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.     

Vibration and length-dependent flexural rigidity of protein microtubules using higher order shear deformation theory

Microtubules are hollow cylindrical filaments of the eukaryotic cytoskeleton characterized by extremely low shear modulus. A remarkable controversy has occurred in the literature, regarding the length dependence of flexural rigidity of microtubules predicted by the classical elastic beam model. In this study, a higher order shear deformable beam model for microtubules is employed to study unexplained length-dependent flexural rigidity and Young’s modulus of microtubules reported in the literature. The formulation allows for warping of the cross-section of the microtubule and eliminates the need for using arbitrary shear correction coefficients as in other theories. It is showed that vibration frequencies predicted by the present parabolic shear deformation theory (PSDT) are much lower than that given by the approximate isotropic beam model for shorter microtubules, although the two models give almost identical results for sufficiently long microtubules. It is confirmed that transverse shearing and the warping of the cross-section of microtubules are mainly responsible for the length-dependent flexural rigidity of an isolated microtubule reported in the literature, which cannot be explained by the widely used Euler-Bernoulli beam model. Indeed, the length-dependent flexural rigidity predicted by the present model is found to be in qualitative agreement with the existing experimental data ( [Kurachi et al., 1995] and [Pampaloni et al., 2006]). These results recommend that the parabolic shear deformation-beam theory offers a unified simple 1D model, which can capture the length dependence of flexural rigidity and be applied to various static and dynamic problems of microtubule mechanics.     

Mechanics of microtubule bundles in pillar cells from the inner ear.

The mechanical properties of cross-linked microtubule bundles were measured from outer pillar cells isolated from the mammalian inner ear. Measurements were made using a three-point bending test and were incorporated into a mathematical model designed to distinguish between the stiffness contributions from microtubules and their cross-linking proteins. Outer pillar cells were composed of 1000-3000 parallel bundled microtubules in a square array that was interdigitated and cross-linked with actin filaments. The average midpoint bending stiffness of intact cells was 7 x 10(-4) N/m. After removal of both the actin filaments and cross-links with detergent in the presence of DNase I, the square array was disrupted and the stiffness decreased by a factor of 4, to 1.7 x 10(-4) N/m. The bending modulus for individual microtubules was calculated to be 7 x 10(-23) Nm2, and the Young's modulus for these 15 protofilament microtubules was 2 x 10(9) Pa. The shear modulus between microtubules in intact cells was calculated to be 10(3) Pa. It was concluded that cross-linking proteins provided shear resistance between microtubules, which resulted in a fourfold increase in stiffness. The model can be used to estimate the mechanical properties of cross-linked microtubule bundles in cells from which direct measurements are not available.     

Wave propagation in protein microtubules modeled as orthotropic elastic shells including transverse shear deformations

Wave propagation along the microtubules is one of the issues of major concern in various microtubule cellular functions. In this study, the general wave propagation behavior in protein microtubules is investigated based on a first-order shear deformation shell theory for orthotropic materials, with particular emphasis on the role of strongly anisotropic elastic properties of microtubules. According to experimental observation, the first-order shear deformation theory is used for the modeling of microtubule walls. A general displacement representation is introduced and a type of coupled polynomial eigenvalue problem is developed. Numerical examples describe the effects of shear deformation and rotary inertia on wave velocities in orthotropic microtubules. Finally, the influences of the microtubule shear modulus, axial external force, effective thickness and material temperature dependency on wave velocities along the microtubule protofilaments, helical pathway and radial directions are elucidated. Most results presented in the present investigation have been absent from the literature for the wave propagation in microtubules.     

Interaction between Microtubules and the Drosophila Formin Cappuccino and Its Effect on Actin Assembly

Formin family actin nucleators are potential coordinators of the actin and microtubule cytoskeletons, as they can both nucleate actin filaments and bind microtubules in vitro. To gain a more detailed mechanistic understanding of formin-microtubule interactions and formin-mediated actin-microtubule cross-talk, we studied microtubule binding by Cappuccino (Capu), a formin involved in regulating actin and microtubule organization during Drosophila oogenesis. We found that two distinct domains within Capu, FH2 and tail, work together to promote high-affinity microtubule binding. The tail domain appears to bind microtubules through nonspecific charge-based interactions. In contrast, distinct residues within the FH2 domain are important for microtubule binding. We also report the first visualization of a formin polymerizing actin filaments in the presence of microtubules. Interestingly, microtubules are potent inhibitors of the actin nucleation activity of Capu but appear to have little effect on Capu once it is bound to the barbed end of an elongating filament. Because Capu does not simultaneously bind microtubules and assemble actin filaments in vitro, its actin assembly and microtubule binding activities likely require spatial and/or temporal regulation within the Drosophila oocyte.     

