Radial compression of microtubules and the mechanism of action of taxol and associated proteins

Structure and dynamics of motor-driven microtubule bundles

Connecting the large-scale emergent behaviors of active cytoskeletal materials to the microscopic properties of their constituents is a challenge due to a lack of data on the multiscale dynamics and structure of such systems. We approach this problem by studying the impact of depletion attraction on bundles of microtubules and kinesin-14 molecular motors. For all depletant concentrations, kinesin-14 bundles generate comparable extensile dynamics. However, this invariable mesoscopic behavior masks the transition in the microscopic motion of microtubules. Specifically, with increasing attraction, we observe a transition from bi-directional sliding with extension to pure extension with no sliding. Small-angle X-ray scattering shows that the transition in microtubule dynamics is concurrent with a structural rearrangement of microtubules from an open hexagonal to a compressed rectangular lattice. These results demonstrate that bundles of microtubules and molecular motors can display the same mesoscopic extensile behaviors despite having different internal structures and microscopic dynamics. They provide essential information for developing multiscale models of active matter.

Microtubules as a potential platform for energy transfer in biological systems: a target for implementing individualized, dynamic variability patterns to improve organ function

Variability characterizes the complexity of biological systems and is essential for their function. Microtubules (MTs) play a role in structural integrity, cell motility, material transport, and force generation during mitosis, and dynamic instability exemplifies the variability in the proper function of MTs. MTs are a platform for energy transfer in cells. The dynamic instability of MTs manifests itself by the coexistence of growth and shortening, or polymerization and depolymerization. It results from a balance between attractive and repulsive forces between tubulin dimers. The paper reviews the current data on MTs and their potential roles as energy-transfer cellular structures and presents how variability can improve the function of biological systems in an individualized manner. The paper presents the option for targeting MTs to trigger dynamic improvement in cell plasticity, regulate energy transfer, and possibly control quantum effects in biological systems. The described system quantifies MT-dependent variability patterns combined with additional personalized signatures to improve organ function in a subject-tailored manner. The platform can regulate the use of MT-targeting drugs to improve the response to chronic therapies. Ongoing trials test the effects of this platform on various disorders.

Active Bending of Disordered Microtubule Bundles by Kinesin Motors

Active networks of biopolymers and motor proteins in vitro self-organize and exhibit dynamic structures on length scales much larger than the interacting individual components of which they consist. How the dynamics is related across the range of length scales is still an open question. Here, we experimentally characterize and quantify the dynamic behavior of isolated microtubule bundles that bend due to the activity of motor proteins. At the motor level, we track and describe the motion features of kinesin-1 clusters stepping within the bending bundles. We find that there is a separation of length scales by at least 1 order of magnitude. At a run length of <1 μm, kinesin-1 activity leads to a bundle curvature in the range of tens of micrometers. We propose that the distribution of microtubule polarity plays a crucial role in the bending dynamics that we observe at both the bundle and motor levels. Our results contribute to the understanding of fundamental principles of vital intracellular processes by disentangling the multiscale dynamics in out-of-equilibrium active networks composed of cytoskeletal elements.

Cell line-directed breast cancer research based on glucose metabolism status

Metabolic reprogramming is a potential hallmark of tumor cells to support continuous proliferation. Metabolic heterogeneity in breast cancer patients has been highlighted as the driving cause of tumor progression and resistance to anticancer drugs. Studying and identifying distinct metabolic alterations in breast cancer subtypes could offer new perspectives for faster diagnosis and treatment. Given cancer cell dependency on glycolysis, the primary energy source, this enzymatic pathway will play a critical role in targeting therapies. Knowledge about the specific metabolic dependencies of tumors for growth and proliferation can be promising for novel targeted and cell-based therapies. Here, the metabolic status with emphasis on glycolysis of breast cancer cell lines according to their classification was reviewed.

Tuning the Properties of Active Microtubule Networks by Depletion Forces

Suspensions of microtubules and nonadsorbing particles form thick and long bundles due to depletion forces. Such interactions act at the nanometer scale and define the structural and dynamical properties of the resulting networks. In this study, we analyze the depletion forces exerted by two types of nonadsorbing particles, namely, the polymer, poly(ethylene glycol) (PEG), and the block copolymer, Pluronic. We characterize their effects both in passive and active networks by adding motor proteins to the suspensions. By exploiting its bundling effect via entropic forces, we observed that PEG generates a network with thick structures showing a nematic order and larger mesh size. On the other hand, Pluronic builds up a much denser gel-like network without a recognizable mesh structure. This difference is also reflected in the network activity. PEG networks show moderate contraction in lateral directions while Pluronic networks exhibit faster and isotropic contraction. Interestingly, by mixing the two nonadsorbing polymers in different ratios, we observed that the system showed a behavior that exhibited properties of both agents, leading to a robust and fast responsive structure compared to the single-depletant networks. In conclusion, we show how passive osmotic compression modifies the distribution of biopolymers. Its combination with active motors results in a new active material with potential for nanotechnological applications.

Crowder and surface effects on self-organization of microtubules

Microtubules are an essential physical building block of cellular systems. They are organized using specific crosslinkers, motors, and influencers of nucleation and growth. With the addition of antiparallel crosslinkers, microtubule self-organization patterns go through a transition from fanlike structures to homogeneous tactoid condensates in vitro. Tactoids are reminiscent of biological mitotic spindles, the cell division machinery. To create these organizations, we previously used polymer crowding agents. Here we study how altering the properties of the crowders, such as type, size, and molecular weight, affects microtubule organization. Comparing simulations with experiments, we observe a scaling law associated with the fanlike patterns in the absence of crosslinkers. Tactoids formed in the presence of crosslinkers show variable length, depending on the crowders. We correlate the subtle differences to filament contour length changes, affected by nucleation and growth rate changes induced by the polymers in solution. Using quantitative image analysis, we deduce that the tactoids differ from traditional liquid crystal organization, as they are limited in width irrespective of crowders and surfaces, and behave as solidlike condensates.

