Elastic response, buckling, and instability of microtubules under radial indentation

Tensile Stress on Microtubules Facilitates Dynein-Driven Cargo Transport

Mechanical stress significantly affects the physiological functions of cells, including tissue homeostasis, cytoskeletal alterations, and intracellular transport. As a major cytoskeletal component, microtubules respond to mechanical stimulation by altering their alignment and polymerization dynamics. Previously, we reported that microtubules may modulate cargo transport by one of the microtubule-associated motor proteins, dynein, under compressive mechanical stress. Despite the critical role of tensile stress in many biological functions, how tensile stress on microtubules regulates cargo transport is yet to be unveiled. The present study demonstrates that the low-level tensile stress-induced microtubule deformation facilitates dynein-driven transport. We validate our experimental findings using all-atom molecular dynamics simulation. Our study may provide important implications for developing new therapies for diseases that involve impaired intracellular transport.

Critical review of single-cell mechanotyping approaches for biomedical applications

Accurate mechanical measurements of cells has the potential to improve diagnostics, therapeutics and advance understanding of disease mechanisms, where high-resolution mechanical information can be measured by deforming individual cells. Here we evaluate recently developed techniques for measuring cell-scale stiffness properties; while many such techniques have been developed, much of the work examining single-cell stiffness is impacted by difficulties in standardization and comparability, giving rise to large variations in reported mechanical moduli. We highlight the role of underlying mechanical theories driving this variability, and note opportunities to develop novel mechanotyping devices and theoretical models that facilitate convenient and accurate mechanical characterisation. Moreover, many high-throughput approaches are confounded by factors including cell size, surface friction, natural population heterogeneity and convolution of elastic and viscous contributions to cell deformability. We nevertheless identify key approaches based on deformability cytometry as a promising direction for further development, where both high-throughput and accurate single-cell resolutions can be realized.

Measuring mechanical properties with high-speed atomic force microscopy

High-speed atomic force microscopy (HS-AFM) is now a widely used technique to study the dynamics of single biomolecules and complex structures. In the past, it has mainly been used to capture surface topography as structural analysis, leading to important discoveries not attainable by other methods. Similar to conventional AFM, the scope of HS-AFM was recently expanded to encompass quantities beyond topography, such as the measurement of mechanical properties. This review delves into various methodologies for assessing mechanical properties, ranging from semi-quantitative approaches to precise force measurements and their corresponding sample responses. We will focus on the application to single proteins such as bridging integrator-1, ion channels such as Piezo1, complex structures such as microtubules and supramolecular fibers. In all these examples, the unique combination of quantifiable force application and high spatiotemporal resolution allows to unravel mechanisms that cannot be investigated by conventional means.

Geometric mapping from rectilinear material orthotropy to isotropy: Insights into plates and shells

Orthotropic shell structures are ubiquitous in biology and engineering, from bacterial cell walls to reinforced domes. We present a rescaling transformation that maps an orthotropic shallow shell to an isotropic one with a different local geometry. The mapping is applicable to any shell section for which the material orthotropy directions match the principal curvature directions, assuming the commonly used Huber form for the orthotropic shear modulus. Using the rescaling transformation, we derive exact expressions for the buckling pressure as well as the linear indentation response of orthotropic cylinders and general ellipsoids of revolution, which we verify against numerical simulations. Our analysis disentangles the separate contributions of geometric and material anisotropy to shell rigidity. In particular, we identify the geometric mean of orthotropic elastic constants as the key quantifier of material stiffness, playing a role akin to the Gaussian curvature which captures the geometric stiffness contribution. Besides providing insights into the mechanical response of orthotropic shells, our work rigorously establishes the validity of isotropic approximations to orthotropic shells and also identifies situations in which these approximations might fail.

