Thermal fluctuations of grafted microtubules provide evidence of a length-dependent persistence length

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.

Tissue loading and microstructure regulate the deformation of embedded nerve fibres: predictions from single-scale and multiscale simulations

Excessive deformation of nerve fibres (axons) in the spinal facet capsular ligaments (FCLs) can be a cause of pain. The axons are embedded in the fibrous extracellular matrix (ECM) of FCLs, so understanding how local fibre organization and micromechanics modulate their mechanical behaviour is essential. We constructed a computational discrete-fibre model of an axon embedded in a collagen fibre network attached to the axon by distinct fibre-axon connections. This model was used to relate the axonal deformation to the fibre alignment and collagen volume concentration of the surrounding network during transverse, axial and shear deformations. Our results showed that fibre alignment affects axonal deformation only during transverse and axial loading, but higher collagen volume concentration results in larger overall axonal strains for all loading cases. Furthermore, axial loading leads to the largest stretch of axonal microtubules and induces the largest forces on axon's surface in most cases. Comparison between this model and a multiscale continuum model for a representative case showed that although both models predicted similar averaged axonal strains, strain was more heterogeneous in the discrete-fibre model.

Fiber Network Formation in Semi-Flexible Polymer Solutions: An Exploratory Computational Study

The formation of gels through the bundling of semi-flexible polymer chains into fiber networks is ubiquitous in diverse manufactured and natural materials, and, accordingly, we perform exploratory molecular dynamics simulations of a coarse-grained model of semi-flexible polymers in a solution with attractive lateral interchain interactions to understand essential features of this type of gel formation. After showing that our model gives rise to fibrous gels resembling real gels of this kind, we investigate how the extent of fiber bundling influences the "melting" temperature, T m , and the emergent rigidification of model bundled fibers having a fixed number of chains, N, within them. Based on our preliminary observations, we suggest the fiber size is kinetically selected by a reduced thermodynamic driving force and a slowing of the dynamics within the fibers associated with their progressive rigidification with the inclusion of an increasing number of chains in the bundle.

Catastrophic depolymerization of microtubules driven by subunit shape change

Microtubules exhibit a dynamic instability between growth and catastrophic depolymerization. GTP-tubulin (αβ-dimer bound to GTP) self-assembles, but dephosphorylation of GTP- to GDP-tubulin within the tubule results in destabilization. While the mechanical basis for destabilization is not fully understood, one hypothesis is that dephosphorylation causes tubulin to change shape, frustrating bonds and generating stress. To test this idea, we perform molecular dynamics simulations of microtubules built from coarse-grained models of tubulin, incorporating a small compression of α-subunits associated with dephosphorylation in experiments. We find that this shape change induces depolymerization of otherwise stable systems via unpeeling "ram's horns" characteristic of microtubules. Depolymerization can be averted by caps with uncompressed α-subunits, i.e., GTP-rich end regions. Thus, the shape change is sufficient to yield microtubule behavior.

The counterbend dynamics of cross-linked filament bundles and flagella

Cross-linked filament bundles, such as in cilia and flagella, are ubiquitous in biology. They are considered in textbooks as simple filaments with larger stiffness. Recent observations of flagellar counterbend, however, show that induction of curvature in one section of a passive flagellum instigates a compensatory counter-curvature elsewhere, exposing the intricate role of the diminutive cross-linking proteins at large scales. We show that this effect, a material property of the cross-linking mechanics, modifies the bundle dynamics and induces a bimodal L² - L³ length-dependent material response that departs from the Euler-Bernoulli theory. Hence, the use of simpler theories to analyse experiments can result in paradoxical interpretations. Remarkably, the counterbend dynamics instigates counter-waves in opposition to driven oscillations in distant parts of the bundle, with potential impact on the regulation of flagellar bending waves. These results have a range of physical and biological applications, including the empirical disentanglement of material quantities via counterbend dynamics.

A computational framework for cortical microtubule dynamics in realistically shaped plant cells

Plant morphogenesis is strongly dependent on the directional growth and the subsequent oriented division of individual cells. It has been shown that the plant cortical microtubule array plays a key role in controlling both these processes. This ordered structure emerges as the collective result of stochastic interactions between large numbers of dynamic microtubules. To elucidate this complex self-organization process a number of analytical and computational approaches to study the dynamics of cortical microtubules have been proposed. To date, however, these models have been restricted to two dimensional planes or geometrically simple surfaces in three dimensions, which strongly limits their applicability as plant cells display a wide variety of shapes. This limitation is even more acute, as both local as well as global geometrical features of cells are expected to influence the overall organization of the array. Here we describe a framework for efficiently simulating microtubule dynamics on triangulated approximations of arbitrary three dimensional surfaces. This allows the study of microtubule array organization on realistic cell surfaces obtained by segmentation of microscopic images. We validate the framework against expected or known results for the spherical and cubical geometry. We then use it to systematically study the individual contributions of global geometry, cell-edge induced catastrophes and cell-face induced stability to array organization in a cuboidal geometry. Finally, we apply our framework to analyze the highly non-trivial geometry of leaf pavement cells of Arabidopsis thaliana, Nicotiana benthamiana and Hedera helix. We show that our simulations can predict multiple features of the microtubule array structure in these cells, revealing, among others, strong constraints on the orientation of division planes.

