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.     

Spontaneous circulation of active microtubules confined by optical traps

We propose an experiment to demonstrate spontaneous ordering and symmetry breaking of kinesin-driven microtubules confined to an optical trap. Calculations involving the feasibility of such an experiment are first performed which analyze the power needed to confine microtubules and address heating concerns. We then present the results of first-principles simulations of active microtubules confined in such a trap and analyze the types of motion observed by the microtubules as well as the velocity of the surrounding fluid, both near the trap and in the far-field. We find three distinct phases characterized by breaking of distinct symmetries and also analyze the power spectrum of the angular momenta of polymers to further quantify the differences between these phases. Under the correct conditions, microtubules were found to spontaneously align with one another and circle the trap in one direction.     

Volume changes of individual melanosomes measured by scanning force microscopy.

Black pigment cells, melanophores, e.g. located in the epidermis and dermis of frogs, are large flat cells having intracellular black pigment granules, called melanosomes. Due to a large size, high optical contrast, and quick response to drugs, melanophores are attractive as biosensors as well as for model studies of intracellular processes; e.g. organelle transport and G-protein coupled receptors. The geometry of melanosomes from African clawed toad, Xenopus laevis, has been measured using scanning force microscopy (SFM). Three-dimensional images from SFM were used to measure height, width, and length of the melanosomes (100 from aggregated cells and 100 from dispersed cells). The volumes of melanosomes isolated from aggregated and dispersed melanophores were significantly different (P < 0.05, n=200). The average ellipsoidal volume was 0.14+/-0.01 (aggregated) and 0.17+/-0.01 microm3 (dispersed), a difference of 18%. The average major diameter was 810+/-20 and 880+/-20 nm for aggregated and dispersed melanosomes, respectively. To our knowledge, this is the first time SFM has been used to study melanosomes. This may provide an alternative non-destructive technique that may be particularly suitable for studying morphological aspects of various melanin granules.     

Flexural rigidity of singlet microtubules estimated from statistical analysis of their contour lengths and end-to-end distances

Microtubules in solutions, observed under a dark-field microscope, show incessant Brownian movement such as translational, rotational and flexing motion. A large number of microtubules, spontaneously stuck to the under surface of a coverslip, were photographed and the contour lengths and end-to-end distances of their images were measured. From the statistical analysis of the contour lengths and end-to-end distances, a value for the parameter γ representing the flexibility of singlet microtubules was estimated to γ = (6.8 ± 0.8) · 10^?3μm^?1. From the value of γ, the elastic modulus for bending, ε, and Young's modulus, Y, of singlet microtubules were computed to be ε = ～ 10^?16 dyne·cm² and Y = ～ 10⁹ dyne·cm^?2, respectively. The microscopic elastic constant, k, of bonding between two tubulin monomers neighboring along the singlet microtubule was computed to be k = ～ 10² dyne·cm^?1. A singlet microtubule is an order of magnitude as strong against bending and as weak against stretching as an F-actin filament.     

Load-dependent kinetics of force production by smooth muscle myosin measured with optical tweezers

Muscle contraction is driven by the cyclical interaction of myosin with actin, coupled with ATP hydrolysis. Myosin attaches to actin, forming a crossbridge that produces force and movement as it tilts or rocks into subsequent bound states before finally detaching. It has been hypothesized that the kinetics of one or more of these mechanical transitions are dependent on load, allowing muscle to shorten quickly under low load, but to sustain tension economically, with slowly cycling crossbridges under high load conditions. The idea that muscle biochemistry depends on mechanical output is termed the 'Fenn effect'. However, the molecular details of how load affects the kinetics of a single crossbridge are unknown. Here, we describe a new technique based on optical tweezers to rapidly apply force to a single smooth muscle myosin crossbridge. The crossbridge produced movement in two phases that contribute 4 nm + 2 nm of displacement. Duration of the first phase depended in an exponential manner on the amplitude of applied load. Duration of the second phase was much less affected by load, but was significantly shorter at high ATP concentration. The effect of load on the lifetime of the bound crossbridge is to prolong binding when load is high, but to accelerate release when load is low or negative.     