The Influence of Nucleus Mechanics in Modelling Adhesion-independent Cell Migration in Structured and Confined Environments

Recent biological experiments (Lämmermann et al. in Nature 453(7191):51-55, 2008; Reversat et al. in Nature 7813:582-585, 2020; Balzer et al. in ASEB J Off Publ Fed Am Soc Exp Biol 26(10):4045-4056, 2012) have shown that certain types of cells are able to move in structured and confined environments even without the activation of focal adhesion. Focusing on this particular phenomenon and based on previous works (Jankowiak et al. in Math Models Methods Appl Sci 30(03):513-537, 2020), we derive a novel two-dimensional mechanical model, which relies on the following physical ingredients: the asymmetrical renewal of the actin cortex supporting the membrane, resulting in a backward flow of material; the mechanical description of the nuclear membrane and the inner nuclear material; the microtubule network guiding nucleus location; the contact interactions between the cell and the external environment. The resulting fourth order system of partial differential equations is then solved numerically to conduct a study of the qualitative effects of the model parameters, mainly those governing the mechanical properties of the nucleus and the geometry of the confining structure. Coherently with biological observations, we find that cells characterized by a stiff nucleus are unable to migrate in channels that can be crossed by cells with a softer nucleus. Regarding the geometry, cell velocity and ability to migrate are influenced by the width of the channel and the wavelength of the external structure. Even though still preliminary, these results may be potentially useful in determining the physical limit of cell migration in confined environments and in designing scaffolds for tissue engineering.

Conformational dynamics and mechanical properties of biomimetic RNA, DNA, and RNA-DNA hybrid nanotubes: an atomistic molecular dynamics study

With the nanotechnology boom, artificially designed nucleic acid nanotubes have aroused interest due to their practical applications in nanorobotics, vaccine design, membrane channels, drug delivery, and force sensing. In this paper, computational study was performed to investigate the structural dynamics and mechanical properties of RNA nanotubes (RNTs), DNA nanotubes (DNTs), and RNA-DNA hybrid nanotubes (RDHNTs). So far, the structural and mechanical properties of RDHNTs have not been examined in experiments or theoretical calculations, and there is limited knowledge regarding these properties for RNTs. Here, the simulations were carried out using the equilibrium molecular dynamics (MD) and steered molecular dynamics (SMD) approaches. Using in-house scripting, we modeled hexagonal nanotubes composed of six double-stranded molecules connected by four-way Holliday junctions. Classical MD analyses were performed on the collected trajectory data to investigate structural properties. Analyses of the microscopic structural parameters of RDHNT indicated a structural transition from the A-form to a conformation between the A- and B-forms, which may be attributable to the increased rigidity of RNA scaffolds compared to DNA staples. Comprehensive research on the elastic mechanical properties was also conducted based on spontaneous thermal fluctuations of nanotubes and employing the equipartition theorem. The Young's modulus of RDHNT (E = 165 MPa) and RNT (E = 144 MPa) was found to be almost the same and nearly half of that found for DNT (E = 325 MPa). Furthermore, the results showed that RNT was more resistant to bending, torsional, and volumetric deformations than DNT and RDHNT. We also used non-equilibrium SMD simulations to acquire comprehensive knowledge of the mechanical response of nanotubes to tensile stress.

Effect of the Rho-Kinase/ROCK Signaling Pathway on Cytoskeleton Components

The mechanical properties of cells are important in tissue homeostasis and enable cell growth, division, migration and the epithelial-mesenchymal transition. Mechanical properties are determined to a large extent by the cytoskeleton. The cytoskeleton is a complex and dynamic network composed of microfilaments, intermediate filaments and microtubules. These cellular structures confer both cell shape and mechanical properties. The architecture of the networks formed by the cytoskeleton is regulated by several pathways, a key one being the Rho-kinase/ROCK signaling pathway. This review describes the role of ROCK (Rho-associated coiled-coil forming kinase) and how it mediates effects on the key components of the cytoskeleton that are critical for cell behaviour.