Modeling the effects of lattice defects on microtubule breaking and healing

Microtubule reorganization often results from the loss of polymer induced through breakage or active destruction by energy-using enzymes. Pre-existing defects in the microtubule lattice likely lower structural integrity and aid filament destruction. Using large-scale molecular simulations, we model diverse microtubule fragments under forces generated at specific positions to locally crush the filament. We show that lattices with 2% defects are crushed and severed by forces three times smaller than defect-free ones. We validate our results with direct comparisons of microtubule kinking angles during severing. We find a high statistical correlation between the angle distributions from experiments and simulations indicating that they sample the same population of structures. Our simulations also indicate that the mechanical environment of the filament affects breaking: local mechanical support inhibits healing after severing, especially in the case of filaments with defects. These results recall reports of microtubule healing after flow-induced bending and corroborate prior experimental studies that show severing is more likely at locations where microtubules crossover in networks. Our results shed new light on mechanisms underlying the ability of microtubules to be destroyed and healed in the cell, either by external forces or by severing enzymes wedging dimers apart. © 2016 Wiley Periodicals, Inc.

Molecular rigidity and enthalpy-entropy compensation in DNA melting

Enthalpy-entropy compensation (EEC) is observed in diverse molecular binding processes of importance to living systems and manufacturing applications, but this widely occurring phenomenon is not sufficiently understood from a molecular physics standpoint. To gain insight into this fundamental problem, we focus on the melting of double-stranded DNA (dsDNA) since measurements exhibiting EEC are extensive for nucleic acid complexes and existing coarse-grained models of DNA allow us to explore the influence of changes in molecular parameters on the energetic parameters by using molecular dynamics simulations. Previous experimental and computational studies have indicated a correlation between EEC and changes in molecular rigidity in certain binding-unbinding processes, and, correspondingly, we estimate measures of DNA molecular rigidity under a wide range of conditions, along with resultant changes in the enthalpy and entropy of binding. In particular, we consider variations in dsDNA rigidity that arise from changes of intrinsic molecular rigidity such as varying the associative interaction strength between the DNA bases, the length of the DNA chains, and the bending stiffness of the individual DNA chains. We also consider extrinsic changes of molecular rigidity arising from the addition of polymer additives and geometrical confinement of DNA between parallel plates. All our computations confirm EEC and indicate that this phenomenon is indeed highly correlated with changes in molecular rigidity. However, two distinct patterns relating to how DNA rigidity influences the entropy of association emerge from our analysis. Increasing the intrinsic DNA rigidity increases the entropy of binding, but increases in molecular rigidity from external constraints decreases the entropy of binding. EEC arises in numerous synthetic and biological binding processes and we suggest that changes in molecular rigidity might provide a common origin of this ubiquitous phenomenon in the mutual binding and unbinding of complex molecules.

Mechanical Properties of the Cytoskeleton and Cells

SUMMARYThe cytoskeleton is the major mechanical structure of the cell; it is a complex, dynamic biopolymer network comprising microtubules, actin, and intermediate filaments. Both the individual filaments and the entire network are not simple elastic solids but are instead highly nonlinear structures. Appreciating the mechanics of biopolymer networks is key to understanding the mechanics of cells. Here, we review the mechanical properties of cytoskeletal polymers and discuss the implications for the behavior of cells.

Single Actin Bundle Rheology

Bundled actin structures play an essential role in the mechanical response of the actin cytoskeleton in eukaryotic cells. Although responsible for crucial cellular processes, they are rarely investigated in comparison to single filaments and isotropic networks. Presenting a highly anisotropic structure, the determination of the mechanical properties of individual bundles was previously achieved through passive approaches observing bending deformations induced by thermal fluctuations. We present a new method to determine the bending stiffness of individual bundles, by measuring the decay of an actively induced oscillation. This approach allows us to systematically test anisotropic, bundled structures. Our experiments revealed that thin, depletion force-induced bundles behave as semiflexible polymers and obey the theoretical predictions determined by the wormlike chain model. Thickening an individual bundle by merging it with other bundles enabled us to study effects that are solely based on the number of involved filaments. These thicker bundles showed a frequency-dependent bending stiffness, a behavior that is inconsistent with the predictions of the wormlike chain model. We attribute this effect to internal processes and give a possible explanation with regard to the wormlike bundle theory.

Structure-property relation and relevance of beam theories for microtubules: a coupled molecular and continuum mechanics study

Quasi-one-dimensional microtubules (MTs) in cells enjoy high axial rigidity but large transverse flexibility due to the inter-protofilament (PF) sliding. This study aims to explore the structure–property relation for MTs and examine the relevance of the beam theories to their unique features. A molecular structural mechanics (MSM) model was used to identify the origin of the inter-PF sliding and its role in bending and vibration of MTs. The beam models were then fitted to the MSM to reveal how they cope with the distinct mechanical responses induced by the inter-PF sliding. Clear evidence showed that the inter-PF sliding is due to the soft inter-PF bonds and leads to the length-dependent bending stiffness. The Euler beam theory is found to adequately describe MT deformation when the inter-PF sliding is largely prohibited. Nevertheless, neither shear deformation nor the nonlocal effect considered in the ‘more accurate’ beam theories can fully capture the effect of the inter-PF sliding. This reflects the distinct deformation mechanisms between an MT and its equivalent continuous body.

