Buckling Behavior of Individual and Bundled Microtubules

As the major structural constituent of the cytoskeleton, microtubules (MTs) serve a variety of biological functions that range from facilitating organelle transport to maintaining the mechanical integrity of the cell. Neuronal MTs exhibit a distinct configuration, hexagonally packed bundles of MT filaments, interconnected by MT-associated protein (MAP) tau. Building on our previous work on mechanical response of axonal MT bundles under uniaxial tension, this study is focused on exploring the compression scenarios. Intracellular MTs carry a large fraction of the compressive loads sensed by the cell and therefore, like any other column-like structure, are prone to substantial bending and buckling. Various biological activities, e.g., actomyosin contractility and many pathological conditions are driven or followed by bending, looping, and buckling of MT filaments. The coarse-grained model previously developed in our lab has been used to study the mechanical behavior of individual and bundled in vivo MT filaments under uniaxial compression. Both configurations show tip-localized, decaying, and short-wavelength buckling. This behavior highlights the role of the surrounding cytoplasm and MAP tau on MT buckling behavior, which allows MT filaments to bear much larger compressive forces. It is observed that MAP tau interconnections improve this effect by a factor of two. The enhanced ability of MT bundles to damp buckling waves relative to individual MT filaments, may be interpreted as a self-defense mechanism because it helps axonal MTs to endure harsher environments while maintaining their function. The results indicate that MT filaments in a bundle do not buckle simultaneously implying that the applied stress is not equally shared among the MT filaments, that is a consequence of the nonuniform distribution of MAP tau proteins along the bundle length. Furthermore, from a pathological perspective, it is observed that axonal MT bundles are more vulnerable to failure in compression than tension.     

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.     

Mechanics of Individual Keratin Bundles in Living Cells

Along with microtubules and microfilaments, intermediate filaments are a major component of the eukaryotic cytoskeleton and play a key role in cell mechanics. In cells, keratin intermediate filaments form networks of bundles that are sparser in structure and have lower connectivity than, for example, actin networks. Because of this, bending and buckling play an important role in these networks. Buckling events, which occur due to compressive intracellular forces and cross-talk between the keratin network and other cytoskeletal components, are measured here in situ. By applying a mechanical model for the bundled filaments, we can access the mechanical properties of both the keratin bundles themselves and the surrounding cytosol. Bundling is characterized by a coupling parameter that describes the strength of the linkage between the individual filaments within a bundle. Our findings suggest that coupling between the filaments is mostly complete, although it becomes weaker for thicker bundles, with some relative movement allowed.     

A mechanics model of microtubule buckling in living cells

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

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.     

The Mechanical Role of Microtubules in Tissue Remodeling

During morphogenesis, tissues undergo extensive remodeling to get their final shape. Such precise sculpting requires the application of forces generated within cells by the cytoskeleton and transmission of these forces through adhesion molecules within and between neighboring cells. Within individual cells, microtubules together with actomyosin filaments and intermediate filaments form the composite cytoskeleton that controls cell mechanics during tissue rearrangements. While studies have established the importance of actin-based mechanical forces that are coupled via intercellular junctions, relatively little is known about the contribution of other cytoskeletal components such as microtubules to cell mechanics during morphogenesis. In this review the focus is on recent findings, highlighting the direct mechanical role of microtubules beyond its well-established role in trafficking and signaling during tissue formation.     

Intermediate filaments against actomyosin: the david and goliath of cell migration

Intermediate filaments (IFs), together with actin and microtubules, constitute the cytoskeleton and regulate essential biological processes including cell migration. Despite the well-described changes in the composition of IFs in migrating cells, the mechanism by which these changes may contribute to cell migration remains elusive. Recent studies show that IFs control cell migration by impacting the actomyosin machinery. This review discusses how the unique physical properties of IFs, the interplay between IFs and the actomyosin network, and the connection of IFs with cell adhesive structures participate in cell migration. We highlight the biochemical and mechanical mechanisms by which IFs control actomyosin-generated forces to influence migration speed and contribute to nuclear integrity and cell resilience to compressive forces in 2D, as well as in confined 3D migration.     

