Analysis of microtubule curvature

The microtubule-severing protein UNC-45A preferentially binds to curved microtubules and counteracts the microtubule-straightening effects of Taxol

Uncoordinated protein 45A (UNC-45A) is the only known ATP-independent microtubule (MT)-severing protein. Thus, it severs MTs via a novel mechanism. In vitro and in cells, UNC-45A-mediated MT severing is preceded by the appearance of MT bends. While MTs are stiff biological polymers, in cells, they often curve, and the result of this curving can be breaking off. The contribution of MT-severing proteins on MT lattice curvature is largely undefined. Here, we show that UNC-45A curves MTs. Using in vitro biophysical reconstitution and total internal fluorescence microscopy analysis, we show that UNC-45A is enriched in the areas where MTs are curved versus the areas where MTs are straight. In cells, we show that UNC-45A overexpression increases MT curvature and its depletion has the opposite effect. We also show that this effect occurs is independent of actomyosin contractility. Lastly, we show for the first time that in cells, Paclitaxel straightens MTs, and that UNC-45A can counteracts the MT-straightening effects of the drug.

The Microtubule Severing Protein UNC-45A Counteracts the Microtubule Straightening Effects of Taxol

UNC-45A is the only known ATP-independent microtubule (MT) severing protein. Thus, it severs MTs via a novel mechanism. In vitro and in cells UNC-45A-mediated MT severing is preceded by the appearance of MT bends. While MTs are stiff biological polymers, in cells, they often curve, and the result of this curving can be breaking off. The contribution of MT severing proteins on MT lattice curvature is largely undefined. Here we show that UNC-45A curves MTs. Using in vitro biophysical reconstitution and TIRF microscopy analysis, we show that UNC-45A is enriched in the areas where MTs are curved versus the areas where MTs are straight. In cells, we show that UNC-45A overexpression increases MT curvature and its depletion has the opposite effect. We also show that this effect occurs is independent of actomyosin contractility. Lastly, we show for the first time that in cells, Paclitaxel straightens MTs, and that UNC-45A can counteracts the MT straightening effects of the drug. Significance: Our findings reveal for the first time that UNC-45A increases MT curvature. This hints that UNC-45A-mediated MT severing could be due to the worsening of MT curvature and provide a mechanistic understanding of how this MT-severing protein may act. UNC-45A is the only MT severing protein expressed in human cancers, including paclitaxel-resistant ovarian cancer. Our finding that UNC-45A counteracts the paclitaxel-straightening effects of MTs in cells suggests an additional mechanism through which cancer cells escape drug treatment.

The rate of microtubule breaking increases exponentially with curvature

Microtubules, cylindrical assemblies of tubulin proteins with a 25 nm diameter and micrometer lengths, are a central part of the cytoskeleton and also serve as building blocks for nanobiodevices. Microtubule breaking can result from the activity of severing enzymes and mechanical stress. Breaking can lead to a loss of structural integrity, or an increase in the numbers of microtubules. We observed breaking of taxol-stabilized microtubules in a gliding motility assay where microtubules are propelled by surface-adhered kinesin-1 motor proteins. We find that over 95% of all breaking events are associated with the strong bending following pinning events (where the leading tip of the microtubule becomes stuck). Furthermore, the breaking rate increased exponentially with increasing curvature. These observations are explained by a model accounting for the complex mechanochemistry of a microtubule. The presence of severing enzymes is not required to observe breaking at rates comparable to those measured previously in cells.