Multi-curve fitting and tubulin-lattice signal removal for structure determination of large microtubule-based motors

Revealing high-resolution structures of microtubule-associated proteins (MAPs) is critical for understanding their fundamental roles in various cellular activities, such as cell motility and intracellular cargo transport. Nevertheless, large flexible molecular motors that dynamically bind and release microtubule networks are challenging for cryo-electron microscopy (cryo-EM). Traditional structure determination of MAPs bound to microtubules needs alignment information from the reconstruction of microtubules, which cannot be readily applied to large MAPs without a fixed binding pattern. Here, we developed a comprehensive approach to estimate the microtubule networks (multi-curve fitting), model the tubulin-lattice signals, and remove them (tubulin-lattice subtraction) from the raw cryo-EM micrographs. The approach does not require an ordered binding pattern of MAPs on microtubules, nor does it need a reconstruction of the microtubules. We demonstrated the capability of our approach using the reconstituted outer-arm dynein (OAD) bound to microtubule doublets. The tubulin-lattice subtraction improves the OAD alignment, thus leading to high-resolution reconstructions. In addition, the multi-curve fitting approach provides an accurate automatic alternative method to pick or segment filaments in 2D images and potentially in 3D tomograms. The accuracy of our approach has been demonstrated by using several other biological filaments. Our work provides a new tool to determine high-resolution structures of large MAPs bound to curved microtubule networks.     

Association of actin filaments with axonal microtubule tracts

Axoplasmic organelles move on actin as well as microtubules in vitro and axons contain a large amount of actin, but little is known about the organization and distribution of actin filaments within the axon. Here we undertake to define the relationship of the microtubule bundles typically found in axons to actin filaments by applying three microscopic techniques: laser-scanning confocal microscopy of immuno-labeled squid axoplasm; electronmicroscopy of conventionally prepared thin sections; and electronmicroscopy of touch preparations-a thin layer of axoplasm transferred to a specimen grid and negatively stained. Light microscopy shows that longitudinal actin filaments are abundant and usually coincide with longitudinal microtubule bundles. Electron microscopy shows that microfilaments are interwoven with the longitudinal bundles of microtubules. These bundles maintain their integrity when neurofilaments are extracted. Some, though not all microfilaments decorate with the S1 fragment of myosin, and some also act as nucleation sites for polymerization of exogenous actin, and hence are definitively identified as actin filaments. These actin filaments range in minimum length from 0.5 to 1.5 µm with some at least as long as 3.5 µm. We conclude that the microtubule-based tracks for fast organelle transport also include actin filaments. These actin filaments are sufficiently long and abundant to be ancillary or supportive of fast transport along microtubules within bundles, or to extend transport outside of the bundle. These actin filaments could also be essential for maintaining the structural integrity of the microtubule bundles.     

Immunodetection of cytoskeletal structures and the Eg5 motor protein on deep-etch replicas of Xenopus egg cortices isolated during the cortical rotation

Summary— We have developed a new method for immunogold detection on deep-etch replicas of isolated Xenopus egg cortices in order to examine the interactions of different cortical elements in three dimensions at high resolution. We have applied this technique to vegetal cortices isolated during the second half of the first cell cycle. The vegetal cortical region at this time is the site of cellular machinery responsible for the ‘cortical rotation’. The entire cortex translocates with respect to the inner cytoplasm, relocating dorsalising determinants to the future dorsal side of the egg. The aligned microtubules in the shear zone between cytoplasm and cortex, implicated in the cortical rotation, were found to be organised as interweaving loose bundles. Interleaved amongst these aligned microtubules were extensive sheets of ER lying in layers parallel to the egg surface. Cytokeratin filaments were found to associate closely with the microtubules over short stretches. Putative actin filaments were present in the shear zone and in the cortex. Eg5, an abundant kinesin-related microtubule motor protein, and candidate for a role in generating cortical rotation movement, showed an almost exclusive localisation to microtubules. Immunofluorescence studies of cortices treated with detergent to disrupt ER or cold to depolymerise microtubules confirmed that Eg5 associates primarily with microtubules. We propose revised models for the mechanism of cortical rotation based on these observations and conclude that Eg5 is unlikely to move ER relative to microtubules during the cortical rotation.     