Pollen tube growth: coping with mechanical obstacles involves the cytoskeleton

Cellular growth and movement require both the control of direction and the physical capacity to generate forces. In animal cells directional control and growth forces are generated by the polymerization of and traction between the elements of the cytoskeleton. Whether actual forces generated by the cytoskeleton play a role in plant cell growth is largely unknown as the interplay between turgor and cell wall is considered to be the predominant structural feature in plant cell morphogenesis. We investigated the mechano-structural role of the cytoskeleton in the invasive growth of pollen tubes. These cells elongate rapidly by tip growth and have the ability to penetrate the stigmatic and stylar tissues in order to drill their way to the ovule. We used agents interfering with cytoskeletal functioning, latrunculin B and oryzalin, in combination with mechanical in vitro assays. While microtubule degradation had no significant effect on the pollen tubes’ capacity to invade a mechanical obstacle, latrunculin B decreased the pollen tubes’ ability to elongate in stiffened growth medium and to penetrate an obstacle. On the other hand, the ability to maintain a certain growth direction in vitro was affected by the degradation of microtubules but not actin filaments. To find out whether both cytoskeletal elements share functions or interact we used both drugs in combination resulting in a dramatic synergistic response. Fluorescent labeling revealed that the integrity of the microtubule cytoskeleton depends on the presence of actin filaments. In contrast, actin filaments seemed independent of the configuration of microtubules.     

Intracellular mechanics of migrating fibroblasts

Cell migration is a highly coordinated process that occurs through the translation of biochemical signals into specific biomechanical events. The biochemical and structural properties of the proteins involved in cell motility, as well as their subcellular localization, have been studied extensively. However, how these proteins work in concert to generate the mechanical properties required to produce global motility is not well understood. Using intracellular microrheology and a fibroblast scratch-wound assay, we show that cytoskeleton reorganization produced by motility results in mechanical stiffening of both the leading lamella and the perinuclear region of motile cells. This effect is significantly more pronounced in the leading edge, suggesting that the mechanical properties of migrating fibroblasts are spatially coordinated. Disruption of the microtubule network by nocodazole treatment results in the arrest of cell migration and a loss of subcellular mechanical polarization; however, the overall mechanical properties of the cell remain mostly unchanged. Furthermore, we find that activation of Rac and Cdc42 in quiescent fibroblasts elicits mechanical behavior similar to that of migrating cells. We conclude that a polarized mechanics of the cytoskeleton is essential for directed cell migration and is coordinated through microtubules.     

Type-I IFN signaling is required for the induction of antigen-specific CD8(+) T cell responses by adenovirus vector vaccine in the gut-mucosa

Microtubules in living cells are very important component for various cellular functions as well as to maintain the cell shape. Mechanical properties of microtubules play a vital role in their functions and structure. To understand the mechanical properties of microtubules in living cells, we developed an orthotropic-Pasternak model and investigated the vibrational behavior when microtubules are embedded in surrounding elastic medium. We considered microtubules as orthotropic elastic shell and its surrounding elastic matrix as Pasternak foundation. We found that due to mechanical coupling of microtubules with elastic medium, the flexural vibration is increased with the stiffening of elastic medium. We noticed that foundation modulus (H) and shear modulus (G) have more effect on radial vibrational mode as compared to longitudinal vibrational mode and torsional vibrational mode.     

Contribution of the Cytoskeleton to the Compressive Properties and Recovery Behavior of Single Cells

The cytoskeleton is known to play an important role in the biomechanical nature and structure of cells, but its particular function in compressive characteristics has not yet been fully examined. This study focused on the contribution of the main three cytoskeletal elements to the bulk compressive stiffness (as measured by the compressive modulus), volumetric or apparent compressibility changes (as further indicated by apparent Poisson's ratio), and recovery behavior of individual chondrocytes. Before mechanical testing, cytochalasin D, acrylamide, or colchicine was used to disrupt actin microfilaments, intermediate filaments, or microtubules, respectively. Cells were subjected to a range of compressive strains and allowed to recover to equilibrium. Analysis of the video recording for each mechanical event yielded relevant compressive properties and recovery characteristics related to the specific cytoskeletal disrupting agent and as a function of applied axial strain. Inhibition of actin microfilaments had the greatest effect on bulk compressive stiffness (∼50% decrease compared to control). Meanwhile, intermediate filaments and microtubules were each found to play an integral role in either the diminution (compressibility) or retention (incompressibility) of original cell volume during compression. In addition, microtubule disruption had the largest effect on the “critical strain threshold” in cellular mechanical behavior (33% decrease compared to control), as well as the characteristic time for recovery (∼100% increase compared to control). Elucidating the role of the cytoskeleton in the compressive biomechanical behavior of single cells is an important step toward understanding the basis of mechanotransduction and the etiology of cellular disease processes.     