Measurement of the Persistence Length of Cytoskeletal Filaments using Curvature Distributions

Cytoskeletal filaments such as microtubules and actin filaments play important roles in the mechanical integrity of cells and the ability of cells to respond to their environment. Measuring the mechanical properties of cytoskeletal structures is crucial for gaining insight into intracellular mechanical stresses and their role in regulating cellular processes. One of the ways to characterize these mechanical properties is by measuring their persistence length, the average length over which filaments stay straight. There are several approaches in the literature for measuring filament deformations, such as Fourier analysis of images obtained using fluorescence microscopy. Here, we show how curvature distributions can be used as an alternative tool to quantify bio-filament deformations, and investigate how the apparent stiffness of filaments depends on the resolution and noise of the imaging system. We present analytical calculations of the scaling curvature distributions as a function of filament discretization, and test our predictions by comparing Monte Carlo simulations to results from existing techniques. We also apply our approach to microtubules and actin filaments obtained from in vitro gliding assay experiments with high densities of non-functional motors, and calculate the persistence length of these filaments. The presented curvature analysis is significantly more accurate compared to existing approaches for small data sets, and can be readily applied to both in vitro or in vivo filament data through the use of the open-source codes we provide.

Actomyosin dynamics modulate microtubule deformation and growth during T-cell activation

Activation of T-cells leads to the formation of immune synapses (ISs) with antigen-presenting cells. This requires T-cell polarization and coordination between the actomyosin and microtubule cytoskeletons. The interactions between these two cytoskeletal components during T-cell activation are not well understood. Here, we elucidate the interactions between microtubules and actin at the IS with high-resolution fluorescence microscopy. We show that microtubule growth dynamics in the peripheral actin-rich region is distinct from that in the central actin-free region. We further demonstrate that these differences arise from differential involvement of Arp2/3- and formin-nucleated actin structures. Formin inhibition results in a moderate decrease in microtubule growth rates, which is amplified in the presence of integrin engagement. In contrast, Arp2/3 inhibition leads to an increase in microtubule growth rates. We find that microtubule filaments are more deformed and exhibit greater shape fluctuations in the periphery of the IS than at the center. Using small molecule inhibitors, we show that actin dynamics and actomyosin contractility play key roles in defining microtubule deformations and shape fluctuations. Our results indicate a mechanical coupling between the actomyosin and microtubule systems during T-cell activation, whereby different actin structures influence microtubule dynamics in distinct ways.

Prior-Apprised Unsupervised Learning of Subpixel Curvilinear Features in Low Signal/Noise Images

Many biophysical problems involve molecular and nanoscale targets moving next to a curvilinear track, e.g., a cytosolic cargo transported by motor proteins moving along a microtubule. For this type of problem, fluorescence imaging is usually the primary tool of choice. There is, however, an ∼20-fold mismatch between target-localization precision and track-imaging resolution such that questions requiring high-fidelity definition of the target's track remain inaccessible. On the other hand, if the contextual image of the tracks can be refined to a level comparable to that of the target, many intuitive yet mechanistically important issues can begin to be addressed. This work demonstrates that it is possible to statistically infer, to subpixel precision, curvilinear features in a low signal/noise image. This is achieved by a framework that consists of three stages: the Hessian-based feature enhancement, the subimage feature sampling and registration, and the statistical learning of the underlying curvilinear structure using a new, to our knowledge, method developed here for inferring the principal curves. In each stage, the descriptive prior information that the features come from curvilinear elements is explicitly taken into account. It is fully automated without user supervision, which is distinctly different from approaches that require user seeding or well-defined training data sets. Computer simulations of realistic images are used to investigate the performance of the framework and its implementation. The characterization results suggest that curvilinear features are refined to the same order of precision as that of the target and that the bootstrap confidence intervals from the analysis allow an estimate for the statistical bounds of the simulated "true" curve. Also shown are analyses of experimental images from three different microscopy modalities: two-photon laser-scanning microscopy, epifluorescence microscopy, and total internal reflection fluorescence microscopy. The practical application of this prior-apprised unsupervised learning framework as well as its potential outlook are discussed.

