to focus stresses on specific mechanotransducer molecules. A key feature of these networks is that they are in a state of isometric tension (i.e., experience a tensile prestress), which ensures that various molecular-scale mechanochemical transduction mechanisms proceed simultaneously and produce a concerted response. These features of living architecture are the same principles that govern tensegrity (tensional integrity) architecture, and mathematical models based on tensegrity are beginning to provide new and useful descriptions of living materials, including mammalian cells. This article reviews how the use of tensegrity at multiple size scales in our bodies guides mechanical force transfer from the macro to the micro, as well as how it facilitates conversion of mechanical signals into changes in ion flux, molecular binding kinetics, signal transduction, gene transcription, cell fate switching and developmental patterning.

Modeling the effect of stretch and plasma membrane tension on Na+-K+-ATPase activity in alveolar epithelial cells

While a number of whole cell mechanical models have been proposed, few, if any, have focused on the relationship among plasma membrane tension, plasma membrane unfolding, and plasma membrane expansion and relaxation via lipid insertion. The goal of this communication is to develop such a model to better understand how plasma membrane tension, which we propose stimulates Na+-K+-ATPase activity but possibly also causes cell injury, may be generated in alveolar epithelial cells during mechanical ventilation. Assuming basic relationships between plasma membrane unfolding and tension and lipid insertion as the result of tension, we have captured plasma membrane mechanical responses observed in alveolar epithelial cells: fast deformation during fast cyclic stretch, slower, time-dependent deformation via lipid insertion during tonic stretch, and cell recovery after release from stretch. The model estimates plasma membrane tension and predicts Na+-K+-ATPase activation for a specified cell deformation time course. Model parameters were fit to plasma membrane tension, whole cell capacitance, and plasma membrane area data collected from the literature for osmotically swollen and shrunken cells. Predictions of membrane tension and stretch-stimulated Na+-K+-ATPase activity were validated with measurements from previous studies. As a proof of concept, we demonstrate experimentally that tonic stretch and consequent plasma membrane recruitment can be exploited to condition cells against subsequent cyclic stretch and hence mitigate stretch-induced responses, including stretch-induced cell death and stretch-induced modulation of Na+-K+-ATPase activity. Finally, the model was exercised to evaluate plasma membrane tension and potential Na+-K+-ATPase stimulation for an assortment of traditional and novel ventilation techniques.

Divided medium-based model for analyzing the dynamic reorganization of the cytoskeleton during cell deformation

Cell deformability and mechanical responses of living cells depend closely on the dynamic changes in the structural architecture of the cytoskeleton (CSK). To describe the dynamic reorganization and the heterogeneity of the prestressed multi-modular CSK, we developed a two-dimensional model for the CSK which was taken to be a system of tension and compression interactions between the nodes in a divided medium. The model gives the dynamic reorganization of the CSK consisting of fast changes in connectivity between nodes during medium deformation and the resulting mechanical behavior is consistent with the strain-hardening and prestress-induced stiffening observed in cells in vitro. In addition, the interaction force networks which occur and balance to each other in the model can serve to identify the main CSK substructures: cortex, stress fibers, intermediate filaments, microfilaments, microtubules and focal adhesions. Removing any of these substructures results in a loss of integrity in the model and a decrease in the prestress and stiffness, and suggests that the CSK substructures are highly interdependent. The present model may therefore provide a useful tool for understanding the cellular processes involving CSK reorganization, such as mechanotransduction, migration and adhesion processes.

Isostaticity and controlled force transmission in the cytoskeleton: A model awaiting experimental evidence

