Cell cytoskeleton and tensegrity

The role of tensegrity architecture of the cytoskeleton in the mechanical behavior of living cells is examined by computational studies. Plane and spatial tensegrity models of the cytoskeleton are considered as well as their non-tensegrity counterparts. Local buckling including deep postbuckling response of the compressed microtubules of the cytoskeleton is considered. The tensioned microfilaments cannot sustain compression. Large deformation of the whole model is accounted and fully nonlinear analysis is performed. It is shown that in the case of local buckling of the microtubules non-tensegrity models exhibit qualitatively the same linear stiffening as their tensegrity counterparts. This result raises the question of experimental validation of the local buckling of microtubules. If the microtubules of real cells are not straight, then tensegrity (in a narrow sense) is not a necessary attribute of the cytoskeleton architecture. If the microtubules are straight then tensegrity is more likely to be the cytoskeletal architecture.     

Toward a generalised tensegrity model describing the mechanical behaviour of the cytoskeleton structure

The control of many cell functions including growth, migration and mechanotransduction, depends crucially on stress-induced mechanical changes in cell shape and cytoskeleton (CSK) structure. Quantitative studies have been carried out on 6-bar tensegrity models to analyse several mechanical parameters involved in the mechanical responses of adherent cells (i.e. strain hardening, internal stress and scale effects). In the present study, we attempt to generalize some characteristic mechanical laws governing spherical tensegrity structures, with a view of evaluating the mechanical behaviour of the hierarchical multi-modular CSK-structure. The numerical results obtained by studying four different tensegrity models are presented in terms of power laws and point to the existence of unique and constant relationships between the overall structural stiffness and the local properties (length, number and internal stress) of the constitutive components.     

Toward a Generalised Tensegrity Model Describing the Mechanical Behaviour of the Cytoskeleton Structure

The control of many cell functions including growth, migration and mechanotransduction, depends crucially on stress-induced mechanical changes in cell shape and cytoskeleton (CSK) structure. Quantitative studies have been carried out on 6-bar tensegrity models to analyse several mechanical parameters involved in the mechanical responses of adherent cells (i.e. strain hardening, internal stress and scale effects). In the present study, we attempt to generalize some characteristic mechanical laws governing spherical tensegrity structures, with a view of evaluating the mechanical behaviour of the hierarchical multi-modular CSK-structure. The numerical results obtained by studying four different tensegrity models are presented in terms of power laws and point to the existence of unique and constant relationships between the overall structural stiffness and the local properties (length, number and internal stress) of the constitutive components.     

Experimental tests of the cellular tensegrity hypothesis

The tensegrity model depicts the cytoskeleton (CSK) as a prestressed network of interconnected filaments. The prestress is generated by the CSK contractile apparatus and is partly balanced by traction at the cell-substrate interface and partly by CSK internal compression elements such as microtubules (MTs). A key feature of tensegrity is that the shear modulus (G) must increase in proportion with the prestress. Here we have tested that prediction as well as the idea that compression of MTs balance a portion of the cell prestress. Airway smooth muscle cells were studied. Traction microscopy was used to calculate traction. Because traction must be balanced by the stress within the cell, the prestress could be computed. Cell G was measured by oscillatory magnetic cytometry. The prestress was modulated using graded concentrations of contracting (histamine) or relaxing (isoproterenol) agonists and by disrupting MTs by colchicine. It was found that G increased in proportion with the prestress and that compression of MTs balanced a significant, but a relatively small fraction of the prestress. Taken together, these results do not disprove other models of cell deformability, nor they prove tensegrity. However, they do support a priori predictions of tensegrity. As such, it may not be necessary to invoke more complex mechanisms to explain these central features of cell deformability.     

Cytoskeletal architecture and mechanical behavior of living cells

Conventional continuum mechanics models considering living cells as viscous fluid balloons are unable to explain some recent experimental observations. In contrast, new microstructural models provide the desirable explanations. These models emphasize the role of the cell cytoskeleton built of struts-microtubules and cables-microfilaments. A specific architectural model of the cytoskeletal framework called "tensegrity" deserved wide attention recently. Tensegrity models particularly account for the phenomenon of linear stiffening of living cells. These models are discussed from the structural mechanics perspective. Classification of structural assemblies is given and the meaning of "tensegrity" is pinpointed. Possible sources of non-linearity leading to cell stiffening are emphasized. The role of local buckling of microtubules and overall stability of the cytoskeleton is stressed. Computational studies play a central role in the development of the microstructural theoretical framework allowing for the prediction of the cell behavior from "first principles". Algorithms of computer analysis of the cytoskeleton that consider unilateral response of microfilaments and deep postbuckling of microtubules are addressed.     

