Buckling Of Microtubules Research Articles

Wave-like oscillations of clamped microtubules driven by collective dynein transport

Microtubules (MTs) are observed to move and buckle driven by ATP-dependent molecular motors in both mitotic and interphasic eukaryotic cells as well as in specialized structures such as flagella and cilia with a stereotypical geometry. In previous work, clamped MTs driven by a few kinesin motors were seen to buckle and occasionally flap in what was referred to as flagella-like motion. Theoretical models of active-filament dynamics and a following force have predicted that, with sufficient force and binding-unbinding, such clamped filaments should spontaneously undergo periodic buckling oscillations. However, a systematic experimental test of the theory and reconciliation to a model was lacking. Here, we have engineered a minimal system of MTs clamped at their plus ends and transported by a sheet of dynein motors that demonstrate the emergence of spontaneous traveling-wave oscillations along single filaments. The frequencies of tip oscillations are in the millihertz range and are statistically indistinguishable in the onset and recovery phases. We develop a 2D computational model of clamped MTs binding and unbinding stochastically to motors in a “gliding-assay” geometry. The simulated MTs oscillate with a frequency comparable to experiment. The model predicts the effect of MT length and motor density on qualitative transitions between distinct phases of flapping, regular oscillations, and looping. We develop an effective “order parameter” based on the relative deflection along the filament and orthogonal to it. The transitions predicted in simulations are validated by experimental data. These results demonstrate a role for geometry, MT buckling, and collective molecular motor activity in the emergence of oscillatory dynamics.

Torsion Geometry 5-Fold Symmetry, Anholonomic Phases, Klein Bottle Logophysics, Chaos, Resonance: Applications Towards a Novel Paradigm for the Neurosciences and Consciousness

Torsion Geometry 5-Fold Symmetry, Anholonomic Phases, Klein Bottle Logophysics, Chaos, Resonance: Applications Towards a Novel Paradigm for the Neurosciences and Consciousness

Tip-scan high-speed atomic force microscopy with a uniaxial substrate stretching device for studying dynamics of biomolecules under mechanical stress.

High-speed atomic force microscopy (HS-AFM) is a powerful tool for studying the dynamics of biomolecules in vitro because of its high temporal and spatial resolution. However, multi-functionalization, such as combination with complementary measurement methods, environment control, and large-scale mechanical manipulation of samples, is still a complex endeavor due to the inherent design and the compact sample scanning stage. Emerging tip-scan HS-AFM overcame this design hindrance and opened a door for additional functionalities. In this study, we designed a motor-driven stretching device to manipulate elastic substrates for HS-AFM imaging of biomolecules under controllable mechanical stimulation. To demonstrate the applicability of the substrate stretching device, we observed a microtubule buckling by straining the substrate and actin filaments linked by α-actinin on a curved surface. In addition, a BAR domain protein BIN1 that senses substrate curvature was observed while dynamically controlling the surface curvature. Our results clearly prove that large-scale mechanical manipulation can be coupled with nanometer-scale imaging to observe biophysical effects otherwise obscured.

Stiffening and softening in the power-law rheological behaviors of cells

Living cells are a complex soft material with fascinating mechanical properties. Confusingly, experiments have shown that cells exhibit stiffening and more solid-like behaviors under uniaxial stretches or shear, while they present softening and more fluid-like behaviors under biaxial stretches. For both of these seemingly paradoxical stiffening and softening rheological behaviors, cells often exhibit a robust power-law rheological characteristic. Here, based on the structural features, we propose a cellular structural model to investigate these rheological behaviors of cells under different loading conditions. It is found that this structural model can naturally capture the stiffening and softening behaviors in the power-law rheological responses of cells, depending on the loading conditions. Both stiffening and softening of cells originate from changes in the configuration of the discrete cytoskeleton: stiffening from the rotation of the microtubules to the loading direction and softening from the elastic buckling of individual microtubules. Moreover, for both stiffening and softening in the rheological behaviors of cells, there exists a unified relationship that the power-law exponent decreases linearly with the cellular stiffness in a semi-logarithmic coordination. We further present that a self-similar hierarchical model can be used to analyze this unified relationship. This study not only provides a discrete cellular structural model to capture the essential mechanisms of cellular rheology, but also suggests that the scaling rheological exponent may be treated as a mechanical marker for monitoring cellular healthy states.