The elasticity of individual titin PEVK exons measured by single molecule atomic force microscopy

The I-band region of the giant muscle protein titin contains a large domain enriched for the amino acids proline, glutamate, valine, and lysine and is denoted the PEVK domain. The PEVK domain of titin encodes a random coil shown to be an important factor in the passive elasticity of titin. Muscle-specific splicing of 116 PEVK exons encodes this domain. It has been proposed that proline contents determine the elasticity of the PEVK polypeptide, where the individual exons code for "flexibility cassettes." To test this hypothesis, we have measured the elasticity of three distinct polypeptides encoded by individual PEVK exons (161, 120 and 184) that varied greatly in their proline contents (7, 14, and 37% respectively) and total PEVK contents (55, 70, and 87%). We used single molecule atomic force microscopy techniques to measure the persistence length, p, of the engineered PEVK proteins. Surprisingly, all three exons 161, 120, and 184 coded for proteins with similar values of persistence length, p = 0.92 +/- 0.38, 0.89 +/- 0.42, and 0.98 +/- 0.4 nm, respectively. We conclude that the PEVK exons encode polypeptides of similar elastic properties, unrelated to their total PEVK contents. Hence, alternative splicing solely adjusts the length of the PEVK domain of titin.     

Sedimentation rates in a Swiss-Italian lake measured with sediment traps

Tripton sedimentation was investigated in the eutrophic Lake Lugano (Ponte Tresa basin) from October 1979 to October 1980. The annual amount of tripton collected was 748 g · m^–2 · y^–1. Phosphorus, nitrogen and organic carbon fluxes into the hypolimnion were estimated to be 1.9, 16.2 and 121 g · m^–2y^–1 respectively. Mineralization rates into the trophogenic layer varied from 11% to 19% per day during summer stratification. The regeneration processes contribute about 60% of the calculated P deficit in the epilimnion. The tripton is decomposed mostly in the metalimnion, out of the euphotic zone; from here the phosphorus is carried back to the overlying waters by diffusion processes.     

Mechanical response of individual collagen fibrils in loaded tendon as measured by atomic force microscopy

A precise analysis of the mechanical response of collagen fibrils in tendon tissue is critical to understanding the ultrastructural mechanisms that underlie collagen fibril interactions (load transfer), and ultimately tendon structure–function. This study reports a novel experimental approach combining macroscopic mechanical loading of tendon with a morphometric ultrascale assessment of longitudinal and cross-sectional collagen fibril deformations. An atomic force microscope was used to characterize diameters and periodic banding (D-period) of individual type-I collagen fibrils within murine Achilles tendons that were loaded to 0%, 5%, or 10% macroscopic nominal strain, respectively. D-period banding of the collagen fibrils increased with increasing tendon strain (2.1% increase at 10% applied tendon strain, p < 0.05), while fibril diameter decreased (8% reduction, p < 0.05). No statistically significant differences between 0% and 5% applied strain were observed, indicating that the onset of fibril (D-period) straining lagged macroscopically applied tendon strains by at least 5%. This confirms previous reports of delayed onset of collagen fibril stretching and the role of collagen fibril kinematics in supporting physiological tendon loads. Fibril strains within the tissue were relatively tightly distributed in unloaded and highly strained tendons, but were more broadly distributed at 5% applied strain, indicating progressive recruitment of collagen fibrils. Using these techniques we also confirmed that collagen fibrils thin appreciably at higher levels of macroscopic tendon strain. Finally, in contrast to prevalent tendon structure–function concepts data revealed that loading of the collagen network is fairly homogenous, with no apparent predisposition for loading of collagen fibrils according to their diameter.     

Dynamic instability of microtubules is regulated by force

Microtubules are long filamentous protein structures that randomly alternate between periods of elongation and shortening in a process termed dynamic instability. The average time a microtubule spends in an elongation phase, known as the catastrophe time, is regulated by the biochemical machinery of the cell throughout the cell cycle. In this light, observed changes in the catastrophe time near cellular boundaries (Brunner, D., and P. Nurse. 2000. Cell. 102:695-704; Komarova, Y.A., I.A. Vorobjev, and G.G. Borisy. 2002. J. Cell Sci. 115:3527-3539) may be attributed to regulatory effects of localized proteins. Here, we argue that the pushing force generated by a microtubule when growing against a cellular object may itself provide a regulatory mechanism of the catastrophe time. We observed an up to 20-fold, force-dependent decrease in the catastrophe time when microtubules grown from purified tubulin were polymerizing against microfabricated barriers. Comparison with catastrophe times for microtubules growing freely at different tubulin concentrations leads us to conclude that force reduces the catastrophe time only by limiting the rate of tubulin addition.     