Intramolecular covalent bonds in Gram-positive bacterial surface proteins

Gram-positive bacteria experience considerable mechanical perturbation when adhering to host surfaces during colonization and infection. They have evolved various adhesion proteins that are mechanically robust to ensure strong surface adhesion. Recently, it was discovered that these adhesion proteins contain rare, extra intramolecular covalent bonds that stabilize protein structures and participate in surface bonding. These intramolecular covalent bonds include isopeptides, thioesters, and ester bonds, which often form spontaneously without the need for additional enzymes. With the development of single-molecule force spectroscopy techniques, the detailed mechanical roles of these intramolecular covalent bonds have been revealed. In this review, we summarize the recent advances in this area of research, focusing on the link between the mechanical stability and function of these covalent bonds in Gram-positive bacterial surface proteins. We also highlight the potential impact of these discoveries on the development of novel antibiotics and chemical biology tools.

A modeling study of the effect of an alternating magnetic field on magnetite nanoparticles in proximity of the neuronal microtubules: A proposed mechanism for detachment of tau proteins

BACKGROUND AND OBJECTIVE

It is known that the disintegration of microtubules in neurons occurs in response to the phosphorylation of the tau proteins that promotes the structural instability of the microtubules, as one of the factors underlying the onset of Alzheimer's disease (AD).

METHODS

In this study, the mechanical variations undergone by the tau protein's and microtubule's structures due to the action of intrinsic magnetite nanoparticles inside the brain tissue have been computationally modeled using the finite element (FEM) method.

RESULTS

The von Mises stress induced by magnetite nanoparticles, subject to an applied alternating magnetic field, leads to local heating and mechanical forces, prompting a corresponding deformation in, and displacement of, the microtubule and the tau protein.

CONCLUSIONS

The induction of these deformations would increase the probability of the microtubules' depolymerization, and hence their eventual structural disintegration.

Feature Extraction of 3T3 Fibroblast Microtubule Based on Discrete Wavelet Transform and Lucy–Richardson Deconvolution Methods

Accompanied by the increasing requirements of the probing micro/nanoscopic structures of biological samples, various image-processing algorithms have been developed for visualization or to facilitate data analysis. However, it remains challenging to enhance both the signal-to-noise ratio and image resolution using a single algorithm. In this investigation, we propose a composite image processing method by combining discrete wavelet transform (DWT) and the Lucy–Richardson (LR) deconvolution method, termed the DWDC method. Our results demonstrate that the signal-to-noise ratio and resolution of live cells’ microtubule networks are considerably improved, allowing the recognition of features as small as 120 nm. The method shows robustness in processing the high-noise images of filament-like biological structures, e.g., the cytoskeleton networks captured by fluorescent microscopes.

The chirality of the mitotic spindle provides a mechanical response to forces and depends on microtubule motors and augmin

Forces produced by motor proteins and microtubule dynamics within the mitotic spindle are crucial for proper chromosome segregation. In addition to linear forces, rotational forces or torques are present in the spindle, which are reflected in the left-handed twisted shapes of microtubule bundles that make the spindle chiral. However, the biological role and molecular origins of spindle chirality are unknown. By developing methods for measuring the spindle twist, we show that spindles are most chiral near the metaphase-to-anaphase transition. To assess the role of chirality in spindle mechanics, we compressed the spindles along their axis. This resulted in a stronger left-handed twist, suggesting that the twisted shape allows for a mechanical response to forces. Inhibition or depletion of motor proteins that perform chiral stepping, Eg5/kinesin-5, Kif18A/kinesin-8, MKLP1/kinesin-6, and dynein, decreased the left-handed twist or led to right-handed twist, implying that these motors regulate the twist by rotating microtubules within their antiparallel overlaps or at the spindle pole. A right-handed twist was also observed after the depletion of the microtubule nucleator augmin, indicating its contribution to the twist through the nucleation of antiparallel bridging microtubules. The uncovered switch from left-handed to right-handed twist reveals the existence of competing mechanisms that promote twisting in opposite directions. As round spindles are more twisted than the elongated ones are, we infer that bending and twisting moments are generated by similar molecular mechanisms and propose a physiological role for spindle chirality in allowing the spindle to absorb mechanical load.