Actomyosin contractility and buckling of microtubules in nucleation, growth and disassembling of focal adhesions

Building up and maintenance of cytoskeletal structure in living cells are force-dependent processes involving a dynamic chain of polymerization and depolymerization events, which are also at the basis of cells’ remodelling and locomotion. All these phenomena develop by establishing cell–matrix interfaces made of protein complexes, known as focal adhesions, which govern mechanosensing and mechanotransduction mechanisms mediated by stress transmission between cell interior and external environment. Within this framework, by starting from a work by Cao et al. (Biophys J 109:1807–1817, 2015), we here investigate the role played by actomyosin contractility of stress fibres in nucleation, growth and disassembling of focal adhesions. In particular, we propose a tensegrity model of an adherent cell incorporating nonlinear elasticity and unstable behaviours, which provides a new kinematical interpretation of cellular contractile forces and describes how stress fibres, microtubules and adhesion plaques interact mechanobiologically. The results confirm some experimental evidences and suggest how the actomyosin contraction level could be exploited by cells to actively control their adhesion, eventually triggering cytoskeleton reconfigurations and migration processes observed in both physiological conditions and diseases.

Isolating the Pathological Contribution of Detyrosinated Microtubules in Human Myocardial Mechanics

Detyrosinated microtubules (dTyr MTs) buckle and bear load during myocyte contraction providing a viscoelastic resistance to myocyte shortening. The proliferation of dTyr MTs observed in heart failure increases myocyte viscoelasticity but the pathological consequences on myocyte and myocardial function remain to be quantitatively assessed. To determine whether suppressing dTyr MTs will reduce viscoelasticity and improve contractile dynamics proportional to the severity of disease, we utilize parallel genetic and pharmaceutical approaches to suppress MT dTyr in freshly isolated human cardiomyocytes and myocardial strips and measure active and passive mechanical properties. Compared to myocytes isolated from non-failing human hearts, suppression of dTyr MTs reduces viscoelasticity and increases unloaded shortening to a greater degree in failing cardiomyocytes. Manipulation of dTyr MT levels does not significantly impact excitation-contraction coupling and de novo mathematical modelling demonstrates that increased contractile dynamics can be attributed to the experimentally measured decrease in viscoelasticity. Preliminary results in myocardial strips from failing hearts display greater viscoelasticity than non-failing myocardium, with depolymerization of MTs in failing myocardium partially restoring passive mechanical properties. The results indicate that dTyr microtubules constrain myocyte contractile dynamics in heart failure. Moreover, the microtubules’ impact in regulating myocardial mechanical properties at rates consistent with diastolic filling is evident in the presence of an intact extracellular matrix.

Microtubule buckling in an elastic matrix with quenched disorder.

The intracellular elastic matrix has been recognized as an important factor to stabilize microtubules and increase their critical buckling force P c in vivo. This phenomenon was qualitatively explained by the Winkler model, which investigated the buckling of a filament embedded in a homogeneous elastic medium. However, the assumption of homogeneity of the matrix in Winkler's, and other advanced models, is unrealistic inside cells, where the local environment is highly variable along the filament. Considering this to be a quenched-disorder system, we use a Poisson distribution for confinements and apply the replica technique combined with the Gaussian variational method to study the buckling of a long filament. The results show two types of filament bucklings: one corresponding to the first-order, and the other to a continuous second-order phase transition. The critical point, i.e., the switch from first- to second-order buckling transition, is induced by the increase in disorder strength. We also discover that this random disorder of the elastic environment destabilizes the filament by decreasing P c from the Winkler result and the matrix with stronger mean elasticity has a stronger role of disorder (inhomogeneity). For microtubules in vivo, buckling follows the discontinuous first-order transition, with P c reduced to the fraction between 0.9 and 0.75 of the Winkler prediction for the homogeneous elastic matrix. We also show that disorder can affect the force-displacement relationship at non-zero temperature, while at zero temperature this effect vanishes.

Microtubules Provide a Viscoelastic Resistance to Myocyte Motion

Background: Microtubules (MTs) buckle and bear load during myocyte contraction, a behavior enhanced by post-translational detyrosination. This buckling suggests a spring-like resistance against myocyte shortening, which could store energy and aid myocyte relaxation. Despite this visual suggestion of elastic behavior, the precise mechanical contribution of the cardiac MT network remains to be defined.Methods: Here we experimentally and computationally probe the mechanical contribution of stable MTs and their influence on myocyte function. We use multiple approaches to interrogate viscoelasticity and cell shortening in primary murine myocytes in which either MTs are depolymerized or detyrosination is suppressed and use the results to inform a mathematical model of myocyte viscoelasticity.Results: MT ablation by colchicine concurrently enhances both the degree of shortening and speed of relaxation, a finding inconsistent with simple spring-like MT behavior and suggestive of a viscoelastic mechanism. Axial stretch and transverse indentation confirm that MTs increase myocyte viscoelasticity. Specifically, increasing the rate of strain amplifies the MT contribution to myocyte stiffness. Suppressing MT detyrosination with parthenolide or via overexpression of tubulin tyrosine ligase has mechanical consequences that closely resemble colchicine, suggesting that the mechanical impact of MTs relies on a detyrosination-dependent linkage with the myocyte cytoskeleton. Mathematical modeling affirms that alterations in cell shortening conferred by either MT destabilization or tyrosination can be attributed to internal changes in myocyte viscoelasticity.Conclusions: The results suggest that the cardiac MT network regulates contractile amplitudes and kinetics by acting as a cytoskeletal shock-absorber, whereby MTs provide breakable cross-links between the sarcomeric and nonsarcomeric cytoskeleton that resist rapid length changes during both shortening and stretch.