Control of molecular shuttles by designing electrical and mechanical properties of microtubules

Kinesin-driven microtubules have been focused on to serve as molecular transporters, called "molecular shuttles," to replace micro/nanoscale molecular manipulations necessitated in micro total analysis systems. Although transport, concentration, and detection of target molecules have been demonstrated, controllability of the transport directions is still a major challenge. Toward broad applications of molecular shuttles by defining multiple moving directions for selective molecular transport, we integrated a bottom-up molecular design of microtubules and a top-down design of a microfluidic device. The surface charge density and stiffness of microtubules were controlled, allowing us to create three different types of microtubules, each with different gliding directions corresponding to their electrical and mechanical properties. The measured curvature of the gliding microtubules enabled us to optimize the size and design of the device for molecular sorting in a top-down approach. The integrated bottom-up and top-down design achieved separation of stiff microtubules from negatively charged, soft microtubules under an electric field. Our method guides multiple microtubules by integrating molecular control and microfluidic device design; it is not only limited to molecular sorters but is also applicable to various molecular shuttles with the high controllability in their movement directions.

Persistence length of collagen molecules based on nonlocal viscoelastic model

Persistence length is one of the most interesting properties of a molecular chain, which is used to describe the stiffness of a molecule. The experimentally measured values of the persistence length of the collagen molecule are widely scattered from 14 to 180 nm. Therefore, an alternative approach is highly desirable to predict the persistence length of a molecule and also to explain the experimental results. In this paper, a nonlocal viscoelastic model is developed to obtain the persistence length of the collagen molecules in solvent. A new explicit formula is proposed for the persistence length of the molecule with the consideration of the small-scale effect, viscoelastic properties of the molecule, loading frequency, and viscosity of the solvent. The presented model indicates that there exists a range of molecule lengths in which the persistence length strongly depends on the frequency and spatial mode of applied loads, small-scale effect, and viscoelastic properties of the collagen.

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.

Single microtubules and small networks become significantly stiffer on short time-scales upon mechanical stimulation

The transfer of mechanical signals through cells is a complex phenomenon. To uncover a new mechanotransduction pathway, we study the frequency-dependent transport of mechanical stimuli by single microtubules and small networks in a bottom-up approach using optically trapped beads as anchor points. We interconnected microtubules to linear and triangular geometries to perform micro-rheology by defined oscillations of the beads relative to each other. We found a substantial stiffening of single filaments above a characteristic transition frequency of 1–30 Hz depending on the filament’s molecular composition. Below this frequency, filament elasticity only depends on its contour and persistence length. Interestingly, this elastic behavior is transferable to small networks, where we found the surprising effect that linear two filament connections act as transistor-like, angle dependent momentum filters, whereas triangular networks act as stabilizing elements. These observations implicate that cells can tune mechanical signals by temporal and spatial filtering stronger and more flexibly than expected.

Deformation pattern in vibrating microtubule: Structural mechanics study based on an atomistic approach

The mechanical properties of microtubules are of great importance for understanding their biological function and for applications in artificial devices. Although microtubule mechanics has been extensively studied both theoretically and experimentally, the relation to its molecular structure is understood only partially. Here, we report on the structural analysis of microtubule vibration modes calculated by an atomistic approach. Molecular dynamics was applied to refine the atomic structure of a microtubule and a C_α elastic network model was analyzed for its normal modes. We mapped fluctuations and local deformations up to the level of individual aminoacid residues. The deformation is mode-shape dependent and principally different in α-tubulins and β-tubulins. Parts of the tubulin dimer sequence responding specifically to longitudinal and radial stress are identified. We show that substantial strain within a microtubule is located both in the regions of contact between adjacent dimers and in the body of tubulins. Our results provide supportive evidence for the generally accepted assumption that the mechanics of microtubules, including its anisotropy, is determined by the bonds between tubulins.

Direct measurement of conformational strain energy in protofilaments curling outward from disassembling microtubule tips

Disassembling microtubules can generate movement independently of motor enzymes, especially at kinetochores where they drive chromosome motility. A popular explanation is the 'conformational wave' model, in which protofilaments pull on the kinetochore as they curl outward from a disassembling tip. But whether protofilaments can work efficiently via this spring-like mechanism has been unclear. By modifying a previous assay to use recombinant tubulin and feedback-controlled laser trapping, we directly demonstrate the spring-like elasticity of curling protofilaments. Measuring their mechanical work output suggests they carry ~25% of the energy of GTP hydrolysis as bending strain, enabling them to drive movement with efficiency similar to conventional motors. Surprisingly, a β-tubulin mutant that dramatically slows disassembly has no effect on work output, indicating an uncoupling of disassembly speed from protofilament strain. These results show the wave mechanism can make a major contribution to kinetochore motility and establish a direct approach for measuring tubulin mechano-chemistry.

Exact solution for the force-extension relation of a semiflexible polymer under compression

Exact solutions for the elastic and thermodynamic properties for the wormlike chain model are elaborated in terms of Mathieu functions. The smearing of the classical Euler buckling instability for clamped polymers is analyzed for the force-extension relation. Interestingly, at strong compression forces the thermal fluctuations lead to larger elongations than for the elastic rod. The susceptibility defined as the derivative of the force-extension relation displays a prominent maximum at a force that approaches the critical Euler buckling force as the persistence length is increased. We also evaluate the excess entropy and heat capacity induced by the compression and find that they vary nonmonotonically with the load. These findings are corroborated by pseudo-Brownian simulations.