Modeling the Mechanical Response of Microtubule Lattices to Pressure

Microtubules, the largest and stiffest filaments of the cytoskeleton, have to be well adapted to the high levels of crowdedness in cells to perform their multitude of functions. Furthermore, fundamental processes that involve microtubules, such as the maintenance of the cellular shape and cellular motion, are known to be highly dependent on external pressure. In light of the importance of pressure for the functioning of microtubules, numerous studies interrogated the response of these cytoskeletal filaments to osmotic pressure, resulting from crowding by osmolytes, such as poly(ethylene glycol)/poly(ethylene oxide) (PEG/PEO) molecules, or to direct applied pressure. The interpretation of experiments is usually based on the assumptions that PEG molecules have unfavorable interactions with the microtubule lattices and that the behavior of microtubules under pressure can be described by using continuous models. We probed directly these two assumptions. First, we characterized the interaction between the main interfaces in a microtubule filament and PEG molecules of various sizes using a combination of docking and molecular dynamics simulations. Second, we studied the response of a microtubule filament to compression using a coarse-grained model that allows for the breaking of lattice interfaces. Our results show that medium length PEG molecules do not alter the energetics of the lateral interfaces in microtubules but rather target and can penetrate into the voids between tubulin monomers at these interfaces, which can lead to a rapid loss of lateral interfaces under pressure. Compression of a microtubule under conditions corresponding to high osmotic pressure results in the formation of the deformed phase found in experiments. Our simulations show that the breaking of lateral interfaces, rather than the buckling of the filament inferred from the continuous models, accounts for the deformation.

Tubulin Double Helix: Lateral and Longitudinal Curvature Changes of Tubulin Protofilament

By virtue of their native structures, tubulin dimers are protein building blocks that are naturally preprogrammed to assemble into microtubules (MTs), which are cytoskeletal polymers. Here, polycation-directed (i.e., electrostatically tunable) assembly of tubulins is demonstrated by conformational changes to the tubulin protofilament in longitudinal and lateral directions, creating tubulin double helices and various tubular architectures. Synchrotron small-angle X-ray scattering and transmission electron microscopy reveal a remarkable range of nanoscale assembly structures: single- and double-layered double-helix tubulin tubules. The phase transitions from MTs to the new assemblies are dependent on the size and concentration of polycations. Two characteristic scales that determine the number of observed phases are the size of polycation compared to the size of tubulin (≈4 nm) and to MT diameter (≈25 nm). This work suggests the feasibility of using polycations that have scissor- and glue-like properties to achieve "programmable breakdown" of protein nanotubes, tearing MTs into double-stranded tubulins and building up previously undiscovered nanostructures. Importantly, a new role of tubulins is defined as 2D shape-controllable building blocks for supramolecular architectures. These findings provide insight into the design of protein-based functional materials, for example, as metallization templates for nanoscale electronic devices, molecular screws, and drug delivery vehicles.

GC-MS based comparative metabolomic analysis of MCF-7 and MDA-MB-231 cancer cells treated with Tamoxifen and/or Paclitaxel

Breast cancer cells MCF-7 and MDA-MB-231 were treated with Tamoxifen (5 μM) or Paclitaxel (1 μM) or with a combination of the two drugs. Herein, we have employed gas chromatography coupled with mass spectroscopy to identify metabolic changes occurring as response to different drug treatments. We report the identification of sixty-one metabolites and overall the two studied cell lines showed a distinct metabolomic profile from each other. Further data analysis indicates that a total of 30 metabolites were significantly differentially abundant in MCF-7 drug-treated cells, most of the metabolic changes occurred when cells were treated with either Tamoxifen (15) or Paclitaxel (25). On the other side, a total of 31 metabolites were significantly differentially abundant in MDA-MB-31 cells with drug treatment. Similarly, to MCF-7 most of the metabolic changes occurred when cells were treated with either Tamoxifen (19) or Paclitaxel (20). In conclusion, this report demonstrates that Tamoxifen and/or Paclitaxel treatment have a pronounced effect on the main metabolic pathways in both breast cancer (BC) cell lines (MCF-7 and MDA-MB231), which could be used as a foundation for future investigations to understand the possible effect of these drugs on different metabolic pathways. SIGNIFICANCE: Metabolic profiling of cancer cells is a promising tool in tumor diagnosis, biomarker discovery and drug treatment protocols, since cancer cells exhibit altered metabolism when compared to normal cells. Although numerous studies have reported the use of various OMICs applications to investigate breast cancer cells, very few of these have performed thorough screening of metabolites in such cells. Our investigation highlights the first study to characterize MCF7 and MDA-MB-231 cancer cells treated with Tamoxifen and/or Paclitaxel and to identify the affected metabolic pathways. Such findings might play an important role in revealing the molecular bases of the underlying mechanism of action of these two frontline anti-breast cancer drugs.

Downregulation of GPSM2 is associated with primary resistance to paclitaxel in breast cancer

Paclitaxel is one of the most effective chemotherapy drugs for breast cancer worldwide but 20–30% patients show primary resistance to the drug. Screening and identification of markers that facilitate effective and rapid prediction of sensitivity to paclitaxel is therefore an urgent medical requirement. In the present study, G protein signaling modulator 2 (GPSM2) mRNA levels were significantly associated with taxane sensitivity in experiments based on the Gene Expression Omnibus (GEO) online database. Immunohistochemical analysis consistently revealed a significant association of GPSM2 protein levels with paclitaxel sensitivity in breast cancer patients. Knockdown of GPSM2 reduced the sensitivity of breast cancer cells to paclitaxel via regulation of the cell cycle. Animal experiments further corroborated our in vitro findings. These results suggest that GPSM2 plays an important role in breast cancer resistance, supporting its utility as a potential target for improving drug susceptibility in patients as well as a marker of paclitaxel sensitivity.

Structural analysis of healthy and cancerous epithelial-type breast cells by nanomechanical spectroscopy allows us to obtain peculiarities of the skeleton and junctions

The transition of healthy epithelial cells to carcinoma is associated with an alteration in the structure and organization of the cytoskeleton of the cells. A comparison of the mechanical properties of cancerous and healthy cells indicated a higher deformability of the cancer cells based on averaging the mechanical properties of single cells. However, the exact reason for softening of the cancerous cells compared to their counterparts remains unclear. Here, we focused on nanomechanical spectroscopy of healthy and cancerous ductal epithelial-type breast cells by means of atomic force microscopy with high lateral and depth precision. As a result, based on atomic force microscopy measurements formation of significantly fewer microtubules in cancerous cells which was observed in our study is most likely one of the main causes for the overall change in mechanical properties without any phenotypic shift. Strikingly, in a confluent layer of invasive ductal carcinoma cells, we observed the formation of cell-cell junctions that have the potential for signal transduction among neighboring cells such as desmosomes and adherens junctions. This increases the possibility of cancerous cell collaboration in malignancy, infiltration or metastasis phenomena.

