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.     

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.     

Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape

Microtubules are long, proteinaceous filaments that perform structural functions in eukaryotic cells by defining cellular shape and serving as tracks for intracellular motor proteins. We report the first accurate measurements of the flexural rigidity of microtubules. By analyzing the thermally driven fluctuations in their shape, we estimated the mean flexural rigidity of taxol-stabilized microtubules to be 2.2 x 10(-23) Nm2 (with 6.4% uncertainty) for seven unlabeled microtubules and 2.1 x 10(-23) Nm2 (with 4.7% uncertainty) for eight rhodamine-labeled microtubules. These values are similar to earlier, less precise estimates of microtubule bending stiffness obtained by modeling flagellar motion. A similar analysis on seven rhodamine-phalloidin- labeled actin filaments gave a flexural rigidity of 7.3 x 10(-26) Nm2 (with 6% uncertainty), consistent with previously reported results. The flexural rigidity of these microtubules corresponds to a persistence length of 5,200 microns showing that a microtubule is rigid over cellular dimensions. By contrast, the persistence length of an actin filament is only approximately 17.7 microns, perhaps explaining why actin filaments within cells are usually cross-linked into bundles. The greater flexural rigidity of a microtubule compared to an actin filament mainly derives from the former's larger cross-section. If tubulin were homogeneous and isotropic, then the microtubule's Young's modulus would be approximately 1.2 GPa, similar to Plexiglas and rigid plastics. Microtubules are expected to be almost inextensible: the compliance of cells is due primarily to filament bending or sliding between filaments rather than the stretching of the filaments themselves.     

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.     

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.     

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.     

An epidermal plakin that integrates actin and microtubule networks at cellular junctions

Plakins are cytoskeletal linker proteins initially thought to interact exclusively with intermediate filaments (IFs), but recently were found to associate additionally with actin and microtubule networks. Here, we report on ACF7, a mammalian orthologue of the Drosophila kakapo plakin genetically involved in epidermal-muscle adhesion and neuromuscular junctions. While ACF7/kakapo is divergent from other plakins in its IF-binding domain, it has at least one actin (K(d) = 0.35 microM) and one microtubule (K(d) approximately 6 microM) binding domain. Similar to its fly counterpart, ACF7 is expressed in the epidermis. In well spread epidermal keratinocytes, ACF7 discontinuously decorates the cytoskeleton at the cell periphery, including microtubules (MTs) and actin filaments (AFs) that are aligned in parallel converging at focal contacts. Upon calcium induction of intercellular adhesion, ACF7 and the cytoskeleton reorganize at cell-cell borders but with different kinetics from adherens junctions and desmosomes. Treatments with cytoskeletal depolymerizing drugs reveal that ACF7's cytoskeletal association is dependent upon the microtubule network, but ACF7 also appears to stabilize actin at sites where microtubules and microfilaments meet. We posit that ACF7 may function in microtubule dynamics to facilitate actin-microtubule interactions at the cell periphery and to couple the microtubule network to cellular junctions. These attributes provide a clear explanation for the kakapo mutant phenotype in flies.     

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.     

Lateral Motion and Bending of Microtubules Studied with a New Single-Filament Tracking Routine in Living Cells

The cytoskeleton is involved in numerous cellular processes such as migration, division, and contraction and provides the tracks for transport driven by molecular motors. Therefore, it is very important to quantify the mechanical behavior of the cytoskeletal filaments to get a better insight into cell mechanics and organization. It has been demonstrated that relevant mechanical properties of microtubules can be extracted from the analysis of their motion and shape fluctuations. However, tracking individual filaments in living cells is extremely complex due, for example, to the high and heterogeneous background. We introduce a believed new tracking algorithm that allows recovering the coordinates of fluorescent microtubules with ∼9 nm precision in in vitro conditions. To illustrate potential applications of this algorithm, we studied the curvature distributions of fluorescent microtubules in living cells. By performing a Fourier analysis of the microtubule shapes, we found that the curvatures followed a thermal-like distribution as previously reported with an effective persistence length of ∼20 μm, a value significantly smaller than that measured in vitro. We also verified that the microtubule-associated protein XTP or the depolymerization of the actin network do not affect this value; however, the disruption of intermediate filaments decreased the persistence length. Also, we recovered trajectories of microtubule segments in actin or intermediate filament-depleted cells, and observed a significant increase of their motion with respect to untreated cells showing that these filaments contribute to the overall organization of the microtubule network. Moreover, the analysis of trajectories of microtubule segments in untreated cells showed that these filaments presented a slower but more directional motion in the cortex with respect to the perinuclear region, and suggests that the tracking routine would allow mapping the microtubule dynamical organization in cells.     