Vaults bind directly to microtubules via their caps and not their barrels

Vaults are large (13 Mda) ribonucleoprotein particles that are especially abundant in multidrug resistant cancer cells and have been implicated in nucleocytoplasmic drug transport. To understand how these large barrel-shaped complexes are transported through the cytosol, we examined the association of vaults with microtubules both in vitro and in vivo. Within cells, a subpopulation of vaults clearly associates with microtubules, and these vaults remain associated with tubulin dimers/oligomers when microtubules are disassembled by nocodazole treatment. In vitro, a microtubule-pull down assay using highly purified rat vaults and reassembled microtubules reveals that vaults exhibit concentration-dependent binding to microtubules that does not require the carboxyl terminal end of tubulin. Remarkably, negative staining for electron microscopy reveals that vault binding to microtubules is mediated by the vault caps; more than 82% of bound vaults attach to the microtubule lattice with their long axes perpendicular to the long axis of the microtubule. Five to six vault particles were bound per micron of microtubule, with no crosslinking of microtubules observed, suggesting that only one end of the vault can bind microtubules. Taken together, the data support the model of vaults as barrel-shaped containers that transiently interact with microtubules.     

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.     

Myosin-Va binds to and mechanochemically couples microtubules to actin filaments

Myosin-Va was identified as a microtubule binding protein by cosedimentation analysis in the presence of microtubules. Native myosin-Va purified from chick brain, as well as the expressed globular tail domain of this myosin, but not head domain bound to microtubule-associated protein-free microtubules. Binding of myosin-Va to microtubules was saturable and of moderately high affinity (approximately 1:24 Myosin-Va:tubulin; Kd = 70 nM). Myosin-Va may bind to microtubules via its tail domain because microtubule-bound myosin-Va retained the ability to bind actin filaments resulting in the formation of cross-linked gels of microtubules and actin, as assessed by fluorescence and electron microscopy. In low Ca2+, ATP addition induced dissolution of these gels, but not release of myosin-Va from MTs. However, in 10 microM Ca2+, ATP addition resulted in the contraction of the gels into aster-like arrays. These results demonstrate that myosin-Va is a microtubule binding protein that cross-links and mechanochemically couples microtubules to actin filaments.     

Cytoskeletal networks and the regulation of cardiac contractility: microtubules, hypertrophy, and cardiac dysfunction

The cytoskeleton as classically defined for eukaryotic cells consists of three systems of protein filaments: the microtubules, the intermediate filaments, and the microfilaments. In mature striated muscle such as the heart of the adult mammal, these three types of cytoskeletal filaments are superimposed spatially on the myofilaments, a specialized system of contractile protein filaments. Each of these systems of protein filaments has the potential to respond in an adaptive or maladaptive manner during load-induced hypertrophic cardiac growth. However, the extent to which such hypertrophy is compensatory is also critically dependent on the type of hemodynamic overload that serves as the hypertrophic stimulus. Thus cardiac hypertrophy is not intrinsically maladaptive; rather, it is the nature of the inducing load rather than hypertrophy itself that is responsible, through effects on structural and/or regulatory proteins, for the frequent deterioration of initially compensatory hypertrophy into the congestive heart failure state. As one example reviewed here of this load specificity of maladaptation, increased microtubule network density is a persistent feature of severely pressure-overloaded, hypertrophied, and failing myocardium that imposes a primarily viscous load on active myofilaments during contraction.     

Electric field generated by axial longitudinal vibration modes of microtubule

Microtubules are electrically polar structures fulfilling prerequisites for generation of oscillatory electric field in the kHz to GHz region. Energy supply for excitation of elasto-electrical vibrations in microtubules may be provided from GTP-hydrolysis; motor protein–microtubule interactions; and energy efflux from mitochondria. We calculated electric field generated by axial longitudinal vibration modes of microtubules for random, and coherent excitation. In case of coherent excitation of vibrations, the electric field intensity is highest at the end of microtubule. The dielectrophoretic force exerted by electric field on the surrounding molecules will influence the kinetics of microtubule polymerization via change in the probability of the transport of charge and mass particles. The electric field generated by vibrations of electrically polar cellular structures is expected to play an important role in biological self-organization.     