Actomyosin Pulls to Advance the Nucleus in a Migrating Tissue Cell

The cytoskeletal forces involved in translocating the nucleus in a migrating tissue cell remain unresolved. Previous studies have variously implicated actomyosin-generated pushing or pulling forces on the nucleus, as well as pulling by nucleus-bound microtubule motors. We found that the nucleus in an isolated migrating cell can move forward without any trailing-edge detachment. When a new lamellipodium was triggered with photoactivation of Rac1, the nucleus moved toward the new lamellipodium. This forward motion required both nuclear-cytoskeletal linkages and myosin activity. Apical or basal actomyosin bundles were found not to translate with the nucleus. Although microtubules dampen fluctuations in nuclear position, they are not required for forward translocation of the nucleus during cell migration. Trailing-edge detachment and pulling with a microneedle produced motion and deformation of the nucleus suggestive of a mechanical coupling between the nucleus and the trailing edge. Significantly, decoupling the nucleus from the cytoskeleton with KASH overexpression greatly decreased the frequency of trailing-edge detachment. Collectively, these results explain how the nucleus is moved in a crawling fibroblast and raise the possibility that forces could be transmitted from the front to the back of the cell through the nucleus.     

Actomyosin Pulls to Advance the Nucleus in a Migrating Tissue Cell

The cytoskeletal forces involved in translocating the nucleus in a migrating tissue cell remain unresolved. Previous studies have variously implicated actomyosin-generated pushing or pulling forces on the nucleus, as well as pulling by nucleus-bound microtubule motors. We found that the nucleus in an isolated migrating cell can move forward without any trailing-edge detachment. When a new lamellipodium was triggered with photoactivation of Rac1, the nucleus moved toward the new lamellipodium. This forward motion required both nuclear-cytoskeletal linkages and myosin activity. Apical or basal actomyosin bundles were found not to translate with the nucleus. Although microtubules dampen fluctuations in nuclear position, they are not required for forward translocation of the nucleus during cell migration. Trailing-edge detachment and pulling with a microneedle produced motion and deformation of the nucleus suggestive of a mechanical coupling between the nucleus and the trailing edge. Significantly, decoupling the nucleus from the cytoskeleton with KASH overexpression greatly decreased the frequency of trailing-edge detachment. Collectively, these results explain how the nucleus is moved in a crawling fibroblast and raise the possibility that forces could be transmitted from the front to the back of the cell through the nucleus.     

Integrins and extracellular matrix in mechanotransduction

Integrins bind extracellular matrix fibrils and associate with intracellular actin filaments through a variety of cytoskeletal linker proteins to mechanically connect intracellular and extracellular structures. Each component of the linkage from the cytoskeleton through the integrin-mediated adhesions to the extracellular matrix therefore transmits forces that may derive from both intracellular, myosin-generated contractile forces and forces from outside the cell. These forces activate a wide range of signaling pathways and genetic programs to control cell survival, fate, and behavior. Additionally, cells sense the physical properties of their surrounding environment through forces exerted on integrin-mediated adhesions. This article first summarizes current knowledge about regulation of cell function by mechanical forces acting through integrin-mediated adhesions and then discusses models for mechanotransduction and sensing of environmental forces.     

Mitochondrial displacements in response to nanomechanical forces

Mechanical stress affects and regulates many aspects of the cell, including morphology, growth, differentiation, gene expression and apoptosis. In this study we show how mechanical stress perturbs the intracellular structures of the cell and induces mechanical responses. In order to correlate mechanical perturbations to cellular responses, we used a combined fluorescence-atomic force microscope (AFM) to produce well defined nanomechanical perturbations of 10 nN while simultaneously tracking the real-time motion of fluorescently labelled mitochondria in live cells. The spatial displacement of the organelles in response to applied loads demonstrates the highly dynamic mechanical response of mitochondria in fibroblast cells. The average displacement of all mitochondrial structures analysed showed an increase of approximately 40%, post-perturbation ( approximately 160 nm in comparison to basal displacements of approximately 110 nm). These results show that local forces can produce organelle displacements at locations far from the initial point of contact (up to approximately 40 microm). In order to examine the role of the cytoskeleton in force transmission and its effect on mitochondrial displacements, both the actin and microtubule cytoskeleton were disrupted using Cytochalasin D and Nocodazole, respectively. Our results show that there is no significant change in mitochondrial displacement following indentation after such treatments. These results demonstrate the role of the cytoskeleton in force transmission through the cell and on mitochondrial displacements. In addition, it is suggested that care must be taken when performing mechanical experiments on living cells with the AFM, as these local mechanical perturbations may have significant structural and even biochemical effects on the cell.     