Microtubule stabilizer reveals requirement of Ca2+-dependent conformational changes of microtubules for rapid coiling of haptonema in haptophyte algae

A haptonema is an elongated microtubule-based motile organelle uniquely present in haptophytes. The most notable and rapid movement of a haptonema is ‘coiling’, which occurs within a few milliseconds following mechanical stimulation in an unknown motor-independent mechanism. Here, we analyzed the coiling process in detail by high-speed filming and showed that haptonema coiling was initiated by left-handed twisting of the haptonema, followed by writhing to form a helix from the distal tip. On recovery from a mechanical stimulus, the helix slowly uncoiled from the proximal region. Electron microscopy showed that the seven microtubules in a haptonema were arranged mostly in parallel but that one of the microtubules often wound around the others in the extended state. A microtubule stabilizer, paclitaxel, inhibited coiling and induced right-handed twisting of the haptonema in the absence of Ca²⁺, suggesting changes in the mechanical properties of microtubules. Addition of Ca²⁺ resulted in the conversion of haptonematal twist into the planar bends near the proximal region. These results indicate that switching microtubule conformation, possibly with the aid of Ca²⁺-binding microtubule-associated proteins is responsible for rapid haptonematal coiling.

Summary: Microscopy observations and pharmacological experiments revealed that the rapid coiling of a non-motor microtubule-based motile organelle, the haptonema, is explained by conformational changes of microtubules, including twisting and writhing.

Damage and Failure of Axonal Microtubule under Extreme High Strain Rate: An In-Silico Molecular Dynamics Study

As a major cytoskeleton element of the axon, the breaking of microtubules (MTs) has been considered as a major cause of the axon degeneration. High strain rate loading is considered as one of the key factors in microtubule breaking. Due to the small size of microtubule, the real-time behavior of microtubule breaking is hard to capture. This study employs fully-atomistic molecular dynamics (MD) simulation to determine the failure modes of microtubule under different loadings conditions such as, unidirectional stretching, bending and hydrostatic expansion. For each loading conditions, MT is subjected to extreme high strain rate (108-109 s-1) loading. We argue that such level of high strain rate may be realized during cavitation bubble implosion. For each loading type, we have determined the critical energy for MT rupture. The associated rupture mechanisms are also discussed. We observed that the stretching has the lowest energy barrier to break the MT at the nanosecond time scale. Moreover, the breakage between the dimers starts at ~16% of total strain when stretched, which is much smaller compared to the reported strain-at-failure (50%) for lower strain rate loading. It suggests that MT fails at a significantly smaller strain states when loaded at higher strain rates.

Pleomorphic linkers as ubiquitous structural organizers of vesicles in axons

Many cellular processes depend on a precise structural organization of molecular components. Here, we established that neurons grown in culture provide a suitable system for in situ structural investigations of cellular structures by cryo-electron tomography, a method that allows high resolution, three-dimensional imaging of fully hydrated, vitrified cellular samples. A higher level of detail of cellular components present in our images allowed us to quantitatively characterize presynaptic and cytoskeletal organization, as well as structures involved in axonal transport and endocytosis. In this way we provide a structural framework into which information from other methods need to fit. Importantly, we show that short pleomorphic linkers (tethers and connectors) extensively interconnect different types of spherical vesicles and other lipid membranes in neurons imaged in a close-to-native state. These linkers likely serve to organize and precisely position vesicles involved in endocytosis, axonal transport and synaptic release. Hence, structural interactions via short linkers may serve as ubiquitous vesicle organizers in neuronal cells.

The self-organization of plant microtubules inside the cell volume yields their cortical localization, stable alignment, and sensitivity to external cues