Mechanics of the Microtubule Seam Interface Probed by Molecular Simulations and in Vitro Severing Experiments

Microtubules (MTs) are structural components essential for cell morphology and organization. It has recently been shown that defects in the filament's lattice structure can be healed to create stronger filaments in a local area and ultimately cause global changes in MT organization and cell mobility. The ability to break, causing a defect, and heal appears to be a physiologically relevant and important feature of the MT structure. Defects can be created by MT severing enzymes and are target sites for complete severing or for healing by newly incorporated dimers. One particular lattice defect, the MT lattice ''seam" interface, is a location often speculated to be a weak site, a site of disassembly, or a target site for MT binding proteins. Despite seams existing in many MT structures, very little is known about the seam's role in MT function and dynamics. In this study, we probed the mechanical stability of the seam interface by applying coarse-grained indenting molecular dynamics. We found that the seam interface is as structurally robust as the typical lattice structure of MTs. Our results suggest that, unlike prior results that claim the seam is a weak site, it is just as strong as any other location on the MT, corroborating recent mechanical measurements.

Altered skeletal muscle microtubule-mitochondrial VDAC2 binding is related to bioenergetic impairments after paclitaxel but not vinblastine chemotherapies

Microtubule-targeting chemotherapies are linked to impaired cellular metabolism, which may contribute to skeletal muscle dysfunction. However, the mechanisms by which metabolic homeostasis is perturbed remains unknown. Tubulin, the fundamental unit of microtubules, has been implicated in the regulation of mitochondrial-cytosolic ADP/ATP exchange through its interaction with the outer membrane voltage-dependent anion channel (VDAC). Based on this model, we predicted that disrupting microtubule architecture with the stabilizer paclitaxel and destabilizer vinblastine would impair skeletal muscle mitochondrial bioenergetics. Here, we provide in vitro evidence of a direct interaction between both α-tubulin and βII-tubulin with VDAC2 in untreated single extensor digitorum longus (EDL) fibers. Paclitaxel increased both α- and βII-tubulin-VDAC2 interactions, whereas vinblastine had no effect. Utilizing a permeabilized muscle fiber bundle preparation that retains the cytoskeleton, paclitaxel treatment impaired the ability of ADP to attenuate H₂O₂ emission, resulting in greater H₂O₂ emission kinetics. Despite no effect on tubulin-VDAC2 binding, vinblastine still altered mitochondrial bioenergetics through a surprising increase in ADP-stimulated respiration while also impairing ADP suppression of H₂O₂ and increasing mitochondrial susceptibility to calcium-induced formation of the proapoptotic permeability transition pore. Collectively, these results demonstrate that altering microtubule architecture with chemotherapeutics disrupts mitochondrial bioenergetics in EDL skeletal muscle. Specifically, microtubule stabilization increases H₂O₂ emission by impairing ADP sensitivity in association with greater tubulin-VDAC binding. In contrast, decreasing microtubule abundance triggers a broad impairment of ADP's governance of respiration and H₂O₂ emission as well as calcium retention capacity, albeit through an unknown mechanism.

Anisotropic mechanics and dynamics of a living mammalian cytoplasm

During physiological processes, cells can undergo morphological changes that can result in a significant redistribution of the cytoskeleton causing anisotropic behavior. Evidence of anisotropy in cells under mechanical stimuli exists; however, the role of cytoskeletal restructuring resulting from changes in cell shape in mechanical anisotropy and its effects remain unclear. In the present study, we examine the role of cell morphology in inducing anisotropy in both intracellular mechanics and dynamics. We change the aspect ratio of cells by confining the cell width and measuring the mechanical properties of the cytoplasm using optical tweezers in both the longitudinal and transverse directions to quantify the degree of mechanical anisotropy. These active microrheology measurements are then combined with intracellular movement to calculate the intracellular force spectrum using force spectrum microscopy (FSM), from which the degree of anisotropy in dynamics and force can be quantified. We find that unrestricted cells with aspect ratio (AR) ∼1 are isotropic; however, when cells break symmetry, they exhibit significant anisotropy in cytoplasmic mechanics and dynamics.

Hypoxia and Noncoding RNAs in Taxane Resistance

Taxanes are chemotherapeutic drugs employed in the clinic to treat a variety of malignancies. Despite their overall efficacy, cancer cells often display resistance to taxanes. Therefore, new strategies to increase the effectiveness of taxane-based chemotherapeutics are urgently needed. Multiple molecular players are linked to taxane resistance; these include efflux pumps, DNA repair mechanisms, and hypoxia-related pathways. In addition, emerging evidence indicates that both non-coding RNAs and epigenetic effectors might also be implicated in taxane resistance. Here we focus on the causes of taxane resistance, with the aim to envisage an integrated model of the 'taxane resistance phenome'. This model could help the development of novel therapeutic strategies to treat taxane-resistant neoplasms.

Microtubules soften due to cross-sectional flattening

We use optical trapping to continuously bend an isolated microtubule while simultaneously measuring the applied force and the resulting filament strain, thus allowing us to determine its elastic properties over a wide range of applied strains. We find that, while in the low-strain regime, microtubules may be quantitatively described in terms of the classical Euler-Bernoulli elastic filament, above a critical strain they deviate from this simple elastic model, showing a softening response with increasingdeformations. A three-dimensional thin-shell model, in which the increased mechanical compliance is caused by flattening and eventual buckling of the filament cross-section, captures this softening effect in the high strain regime and yields quantitative values of the effective mechanical properties of microtubules. Our results demonstrate that properties of microtubules are highly dependent on the magnitude of the applied strain and offer a new interpretation for the large variety in microtubule mechanical data measured by different methods.

Inhibition of Microtubule Depolymerization by Osmolytes

Microtubule dynamics play a critical role in the normal physiology of eukaryotic cells as well as a number of cancers and neurodegenerative disorders. The polymerization/depolymerization of microtubules is regulated by a variety of stabilizing and destabilizing factors, including microtubule-associated proteins and therapeutic agents (e.g., paclitaxel, nocodazole). Here we describe the ability of the osmolytes polyethylene glycol (PEG) and trimethylamine- N-oxide (TMAO) to inhibit the depolymerization of individual microtubule filaments for extended periods of time (up to 30 days). We further show that PEG stabilizes microtubules against both temperature- and calcium-induced depolymerization. Our results collectively suggest that the observed inhibition may be related to combination of the kosmotropic behavior and excluded volume/osmotic pressure effects associated with PEG and TMAO. Taken together with prior studies, our data suggest that the physiochemical properties of the local environment can regulate microtubule depolymerization and may potentially play an important role in in vivo microtubule dynamics.