Computational model for the cell-mechanical response of the osteocyte cytoskeleton based on self-stabilizing tensegrity structures

The mechanism by which mechanical stimulation on osteocytes results in biochemical signals that initiate the remodeling process inside living bone tissue is largely unknown. Even the type of stimulation acting on these cells is not yet clearly identified. However, the cytoskeleton of osteocytes is suggested to play a major role in the mechanosensory process due to the direct connection to the nucleus. In this paper, a computational approach to model and simulate the cell structure of osteocytes based on self-stabilizing tensegrity structures is suggested. The computational model of the cell consists of the major components with respect to mechanical aspects: the integrins that connect the cell with the extracellular bone matrix, and different types of protein fibers (microtubules and intermediate filaments) that form the cytoskeleton, the membrane-cytoskeleton (microfilaments), the nucleus and the centrosome. The proposed geometrical cell models represent the cell in its physiological environment which is necessary in order to give a statement on the cell behavior in vivo. Studies on the mechanical response of osteocytes after physiological loading and in particular the mechanical response of the nucleus show that the load acting on the nucleus is rising with increasing deformation applied to the integrins.     

A multi-modular tensegrity model of an actin stress fiber

Stress fibers are contractile bundles in the cytoskeleton that stabilize cell structure by exerting traction forces on the extracellular matrix. Individual stress fibers are molecular bundles composed of parallel actin and myosin filaments linked by various actin-binding proteins, which are organized end-on-end in a sarcomere-like pattern within an elongated three-dimensional network. While measurements of single stress fibers in living cells show that they behave like tensed viscoelastic fibers, precisely how this mechanical behavior arises from this complex supramolecular arrangement of protein components remains unclear. Here we show that computationally modeling a stress fiber as a multi-modular tensegrity network can predict several key behaviors of stress fibers measured in living cells, including viscoelastic retraction, fiber splaying after severing, non-uniform contraction, and elliptical strain of a puncture wound within the fiber. The tensegrity model can also explain how they simultaneously experience passive tension and generate active contraction forces; in contrast, a tensed cable net model predicts some, but not all, of these properties. Thus, tensegrity models may provide a useful link between molecular and cellular scale mechanical behaviors and represent a new handle on multi-scale modeling of living materials.     

Tensegrity architecture explains linear stiffening and predicts softening of living cells

The problem of theoretical explanation of the experimentally observed linear stiffening of living cells is addressed. This explanation is based on Ingber's assumption that the cell cytoskeleton, which enjoys tensegrity architecture with compressed microtubules that provide tension to the microfilaments, affects the mechanical behavior of the living cell. Moreover, it is shown that the consideration of the extreme flexibility of microtubules and the unilateral response of microfilaments is crucial for the understanding of the living cell overall behavior. Formal nonlinear structural analysis of the cell cytoskeleton under external mechanical loads is performed. For this purpose, a general computer model for tensegrity assemblies with unilateral microfilaments and buckled microtubules is developed and applied to the theoretical analysis of the mechanical response of 2D and 3D examples of tensegrity cells mimicking the behavior of real living cells. Results of the computer simulations explain the experimentally observed cell stiffening. Moreover, the theoretical results predict the possible existence of a transient softening behavior of cells, a phenomenon, which has not been observed in experiments yet.     