Axon tension regulates fasciculation/defasciculation through the control of axon shaft zippering

While axon fasciculation plays a key role in the development of neural networks, very little is known about its dynamics and the underlying biophysical mechanisms. In a model system composed of neurons grown ex vivo from explants of embryonic mouse olfactory epithelia, we observed that axons dynamically interact with each other through their shafts, leading to zippering and unzippering behavior that regulates their fasciculation. Taking advantage of this new preparation suitable for studying such interactions, we carried out a detailed biophysical analysis of zippering, occurring either spontaneously or induced by micromanipulations and pharmacological treatments. We show that zippering arises from the competition of axon-axon adhesion and mechanical tension in the axons, and provide the first quantification of the force of axon-axon adhesion. Furthermore, we introduce a biophysical model of the zippering dynamics, and we quantitatively relate the individual zipper properties to global characteristics of the developing axon network. Our study uncovers a new role of mechanical tension in neural development: the regulation of axon fasciculation.

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.

Optical detection of nanometric thermal fluctuations to measure the stiffness of rigid superparamagnetic microrods

The rigidity of numerous biological filaments and crafted microrods has been conveniently deduced from the analysis of their thermal fluctuations. However, the difficulty of measuring nanometric displacements with an optical microscope has so far limited such studies to sufficiently flexible rods, of which the persistence length ([Formula: see text]) rarely exceeds 1 m at room temperature. Here, we demonstrate the possibility to probe 10-fold stiffer rods by a combination of superresolutive optical methods and a statistical analysis of the data based on a recent theoretical model that predicts the amplitude of the fluctuations at any location of the rod [Benetatos P, Frey E (2003) Phys Rev E Stat Nonlin Soft Matter Phys 67(5):051108]. Using this approach, we report measures of [Formula: see text] up to 0.5 km. We obtained these measurements on recently designed superparamagnetic [Formula: see text]40-[Formula: see text]m-long microrods containing iron-oxide nanoparticles connected by a polymer mesh. Using their magnetic properties, we provide an alternative proof of validity of these thermal measurements: For each individual studied rod, we performed a second measure of its rigidity by deflecting it with a uniform magnetic field. The agreement between the thermal and the magnetoelastic measures was realized with more than a decade of values of [Formula: see text] from 5.1 m to 129 m, corresponding to a bending modulus ranging from 2.2 to 54 (×[Formula: see text] Jm). Despite the apparent homogeneity of the analyzed microrods, their Young modulus follows a broad distribution from 1.9 MPa to 59 MPa and up to 200 MPa, depending on the size of the nanoparticles.

Introduction to Optical Tweezers

Thirty years after their invention by Arthur Ashkin and colleagues at Bell Labs in 1986 [1], optical tweezers (or traps) have become a versatile tool to address numerous biological problems. Put simply, an optical trap is a highly focused laser beam that is capable of holding and applying forces to micron-sized dielectric objects. However, their development over the last few decades has converted these tools from boutique instruments into highly versatile instruments of molecular biophysics. This introductory chapter intends to give a brief overview of the field, highlight some important scientific achievements, and demonstrate why optical traps have become a powerful tool in the biological sciences. We introduce a typical optical setup, describe the basic theoretical concepts of how trapping forces arise, and present the quantitative position and force measurement techniques that are most widely used today.

Altered nuclear dynamics in MDX myofibers

Duchenne muscular dystrophy (DMD) is a genetic disorder in which the absence of dystrophin leads to progressive muscle degeneration and weakness. Although the genetic basis is known, the pathophysiology of dystrophic skeletal muscle remains unclear. We examined nuclear movement in wild-type (WT) and muscular dystrophy mouse model for DMD (MDX) (dystrophin-null) mouse myofibers. We also examined expression of proteins in the linkers of nucleoskeleton and cytoskeleton (LINC) complex, as well as nuclear transcriptional activity via histone H3 acetylation and polyadenylate-binding nuclear protein-1. Because movement of nuclei is not only LINC dependent but also microtubule dependent, we analyzed microtubule density and organization in WT and MDX myofibers, including the application of a unique 3D tool to assess microtubule core structure. Nuclei in MDX myofibers were more mobile than in WT myofibers for both distance traveled and velocity. MDX muscle shows reduced expression and labeling intensity of nesprin-1, a LINC protein that attaches the nucleus to the microtubule and actin cytoskeleton. MDX nuclei also showed altered transcriptional activity. Previous studies established that microtubule structure at the cortex is disrupted in MDX myofibers; our analyses extend these findings by showing that microtubule structure in the core is also disrupted. In addition, we studied malformed MDX myofibers to better understand the role of altered myofiber morphology vs. microtubule architecture in the underlying susceptibility to injury seen in dystrophic muscles. We incorporated morphological and microtubule architectural concepts into a simplified finite element mathematical model of myofiber mechanics, which suggests a greater contribution of myofiber morphology than microtubule structure to muscle biomechanical performance.NEW & NOTEWORTHY Microtubules provide the means for nuclear movement but show altered organization in the muscular dystrophy mouse model (MDX) (dystrophin-null) muscle. Here, MDX myofibers show increased nuclear movement, altered transcriptional activity, and altered linkers of nucleoskeleton and cytoskeleton complex expression compared with healthy myofibers. Microtubule architecture was incorporated in finite element modeling of passive stretch, revealing a role of fiber malformation, commonly found in MDX muscle. The results suggest that alterations in microtubule architecture in MDX muscle affect nuclear movement, which is essential for muscle function.