Mechanics of microtubules

Microtubules are rigid cytoskeletal filaments, and their mechanics affect cell morphology and cellular processes. For instance, microtubules for the support structures for extended morphologies, such as axons and cilia. Further, microtubules act as tension rods to pull apart chromosomes during cellular division. Unlike other cytoskeletal filaments (e.g., actin) that work as large networks, microtubules work individually or in small groups, so their individual mechanical properties are quite important to their cellular function. In this review, we explore the past work on the mechanics of individual microtubules, which have been studied for over a quarter of a century. We also present some prospective on future endeavors to determine the molecular mechanisms that control microtubule rigidity.     

Hypaphorine, an indole-3-acetic acid antagonist delivered by the ectomycorrhizal fungus Pisolithus tinctorius, induces reorganisation of actin and the microtubule cytoskeleton in Eucalyptus globulus ssp bicostata root hairs

Hypaphorine, an indole alkaloid from the ectomycorrhizal fungus Pisolithus tinctorius Coker & Couch., counteracts indole-3-acetic acid (IAA) activity and controls the rate of root hair elongation in Eucalyptus globulus ssp. bicostata. The present investigation shows that hypaphorine changes cytoskeletal organisation in elongating root hairs of the host. The actin cytoskeleton was investigated by two different fixation and labelling procedures, which gave similar results. In control root hairs, actin organisation was characterised by (i) an actin cap at the very tip region, (ii) a subapical region with reduced labelling and containing fine actin filaments, and (iii) axial bundles of actin filaments running from the subapical part to the base of the root hair. In the hypaphorine-treated root hairs no actin cap was distinguished. The fine actin filaments occurring in the subapical region were replaced by a few thick actin filament bundles that extended from the subapical region toward the root hair tip. In the hypaphorine-treated hairs the total number of actin filament bundles along most of the root hair length was significantly reduced, presumably due to aggregation of pre-existing actin filaments. The first signs of alteration to the cytoskeleton could be detected as soon as 15 min after hypaphorine treatment. In hypaphorine-treated, but not in control root hairs, a patch of aggregated microtubules regularly occurred at a distance of approximately 10 m from the tip, possibly as a consequence of changes induced by hypaphorine in the actin cytoskeleton. The hypaphorine-induced aggregations in the actin and microtubule cytoskeletons could stabilise the structure of cytoskeletal elements, which in turn could hinder the vesicle delivery at the tip necessary for elongation. Such cytoskeletal alterations may be a consequence of the antagonism between IAA and hypaphorine. The latter view was supported by restoration of the actin cytoskeleton in hypaphorine-treated root hairs by IAA application.     

SB401, a pollen-specific protein from Solanum berthaultii, binds to and bundles microtubules and F-actin

We characterize a novel, pollen-specific, microtubule-associated protein, SB401, found in Solanum berthaultii. This protein binds to and bundles taxol-stabilized microtubules and enhances tubulin polymerization in a concentration-dependent manner, particularly at lower temperatures. Electron microscopy revealed that the protein decorates the entire length of microtubules. Cross-linking and electrophoresis studies showed that SB401 protein forms dimers, and suggest that dimerization could account for bundling. Double immunofluorescent staining of pollen tubes of S. berthaultii showed that SB401 protein co-localized with cortical microtubule bundles. SB401 protein also binds to and bundles actin filaments, and could connect actin filaments to microtubules. SB401 protein had a much higher affinity for microtubules than for actin filaments. In the presence of both cytoskeletal elements, the protein preferentially bound microtubules to form bundles. These results demonstrate that SB401 protein may have important roles in organizing the cytoskeleton in pollen tubes.     

Effects of microtubule disruption on force, velocity, stiffness and [Ca(2+)](i) in porcine coronary arteries

Force generated by smooth muscle cells is believed to result from the interaction of actin and myosin filaments and is regulated through phosphorylation of the myosin regulatory light chain (LC(20)). The role of other cytoskeleton filaments, such as microtubules and intermediate filaments, in determining the mechanical output of smooth muscle is unclear. In cultured fibroblasts, microtubule disruption results in large increases in force similar to contractions associated with LC(20) phosphorylation (15). One hypothesis, the "tensegrity" or "push-pull" model, attributes this increase in force to the disruption of microtubules functioning as rigid struts to resist force generated by actin-myosin interaction (9). In porcine coronary arteries, the disruption of microtubules by nocodazole (11 microM) also elicited moderate but significant increases in isometric force (10-40% of a KCl contracture), which could be blocked or reversed by taxol (a microtubule stabilizer). We tested whether this nocodazole-induced force was accompanied by changes in coronary artery stiffness or unloaded shortening velocity, parameters likely to be highly sensitive to microtubule resistance elements. Few changes were seen, ruling out push-pull mechanisms for the increase in force by nocodazole. In contrast, the intracellular calcium concentration, measured by fura 2 in the intact artery, was increased by nocodazole in parallel with force, and this was inhibited and/or reversed by taxol. Our results indicate that microtubules do not significantly contribute to vascular smooth muscle mechanical characteristics but, importantly, may play a role in modulation of Ca(2+) signal transduction.     