Equilibria of idealized confined astral microtubules and coupled spindle poles

Positioning of the mitotic spindle through the interaction of astral microtubules with the cell boundary often determines whether the cell division will be symmetric or asymmetric. This process plays a crucial role in development. In this paper, a numerical model is presented that deals with the force exerted on the spindle by astral microtubules that are bent by virtue of their confinement within the cell boundary. It is found that depending on parameters, the symmetric position of the spindle can be stable or unstable. Asymmetric stable equilibria also exist, and two or more stable positions can exist simultaneously. The theory poses new types of questions for experimental research. Regarding the cases of symmetric spindle positioning, it is necessary to ask whether the microtubule parameters are controlled by the cell so that the bending mechanics favors symmetry. If they are not, then it is necessary to ask what forces external to the microtubule cytoskeleton counteract the bending effects sufficiently to actively establish symmetry. Conversely, regarding the cases with asymmetry, it is now necessary to investigate whether the cell controls the microtubule parameters so that the bending favors asymmetry apart from any forces that are external to the microtubule cytoskeleton.     

Osmotic Regulation Is Required for Cancer Cell Survival under Solid Stress

For a solid tumor to grow, it must be able to support the compressive stress that is generated as it presses against the surrounding tissue. Although the literature suggests a role for the cytoskeleton in counteracting these stresses, there has been no systematic evaluation of which filaments are responsible or to what degree. Here, using a three-dimensional spheroid model, we show that cytoskeletal filaments do not actively support compressive loads in breast, ovarian, and prostate cancer. However, modulation of tonicity can induce alterations in spheroid size. We find that under compression, tumor cells actively efflux sodium to decrease their intracellular tonicity, and that this is reversible by blockade of sodium channel NHE1. Moreover, although polymerized actin does not actively support the compressive load, it is required for sodium efflux. Compression-induced cell death is increased by both sodium blockade and actin depolymerization, whereas increased actin polymerization offers protective effects and increases sodium efflux. Taken together, these results demonstrate that cancer cells modulate their tonicity to survive under compressive solid stress.     

Apparent stiffness of vimentin intermediate filaments in living cells and its relation with other cytoskeletal polymers

The cytoskeleton is a complex network of interconnected biopolymers intimately involved in the generation and transmission of forces. Several mechanical properties of microtubules and actin filaments have been extensively explored in cells. In contrast, intermediate filaments (IFs) received comparatively less attention despite their central role in defining cell shape, motility and adhesion during physiological processes as well as in tumor progression. Here, we explored relevant biophysical properties of vimentin IFs in living cells combining confocal microscopy and a filament tracking routine that allows localizing filaments with ~20 nm precision. A Fourier-based analysis showed that IFs curvatures followed a thermal-like behavior characterized by an apparent persistence length (lp*) similar to that measured in aqueous solution. Additionally, we determined that certain perturbations of the cytoskeleton affect lp* and the lateral mobility of IFs as assessed in cells in which either the microtubule dynamic instability was reduced or actin filaments were partially depolymerized. Our results provide relevant clues on how vimentin IFs mechanically couple with microtubules and actin filaments in cells and support a role of this network in the response to mechanical stress.     

The mechanical basis of cell rearrangement. I. Epithelial morphogenesis during Fundulus epiboly

Many morphogenetic processes are accomplished by coordinated cell rearrangements. These rearrangements are accompanied by substantial shifts in the neighbor relationships between cells. Here we propose a model for studying morphogenesis in epithelial sheets by directed cell neighbor change. Our model describes cell rearrangements by accounting for the balance of forces between neighboring cells within an epithelium. Cell rearrangement and cell shape changes occur when these forces are not in mechanical equilibrium. We will show that cell rearrangement within the epidermal enveloping layer (EVL) of the teleost fish Fundulus during epiboly can be explained solely in terms of the balance of forces generated among constituent epithelial cells. Within a cell, we account for circumferential elastic forces and the force generated by hydrostatic and osmotic pressure. The model treats epithelial cells as two-dimensional polygons where the mechanical forces are applied to the polygonal nodes. A cell node protrudes or contracts when the nodal forces are not in mechanical equilibrium. In an epithelial sheet, adjacent cells share common boundary nodes; in this way, mechanical force is transmitted from cell to cell, mimicking junctional coupling. These junctional nodes can slide, and nodes may appear or disappear, so that the number of polygonal sides is variable. Computer graphics allows us to compare numerical simulations of the model with time-lapse cinemicroscopy of cell rearrangements in the living embryo, and data obtained from fixed and silver stained embryos. By manipulating the mechanical properties of the model cells we can study the conditions necessary to reproduce normal cell behavior during Fundulus epiboly. We find that simple stress relaxation is sufficient to account for cell rearrangements among interior cells of the EVL when they are isotropically contractile. Experimental observations show that the number of EVL marginal cells continuously decreases throughout epiboly. In order for the simulation to reproduce this behavior, cells at the EVL boundary must generate protrusive forces rather than contractile tension forces. Therefore, the simulation results suggest that the mechanical properties of EVL marginal cells at their leading edge must be quite different from EVL interior cells.