Models of cytoskeletal mechanics of adherent cells

 Adherent cells sense their mechanical environment, which, in turn, regulates their functions. During the past decade, a growing body of evidence has indicated that a deformable, solid-state intracellular structure known as the cytoskeleton (CSK) plays a major role in transmitting and distributing mechanical stresses within the cell as well as in their conversion into a chemical response. Therefore in order to understand mechanical regulation and control of cellular functions, one needs to understand mechanisms that determine how the CSK changes its shape and mechanics in response to stress. In this survey, we examined commonly used structurally based models of the CSK. In particular, we focused on two classes of these models: open-cell foam networks and stress-supported structures. We identified the underlying mechanisms that determine deformability of those models and compare model predictions with data previously obtained from mechanical tests on cultured living adherent cells at steady state. We concluded that stress-supported structures appear more suitable for describing cell deformability because this class of structures can explain the central role that the cytoskeletal contractile prestress plays in cellular mechanics. Received: 2 January 2002 / Accepted: 27 February 2002     

Mechanical control of tissue morphogenesis during embryological development

Twenty years ago, we proposed a model of developmental control based on tensegrity architecture, in which tissue pattern formation in the embryo is controlled through mechanical interactions between cells and extracellular matrix (ECM) which place the tissue in a state of isometric tension (prestress). The model proposed that local changes in the mechanical compliance of the ECM, for example, due to regional variations in basement membrane degradation beneath growing epithelium, may result in local stretching of the ECM and associated adherent cells, much like a "run-in-a-stocking". Cell growth and function would be controlled locally though physical distortion of the associated cells, or changes in cytoskeletal tension. Importantly, experimental studies have demonstrated that cultured cells can be switched between different fates, including growth, differentiation, apoptosis, directional motility and different stem cell lineages, by modulating cell shape. Experiments in whole embryonic organ rudiments also have confirmed the tight correlation between basement membrane thinning, cell tension generation and new bud and branch formation during tissue morphogenesis and that this process can be inhibited or accelerated by dissipating or enhancing cytoskeletal tension, respectively. Taken together, this work confirms that mechanical forces generated in the cytoskeleton of individual cells and exerted on ECM scaffolds, play a critical role in the sculpting of the embryo.     

Optical deformability as an inherent cell marker for testing malignant transformation and metastatic competence

The relationship between the mechanical properties of cells and their molecular architecture has been the focus of extensive research for decades. The cytoskeleton, an internal polymer network, in particular determines a cell's mechanical strength and morphology. This cytoskeleton evolves during the normal differentiation of cells, is involved in many cellular functions, and is characteristically altered in many diseases, including cancer. Here we examine this hypothesized link between function and elasticity, enabling the distinction between different cells, by using a microfluidic optical stretcher, a two-beam laser trap optimized to serially deform single suspended cells by optically induced surface forces. In contrast to previous cell elasticity measurement techniques, statistically relevant numbers of single cells can be measured in rapid succession through microfluidic delivery, without any modification or contact. We find that optical deformability is sensitive enough to monitor the subtle changes during the progression of mouse fibroblasts and human breast epithelial cells from normal to cancerous and even metastatic state. The surprisingly low numbers of cells required for this distinction reflect the tight regulation of the cytoskeleton by the cell. This suggests using optical deformability as an inherent cell marker for basic cell biological investigation and diagnosis of disease.     

细胞结构的张力完整性

张力完整性结构由承受压力构件和一系列连续的张力构件相互连接组成.这种结构的稳定性取决于结构内部张力的完整性的保持,因而被称为张力完整性.生物学研究表明细胞的结构符合张力完整性原理.而且细胞骨架的张力完整性影响细胞的形状及其功能.应用张力完整性原理可解释细胞内力化学转导的一些基本规律.     

The Theory of Tensegrity and Spatial Organization of Living Matter

There is still no consensus on the mechanisms regulating the formation and maintenance of morphological structures in the individual development of living organisms. The hypothesis that the mechanical forces are important for biological morphogenesis was put forward more than 100 years ago. In recent decades, studies indicating the regulatory role of mechanical stresses at different levels of organization of life have appeared. The signaling mechanisms that are responsible for the reception of mechanical influences and reprogramming of the properties of cells and tissues are studied. Since the mid-1970s, the principles of selfstressed structures or the tensegrity (tensional integrity) theory have been applied to understand the structure and functions of living structures in statics and dynamics. According to this standpoint, the cell can be represented as a self-stressed structure in which microtubules function as rigid rods and microfilaments serve as elastic threads. Such a system is anchored to extracellular matrix through cellular contacts, since it is adjusted to the external patterns of mechanical stresses. The notion of living systems as self-stressed structures provides a fresh look at the mechanotransduction, developing organism integrity, and biological morphogenesis. Although the application of the ideas of tensegrity to biological systems has not yet received broad support among biologists, the influence of these ideas on the formation of modern mechanobiology and understanding the crucial role of cytoskeletal structures in cellular processes should be mentioned.     