Many cell functions rely on the ability of microtubules to self-organize as complex networks. In plants, cortical microtubules are essential to determine cell shape as they guide the deposition of cellulose microfibrils, and thus control mechanical anisotropy of the cell wall. Here we analyze how, in turn, cell shape may influence microtubule behavior. Building upon previous models that confined microtubules to the cell surface, we introduce an agent model of microtubules enclosed in a three-dimensional volume. We show that the microtubule network has spontaneous aligned configurations that could explain many experimental observations without resorting to specific regulation. In particular, we find that the preferred cortical localization of microtubules emerges from directional persistence of the microtubules, and their interactions with each other and with the stiff wall. We also identify microtubule parameters that seem relatively insensitive to cell shape, such as length or number. In contrast, microtubule array anisotropy depends on local curvature of the cell surface and global orientation follows robustly the longest axis of the cell. Lastly, we find that geometric cues may be overcome, as the network is capable of reorienting toward weak external directional cues. Altogether our simulations show that the microtubule network is a good transducer of weak external polarity, while at the same time, easily reaching stable global configurations.

Plants exhibit an astonishing diversity in architecture and morphology. A key to such diversity is the ability of their cells to coordinate and grow to reach a broad spectrum of sizes and shapes. Cell growth in plants is guided by the microtubule cytoskeleton. Here, we seek to understand how microtubules self-organize close to the cell surface. We build upon previous two-dimensional models and we consider microtubules as lines growing in three dimensions, accounting for interactions between microtubules or between microtubules and the cell surface. We show that microtubule arrays are able to adapt to various cell shapes and to reorient in response to external signals. Altogether, our results help to understand how the microtubule cytoskeleton contributes to the diversity of plant shapes and to how these shapes adapt to environment.

Characterization of microtubule buckling in living cells

Microtubules are filamentous biopolymers involved in essential biological processes. They form key structures in eukaryotic cells, and thus it is very important to determine the mechanisms involved in the formation and maintenance of the microtubule network. Microtubule bucklings are transient and localized events commonly observed in living cells and characterized by a fast bending and its posterior relaxation. Active forces provided by molecular motors have been indicated as responsible for most of these rapid deformations. However, the factors that control the shape amplitude and the time scales of the rising and release stages remain unexplored. In this work, we study microtubule buckling in living cells using Xenopus laevis melanophores as a model system. We tracked single fluorescent microtubules from high temporal resolution (0.3-2 s) confocal movies. We recovered the center coordinates of the filaments with 10-nm precision and analyzed the amplitude of the deformation as a function of time. Using numerical simulations, we explored different force mechanisms resulting in microtubule bending. The simulated events reproduce many features observed for microtubules, suggesting that a mechanistic model captures the essential processes underlying microtubule buckling. Also, we studied the interplay between actively transported vesicles and the microtubule network using a two-color technique. Our results suggest that microtubules may affect transport indirectly besides serving as tracks of motor-driven organelles. For example, they could obstruct organelles at microtubule intersections or push them during filament mechanical relaxation.

Mechanical splitting of microtubules into protofilament bundles by surface-bound kinesin-1

The fundamental biophysics of gliding microtubule (MT) motility by surface-tethered kinesin-1 motor proteins has been widely studied, as well as applied to capture and transport analytes in bioanalytical microdevices. In these systems, phenomena such as molecular wear and fracture into shorter MTs have been reported due the mechanical forces applied on the MT during transport. In the present work, we show that MTs can be split longitudinally into protofilament bundles (PFBs) by the work performed by surface-bound kinesin motors. We examine the properties of these PFBs using several techniques (e.g., fluorescence microscopy, SEM, AFM), and show that the PFBs continue to be mobile on the surface and display very high curvature compared to MT. Further, higher surface density of kinesin motors and shorter kinesin-surface tethers promote PFB formation, whereas modifying MT with GMPCPP or higher paclitaxel concentrations did not affect PFB formation.

Microtubules self-repair in response to mechanical stress

Microtubules--which define the shape of axons, cilia and flagella, and provide tracks for intracellular transport--can be highly bent by intracellular forces, and microtubule structure and stiffness are thought to be affected by physical constraints. Yet how microtubules tolerate the vast forces exerted on them remains unknown. Here, by using a microfluidic device, we show that microtubule stiffness decreases incrementally with each cycle of bending and release. Similar to other cases of material fatigue, the concentration of mechanical stresses on pre-existing defects in the microtubule lattice is responsible for the generation of more extensive damage, which further decreases microtubule stiffness. Strikingly, damaged microtubules were able to incorporate new tubulin dimers into their lattice and recover their initial stiffness. Our findings demonstrate that microtubules are ductile materials with self-healing properties, that their dynamics does not exclusively occur at their ends, and that their lattice plasticity enables the microtubules' adaptation to mechanical stresses.