Temperature dependence rigidity of non-taxol stabilized single microtubules

Competitive inhibitors of lysosomal hydrolases (pharmacological chaperones) have been used to treat some lysosomal storage diseases which result from mis-sense mutations and mis-folded protein but have not been tried in Batten disease, for which there is no current therapy. We synthesized a large number of novel, non-hydrolyzable competitive inhibitors of palmitoyl:protein thioesterase (PPT1) and showed that some could act as chemical chaperones. One inhibitor (CS38: βAGDap(Pal)VKIKK) was taken up by lymphoblasts from patients with mutations leading to the T75P/R151X substitutions and enhanced PPT1 activity 2-fold. A similar 2-fold stimulation with another inhibitor (AcGDap(Palm)GG(R)₇) was observed in patients with a G108R amino acid substitution in PPT1. Residual PPT1 activity in both was thermally unstable at pH 7.4 (but not at 4.7) consistent with a mis-folded, unstable PPT1 degraded by the ER stress response. Patients with null mutations did not respond to the pharmacological chaperones.     

Surface viscoelasticity of individual gram-negative bacterial cells measured using atomic force microscopy

The cell envelope of gram-negative bacteria is responsible for many important biological functions: it plays a structural role, it accommodates the selective transfer of material across the cell wall, it undergoes changes made necessary by growth and division, and it transfers information about the environment into the cell. Thus, an accurate quantification of cell mechanical properties is required not only to understand physiological processes but also to help elucidate the relationship between cell surface structure and function. We have used a novel, atomic force microscopy (AFM)-based approach to probe the mechanical properties of single bacterial cells by applying a constant compressive force to the cell under fluid conditions while measuring the time-dependent displacement (creep) of the AFM tip due to the viscoelastic properties of the cell. For these experiments, we chose a representative gram-negative bacterium, Pseudomonas aeruginosa PAO1, and we used regular V-shaped AFM cantilevers with pyramid-shaped and colloidal tips. We find that the cell response is well described by a three-element mechanical model which describes an effective cell spring constant, k(1), and an effective time constant, tau, for the creep deformation. Adding glutaraldehyde, an agent that increases the covalent bonding of the cell surface, produced a significant increase in k(1) together with a significant decrease in tau. This work represents a new attempt toward the understanding of the nanomechanical properties of single bacteria while they are under fluid conditions, which could be of practical value for elucidating, for instance, the biomechanical effects of drugs (such as antibiotics) on pathogens.     

Temperature dependence of the flexural rigidity of single microtubules

Although the flexural rigidity of a microtubule has previously been estimated by various methods, its temperature dependence has never been systematically examined. Here, we measured the flexural rigidity of a single taxol-stabilized microtubule from thermal fluctuation of the free end of a microtubule, the other end of which was fixed, at different temperatures; the results showed that the flexural rigidity is 2.54 × 10⁻²⁴ N m² independent of temperature in the range of 20-35 °C. Next, we applied temperature pulse microscopy (TPM) [K. Kawaguchi, S. Ishiwata, Thermal activation of single kinesin molecules with temperature pulse microscopy. Cell Motil. Cytoskeleton 49 (2001) 41-47; H. Kato, T. Nishizaka, T. Iga, K. Kinosita Jr., S. Ishiwata, Imaging of thermal activation of actomyosin motors. Proc. Natl. Acad. Sci. USA 96 (1999) 9602-9606], which created the temperature gradient (1-2 °C/μm) along a microtubule gliding on kinesins in the presence of ATP. As a result, the gliding microtubule was buckled between two interacting kinesin molecules, when the microtubule had been propelled faster by the rear kinesin (higher temperature) and slower by the front one (lower temperature). By estimating the critical force to induce buckling of a microtubule, the flexural rigidity of a microtubule was estimated to be (2.7-7.8) × 10⁻²⁴ N m², which was in good agreement with the value determined above. We discuss the buckling process based on the temperature dependence of the force-velocity relationship of kinesin motility.     