Mechanosensitivity as an integrative system in heart: an audit

This review examines a manifold of apparently loosely linked observations and mechanisms, from membrane to man, and assembles them to support the notion that mechanoelectric transduction is an integrative regulatory system in the heart. For this, the assemblage has to satisfy, at least to some extent, criteria that apply to other integrative regulatory systems such as the endocrine and nervous systems. The integrative effectors in the endocrine system are chemical linkages, circulating hormones: in the nervous system the linkage is a network of cables, nerve conduction and neurotransmitters. Mechanical integration is would be effected through mechanical machinery, cardiac contractile and hydraulic function with attendant stress and strain transmitted via "tensegrity". This can, through the cytoskeleton, begin with membrane integrins and transmit intracellularly for example via F actins to reach the rest of the membranous integrins. Further transmission to the organ is via cell-to-cell adhesion complexes and the extracellular matrix. This tensegrity facilitates integration of force and strain changes from area to area. In consequence, and analogous to the neurendocrine system, mechanoelectric transduction should, and does (1) operate at the molecular or membrane level--this would be via mechanotransducers affecting transmembrane ionic flow; (2) operate in the cell--to influence electrophysiology; (3) have a multicellular expression--e.g. mechanical distortion of one cell can raise intracellular calcium of an adjacent cell; (4) express in the intact organ--e.g. an increase in venous return hydraulically distends the sinoatrial node, steepening its pacemaker potential, thus increasing heart rate. It should also (5) demonstrate elements of a feedback system--"mechanoelectric feedback", and (6) interact with other systems--the cytoskeleton incorporates cell signalling complexes intersecting with other signal cascades. Finally, (7) it can malfunction to produce clinical abnormality--it contributes electrophysiologically to lethal cardiac arrhythmia. This anatomical and functional behaviour of mechanoelectric transduction could sanction the prospect of viewing it as analogous to the other integrative physiological systems.     

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

Mechanical properties of adherent cells were investigated using methods of engineering mechanics. The cytoskeleton (CSK) was modeled as a filamentous network and key mechanisms and corresponding molecular structures which determine cell elastic behavior were identified. Three models of the CSK were considered: open-cell foam networks, prestressed cable nets, and a tensegrity model as a special case of the latter. For each model, the modulus of elasticity (i.e. an index of resistance to small deformation) was given as a function of mechanical and geometrical properties of CSK filaments whose values were determined from the data in the literature. Quantitative predictions for the elastic modulus were compared with data obtained previously from mechanical tests on adherent cells. The open-cell foam model yielded the elastic modulus (10(3)-10(4)Pa) which was consistent with measurements which apply a large compressive stress to the cell. This suggests that bending of CSK filaments is the key mechanism for resisting large compression. The prestressed cable net and tensegrity model yielded much lower elastic moduli (10(1)-10(2)Pa) which were consistent with values determined from equilibrium measurements at low applied stress. This suggests that CSK prestress and architecture are the primary determinants of the cell elastic response. The tensegrity model revealed the possibility that buckling of microtubules of the CSK also contributed to cell elasticity.     

Direct observations of the mechanical behaviors of the cytoskeleton in living fibroblasts

Cytoskeletal proteins tagged with green fluorescent protein were used to directly visualize the mechanical role of the cytoskeleton in determining cell shape. Rat embryo (REF 52) fibroblasts were deformed using glass needles either uncoated for purely physical manipulations, or coated with laminin to induce attachment to the cell surface. Cells responded to uncoated probes in accordance with a three-layer model in which a highly elastic nucleus is surrounded by cytoplasmic microtubules that behave as a jelly-like viscoelastic fluid. The third, outermost cortical layer is an elastic shell under sustained tension. Adhesive, laminin-coated needles caused focal recruitment of actin filaments to the contacted surface region and increased the cortical layer stiffness. This direct visualization of actin recruitment confirms a widely postulated model for mechanical connections between extracellular matrix proteins and the actin cytoskeleton. Cells tethered to laminin-treated needles strongly resisted elongation by actively contracting. Whether using uncoated probes to apply simple deformations or laminin-coated probes to induce surface-to-cytoskeleton interaction we observed that experimentally applied forces produced exclusively local responses by both the actin and microtubule cytoskeleton. This local accomodation and dissipation of force is inconsistent with the proposal that cellular tensegrity determines cell shape.     