SOAX: a software for quantification of 3D biopolymer networks

Filamentous biopolymer networks in cells and tissues are routinely imaged by confocal microscopy. Image analysis methods enable quantitative study of the properties of these curvilinear networks. However, software tools to quantify the geometry and topology of these often dense 3D networks and to localize network junctions are scarce. To fill this gap, we developed a new software tool called “SOAX”, which can accurately extract the centerlines of 3D biopolymer networks and identify network junctions using Stretching Open Active Contours (SOACs). It provides an open-source, user-friendly platform for network centerline extraction, 2D/3D visualization, manual editing and quantitative analysis. We propose a method to quantify the performance of SOAX, which helps determine the optimal extraction parameter values. We quantify several different types of biopolymer networks to demonstrate SOAX's potential to help answer key questions in cell biology and biophysics from a quantitative viewpoint.

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.

Quantitative analysis of microtubule self-assembly kinetics and tip structure

Microtubules are dynamic polymers of the cytoskeleton, which play important roles in cell division, polarization, and intracellular transport. Self-assembly of microtubule polymer from αβ-tubulin heterodimers is highly variable, with stochastic switching between alternate states of net growth and net shortening, a phenomenon known as dynamic instability. Microtubule tip structures are also variable and directly influence the kinetics of assembly and vice versa. TipTracker, a semiautomated, image processing-based tool, permits high spatial and temporal resolution measurements from fluorescence microscopy images (~10-40 nm, or 1-5 dimer lengths, at 1-10 Hz) with simultaneous tip structure estimation. We provide a walkthrough of the TipTracker code to demonstrate methods used to (1) fit the coordinates of the microtubule backbone; (2) track microtubule tip position; and (3) estimate tip structure from the spatial decay of the tip fluorescence distribution, discuss possible sources of error, and include an example protocol for nanometer-scale tip tracking in living cells. Additionally, we evaluate TipTracker's accuracy on simulated digital images and fixed microtubules to estimate accuracy under realistic imaging conditions. In summary, this chapter demonstrates the use of TipTracker in making robust, high-resolution measurements of microtubule tip dynamics and structures, facilitating quantitative investigations into nanoscale/molecular control of microtubule assembly. Although our primary focus is on microtubules, these methods are, in principle, suitable for other polymer structures, such as F-actin.

How mechanical stress controls microtubule behavior and morphogenesis in plants: history, experiments and revisited theories

Microtubules have a key role in plant morphogenesis, as they control the oriented deposition of cellulose in the cell wall, and thus growth anisotropy. The idea that mechanical stress could be one of the main determinants behind the orientation of microtubules in plant cells emerged very soon after their discovery. The cause of mechanical stress in plant cells is turgor pressure, which can build up to 1 MPa and is restrained by cell wall stiffness. On the tissue scale, this can lead to regional patterns of tension, in particular in the epidermis of aerial organs, which resist the stress generated by cells in internal tissues. Here we summarize more than 50 years of work on the contribution of mechanical stress in guiding microtubule behavior, and the resulting impact on growth anisotropy and growth heterogeneity. We propose a conceptual model on microtubule dynamics and their ability to self-organize in bundles parallel to the direction of maximal stress, as well as a synthetic representation of the putative mechanotransducers at play.