Synchrotron small-angle X-ray scattering and electron microscopy characterization of structures and forces in microtubule/Tau mixtures

Tau, a neuronal protein known to bind to microtubules and thereby regulate microtubule dynamic instability, has been shown recently to not only undergo conformational transitions on the microtubule surface as a function of increasing microtubule coverage density (i.e., with increasing molar ratio of Tau to tubulin dimers) but also to mediate higher-order microtubule architectures, mimicking fascicles of microtubules found in the axon initial segment. These discoveries would not have been possible without fine structure characterization of microtubules, with and without applied osmotic pressure through the use of depletants. Herein, we discuss the two primary techniques used to elucidate the structure, phase behavior, and interactions in microtubule/Tau mixtures: transmission electron microscopy and synchrotron small-angle X-ray scattering. While the former is able to provide striking qualitative images of bundle morphologies and vacancies, the latter provides angstrom-level resolution of bundle structures and allows measurements in the presence of in situ probes, such as osmotic depletants. The presented structural characterization methods have been applied both to equilibrium mixtures, where paclitaxel is used to stabilize microtubules, and also to dissipative nonequilibrium mixtures at 37°C in the presence of GTP and lacking paclitaxel.

Structure and Intermolecular Interactions between L-Type Straight Flagellar Filaments

Bacterial mobility is powered by rotation of helical flagellar filaments driven by rotary motors. Flagellin isolated from the Salmonella Typhimurium SJW1660 strain, which differs by a point mutation from the wild-type strain, assembles into straight filaments in which flagellin monomers are arranged in a left-handed helix. Using small-angle x-ray scattering and osmotic stress methods, we investigated the structure of SJW1660 flagellar filaments as well as the intermolecular forces that govern their assembly into dense hexagonal bundles. The scattering data were fitted to models, which took into account the atomic structure of the flagellin subunits. The analysis revealed the exact helical arrangement and the super-helical twist of the flagellin subunits within the filaments. Under osmotic stress, the filaments formed two-dimensional hexagonal bundles. Monte Carlo simulations and continuum theories were used to analyze the scattering data from hexagonal arrays, revealing how the bundle bulk modulus and the deflection length of filaments in the bundles depend on the applied osmotic stress. Scattering data from aligned flagellar bundles confirmed the theoretically predicated structure-factor scattering peak line shape. Quantitative analysis of the measured equation of state of the bundles revealed the contributions of electrostatic, hydration, and elastic interactions to the intermolecular forces associated with bundling of straight semi-flexible flagellar filaments.

The Dark Matter of Biology

The inside of the cell is full of important, yet invisible species of molecules and proteins that interact weakly but couple together to have huge and important effects in many biological processes. Such “dark matter” inside cells remains mostly hidden, because our tools were developed to investigate strongly interacting species and folded proteins. Example dark-matter species include intrinsically disordered proteins, posttranslational states, ion species, and rare, transient, and weak interactions undetectable by biochemical assays. The dark matter of biology is likely to have multiple, vital roles to regulate signaling, rates of reactions, water structure and viscosity, crowding, and other cellular activities. We need to create new tools to image, detect, and understand these dark-matter species if we are to truly understand fundamental physical principles of biology.

Optomechanical proposal for monitoring microtubule mechanical vibrations

Microtubules provide the mechanical force required for chromosome separation during mitosis. However, little is known about the dynamic (high-frequency) mechanical properties of microtubules. Here, we theoretically propose to control the vibrations of a doubly clamped microtubule by tip electrodes and to detect its motion via the optomechanical coupling between the vibrational modes of the microtubule and an optical cavity. In the presence of a red-detuned strong pump laser, this coupling leads to optomechanical-induced transparency of an optical probe field, which can be detected with state-of-the art technology. The center frequency and line width of the transparency peak give the resonance frequency and damping rate of the microtubule, respectively, while the height of the peak reveals information about the microtubule-cavity field coupling. Our method opens the new possibilities to gain information about the physical properties of microtubules, which will enhance our capability to design physical cancer treatment protocols as alternatives to chemotherapeutic drugs.

Tubulin acetylation protects long-lived microtubules against mechanical ageing

Long-lived microtubules endow the eukaryotic cell with long-range transport abilities. While long-lived microtubules are acetylated on Lys40 of α-tubulin (αK40), acetylation takes place after stabilization and does not protect against depolymerization. Instead, αK40 acetylation has been proposed to mechanically stabilize microtubules. Yet how modification of αK40, a residue exposed to the microtubule lumen and inaccessible to microtubule-associated proteins and motors, could affect microtubule mechanics remains an open question. Here we develop FRET-based assays that report on the lateral interactions between protofilaments and find that αK40 acetylation directly weakens inter-protofilament interactions. Congruently, αK40 acetylation affects two processes largely governed by inter-protofilament interactions, reducing the nucleation frequency and accelerating the shrinkage rate. Most relevant to the biological function of acetylation, microfluidics manipulations demonstrate that αK40 acetylation enhances flexibility and confers resilience against repeated mechanical stresses. Thus, unlike deacetylated microtubules that accumulate damage when subjected to repeated stresses, long-lived microtubules are protected from mechanical ageing through their acquisition of αK40 acetylation. In contrast to other tubulin post-translational modifications that act through microtubule-associated proteins, motors and severing enzymes, intraluminal acetylation directly tunes the compliance and resilience of microtubules.

Role of tau in the spatial organization of axonal microtubules: keeping parallel microtubules evenly distributed despite macromolecular crowding

Opposing views have been proposed regarding the role of tau, the principal microtubule-associated protein in axons. On the one hand, tau forms cross-bridges at the interface between microtubules and induces microtubule bundling in neurons. On the other hand, tau is also considered a polymer brush which efficiently separates microtubules. In mature axons, microtubules are indeed arranged in parallel arrays and are well separated from each other. To reconcile these views, we developed a mechanistic model based on in vitro and cellular approaches combined to analytical and numerical analyses. The results indicate that tau forms long-range cross-bridges between microtubules under macromolecular crowding conditions. Tau cross-bridges prevent the redistribution of tau away from the interface between microtubules, which would have occurred in the polymer brush model. Consequently, the short-range attractive force between microtubules induced by macromolecular crowding is avoided and thus microtubules remain well separated from each other. Interestingly, in this unified model, tau diffusion on microtubules enables to keep microtubules evenly distributed in axonal sections at low tau levels.