Microtubules may harden or soften cells, depending of the extent of cell distension

Experimental data show that disruption of microtubules causes cells to either become stiffer or softer. Current understanding of these behaviors is based on several different mechanisms, each of which can account for only stiffening or softening. In this study we offer a model that can explain both these features. The model is based on the cellular tensegrity idea. Key premises of the model are that cell shape stability is secured through pre-existing mechanical stress (prestress) borne by the actin cytoskeletal network, and that this prestress is partly balanced by cytoskeletal microtubules and partly by the extracellular matrix. Thus, disturbance of this balance would affect cell deformability. The model predicts that disruption of microtubules causes an increase or a decrease in cell stiffness, depending on the extent to which microtubules participate in balancing the prestress which, in turn, depends on the extent of cell spreading. In highly spread cells microtubules have a minor and negative contribution to cell stiffness, whereas in less spread cells their contribution is positive and substantial. Since in their natural habitat cells seldom exhibit highly spread forms, the above results suggest that the contribution of microtubules to cell deformability cannot be overlooked.     

The plastic cell: mechanical deformation of cells and tissues

Epithelial cells possess the ability to change their shape in response to mechanical stress by remodelling their junctions and their cytoskeleton. This property lies at the heart of tissue morphogenesis in embryos. A key feature of embryonic cell shape changes is that they result from repeated mechanical inputs that make them partially irreversible at each step. Past work on cell rheology has rarely addressed how changes can become irreversible in a complex tissue. Here, we review new and exciting findings dissecting some of the physical principles and molecular mechanisms accounting for irreversible cell shape changes. We discuss concepts of mechanical ratchets and tension thresholds required to induce permanent cell deformations akin to mechanical plasticity. Work in different systems has highlighted the importance of actin remodelling and of E-cadherin endocytosis. We also list some novel experimental approaches to fine-tune mechanical tension, using optogenetics, magnetic beads or stretching of suspended epithelial tissues. Finally, we discuss some mathematical models that have been used to describe the quantitative aspects of accounting for mechanical cell plasticity and offer perspectives on this rapidly evolving field.     

Dissecting the contribution of actin and vimentin intermediate filaments to mechanical phenotype of suspended cells using high-throughput deformability measurements and computational modeling

Mechanical cell properties play an important role in many basic biological functions, including motility, adhesion, proliferation and differentiation. There is a growing body of evidence that the mechanical cell phenotype can be used for detection and, possibly, treatment of various diseases, including cancer. Understanding of pathological mechanisms requires investigation of the relationship between constitutive properties and major structural components of cells, i.e., the nucleus and cytoskeleton. While the contribution of actin und microtubules to cellular rheology has been extensively studied in the past, the role of intermediate filaments has been scarcely investigated up to now. Here, for the first time we compare the effects of drug-induced disruption of actin and vimentin intermediate filaments on mechanical properties of suspended NK cells using high-throughput deformability measurements and computational modeling. Although, molecular mechanisms of actin and vimentin disruption by the applied cytoskeletal drugs, Cytochalasin-D and Withaferin-A, are different, cell softening in both cases can be attributed to reduction of the effective density and stiffness of filament networks. Our experimental data suggest that actin and vimentin deficient cells exhibit, in average, 41% and 20% higher deformability in comparison to untreated control. 3D Finite Element simulation is performed to quantify the contribution of cortical actin and perinuclear vimentin to mechanical phenotype of the whole cell. Our simulation provides quantitative estimates for decreased filament stiffness in drug-treated cells and predicts more than two-fold increase of the strain magnitude in the perinuclear vimentin layer of actin deficient cells relatively to untreated control. Thus, the mechanical function of vimentin becomes particularly essential in motile and proliferating cells that have to dynamically remodel the cortical actin network. These insights add functional cues to frequently observed overexpression of vimentin in diverse types of cancer and underline the role of vimentin targeting drugs, such as Withaferin-A, as a potent cancerostatic supplement.