Emergence of flagellar beating from the collective behavior of individual ATP-powered dyneins

Flagella are hair-like projections from the surface of eukaryotic cells, and they play an important role in many cellular functions, such as cell-motility. The beating of flagella is enabled by their internal architecture, the axoneme, and is powered by a dense distribution of motor proteins, dyneins. The dyneins deliver the required mechanical work through the hydrolysis of ATP. Although the dynein-ATP cycle, the axoneme microstructure, and the flagellar-beating kinematics are well studied, their integration into a coherent picture of ATP-powered flagellar beating is still lacking. Here we show that a time-delayed negative-work-based switching mechanism is able to convert the individual sliding action of hundreds of dyneins into a regular overall beating pattern leading to propulsion. We developed a computational model based on a minimal representation of the axoneme consisting of two representative doublet microtubules connected by nexin links. The relative sliding of the microtubules is incorporated by modeling two groups of ATP-powered dyneins, each responsible for sliding in opposite directions. A time-delayed switching mechanism is postulated, which is key in converting the local individual sliding action of multiple dyneins into global beating. Our results demonstrate that an overall nonreciprocal beating pattern can emerge with time due to the spatial and temporal coordination of the individual dyneins. These findings provide insights in the fundamental working mechanism of axonemal dyneins and could possibly open new research directions in the field of flagellar motility.

Multi scale modeling of 2450MHz electric field effects on microtubule mechanical properties

Microtubule (MT) rigidity and response to 2450MHz electric fields were investigated, via multi scale modeling approach. For this purpose, six systems were designed and simulated to consider all types of feasible interactions between α and β monomers in MT, by using all atom molecular dynamics method. Subsequently, coarse grain modeling was used to design different lengths of MT. Investigation of effects of external 2450MHz electric field on MT showed MT less rigidity in the presence of such field, which may perturb its functions. Moreover, an additional computational setup was designed to study effects of 2450MHz field on MT response to AFM tip. It was found, more tip velocity led to MT faster transformation and less time was required to change MT elastic response to plastic one, applying constant radius. Moreover it was observed smaller tip caused to increase required time to change MT elastic response to plastic one, considering constant velocity. Furthermore, exposing MT to 2450MHz field led to no significant changes in MT response to AFM tip, but quick change in MT elastic response to plastic one.

Paclitaxel suppresses Tau-mediated microtubule bundling in a concentration-dependent manner

BACKGROUND

Microtubules (MTs) are protein nanotubes comprised of straight protofilaments (PFs), head to tail assemblies of αβ-tubulin heterodimers. Previously, it was shown that Tau, a microtubule-associated protein (MAP) localized to neuronal axons, regulates the average number of PFs in microtubules with increasing inner radius <R_in^MT> observed for increasing Tau/tubulin-dimer molar ratio Φ_Tau at paclitaxel/tubulin-dimer molar ratio Λ_Ptxl=1/1.

METHODS

We report a synchrotron SAXS and TEM study of the phase behavior of microtubules as a function of varying concentrations of paclitaxel (1/32≤Λ_Ptxl≤1/4) and Tau (human isoform 3RS, 0≤Φ_3RS≤1/2) at room temperature.

RESULTS

Tau and paclitaxel have opposing regulatory effects on microtubule bundling architectures and microtubule diameter. Surprisingly and in contrast to previous results at Λ_Ptxl=1/1 where microtubule bundles are absent, in the lower paclitaxel concentration regime (Λ_Ptxl≤1/4), we observe both microtubule doublets and triplets with increasing Tau. Furthermore, increasing paclitaxel concentration (up to Λ_Ptxl=1/1) slightly decreased the average microtubule diameter (by ~1 PF) while increasing Tau concentration (up to Φ_3RS=1/2) significantly increased the diameter (by ~2-3 PFs).

CONCLUSIONS

The suppression of Tau-mediated microtubule bundling with increasing paclitaxel is consistent with paclitaxel seeding more, but shorter, microtubules by rapidly exhausting tubulin available for polymerization. Microtubule bundles require the aggregate Tau-Tau attractions along the microtubule length to overcome individual microtubule thermal energies disrupting bundles.

GENERAL SIGNIFICANCE

Investigating MAP-mediated interactions between microtubules (as it relates to in vivo behavior) requires the elimination or minimization of paclitaxel.

Semiflexible Chains at Surfaces: Worm-Like Chains and beyond

We give an extended review of recent numerical and analytical studies on semiflexible chains near surfaces undertaken at Institut Charles Sadron (sometimes in collaboration) with a focus on static properties. The statistical physics of thin confined layers, strict two-dimensional (2D) layers and adsorption layers (both at equilibrium with the dilute bath and from irreversible chemisorption) are discussed for the well-known worm-like-chain (WLC) model. There is mounting evidence that biofilaments (except stable d-DNA) are not fully described by the WLC model. A number of augmented models, like the (super) helical WLC model, the polymorphic model of microtubules (MT) and a model with (strongly) nonlinear flexural elasticity are presented, and some aspects of their surface behavior are analyzed. In many cases, we use approaches different from those in our previous work, give additional results and try to adopt a more general point of view with the hope to shed some light on this complex field.