The effect of multivalent cations and Tau on paclitaxel-stabilized microtubule assembly, disassembly, and structure

In this review we describe recent studies directed at understanding the formation of novel nanoscale assemblies in biological materials systems. In particular, we focus on the effects of multivalent cations, and separately, of microtubule-associated protein (MAP) Tau, on microtubule (MT) ordering (bundling), MT disassembly, and MT structure. Counter-ion directed bundling of paclitaxel-stabilized MTs is a model electrostatic system, which parallels efforts to understand MT bundling by intrinsically disordered proteins (typically biological polyampholytes) expressed in neurons. We describe studies, which reveal an unexpected transition from tightly spaced MT bundles to loose bundles consisting of strings of MTs as the valence of the cationic counter-ion decreases from Z=3 to Z=2. This transition is not predicted by any current theories of polyelectrolytes. Notably, studies of a larger series of divalent counter-ions reveal strong ion specific effects. Divalent counter-ions may either bundle or depolymerize paclitaxel-stabilized MTs. The ion concentration required for depolymerization decreases with increasing atomic number. In a more biologically related system we review synchrotron small angle x-ray scattering (SAXS) studies on the effect of the Tau on the structure of paclitaxel-stabilized MTs. The electrostatic binding of MAP Tau isoforms leads to an increase in the average radius of microtubules with increasing Tau coverage (i.e. a re-distribution of protofilament numbers in MTs). Finally, inspired by MTs as model nanotubes, we briefly describe other more robust lipid-based cylindrical nanostructures, which may have technological applications, for example, in drug encapsulation and delivery.

Cardioprotective effect of royal jelly on paclitaxel-induced cardio-toxicity in rats

OBJECTIVES

Paclitaxel is a potent chemotherapy agent with severe side effects, including allergic reactions, cardiovascular problems, complete hair loss, joint and muscle pain, which may limit its use and lower its efficiency. The cardioprotective effect of royal jelly was investigated on paclitaxel-induced damages.

MATERIALS AND METHODS

Adult male Wistar rats were divided into control and test groups (n=8). The test group was assigned into five subgroups; 4 groups, along with paclitaxel administration (7.5 mg/kg BW, weekly), received various doses of royal jelly (50, 100, and 150 mg/kg BW) for 28 consecutive days. The last group received only royal jelly at 100 mg/kg. In addition to oxidative and nitrosative stress biomarkers, the creatine kinase (CK-BM) level was also determined. To show the cardioprotective effect of royal jelly on paclitaxel-induced damages, histopathological examinations were conducted.

RESULTS

Royal jelly lowered the paclitaxel-elevated malondialdehyde and nitric oxide levels in the heart. Royal jelly could also remarkably reduce the paclitaxel-induced cardiac biomarker of creatine kinase (CK-BM) level and pathological injuries such as diffused edema, hemorrhage, congestion, hyaline exudates, and necrosis. Moreover, royal jelly administration in a dose-dependent manner resulted in a significant (P<0.05) increase in the paclitaxel-reduced total antioxidant capacity.

CONCLUSION

Our data suggest that the paclitaxel-induced histopathological and biochemical alterations could be protected by the royal jelly administration. The cardioprotective effect of royal jelly may be related to the suppression of oxidative and nitrosative stress.

Direct force measurements reveal that protein Tau confers short-range attractions and isoform-dependent steric stabilization to microtubules

Microtubules (MTs) are hollow cytoskeletal filaments assembled from αβ-tubulin heterodimers. Tau, an unstructured protein found in neuronal axons, binds to MTs and regulates their dynamics. Aberrant Tau behavior is associated with neurodegenerative dementias, including Alzheimer's. Here, we report on a direct force measurement between paclitaxel-stabilized MTs coated with distinct Tau isoforms by synchrotron small-angle X-ray scattering (SAXS) of MT-Tau mixtures under osmotic pressure (P). In going from bare MTs to MTs with Tau coverage near the physiological submonolayer regime (Tau/tubulin-dimer molar ratio; ΦTau = 1/10), isoforms with longer N-terminal tails (NTTs) sterically stabilized MTs, preventing bundling up to PB ∼ 10,000-20,000 Pa, an order of magnitude larger than bare MTs. Tau with short NTTs showed little additional effect in suppressing the bundling pressure (PB ∼ 1,000-2,000 Pa) over the same range. Remarkably, the abrupt increase in PB observed for longer isoforms suggests a mushroom to brush transition occurring at 1/13 < ΦTau < 1/10, which corresponds to MT-bound Tau with NTTs that are considerably more extended than SAXS data for Tau in solution indicate. Modeling of Tau-mediated MT-MT interactions supports the hypothesis that longer NTTs transition to a polyelectrolyte brush at higher coverages. Higher pressures resulted in isoform-independent irreversible bundling because the polyampholytic nature of Tau leads to short-range attractions. These findings suggest an isoform-dependent biological role for regulation by Tau, with longer isoforms conferring MT steric stabilization against aggregation either with other biomacromolecules or into tight bundles, preventing loss of function in the crowded axon environment.

Measuring cohesion between macromolecular filaments one pair at a time: depletion-induced microtubule bundling

In the presence of nonadsorbing polymers, colloidal particles experience ubiquitous attractive interactions induced by depletion forces. Here, we measure the depletion interaction between a pair of microtubule filaments using a method that combines single filament imaging with optical trapping. By quantifying the dependence of filament cohesion on both polymer concentration and solution ionic strength, we demonstrate that the minimal model of depletion, based on the Asakura-Oosawa theory, fails to quantitatively describe the experimental data. By measuring the cohesion strength in two- and three- filament bundles, we verify pairwise additivity of depletion interactions for the specific experimental conditions. The described experimental technique can be used to measure pairwise interactions between various biological or synthetic filaments and complements information extracted from bulk osmotic stress experiments.