Length-dependence of flexural rigidity as a result of anisotropic elastic properties of microtubules

Unexplained length-dependence of flexural rigidity and Young's modulus of microtubules is studied using an orthotropic elastic shell model. It is showed that vibration frequencies and buckling load predicted by the accurate orthotropic shell model 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 this inaccuracy of the isotropic beam model used by all previous researchers that leads to reported lower flexural rigidity and Young's modulus for shorter microtubules. In particular, much lower shear modulus and circumferential Young's modulus, which only weaken flexural rigidity of shorter microtubules, are responsible for the observed length-dependence of the flexural rigidity. These results confirm that longitudinal Young's modulus of microtubules is length-independent, and the observed length-dependence of the flexural rigidity and Young's modulus is a result of strongly anisotropic elastic properties of microtubules which have a length-dependent weakening effect on flexural rigidity of shorter microtubules.     

Biomolecular interactions measured by atomic force microscopy

Atomic force microscopy (AFM) is nowadays frequently applied to determine interaction forces between biological molecules. Starting with the detection of the first discrete unbinding forces between ligands and receptors by AFM only several years ago, measurements have become more and more quantitative. At the same time, theories have been developed to describe and understand the dynamics of the unbinding process and experimental techniques have been refined to verify this theory. In addition, the detection of molecular recognition forces has been exploited to map and image the location of binding sites. In this review we discuss the important contributions that have led to the development of this field. In addition, we emphasize the potential of chemically well-defined surface modification techniques to further improve reproducible measurements by AFM. This increased reproducibility will pave the way for a better understanding of molecular interactions in cell biology.     

A bending mode analysis for growing microtubules: evidence for a velocity-dependent rigidity

Microtubules are dynamic protein polymers that continuously switch between elongation and rapid shrinkage. They have an exceptional bending stiffness that contributes significantly to the mechanical properties of eukaryotic cells. Measurements of the persistence length of microtubules have been published since 10 years but the reported values vary over an order of magnitude without an available explanation. To precisely measure the rigidity of microtubules in their native growing state, we adapted a previously developed bending mode analysis of thermally driven shape fluctuations to the case of an elongating filament that is clamped at one end. Microtubule shapes were quantified using automated image processing, allowing for the characterization of up to five bending modes. When taken together with three other less precise measurements, our rigidity data suggest that fast-growing microtubules are less stiff than slow-growing microtubules. This would imply that care should be taken in interpreting rigidity measurements on stabilized microtubules whose growth history is not known. In addition, time analysis of bending modes showed that higher order modes relax more slowly than expected from simple hydrodynamics, possibly by the effects of internal friction within the microtubule.     

Flexural rigidity of marginal bands isolated from erythrocytes of the newt

The marginal band is a bundle of microtubules residing at the periphery of nucleated erythrocytes of nonmammalian vertebrates and some invertebrates. Marginal bands from erythrocytes of the newt (Notopthalmus viridescens) were isolated from the cells as intact structures by treatment with detergent and either mild protease or high salt. Isolated bands were subjected to mechanical testing by stretching the band between a glass microhook and a calibrated glass fiber. The deflection of the fiber provided a measure of the force on the band. The flexural rigidity of the band was determined from measurements of the band deformation as a function of applied force. Bands isolated with either of two proteases (pepsin or elastase) or with high salt exhibited elastic behavior with a flexural rigidity of approximately 9.0 X 10(-12) dyn.cm2. Treatment of bands with chymopapain caused an increase in band rigidity and inelastic behavior. Estimates of the contribution of the band to cellular rigidity are made based on the measurements of the structural properties of the isolated band. The band provides the cell with a large resistance to indentations at the rim and to large extensions, while maintaining a high degree of flexibility in small extensions or flexure.     

Deformability and adhesive force of artificial platelets measured by atomic force microscopy

Platelet glycoprotein GPIaIIa is an adhesive protein that recognizes collagen. We have investigated polymerized albumin particles conjugated with recombinant GPIaIIa (rGPIaIIa-poly Alb) for their platelet-like function. To evaluate the feasibility of these particles to achieve the hemostatic process, we measured the deformability (Young’s modulus and spring constant) and the adhesive force of the particles using atomic force microscopy, which can measure the mechanical properties of individual cells. Our results showed that the Young’s modulus of these particles was 2.3-fold larger than that of natural platelets and 12-fold larger than that of human red blood cells. The Young’s modulus of the particles may have been determined by the properties of the polymerized albumin particle, although the glycoprotein of the platelet surface also contributed to the higher modulus. Our results also showed that the adhesive force of the rGPIaIIa-poly Alb with the collagen ligand was 52% of that of natural platelets. These two mechanical properties (deformability and adhesive force) of cells or particles, such as rGPIaIIa-poly Alb, are important specifications for the optimum design of platelet substitutes.