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.     

The Dynamic Behavior of Individual Microtubules Associated with Chromosomes In Vitro

Mitotic movements of chromosomes are usually coupled to the elongation and shortening of the microtubules to which they are bound. The lengths of kinetochore-associated microtubules change by incorporation or loss of tubulin subunits, principally at their chromosome-bound ends. We have reproduced aspects of this phenomenon in vitro, using a real-time assay that displays directly the movements of individual chromosome-associated microtubules as they elongate and shorten. Chromosomes isolated from cultured Chinese hamster ovary cells were adhered to coverslips and then allowed to bind labeled microtubules. In the presence of tubulin and GTP, these microtubules could grow at their chromosome-bound ends, causing the labeled segments to move away from the chromosomes, even in the absence of ATP. Sometimes a microtubule would switch to shortening, causing the direction of movement to change abruptly. The link between a microtubule and a chromosome was mechanically strong; 15 pN of tension was generally insufficient to detach a microtubule, even though it could add subunits at the kinetochore–microtubule junction. The behavior of the microtubules in vitro was regulated by the chromosomes to which they were bound; the frequency of transitions from polymerization to depolymerization was decreased, and the speed of depolymerization-coupled movement toward chromosomes was only one-fifth the rate of shortening for microtubules free in solution. Our results are consistent with a model in which each microtubule interacts with an increasing number of chromosome-associated binding sites as it approaches the kinetochore.     

Nucleation and growth of microtubules from gamma-tubulin-functionalized gold surfaces

Microtubules are protein filaments that are emerging as potential building blocks in manufacturing nanoscale structures and systems such as interconnecting nanowires. Future development in using microtubules necessitates a control of their nucleation and growth. We report the controlled nucleation and growth of microtubules from functionalized gold on a hydrophilic oxidized silicon wafer. The gold substrate is functionalized with gamma-tubulin, a natural nucleating agent for microtubule growth. We show that the attached gamma-tubulin retains its biological functionality and leads to nucleation and assembly of microtubules from the functionalized gold surface. We also analyze the interplay between the geometry of the nucleating substrates and the morphology of microtubules arrays and networks grown from them. We consider two geometrical arrangements of the substrates: (a) a square lattice of small gold pads on a hydrophilic oxidized silicon wafer and (b) a large flat surface. Fluorescence microscopy and scanning electron microscopy are employed to provide a detailed characterization of the length and morphology of the nucleated and grown microtubules. The observed microtubule morphologies are modeled, analyzed and discussed within the context of reaction-diffusion and nucleation controlled processes.     

Flexural Rigidity Measurements of Biopolymers Using Gliding Assays

Microtubules are cytoskeletal polymers which play a role in cell division, cell mechanics, and intracellular transport. Each of these functions requires microtubules that are stiff and straight enough to span a significant fraction of the cell diameter. As a result, the microtubule persistence length, a measure of stiffness, has been actively studied for the past two decades¹. Nonetheless, open questions remain: short microtubules are 10-50 times less stiff than long microtubules^2-4, and even long microtubules have measured persistence lengths which vary by an order of magnitude^5-9.Here, we present a method to measure microtubule persistence length. The method is based on a kinesin-driven microtubule gliding assay¹⁰. By combining sparse fluorescent labeling of individual microtubules with single particle tracking of individual fluorophores attached to the microtubule, the gliding trajectories of single microtubules are tracked with nanometer-level precision. The persistence length of the trajectories is the same as the persistence length of the microtubule under the conditions used¹¹. An automated tracking routine is used to create microtubule trajectories from fluorophores attached to individual microtubules, and the persistence length of this trajectory is calculated using routines written in IDL.This technique is rapidly implementable, and capable of measuring the persistence length of 100 microtubules in one day of experimentation. The method can be extended to measure persistence length under a variety of conditions, including persistence length as a function of length along microtubules. Moreover, the analysis routines used can be extended to myosin-based acting gliding assays, to measure the persistence length of actin filaments as well.     

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.