Brownian dynamics of subunit addition-loss kinetics and thermodynamics in linear polymer self-assembly

The structure and free energy of multistranded linear polymer ends evolves as individual subunits are added and lost. Thus, the energetic state of the polymer end is not constant, as assembly theory has assumed. Here we utilize a Brownian dynamics approach to simulate the addition and loss of individual subunits at the polymer tip. Using the microtubule as a primary example, we examined how the structure of the polymer tip dictates the rate at which units are added to and lost from individual protofilaments. We find that freely diffusing subunits arrive less frequently to lagging protofilaments but bind more efficiently, such that there is no kinetic difference between leading and lagging protofilaments within a tapered tip. However, local structure at the nanoscale has up to an order-of-magnitude effect on the rate of addition. Thus, the kinetic on-rate constant, integrated across the microtubule tip (kon,MT), is an ensemble average of the varying individual protofilament on-rate constants (kon,PF). Our findings have implications for both catastrophe and rescue of the dynamic microtubule end, and provide a subnanoscale framework for understanding the mechanism of action of microtubule-associated proteins and microtubule-directed drugs. Although we utilize the specific example of the microtubule here, the findings are applicable to multistranded polymers generally.

Simulated cytoskeletal collapse via tau degradation

We present a coarse-grained two dimensional mechanical model for the microtubule-tau bundles in neuronal axons in which we remove taus, as can happen in various neurodegenerative conditions such as Alzheimers disease, tauopathies, and chronic traumatic encephalopathy. Our simplified model includes (i) taus modeled as entropic springs between microtubules, (ii) removal of taus from the bundles due to phosphorylation, and (iii) a possible depletion force between microtubules due to these dissociated phosphorylated taus. We equilibrate upon tau removal using steepest descent relaxation. In the absence of the depletion force, the transverse rigidity to radial compression of the bundles falls to zero at about 60% tau occupancy, in agreement with standard percolation theory results. However, with the attractive depletion force, spring removal leads to a first order collapse of the bundles over a wide range of tau occupancies for physiologically realizable conditions. While our simplest calculations assume a constant concentration of microtubule intercalants to mediate the depletion force, including a dependence that is linear in the detached taus yields the same collapse. Applying percolation theory to removal of taus at microtubule tips, which are likely to be the protective sites against dynamic instability, we argue that the microtubule instability can only obtain at low tau occupancy, from 0.06-0.30 depending upon the tau coordination at the microtubule tips. Hence, the collapse we discover is likely to be more robust over a wide range of tau occupancies than the dynamic instability. We suggest in vitro tests of our predicted collapse.

Mechanical properties of doubly stabilized microtubule filaments

Microtubules are cytoskeletal filaments responsible for cell morphology and intracellular organization. Their dynamical and mechanical properties are regulated through the nucleotide state of the tubulin dimers and the binding of drugs and/or microtubule-associated proteins. Interestingly, microtubule-stabilizing factors have differential effects on microtubule mechanics, but whether stabilizers have cumulative effects on mechanics or whether one effect dominates another is not clear. This is especially important for the chemotherapeutic drug Taxol, an important anticancer agent and the only known stabilizer that reduces the rigidity of microtubules. First, we ask whether Taxol will combine additively with another stabilizer or whether one stabilizer will dominate another. We call microtubules in the presence of Taxol and another stabilizer, doubly stabilized. Second, since Taxol is often added to a number of cell types for therapeutic purposes, it is important from a biomedical perspective to understand how Taxol added to these systems affects the mechanical properties in treated cells. To address these questions, we use the method of freely fluctuating filaments with our recently developed analysis technique of bootstrapping to determine the distribution of persistence lengths of a large population of microtubules treated with different stabilizers, including Taxol, guanosine-5' [(α, β)-methyleno] triphosphate, guanosine-5'-O-(3-thiotriphosphate), tau, and MAP4. We find that combinations of these stabilizers have novel effects on the mechanical properties of microtubules.

Entropic attraction condenses like-charged interfaces composed of self-assembled molecules

Like-charged solid interfaces repel and separate from one another as much as possible. Charged interfaces composed of self-assembled charged-molecules such as lipids or proteins are ubiquitous. The present study shows that although charged lipid-membranes are sufficiently rigid, in order to swell as much as possible, they deviate markedly from the behavior of typical like-charged solids when diluted below a critical concentration (ca. 15 wt %). Unexpectedly, they swell into lamellar structures with spacing that is up to four times shorter than the layers should assume (if filling the entire available space). This process is reversible with respect to changing the lipid concentration. Additionally, the research shows that, although the repulsion between charged interfaces increases with temperature, like-charged membranes, remarkably, condense with increasing temperature. This effect is also shown to be reversible. Our findings hold for a wide range of conditions including varying membrane charge density, bending rigidity, salt concentration, and conditions of typical living systems. We attribute the limited swelling and condensation of the net repulsive interfaces to their self-assembled character. Unlike solids, membranes can rearrange to gain an effective entropic attraction, which increases with temperature and compensates for the work required for condensing the bilayers. Our findings provide new insight into the thermodynamics and self-organization of like-charged interfaces composed of self-assembled molecules such as charged biomaterials and supramolecular assemblies that are widely found in synthetic and natural constructs.

Why is the microtubule lattice helical?

Microtubules polymerize from identical tubulin heterodimers, which form a helical lattice pattern that is the microtubule. This pattern always has left-handed chirality, but it is not known why. But as tubulin, similar to other proteins, evolved for a purpose, the question of the title of this artcile appears to be meaningful. In a computer simulation that explores the 'counterfactual biology' of microtubules without helicity, we demonstrate that these have the same mechanical properties as Nature's microtubules with helicity. Thus only a dynamical reason for helicity is left as potential explanation. We find that helicity solves 'the problem of the blind mason', i.e. how to correctly build a structure, guided only by the shape of the bricks. This answer in turn raises some new questions for researchers to address.

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.

Intrinsic bending of microtubule protofilaments

The complex polymerization dynamics of the microtubule (MT) plus end are closely linked to the hydrolysis of the GTP nucleotide bound to the β-tubulin. The destabilization is thought to be associated with the conformational change of the tubulin dimers from the straight conformation in the MT lattice to a curved conformation. It remains under debate whether this transformation is directly related to the nucleotide state, or a consequence of the longitudinal or lateral contacts in the MT lattice. Here, we present large-scale atomistic simulations of short tubulin protofilaments with both nucleotide states, starting from both extreme conformations. Our simulations indicate that both interdimer and intradimer contacts in both GDP and GTP-bound tubulin dimers and protofilaments in solution bend. There are no observable differences between the mesoscopic properties of the contacts in GTP and GDP-bound tubulin or the intradime and interdimer interfaces.