Surface effect on buckling of microtubules in living cells using first-order shear deformation shell theory and standard linear solid model

In this paper, an orthotropic elastic shell model is developed for the buckling analysis of protein microtubules subjected to an axial force in living cells. Surface effects are taken into consideration based on the Gurtin–Murdoch elasticity theory. To incorporate the small scale effects, the nonlocal elasticity theory is also used. The influences of the viscoelastic surrounding cytoplasm are taken into account employing standard linear solid model. The governing differential equations are derived using the first-order shear deformation theory and the principle of virtual work. A numerical solution is obtained for the governing equations by employing differential quadrature method. To verify the accuracy of the numerical results, the present results for the axial buckling of microtubules stabilized with microtubule-associated proteins and taxol are compared with those of experimental observations in the literature. It is found that the orthotropic shell model with both surface and nonlocal effects can describe the buckling behavior of microtubules accurately, while the nonlocal shell model without surface effects fails to predict the buckling loads.

Microtubule Buckling Affects Cargo Transportation By Molecular Motor

A cell can be best resembled by a metropolitan city where all its functions are driven by the interactions of densely packed proteins. For the traffic system in this ‘city’, the expressway consists of actin and microtubules (MTs). On the other hand, the stepping motor proteins serve as ‘vehicles’ and transport cargo from the nucleus (minus end) to the periphery (plus end) and vice versa [1]. Kinesin-1 and cytoplasmic dynein are the two major cytoplasmic motors that transport cargos towards the plus and minus end of the MT respectively. Stimulated or spontaneous cell contraction, or constrained MT polymerization at the cell periphery give rise to buckling deformation of MT in cells, that may result into buckling with short wavelengths (e.g., several µm) [2-5]. While significant advancement is made in understanding the role of kinesin in transporting cargo individually or as team along undeformed MT [6-8], how the deformity in the MT due to buckling may affect the motility of the motor is overlooked. Kinesin takes regular steps of 8 nm in a hand-over-hand fashion [9] whereas dynein shows variable step sizes ranging from 8 – 32 nm uncoordinatedly [10]. Advanced studies on the structure and mechanism still do not provide clear idea on how the uncoordinated stepping mechanism in dynein responds to the buckled MT. Therefore, the effect of buckling of MT on the cargo transportation has a large scope to explore. Previously, we developed an experimental set-up, micro-stretcher, to control buckling of the MT filaments on a 2D elastic medium [11]. Present study exploits the knowledge from the system of MT buckling to further explore its contribution on the dynein based cargo transportation in vitro. For this, we fixed MTs on a pre-stretched elastic substrate, polydimethylsiloxane (PDMS), through interaction with kinesins. Relaxation of the pre-stretched PDMS consequently developed axial compression stress on the MTs, resulting into their buckling. We controlled the release of tensile strain of the PDMS to tune the buckling extent of MTs. Next, we immobilized the MTs with mild glutaraldehyde treatment and allowed the transportation of Qdots by motors along the undeformed and deformed MTs. We analyzed different parameters, e.g. velocities, pauses and run lengths from the observation of the cargo transportation. With increasing MT buckling we observed changes in the cargo transportation behavior of the motors. For kinesins, we observed that, the cargo velocities decreased with increasing strain in the MTs and finally, cargo transportation was halted at high strain region. While for dynein, cargo transportation prevailed with increased overall velocity with two peaks, one occurring in the low and the other at high strain region. Our goal is to explore the mechanism of how the buckling deformation of MT is affecting the observed phenomena in motor protein-based cargo transportation. Structural deformation in MTs, particularly, have showed to implicate several neurodegenerative diseases such as Alzheimer's disease, cardiovascular syndromes, neurological disorders and cancers etc. [12]. Therefore in vitro study of motor proteins in transporting cargo along deformed MTs will contribute not only in understanding the mechanism of motor motility in cells but also to target specific pathways for various neurodegenerative diseases.