Semiflexible Biopolymers in Bundled Arrangements

Bundles and networks of semiflexible biopolymers are key elements in cells, lending them mechanical integrity while also enabling dynamic functions. Networks have been the subject of many studies, revealing a variety of fundamental characteristics often determined via bulk measurements. Although bundles are equally important in biological systems, they have garnered much less scientific attention since they have to be probed on the mesoscopic scale. Here, we review theoretical as well as experimental approaches, which mainly employ the naturally occurring biopolymer actin, to highlight the principles behind these structures on the single bundle level.

Elastic Anisotropy Scenario for Cooperative Binding of Kinesin-Coated Beads on Microtubules

Muto et al. reported in 2005 an observation called cooperative binding, according to which the initial binding of a bead covered with active kinesins on a microtubule filament was capable of favoring the subsequent binding of similar beads on the same filament up to distances of the order of a few microns. This positive bias is stronger ahead of the initially bound bead than behind. We explain this effect by combining the recently proposed notion of shear screening length with the notion of localized tubulin conformational transition induced by motor binding. Elastic terms linked to the polarity of protofilaments, up to now ignored, provide adequate description to the long-range elastic shear generated by motor binding. The subsequent binding is favored when and where the shear displacement of protofilaments meets the requirement for specific strong binding. We propose experimental tests of our model, which open the way to a new type of spectroscopy for biomolecular processes.

Steering microtubule shuttle transport with dynamically controlled magnetic fields

Nanoscale control of matter is critical to the design of integrated nanosystems. Here, we describe a method to dynamically control directionality of microtubule (MT) motion using programmable magnetic fields. MTs are combined with magnetic quantum dots (i.e., MagDots) that are manipulated by external magnetic fields provided by magnetic nanowires. MT shuttles thus undergo both ATP-driven and externally-directed motion with a fluorescence component that permits simultaneous visualization of shuttle motion. This technology is used to alter the trajectory of MTs in motion and to pin MT motion. Such an approach could be used to evaluate the MT-kinesin transport system and could serve as the basis for improved lab-on-a-chip technologies based on MT transport.

Elastic Properties of Nucleic Acids by Single-Molecule Force Spectroscopy

We review the current knowledge on the use of single-molecule force spectroscopy techniques to extrapolate the elastic properties of nucleic acids. We emphasize the lesser-known elastic properties of single-stranded DNA. We discuss the importance of accurately determining the elastic response in pulling experiments, and we review the simplest models used to rationalize the experimental data as well as the experimental approaches used to pull single-stranded DNA. Applications used to investigate DNA conformational transitions and secondary structure formation are also highlighted. Finally, we provide an overview of the effects of salt and temperature and briefly discuss the effects of contour length and sequence dependence.

The effects of external electric fields of 900 MHz and 2450 MHz frequencies onαβ-tubulin dimer stabilized by paclitaxel: Molecular dynamics approach

Using molecular dynamics simulation method, the effects of external electric fields of 900[Formula: see text]MHz and 2450 frequencies on [Formula: see text]-tubulin dimer stabilized by paclitaxel, have been modeled. Due to this purpose, two systems, (A) [Formula: see text]-tubulin dimer and (B) [Formula: see text]-tubulin dimer stabilized by paclitaxel, were exposed to an external electric field of 0.01[Formula: see text]V/nm with frequency values of 900[Formula: see text]MHz and 2450[Formula: see text]MHz. It was found that application of these fields, which are in the range of cell phone and microwave frequencies, increased the flexibility of each system. Since paclitaxel, as chemotherapy drug, is used to increase the rigidity of dimer, application of such fields may disturb the effect of paclitaxel on the dimer. Consequently, negative side effects on the chemotherapy process may be observed.

Buckling behavior of individual and bundled microtubules

As the major structural constituent of the cytoskeleton, microtubules (MTs) serve a variety of biological functions that range from facilitating organelle transport to maintaining the mechanical integrity of the cell. Neuronal MTs exhibit a distinct configuration, hexagonally packed bundles of MT filaments, interconnected by MT-associated protein (MAP) tau. Building on our previous work on mechanical response of axonal MT bundles under uniaxial tension, this study is focused on exploring the compression scenarios. Intracellular MTs carry a large fraction of the compressive loads sensed by the cell and therefore, like any other column-like structure, are prone to substantial bending and buckling. Various biological activities, e.g., actomyosin contractility and many pathological conditions are driven or followed by bending, looping, and buckling of MT filaments. The coarse-grained model previously developed in our lab has been used to study the mechanical behavior of individual and bundled in vivo MT filaments under uniaxial compression. Both configurations show tip-localized, decaying, and short-wavelength buckling. This behavior highlights the role of the surrounding cytoplasm and MAP tau on MT buckling behavior, which allows MT filaments to bear much larger compressive forces. It is observed that MAP tau interconnections improve this effect by a factor of two. The enhanced ability of MT bundles to damp buckling waves relative to individual MT filaments, may be interpreted as a self-defense mechanism because it helps axonal MTs to endure harsher environments while maintaining their function. The results indicate that MT filaments in a bundle do not buckle simultaneously implying that the applied stress is not equally shared among the MT filaments, that is a consequence of the nonuniform distribution of MAP tau proteins along the bundle length. Furthermore, from a pathological perspective, it is observed that axonal MT bundles are more vulnerable to failure in compression than tension.