A new model is proposed for force transmission through the cytoskeleton (CSK). A general discussion is first presented on the physical principles that underlie the modeling of this phenomenon. Some fundamental problems of conventional models--continuous and discrete--are examined. It is argued that mediation of focused forces is essential for good control over intracellular mechanical signals. The difficulties of conventional continuous models in describing such mediation are traced to a fundamental assumption rather than to their being continuous. Relevant advantages and disadvantages of continuous and discrete modeling are discussed. It is concluded that favoring discrete models is based on two misconceptions, which are clarified. The model proposed here is based on the idea that focused propagation of mechanical stimuli in frameworks over large distances (compared to the mesh size) can only occur when considerable regions of the CSK are isostatic. The concept of isostaticity is explained and a recently developed continuous isostaticity theory is briefly reviewed. The model enjoys several advantages: it leads to good control over force mediation; it explains nonuniform stresses and action at a distance; it is continuous, making it possible to model force propagation over long distances; and it enables prediction of individual force paths. To be isostatic, or nearly so, CSK networks must possess specific structural characteristics, and these are quantified. Finally, several experimental observations are interpreted using the new model and implications are discussed. It is also suggested that this approach may give insight into the dynamics of reorganization of the CSK. Many of the results are amenable to experimental measurements, providing a testing ground for the proposed picture, and generic experiments are suggested.

Frequency response of a viscoelastic tensegrity model: Structural rearrangement contribution to cell dynamics

In an attempt to understand the role of structural rearrangement onto the cell response during imposed cyclic stresses, we simulated numerically the frequency-dependent behavior of a viscoelastic tensegrity structure (VTS model) made of 24 elastic cables and 6 rigid bars. The VTS computational model was based on the nonsmooth 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 normalized 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.

Stress transmission in the lung: pathways from organ to molecule

Gas exchange, the primary function of the lung, can come about only with the application of physical forces on the macroscale and their transmission to the scale of small airway, small blood vessel, and alveolus, where they serve to distend and stabilize structures that would otherwise collapse. The pathway for force transmission then continues down to the level of cell, nucleus, and molecule; moreover, to lesser or greater degrees most cell types that are resident in the lung have the ability to generate contractile forces. At these smallest scales, physical forces serve to distend the cytoskeleton, drive cytoskeletal remodeling, expose cryptic binding domains, and ultimately modulate reaction rates and gene expression. Importantly, evidence has now accumulated suggesting that multiscale phenomena span these scales and govern integrative lung behavior.

The effects of morphology, confluency, and phenotype on whole-cell mechanical behavior

Emerging evidence indicates that cellular mechanical behavior can be altered by disease, drug treatment, and mechanical loading. To effectively investigate how disease and mechanical or biochemical treatments influence cellular mechanical behavior, it is imperative to determine the source of large inter-cell differences in whole-cell mechanical behavior within a single cell line. In this study, we used the atomic force microscope to investigate the effects of cell morphological parameters and confluency on whole-cell mechanical behavior for osteoblastic and fibroblastic cells. For nonconfluent cells, projected nucleus area, cell area, and cell aspect ratio were not correlated with mechanical behavior (p>or=0.46), as characterized by a parallel-spring recruitment model. However, measured force-deformation responses were statistically different between osteoblastic and fibroblastic cells (p<0.001) and between confluent and nonconfluent cells (p<0.001). Osteoblastic cells were 2.3-2.8 times stiffer than fibroblastic cells, and confluent cells were 1.5-1.8 times stiffer than nonconfluent cells. The results indicate that structural differences related to phenotype and confluency affect whole-cell mechanical behavior, while structural differences related to global morphology do not. This suggests that cytoskeleton structural parameters, such as filament density, filament crosslinking, and cell-cell and cell-matrix attachments, dominate inter-cell variability in whole-cell mechanical behavior.

Plant and fungal cytomechanics: quantifying and modeling cellular architectureThis review is one of a selection of papers published in the Special Issue on Plant Cell Biology

Biomechanical studies aim at understanding the relationship between the mechanical properties of biological structures and their function. In cytomechanical investigations, this approach is brought down to the scale of cells and subcellular structures. In plant cells and the hyphae of fungi and water molds, interactions between turgor pressure, the cell wall, and the cytoskeleton are considered of primary importance. This review is an overview of how the mechanical properties of these individual features and their interactions have been measured and how the experimental data are used to produce theoretical mechanical models of cellular architecture and dynamics. Several models are discussed, and focusing on the example of tip-growing cells, various approaches to understanding the mechanical aspects of cellular morphogenesis are analyzed.

Effects of cytoskeletal prestress on cell rheological behavior

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