Effects of the cross-linkers on the buckling of microtubules in cells

In cells, the protein cross-linkers lead to a distinct buckling behavior of microtubules (MTs) different from the buckling of individual MTs. This paper thus aims to examine this issue via the molecular structural mechanics (MSM) simulations. The transition of buckling responses was captured as the two-dimensional-linkers were replaced by the three-dimensional (3D) ones. Then, the effects of the radial orientation and the axial density of the 3D-linkers were examined, showing that more uniform distribution of the radial orientation leads to the higher critical load with 3D buckling modes, while the inhomogeneity of the axial density results in the localized buckling patterns. The results demonstrated the important role of the cross-linker in regulating MT stiffness, revealed the physics of the experimentally observed localized buckling and these results will pave the way to a new multi-component mechanics model for whole cells.

Characterization of microtubule buckling in living cells.

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

Size-dependent axial instability of microtubules surrounded by cytoplasm of a living cell based on nonlocal strain gradient elasticity theory

Microtubules including tubulin heterodimers arranging in a parallel shape of cylindrical hollow plays an important role in the mechanical stiffness of a living cell. In the present study, the nonlocal strain gradient theory of elasticity including simultaneously the both nonlocality and strain gradient size dependency is put to use within the framework of a refined orthotropic shell theory with hyperbolic distribution of shear deformation to analyze the size-dependent buckling and postbuckling characteristics of microtubules embedded in cytoplasm under axial compressive load. The non-classical governing differential equations are deduced via boundary layer theory of shell buckling incorporating the nonlinear prebuckling deformation and microtubule-cytoplasm interaction in the living cell environment. Finally, with the aid of a two-stepped perturbation solution methodology, the explicit analytical expressions for nonlocal strain gradient stability paths of axially loaded microtubules are achieved. It is illustrated that by taking the nonlocal size effect into consideration, the critical buckling load of microtubule and its maximum deflection associated with the minimum postbuckling load decreases, while the strain gradient size dependency causes to increase them.

Microtubule Bundles in the Adult Cardiomyocyte

The role of Microtubules (MTs) in mechanosignalling and mechanical properties has seen a recent surge of interest among the cardiac and skeletal muscle community. We recently reported that MTs buckle and bear load during the cardiac cycle. This has a significant effect on contractile mechanics, suggesting that myocyte function is tunable by any regulatory pathway that alters the mechanical behavior of MTs. Other work ongoing in our lab indicates that a number of Microtubule Associated Proteins (MAPs) are robustly upregulated in human heart disease. Multi-MT assemblies or bundles associated with these and other MAPs have been observed and studied extensively in other contexts, including unicellular motile structures and neuronal axons, but have not been examined in cardiac myocytes. The number of MTs involved, their geometry and the relative abundance of such structures compared to isolated MTs have significant implications for the mechanical properties of a myocyte. Using targeted overexpression of several MAPs in adult rat cardiomyocytes, we examine the structure, magnitude and prevalence of MT bundles by electron microscopy. We find that single MTs are the most prevalent MT elements in the unmanipulated myocyte, accompanied by comparatively rare and small groupings of 2-3 MTs with wide spacing. MTs are preferentially located at the interface between myofibril and mitochondria. Manipulation of MT binding partners can modestly increase the size and likelihood of MT bundles, and also dramatically reduces the inter-tubule spacing to be in-line with canonical bundle spacing. When we further characterized the functional consequences of MT bundling on cardiac contractility, we were surprised to find that the promotion of bundling, at least with certain MAPs, does not appear to impair contraction by reinforcing compliant microtubules, but rather uncouples the MTs from the process of contraction-associated buckling.

Calcium-independent disruption of microtubule dynamics by nanosecond pulsed electric fields in U87 human glioblastoma cells

High powered, nanosecond duration, pulsed electric fields (nsPEF) cause cell death by a mechanism that is not fully understood and have been proposed as a targeted cancer therapy. Numerous chemotherapeutics work by disrupting microtubules. As microtubules are affected by electrical fields, this study looks at the possibility of disrupting them electrically with nsPEF. Human glioblastoma cells (U87-MG) treated with 100, 10 ns, 44 kV/cm pulses at a frequency of 10 Hz showed a breakdown of their interphase microtubule network that was accompanied by a reduction in the number of growing microtubules. This effect is temporally linked to loss of mitochondrial membrane potential and independent of cellular swelling and calcium influx, two factors that disrupt microtubule growth dynamics. Super-resolution microscopy revealed microtubule buckling and breaking as a result of nsPEF application, suggesting that nsPEF may act directly on microtubules.