Constructing 3D microtubule networks using holographic optical trapping

Developing abilities to assemble nanoscale structures is a major scientific and engineering challenge. We report a technique which allows precise positioning and manipulation of individual rigid filaments, enabling construction of custom-designed 3D filament networks. This approach uses holographic optical trapping (HOT) for nano-positioning and microtubules (MTs) as network building blocks. MTs are desirable engineering components due to their high aspect ratio, rigidity, and their ability to serve as substrate for directed nano-transport, reflecting their roles in the eukaryotic cytoskeleton. The 3D architecture of MT cytoskeleton is a significant component of its function, however experimental tools to study the roles of this geometric complexity in a controlled environment have been lacking. We demonstrate the broad capabilities of our system by building a self-supporting 3D MT-based nanostructure and by conducting a MT-based transport experiment on a dynamically adjustable 3D MT intersection. Our methodology not only will advance studies of cytoskeletal networks (and associated processes such as MT-based transport) but will also likely find use in engineering nanostructures and devices.

A nonequilibrium power balance relation for analyzing dissipative filament dynamics

Biofilaments like F-actin or microtubules, as well as cilia, flagella, or filament bundles, are often deformed by distributed and time-dependent external forces. It is highly desirable to characterize these filaments' mechanics in an efficient way, either using a single experiment or a high throughput method. We here propose a dynamic power balance approach to study nonequilibrium filament dynamics and exemplify it both experimentally and theoretically by applying it to microtubule gliding assay dynamics. Its usefulness is highlighted by the experimental determination of the lateral friction coefficient for microtubules on kinesins. In contrast to what is usually assumed, friction is anisotropic, in a similar fashion as hydrodynamic friction. We also exemplify, by considering a microtubule buckling event, that if at least one parameter is known in advance, all other parameters can be determined by analyzing a single time-dependent experiment.

Buckling of Microtubules on a 2D Elastic Medium

We have demonstrated compression stress induced mechanical deformation of microtubules (MTs) on a two-dimensional elastic medium and investigated the role of compression strain, strain rate, and a MT-associated protein in the deformation of MTs. We show that MTs, supported on a two-dimensional substrate by a MT-associated protein kinesin, undergo buckling when they are subjected to compression stress. Compression strain strongly affects the extent of buckling, although compression rate has no substantial effect on the buckling of MTs. Most importantly, the density of kinesin is found to play the key role in determining the buckling mode of MTs. We have made a comparison between our experimental results and the ‘elastic foundation model’ that theoretically predicts the buckling behavior of MTs and its connection to MT-associated proteins. Taking into consideration the role of kinesin in altering the mechanical property of MTs, we are able to explain the buckling behavior of MTs by the elastic foundation model. This work will help understand the buckling mechanism of MTs and its connection to MT-associated proteins or surrounding medium, and consequently will aid in obtaining a meticulous scenario of the compression stress induced deformation of MTs in cells.

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.

Nodal versus Total Axonal Strain and the Role of Cholesterol in Traumatic Brain Injury

Traumatic brain injury (TBI) is a health threat that affects every year millions of people involved in motor vehicle and sporting accidents, and thousands of soldiers in battlefields. Diffuse axonal injury (DAI) is one of the most frequent types of TBI leading to death. In DAI, the initial traumatic event is followed by a cascade of biochemical changes that take time to develop in full, so that symptoms may not become apparent until days or weeks after the original injury. Hence, DAI is a dynamic process, and the opportunity exists to prevent its progression provided the initial trauma can be predicted at the molecular level. Here, we present preliminary evidence from micro-finite element (FE) simulations that the mechanical response of central nervous system myelinated fibers is dependent on the axonal diameter, the ratio between axon diameter and fiber diameter (g-ratio), the microtubules density, and the cholesterol concentration in the axolemma and myelin. A key outcome of the simulations is that there is a significant difference between the overall level of strain in a given axonal segment and the level of local strain in the Ranvier nodes contained in that segment, with the nodal strain being much larger than the total strain. We suggest that the acquisition of this geometric and biochemical information by means of already available high resolution magnetic resonance imaging techniques, and its incorporation in current FE models of the brain will enhance the models capacity to predict the site and magnitude of primary axonal damage upon TBI.

Scattering Function for Branched Wormlike Chains

Wormlike or threadlike structures with local cylindrical geometry are abundantly found in nature and technical products. A thorough structural characterization in the bulk for a whole ensemble, however, is difficult. The inherent semiordered nature of the tortuous large-scale structure and especially the quantification of branching renders an assessment difficult. In the present work we introduce a hybrid function expressing the scattering intensities for X-rays, neutrons, or light in the small-angle regime for this system. The function is termed "hybrid" because it employs terms from different approaches. The large-scale structure is described via a Guinier term as well as a concomitant power-law expression in momentum transfer q taken from the so-called unified function. The local cylindrical shape, however, is taken into account through a form factor for cylinders from rigid-body modeling. In principle, the latter form factor can be replaced by an expression for any other regular body so that the new hybrid function is a versatile tool for studying hierarchical structures assembled from uniform subunits. The appropriateness and capability of the new function for cylindrical structures is exemplified using the example of a wormlike micellar system.