Nanoscale assembly in biological systems: from neuronal cytoskeletal proteins to curvature stabilizing lipids

The review will describe experiments inspired by the rich variety of bundles and networks of interacting microtubules (MT), neurofilaments, and filamentous-actin in neurons where the nature of the interactions, structures, and structure-function correlations remain poorly understood. We describe how three-dimensional (3D) MT bundles and 2D MT bundles may assemble, in cell free systems in the presence of counter-ions, revealing structures not predicted by polyelectrolyte theories. Interestingly, experiments reveal that the neuronal protein tau, an abundant MT-associated-protein in axons, modulates the MT diameter providing insight for the control of geometric parameters in bio- nanotechnology. In another set of experiments we describe lipid-protein-nanotubes, and lipid nano-tubes and rods, resulting from membrane shape evolution processes involving protein templates and curvature stabilizing lipids. Similar membrane shape changes, occurring in cells for the purpose of specific functions, are induced by interactions between membranes and proteins. The biological materials systems described have applications in bio-nanotechnology.

X+: a comprehensive computationally accelerated structure analysis tool for solution X-ray scattering from supramolecular self-assemblies

X+is a user-friendly multi-core accelerated program that fully analyses solution X-ray scattering radially integrated images. This software is particularly useful for analysing supramolecular self-assemblies, often found in biology, and for reconstructing the scattering signal in its entirety. The program enables various ways of subtracting background noise. The user selects a geometric model and defines as many layers of that shape as needed. The thickness and electron density of each layer are the fitting parameters. An initial guess is input by the user and the program calculates the form-factor parameters that best fit the data. The polydispersity of one size parameter at a time can be taken into account. The program can then address the assembly of those shapes into different lattice symmetries. This is accounted for by fitting the parameters of the structure factor, using various peak line shapes. The models of the program and selected features are presented. Among them are the model-fitting procedure, which includes both absolute and relative constraints, data smoothing, signal decomposition for separation of form and structure factors, goodness-of-fit verification procedures, error estimation, and automatic feature recognition in the data, such as correlation peaks and baseline. The program's intuitive graphical user interface runs on Windows PCs. UsingX+, the exact structure of a microtubule in a crowded environment, and the structure, domain size, and elastic and interaction parameters of lipid bilayers, were obtained.

Acute Taxol nephrotoxicity: Histological and ultrastructural studies of mice kidney parenchyma

Taxol is a microtubule inhibitor drug widely used in treatment of many types of cancer. Nephrotoxicity is the most hazardous effect complicating chemotherapy in general and kidney functions must be monitored early during any chemotherapeutic course. The main objective of the present study was to investigate the effect of acute Taxol nephrotoxicity in mice. In the present study Taxol at different doses; MD, ID and MTD (0.6, 1.15 and 1.7 mg/kg), respectively, was given by intra-peritoneal route to 54 adult male mice with an average body weight of 20-25 g. Kidney samples was taken 6, 24, 48 h following administration, fixed in 10% neutral buffered formalin, paraffin sections 5 μm thick were stained by haematoxylin and eosin and PAS and then examined for histological changes. Samples from animals treated by the maximum dose (MTD = 1.7 mg/kg) for 48 h were fixed in 3% gluteraldehyde in phosphate buffer (pH 7.4) and processed for transmission electron microscope. Taxol given for short duration was found to produce marked degenerative changes in kidney parenchyma even in minimum tolerated dose (MD = 0.6 mg/kg). Individual variations were observed regarding the degree of nephrotoxicity. There was marked loss of renal tubules epithelial lining, damage of brush border and formation of hyaline casts within the damaged tubules. The alterations were in the form of both necrotic and apoptotic changes in the kidney tubules. Focal atrophy of glomerular tufts was also observed. Vascular congestion and degenerative changes in renal blood vessels were occasionally evident in some samples. Ultrastructure study revealed damage of glomerular membrane. Proximal tubule showed loss of basal infoldings, damage of brush border, mitochondrial degeneration and nuclear changes. Distal tubules also showed demarked degenerative changes. Increased frequency of micronuclei proved that Taxol had genotoxic effects in mice bone marrow cells. In conclusion Taxol had nephrotoxic effect on mice kidney that must be considered during its use as a chemotherapeutic agent in human.

Microtubule elasticity: connecting all-atom simulations with continuum mechanics

The mechanical properties of microtubules have been extensively studied using a wide range of biophysical techniques, seeking to understand the mechanics of these cylindrical polymers. Here we develop a method for connecting all-atom molecular dynamics simulations with continuum mechanics and show how this can be applied to understand microtubule mechanics. Our coarse-graining technique applied to the microscopic simulation system yields consistent predictions for the Young's modulus and persistence length of microtubules, while clearly demonstrating how binding of the drug Taxol decreases the stiffness of microtubules. The techniques we develop should be widely applicable to other macromolecular systems.

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.

An analysis of FtsZ assembly using small angle X-ray scattering and electron microscopy

Small angle X-ray scattering (SAXS) was used for the first time to study the self-assembly of the bacterial cell division protein, FtsZ, with three different additives: calcium chloride, monosodium glutamate and DEAE-dextran hydrochloride in solution. The SAXS data were analyzed assuming a model form factor and also by a model-independent analysis using the pair distance distribution function. Transmission electron microscopy (TEM) was used for direct observation of the FtsZ filaments. By sectioning and negative staining with glow discharged grids, very high bundling as well as low bundling polymers were observed under different assembly conditions. FtsZ polymers formed different structures in the presence of different additives and these additives were found to increase the bundling of FtsZ protofilaments by different mechanisms. The combined use of SAXS and TEM provided us a significant insight of the assembly of FtsZ and microstructures of the assembled FtsZ polymers.

Effects of osmotic force and torque on microtubule bundling and pattern formation

We report effects of polyethylene glycol (PEG, molecular weight of 35 kDa ) on microtubule (MT) bundling and pattern formation. Without PEG, polymerizing tubulin solutions of a few mg/ml that are initially subjected to a field that aligns MTs can spontaneously form striated birefringence patterns. These patterns form through MT alignment, bundling, and coordinated bundle buckling. With increasing PEG concentrations, solutions form progressively weaker patterns. At a sufficiently high PEG concentration ( approximately 0.5% by weight), the samples maintain a nearly uniform birefringence (i.e., no pattern) and laterally contract at a later stage. Concomitantly, on a microscopic level, the network of dispersed MTs that accompany the bundles in pure solutions disappear and the bundles become more distinct. We attribute the weakening of the pattern to the loss of the dispersed MT network, which is required to mediate the coordination of bundle buckling. We propose that the loss of the dispersed network and the enhanced bundling result from PEG associated osmotic forces that drive MTs together and osmotic torques that facilitate their bundling. Similarly, we attribute the lateral contraction of the samples to osmotic torques that tend to align crossing bundles in the network.