Vibration, buckling and smart control of microtubules using piezoelectric nanoshells under electric voltage in thermal environment

Piezoelectric nanomaterials such as zinc oxide (ZnO) are of low toxicity and have many biomedical applications including optical imaging, drug delivery, biosensing and harvesting biomechanical energy using hybrid nanogenerators. In this paper, the vibration, buckling and smart control of microtubules (MTs) embedded in an elastic medium in thermal environment using a piezoelectric nanoshell (PNS) are investigated. The MT and PNS are considered to be coupled by a filament network. The PNS is subjected to thermal loads and an external electric voltage which operates to control the mechanical behavior of the MT. Using the nonlocal continuum mechanics, the governing differential equations are derived. An exact solution is presented for simply supported boundary conditions. The differential quadrature method is also used to solve the governing equations for other boundary conditions. A detailed parametric study is conducted to investigate the effects of the elastic constants of surrounding medium and internal filament matrix, scale coefficient, electric voltage, the radius-to-thickness ratio of PNSs and temperature change on the smart control of MTs. It is found that the applied electric voltage can be used as an effective controlling parameter for the vibration and buckling of MTs.

Buckling of microtubules on elastic media via breakable bonds

Buckling of microtubules observed in cells has been reconstructed on a two-dimensional elastic medium consisting of kinesins grafted over compressible substrates, enabling precise control of experimental conditions and quantitative analysis. However, interpretations of the observations have ambiguities due to inevitable experimental difficulties. In this study, with computer simulations, we investigated importance of the mode of interaction of microtubule with elastic medium in the buckling behavior of microtubule. By taking into consideration of forced-induced detachments of kinesins from microtubules, our simulations reproduced the previous experimental results, and showed deviations from predictions of the elastic foundation model. On the other hand, with hypothetical linkers permanently bound to microtubules, our simulation reproduced the predictions of the elastic foundation model. By analyzing the results of the simulations, we investigated as to why the difference arose. These findings indicate the importance of the mode of interaction of microtubule with the medium in the buckling behavior of microtubule. Our findings would bring new insights on buckling of microtubules in living cells.

3-D Topological Arrangement of Cytoskeleton Modulated by Environmental Mechanics

In developmental biology and regenerative medicine, one important and long-lasting issue is to understand how mammalian cells spontaneously arrange themselves into specific, 3-D forms of organs. Loss of such ordering is a hallmark of many diseases including malformation and cancer. For decades, emphasis has been placed on spatial pre-patterning and multi-cellular coordination of chemical signals, to explain how such ordering emerges. Not until recently, it is recognized that forces also play an important role. We have, for example, shown that cells can develop long-range multi-cellular coordination (up to 600 microns) in tissue formation and cancer invasion, through cell-matrix mechanical interactions. Here, we report that single epithelial cells can spontaneously break symmetry and partition cytoskeleton into the precursor forms for multi-cellular coordination including the formation of apicobasal polarity, in the absence of pre-patterning of intracellular or extracellular chemical signals. Furthermore, such process provides geometrical cues to guide the spatial patterning of intracellular signals and extracellular matrix molecules. It is specific to normal epithelial cells and not observed in several cancer cell lines, mesenchymal cells, or stem cells. Through manipulating environmental mechanics and mathematical modeling, we find that the spontaneous partition of cytoskeleton arises from the mechanical instability in the counteracting between actomyosin contraction and microtubule buckling, and is modulated by substrate rigidity. Based on these results, we propose that mechanical instability of single cells is sufficient to create a topological precursor as a building block for chemical signaling and multi-cellular coordination in development, and failure in such a process might lead to diseases.

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.

Thermal Fluctuation Induced Piezoelectric Effect in Cytoskeletal Microtubules: Model for Energy Harvesting and Their Intracellular Communication

Cytoskeletal microtubules have long been conjectured to have piezoelectric properties. They have been shown to behave as nematic liquid crystals which oscillate along their director axis due to the prevalent thermal fluctuations. In this work, we develop a theoretical model of the mechanics of microtubules in the cytosolic space based on the buckling of its structure due to these thermal fluctuations. This cytosolic space has been considered as a viscoelastic medium in which microtubule oscillations have been considered. As a result of resilience of cytosol and neighbouring filaments from the axial force due to thermal fluctuations, the surface traction acting laterally on the microtubule structure has been further used to elucidate its piezoelectric behaviour in vivo. After the piezoelectric properties induced by thermal fluctuations (in addition to the buckling) of microtubules have been discussed, we propose a model discussing how microtubules behave as energy harvesters and communicate via electromagnetic radiation, with each other, in an intracellular environment.