Actin filament curvature biases branching direction

Mechanical cues affect many important biological processes in metazoan cells, such as migration, proliferation, and differentiation. Such cues are thought to be detected by specialized mechanosensing molecules linked to the cytoskeleton, an intracellular network of protein filaments that provide mechanical rigidity to the cell and drive cellular shape change. The most abundant such filament, actin, forms branched networks nucleated by the actin-related protein (Arp) 2/3 complex that support or induce membrane protrusions and display adaptive behavior in response to compressive forces. Here we show that filamentous actin serves in a mechanosensitive capacity itself, by biasing the location of actin branch nucleation in response to filament bending. Using an in vitro assay to measure branching from curved sections of immobilized actin filaments, we observed preferential branch formation by the Arp2/3 complex on the convex face of the curved filament. To explain this behavior, we propose a fluctuation gating model in which filament binding or branch nucleation by Arp2/3 occur only when a sufficiently large, transient, local curvature fluctuation causes a favorable conformational change in the filament, and we show with Monte Carlo simulations that this model can quantitatively account for our experimental data. We also show how the branching bias can reinforce actin networks in response to compressive forces. These results demonstrate how filament curvature can alter the interaction of cytoskeletal filaments with regulatory proteins, suggesting that direct mechanotransduction by actin may serve as a general mechanism for organizing the cytoskeleton in response to force.

Effects of dynein on microtubule mechanics and centrosome positioning

When microtubules are severed by laser ablation, newly created minus ends increase in curvature, but they straighten when dynein is inhibited. It is found that cytoplasmic dynein generates tension and friction along microtubule lengths and that these forces govern the dynamics of centrosome centering.

To determine forces on intracellular microtubules, we measured shape changes of individual microtubules following laser severing in bovine capillary endothelial cells. Surprisingly, regions near newly created minus ends increased in curvature following severing, whereas regions near new microtubule plus ends depolymerized without any observable change in shape. With dynein inhibited, regions near severed minus ends straightened rapidly following severing. These observations suggest that dynein exerts a pulling force on the microtubule that buckles the newly created minus end. Moreover, the lack of any observable straightening suggests that dynein prevents lateral motion of microtubules. To explain these results, we developed a model for intracellular microtubule mechanics that predicts the enhanced buckling at the minus end of a severed microtubule. Our results show that microtubule shapes reflect a dynamic force balance in which dynein motor and friction forces dominate elastic forces arising from bending moments. A centrosomal array of microtubules subjected to dynein pulling forces and resisted by dynein friction is predicted to center on the experimentally observed time scale, with or without the pushing forces derived from microtubule buckling at the cell periphery.

Loop formation of microtubules during gliding at high density

The microtubule cytoskeleton, including the associated proteins, forms a complex network essential to multiple cellular processes. Microtubule-associated motor proteins, such as kinesin-1, travel on microtubules to transport membrane bound vesicles across the crowded cell. Other motors, such as cytoplasmic dynein and kinesin-5, are used to organize the cytoskeleton during mitosis. In order to understand the self-organization processes of motors on microtubules, we performed filament-gliding assays with kinesin-1 motors bound to the cover glass with a high density of microtubules on the surface. To observe microtubule organization, 3% of the microtubules were fluorescently labeled to serve as tracers. We find that microtubules in these assays are not confined to two dimensions and can cross one other. This causes microtubules to align locally with a relatively short correlation length. At high density, this local alignment is enough to create 'intersections' of perpendicularly oriented groups of microtubules. These intersections create vortices that cause microtubules to form loops. We characterize the radius of curvature and time duration of the loops. These different behaviors give insight into how crowded conditions, such as those in the cell, might affect motor behavior and cytoskeleton organization.

Segmentation and tracking of cytoskeletal filaments using open active contours

We use open active contours to quantify cytoskeletal structures imaged by fluorescence microscopy in two and three dimensions. We developed an interactive software tool for segmentation, tracking, and visualization of individual fibers. Open active contours are parametric curves that deform to minimize the sum of an external energy derived from the image and an internal bending and stretching energy. The external energy generates (i) forces that attract the contour toward the central bright line of a filament in the image, and (ii) forces that stretch the active contour toward the ends of bright ridges. Images of simulated semiflexible polymers with known bending and torsional rigidity are analyzed to validate the method. We apply our methods to quantify the conformations and dynamics of actin in two examples: actin filaments imaged by TIRF microscopy in vitro, and actin cables in fission yeast imaged by spinning disk confocal microscopy.