Lateral Motion and Bending of Microtubules Studied with a New Single-Filament Tracking Routine in Living Cells

The cytoskeleton is involved in numerous cellular processes such as migration, division, and contraction and provides the tracks for transport driven by molecular motors. Therefore, it is very important to quantify the mechanical behavior of the cytoskeletal filaments to get a better insight into cell mechanics and organization. It has been demonstrated that relevant mechanical properties of microtubules can be extracted from the analysis of their motion and shape fluctuations. However, tracking individual filaments in living cells is extremely complex due, for example, to the high and heterogeneous background. We introduce a believed new tracking algorithm that allows recovering the coordinates of fluorescent microtubules with ∼9 nm precision in in vitro conditions. To illustrate potential applications of this algorithm, we studied the curvature distributions of fluorescent microtubules in living cells. By performing a Fourier analysis of the microtubule shapes, we found that the curvatures followed a thermal-like distribution as previously reported with an effective persistence length of ∼20 μm, a value significantly smaller than that measured in vitro. We also verified that the microtubule-associated protein XTP or the depolymerization of the actin network do not affect this value; however, the disruption of intermediate filaments decreased the persistence length. Also, we recovered trajectories of microtubule segments in actin or intermediate filament-depleted cells, and observed a significant increase of their motion with respect to untreated cells showing that these filaments contribute to the overall organization of the microtubule network. Moreover, the analysis of trajectories of microtubule segments in untreated cells showed that these filaments presented a slower but more directional motion in the cortex with respect to the perinuclear region, and suggests that the tracking routine would allow mapping the microtubule dynamical organization in cells.     

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.     

Exploring the mechanical properties of single vimentin intermediate filaments by atomic force microscopy

Intermediate filaments (IFs), together with actin filaments and microtubules, compose the cytoskeleton. Among other functions, IFs impart mechanical stability to cells when exposed to mechanical stress and act as a support when the other cytoskeletal filaments cannot keep the structural integrity of the cells. Here we present a study on the bending properties of single vimentin IFs in which we used an atomic force microscopy (AFM) tip to elastically deform single filaments hanging over a porous membrane. We obtained a value for the bending modulus of non-stabilized IFs between 300 MPa and 400 MPa. Our results together with previous ones suggest that IFs present axial sliding between their constitutive building blocks and therefore have a bending modulus that depends on the filament length. Measurements of glutaraldehyde-stabilized filaments were also performed to reduce the axial sliding between subunits and therefore provide a lower limit estimate of the Young's modulus of the filaments. The results show an increment of two to three times in the bending modulus for the stabilized IFs with respect to the non-stabilized ones, suggesting that the Young's modulus of vimentin IFs should be around 900 MPa or higher.     

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.     

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.     

Cytoskeletal dynamics and transport in growth cone motility and axon guidance

Recent studies indicate the actin and microtubule cytoskeletons are a final common target of many signaling cascades that influence the developing neuron. Regulation of polymer dynamics and transport are crucial for the proper growth cone motility. This review addresses how actin filaments, microtubules, and their associated proteins play crucial roles in growth cone motility, axon outgrowth, and guidance. We present a working model for cytoskeletal regulation of directed axon outgrowth. An important goal for the future will be to understand the coordinated response of the cytoskeleton to signaling cascades induced by guidance receptor activation.     

Cytoskeletal bundle mechanics

The mechanical properties of cytoskeletal actin bundles play an essential role in numerous physiological processes, including hearing, fertilization, cell migration, and growth. Cells employ a multitude of actin-binding proteins to actively regulate bundle dimensions and cross-linking properties to suit biological function. The mechanical properties of actin bundles vary by orders of magnitude depending on diameter and length, cross-linking protein type and concentration, and constituent filament properties. Despite their importance to cell function, the molecular design principles responsible for this mechanical behavior remain unknown. Here, we examine the mechanics of cytoskeletal bundles using a molecular-based model that accounts for the discrete nature of constituent actin filaments and their distinct cross-linking proteins. A generic competition between filament stretching and cross-link shearing determines three markedly different regimes of mechanical response that are delineated by the relative values of two simple design parameters, revealing the universal nature of bundle-bending mechanics. In each regime, bundle-bending stiffness displays distinct scaling behavior with respect to bundle dimensions and molecular composition, as observed in reconstituted actin bundles in vitro. This mechanical behavior has direct implications on the physiological bending, buckling, and entropic stretching behavior of cytoskeletal processes, as well as reconstituted actin systems. Results are used to predict the bending regimes of various in vivo cytoskeletal bundles that are not easily accessible to experiment and to generate hypotheses regarding implications of the isolated behavior on in vivo bundle function.