Mechanical design of DNA nanostructures

Structural DNA nanotechnology is a rapidly emerging field that has demonstrated great potential for applications such as single molecule sensing, drug delivery, and templating molecular components. As the applications of DNA nanotechnology expand, a consideration of their mechanical behavior is becoming essential to understand how these structures will respond to physical interactions. This review considers three major avenues of recent progress in this area: (1) measuring and designing mechanical properties of DNA nanostructures, (2) designing complex nanostructures based on imposed mechanical stresses, and (3) designing and controlling structurally dynamic nanostructures. This work has laid the foundation for mechanically active nanomachines that can generate, transmit, and respond to physical cues in molecular systems.

Why microtubules run in circles: mechanical hysteresis of the tubulin lattice

The fate of every eukaryotic cell subtly relies on the exceptional mechanical properties of microtubules. Despite significant efforts, understanding their unusual mechanics remains elusive. One persistent, unresolved mystery is the formation of long-lived arcs and rings, e.g., in kinesin-driven gliding assays. To elucidate their physical origin we develop a model of the inner workings of the microtubule's lattice, based on recent experimental evidence for a conformational switch of the tubulin dimer. We show that the microtubule lattice itself coexists in discrete polymorphic states. Metastable curved states can be induced via a mechanical hysteresis involving torques and forces typical of few molecular motors acting in unison, in agreement with the observations.

Microtubule teardrop patterns

Several strategies for controlling microtubule patterns are developed because of the rigidity determined from the molecular structure and the geometrical structure. In contrast to the patterns in co-operation with motor proteins or associated proteins, microtubules have a huge potential for patterns via their intrinsic flexural rigidity. We discover that a microtubule teardrop pattern emerges via self-assembly under hydrodynamic flow from the parallel bundles without motor proteins. In the growth process, the bundles ultimately bend according to the critical bending curvature. Such protein pattern formation utilizing the intrinsic flexural rigidity will provide broad understandings of self-assembly of rigid rods, not only in biomolecules, but also in supramolecules.

Influence of GHz electric fields on the mechanical properties of a microtubule

The effects of external GHz electric fields on the mechanical properties of a microtubule (MT) have been modeled through the application of a molecular dynamics simulation method. To explore the properties of the MT, two different systems each consisting of a pair of dimers were exposed to an 0.03 V/nm electric field with a frequency ranging between 1 to 10 GHz. It was found that the Young's modulus of each system, which is related to the flexibility of the MT, was lower at some frequencies and higher at others in comparison with normal biological conditions. Hence, the application of such an electric field with a frequency in this range may affect MT function, which could have positive or negative effects on cell health. Positive effects include its potential use in cancer treatment, where the application of such a field could lead to a decrease in MT rigidity, similar to the effect of Taxol on MTs. Negative effects include unwanted changes to the mechanical properties of MTs (e.g., disturbing the cell division process and in turn increasing the risk of cancer) upon the application of such a field.

Nanomechanics and intermolecular forces of amyloid revealed by four-dimensional electron microscopy

The amyloid state of polypeptides is a stable, highly organized structural form consisting of laterally associated β-sheet protofilaments that may be adopted as an alternative to the functional, native state. Identifying the balance of forces stabilizing amyloid is fundamental to understanding the wide accessibility of this state to peptides and proteins with unrelated primary sequences, various chain lengths, and widely differing native structures. Here, we use four-dimensional electron microscopy to demonstrate that the forces acting to stabilize amyloid at the atomic level are highly anisotropic, that an optimized interbackbone hydrogen-bonding network within β-sheets confers 20 times more rigidity on the structure than sequence-specific sidechain interactions between sheets, and that electrostatic attraction of protofilaments is only slightly stronger than these weak amphiphilic interactions. The potential biological relevance of the deposition of such a highly anisotropic biomaterial in vivo is discussed.

Control of microtubule trajectory within an electric field by altering surface charge density

One of challenges for using microtubules (MTs) driven by kinesin motors in microfluidic environments is to control their direction of movement. Although applying physical biases to rectify MTs is prevalent, it has not been established as a design methodology in conjunction with microfluidic devices. In the future, the methodology is expected to achieve functional motor-driven nanosystems. Here, we propose a method to guide kinesin-propelled MTs in multiple directions under an electric field by designing a charged surface of MT minus ends labeled with dsDNA via a streptavidin-biotin interaction. MTs labeled with 20-bp or 50-bp dsDNA molecules showed significantly different trajectories according to the DNA length, which were in good agreement with values predicted from electrophoretic mobilities measured for their minus ends. Since the effective charge of labeled DNA molecules was equal to that of freely dispersed DNA molecules in a buffer solution, MT trajectory could be estimated by selecting labeling molecules with known charges. Moreover, the estimated trajectory enables to define geometrical sizes of a microfluidic device. This rational molecular design and prediction methodology allows MTs to be guided in multiple directions, demonstrating the feasibility of using molecular sorters driven by motor proteins.