Microtubule Tip Tracking and Tip Structures at the Nanometer Scale Using Digital Fluorescence Microscopy

Microtubules (MTs) are central to fundamental cellular processes including mitosis, polarization, and axon extension. A key issue is to understand how MT-associated proteins and therapeutic drugs, such as the anticancer drug paclitaxel, control MT self-assembly. To facilitate this research, it would be helpful to have automated methods that track the tip of dynamically assembling MTs as observed via fluorescence microscopy. Through a combination of digital fluorescence imaging with MT modeling, model-convolution, and automated image analysis of live and fixed MTs, we developed a method for MT tip tracking that includes estimation of the measurement error. We found that the typical single-frame tip tracking accuracy of GFP-tubulin labeled MTs in living LLC-PK1α cells imaged with a standard widefield epifluorescence digital microscope system is ~36 nm, the equivalent of ~4.5 tubulin dimer layers. However, if the MT tips are blunt, the tip tracking accuracy can be as accurate as ~15 nm (~2 dimer layers). By fitting a Gaussian survival function to the MT tip intensity profiles, we also established that MTs within living cells are not all blunt, but instead exhibit highly variable tapered tip structures with a protofilament length standard deviation of ~180 nm. More generally, the tip tracking method can be extended to track the tips of any individual fluorescently labeled filament, and can estimate filament tip structures both in vivo and in vitro with single-frame accuracy on the nanoscale.

Measuring the number and spacing of molecular motors propelling a gliding microtubule

The molecular motor gliding assay, in which a microtubule or other filament moves across a surface coated with motors, has provided much insight into how molecular motors work. The kinesin-microtubule system is also a strong candidate for the job of nanoparticle transporter in nanotechnology devices. In most cases, several motors transport each filament. Each motor serves both to bind the microtubule to a stationary surface and to propel the microtubule along the surface. By applying a uniform transverse force of 4-19 pN to a superparamagnetic bead attached to the trailing end of the microtubule, we have measured the distance d between binding points (motors). The average value of d was determined as a function of motor surface density σ. The measurements agree well with the scaling model of Duke, Holy, and Liebler, which predicts that (d)~σ(-2/5) if 0.05≤σ≤20 μm(-2) [Phys. Rev. Lett. 74, 330 (1995)]. The distribution of d fits an extension of the model. The radius of curvature of a microtubule bent at a binding point by the force of the magnetic bead was ≈1 μm, 5000-fold smaller than the radius of curvature of microtubules subjected only to thermal forces. This is evidence that at these points of high bending stress, generated by the force on the magnetic bead, the microtubule is in the more flexible state of a two-state model of microtubule bending proposed by Heussinger, Schüller, and Frey [Phys. Rev. E 81, 021904 (2010)].

ER sliding dynamics and ER-mitochondrial contacts occur on acetylated microtubules

Movement of the ER and mitochondria is coupled by limited interactions of the ER with a subset of posttranslationally modified microtubules.

The endoplasmic reticulum (ER) network is extremely dynamic in animal cells, yet little is known about the mechanism and function of its movements. The most common ER dynamic, termed ER sliding, involves ER tubule extension along stable microtubules (MTs). In this study, we show that ER sliding occurs on nocodazole-resistant MTs that are posttranslationally modified by acetylation. We demonstrate that high MT curvature is a good indicator of MT acetylation and show in live cells that ER sliding occurs predominantly on these curved, acetylated MTs. Furthermore, increasing MT acetylation by drug treatment increases the frequency of ER sliding. One purpose of the ER sliding on modified MT tracts could be to regulate its interorganelle contacts. We find that all mitochondria and many endosomes maintain contact with the ER despite the movements of each. However, mitochondria, but not endosomes, preferentially localize to acetylated MTs. Thus, different ER dynamics may occur on distinct MT populations to establish or maintain contacts with different organelles.