Taxol allosterically alters the dynamics of the tubulin dimer and increases the flexibility of microtubules

Taxol is a commonly used antitumor agent that hyperstabilizes microtubules and prevents cell division. The interaction of Taxol with tubulin and the microtubule has been studied through a wide array of experimental techniques; however, the exact molecular mechanism by which Taxol stabilizes microtubules has remained elusive. In this study, through the use of large-scale molecular simulations, we show that Taxol affects the interactions between the M and H1-S2 loops of adjacent tubulin dimers leading to more stable interprotofilament interactions. More importantly, we demonstrate that Taxol binding leads to a significant increase in the dynamics and flexibility of the portion of beta-tubulin that surrounds the bound nucleotide and makes contact with the alpha-monomer of the next dimer in the protofilament. We conclude that this increase in flexibility allows the microtubule to counteract the conformational changes induced by nucleotide hydrolysis and keeps the protofilaments in a straight conformation, resulting in a stable microtubule.

Three-dimensional microtubule behavior in Xenopus egg extracts reveals four dynamic states and state-dependent elastic properties

Although microtubules are key players in many cellular processes, very little is known about their dynamic and mechanical properties in physiological three-dimensional environments. The conventional model of microtubule dynamic instability postulates two dynamic microtubule states, growth and shrinkage. However, several studies have indicated that such a model does not provide a comprehensive quantitative and qualitative description of microtubule behavior. Using three-dimensional laser light-sheet fluorescence microscopy and a three-dimensional sample preparation in spacious Teflon cylinders, we measured microtubule dynamic instability and elasticity in interphase Xenopus laevis egg extracts. Our data are inconsistent with a two-state model of microtubule dynamic instability and favor an extended four-state model with two independent metastable pause states over a three-state model with a single pause state. Moreover, our data on kinetic state transitions rule out a simple GTP cap model as the driving force of microtubule stabilization in egg extracts on timescales of a few seconds or longer. We determined the three-dimensional elastic properties of microtubules as a function of both the contour length and the dynamic state. Our results indicate that pausing microtubules are less flexible than growing microtubules and suggest a growth-speed-dependent persistence length. These data might hint toward mechanisms that enable microtubules to efficiently perform multiple different tasks in the cell and suggest the development of a unified model of microtubule dynamics and microtubule mechanics.

Microtubule architecture: inspiration for novel carbon nanotube-based biomimetic materials

Microtubules are self-assembling biological nanotubes that are essential for cell motility, cell division and intracellular trafficking. Microtubules have outstanding mechanical properties, combining high resilience and stiffness. Such a combination allows microtubules to accomplish multiple cellular functions and makes them interesting for material sciences. We review recent experiments that elucidate the relationship between molecular architecture and mechanics in microtubules and examine analogies and differences between microtubules and carbon nanotubes, which are their closest equivalent in nanotechnology. We suggest that a long-term goal in bionanotechnology should be mimicking the properties of microtubules and microtubule bundles to produce new functional nanomaterials.

A finite element framework for computation of protein normal modes and mechanical response

A computational framework based on the Finite Element Method is presented to calculate the normal modes and mechanical response of proteins and their supramolecular assemblies. Motivated by elastic network models, proteins are treated as continuum elastic solids with molecular volume defined by their solvent-excluded surface. The discretized Finite Element representation is obtained using a surface simplification algorithm that facilitates the generation of models of arbitrary prescribed spatial resolution. The procedure is applied to a mutant of T4 phage lysozyme, G-actin, syntenin, cytochrome-c', beta-tubulin, and the supramolecular assembly filamentous actin (F-actin). Equilibrium thermal fluctuations of alpha-carbon atoms and their inter-residue correlations compare favorably with all-atom-based results, the Rotational-Translational Block procedure, and experiment. Additionally, the free vibration and compressive buckling responses of F-actin are in quantitative agreement with experiment. The proposed methodology is applicable to any protein or protein assembly and facilitates the incorporation of specific atomic-level interactions, including aqueous-electrolyte-mediated electrostatic effects and solvent damping. The procedure is equally applicable to proteins with known atomic coordinates as it is to electron density maps of proteins, protein complexes, and supramolecular assemblies of unknown atomic structure.

Surface deflection of a microtubule loaded by a concentrated radial force

Microtubules are hollow cylindrical filaments of a eukaryotic cytoskeleton which are sensitive to externally applied radial forces due to their low circumferential elastic modulus. In this work, an orthotropic elastic shell model for microtubules is used to study the surface radial deflection of a microtubule loaded by a concentrated radial force generated by either a single molecular motor or a radial indentation tip. Our results show that the maximum surface radial deflection of a microtubule generated by a concentrated radial force of a few pN can be as large as a few nanometers (a significant fraction of the radius of microtubules), which could cause significant surface morphological non-uniformity of the microtubule. In contrast, radial indentation under a much larger compressive force, which can be as large as a few hundreds of pN, will cause hardening of the circumferential elastic modulus almost equal to the longitudinal modulus of microtubules. In this case, our results show that a microtubule can withstand a concentrated radial compressive force as large as a few hundreds of pN, with a maximum radial deflection not more than a few nanometers, in good agreement with recent experiments on radial indentation of microtubules. These results offer useful data and new insights into the basic understanding of elastic interaction between microtubules and molecular motors and radial indentation of microtubules.

Orthotropic elastic shell model for buckling of microtubules

In view of the fact that microtubules exhibit strong anisotropic elastic properties, an orthotropic elastic shell model for microtubules is developed to study buckling behavior of microtubules. The predicted critical pressure is found to agree well with recent unexplained experimental data on pressure-induced buckling of microtubules [Needleman, Phys. Rev. Lett. 93, 198104 (2004); Biophys. J. 89, 3410 (2005)] which are lower than that predicted by the isotropic shell model by four orders of magnitude. General buckling behavior of microtubules under axial compression or radial pressure is studied. The results show that the isotropic shell model greatly overestimates the bucking loads of microtubules, except columnlike axially compressed buckling of long microtubules (of length-to-diameter ratio larger than, say, 150). In particular, the present results also offer a plausible explanation for the length dependency of flexibility of microtubules reported in the literature.