Model Convolution: A Computational Approach to Digital Image Interpretation

Digital fluorescence microscopy is commonly used to track individual proteins and their dynamics in living cells. However, extracting molecule-specific information from fluorescence images is often limited by the noise and blur intrinsic to the cell and the imaging system. Here we discuss a method called “model-convolution,” which uses experimentally measured noise and blur to simulate the process of imaging fluorescent proteins whose spatial distribution cannot be resolved. We then compare model-convolution to the more standard approach of experimental deconvolution. In some circumstances, standard experimental deconvolution approaches fail to yield the correct underlying fluorophore distribution. In these situations, model-convolution removes the uncertainty associated with deconvolution and therefore allows direct statistical comparison of experimental and theoretical data. Thus, if there are structural constraints on molecular organization, the model-convolution method better utilizes information gathered via fluorescence microscopy, and naturally integrates experiment and theory.

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.

Anterograde microtubule transport drives microtubule bending in LLC-PK1 epithelial cells

Microtubules (MTs) have been proposed to act mechanically as compressive struts that resist both actomyosin contractile forces and their own polymerization forces to mechanically stabilize cell shape. To identify the origin of MT bending, we directly observed MT bending and F-actin transport dynamics in the periphery of LLC-PK1 epithelial cells. We found that F-actin is nearly stationary in these cells even as MTs are deformed, demonstrating that MT bending is not driven by actomyosin contractility. Furthermore, the inhibition of myosin II activity through the use of blebbistatin results in microtubules that are still dynamically bending. In addition, as determined by fluorescent speckle microscopy, MT polymerization rarely results, if ever, in bending. We suppressed dynamic instability using nocodazole, and we observed no qualitative change in the MT bending dynamics. Bending most often results from anterograde transport of proximal portions of the MT toward a nearly stationary distal tip. Interestingly, we found that in an in vitro kinesin-MT gliding assay, MTs buckle in a similar manner. To make quantitative comparisons, we measured curvature distributions of observed MTs and found that the in vivo and in vitro curvature distributions agree quantitatively. In addition, the measured MT curvature distribution is not Gaussian, as expected for a thermally driven semiflexible polymer, indicating that thermal forces play a minor role in MT bending. We conclude that many of the known mechanisms of MT deformation, such as polymerization and acto-myosin contractility, play an inconsequential role in mediating MT bending in LLC-PK1 cells and that MT-based molecular motors likely generate most of the strain energy stored in the MT lattice. The results argue against models in which MTs play a major mechanical role in LLC-PK1 cells and instead favor a model in which mechanical forces control the spatial distribution of the MT array.

Chapter 19: Mechanical response of cytoskeletal networks

The cellular cytoskeleton is a dynamic network of filamentous proteins, consisting of filamentous actin (F-actin), microtubules, and intermediate filaments. However, these networks are not simple linear, elastic solids; they can exhibit highly nonlinear elasticity and a thermal dynamics driven by ATP-dependent processes. To build quantitative mechanical models describing complex cellular behaviors, it is necessary to understand the underlying physical principles that regulate force transmission and dynamics within these networks. In this chapter, we review our current understanding of the physics of networks of cytoskeletal proteins formed in vitro. We introduce rheology, the technique used to measure mechanical response. We discuss our current understanding of the mechanical response of F-actin networks, and how the biophysical properties of F-actin and actin cross-linking proteins can dramatically impact the network mechanical response. We discuss how incorporating dynamic and rigid microtubules into F-actin networks can affect the contours of growing microtubules and composite network rigidity. Finally, we discuss the mechanical behaviors of intermediate filaments.