Video abstract

•

Spindle twist depends on torque-generating motors Eg5, Kif18A, MKLP1, and dynein

•

Without the microtubule nucleator augmin, spindles show right-handed twist

•

Compression of the spindle along the axis increases the left-handed twist

•

Rounder spindles are more twisted than elongated ones are

Microtubule Preparation for Investigation with High-Speed Atomic Force Microscopy

High-speed atomic force microscopy (AFM) is a versatile method that can visualize proteins and protein systems on the nanometer scale and at a temporal resolution of 100 ms. The application to microtubules can not only reveal structural information with single-tubulin resolution but can also extract mechanical information and allows to study single motor proteins walking on microtubules, among others. This chapter provides a step-by-step guide from microtubule polymerization to successful observation with high-speed AFM.

Mechanical Deformation of Microtubules on a Two-Dimensional Elastic Medium

Microtubule, the most rigid filamentous protein in cytoskeleton, plays significant roles in cellular mechano-transduction and mechano-regulation of cellular functions. In cells, the mechanical stress serves as a prevalent stimulus to frequently cause deformation of the microtubules participating in various cellular events. While the experimental and simulation-based approaches have confirmed the role of mechanical stress to tune mechanical properties of microtubule. Yet, the effect of mechanical force on the structural stability and the mechanism of microtubule deformation have remained obscure. Here, we describe the mechanical stress-induced deformation of microtubules using a custom-made mechanical device. We designed the device in a way which allows the microtubules to undergo deformation as response to the applied stress while attached on a two-dimensional elastic substrate through interaction with microtubule-associated motor protein, kinesin. We provide here the method to cause controlled bucking or fragmentation of microtubules by applying compressive or tensile stress on the microtubules, respectively. Such study is crucial to understand the mechanism of deformation in microtubules in cellular environment and their consequences in physiological activities.

Indentation responses of pressurized ellipsoidal and cylindrical elastic shells: Insights from shallow-shell theory

Pressurized elastic shells are ubiquitous in nature and technology, from the outer walls of yeast and bacterial cells to artificial pressure vessels. Indentation measurements simultaneously probe the internal pressure and elastic properties of thin shells and serve as a useful tool for strength testing and for inferring internal biological functions of living cells. We study the effects of geometry and pressure-induced stress on the indentation stiffness of ellipsoidal and cylindrical elastic shells using shallow-shell theory. We show that the linear indentation response reduces to a single integral with two dimensionless parameters that encode the asphericity and internal pressure. This integral can be numerically evaluated in all regimes and is used to generate compact analytical expressions for the indentation stiffness in various regimes of technological and biological importance. Our results provide theoretical support for previous scaling and numerical results describing the stiffness of ellipsoids, reveal a new pressure scale that dictates the large-pressure response, and give new insights to the linear indentation response of pressurized cylinders.

Pulling the springs of a cell by single-molecule force spectroscopy

The fundamental unit of the human body comprises of the cells which remain embedded in a fibrillar network of extracellular matrix proteins which in turn provides necessary anchorage the cells. Tissue repair, regeneration and reprogramming predominantly involve a traction force mediated signalling originating in the ECM and travelling deep into the cell including the nucleus via circuitry of spring-like filamentous proteins like microfilaments or actin, intermediate filaments and microtubules to elicit a response in the form of mechanical movement as well as biochemical changes. The 'springiness' of these proteins is highlighted in their extension-contraction behaviour which is manifested as an effect of differential traction force. Atomic force microscope (AFM) provides the magic eye to visualize and quantify such force-extension/indentation events in these filamentous proteins as well as in whole cells. In this review, we have presented a summary of the current understanding and advancement of such measurements by AFM based single-molecule force spectroscopy in the context of cytoskeletal and nucleoskeletal proteins which act in tandem to facilitate mechanotransduction.

Coarse-Grained Simulation of Mechanical Properties of Single Microtubules With Micrometer Length

Microtubules are one of the most important components in the cytoskeleton and play a vital role in maintaining the shape and function of cells. Because single microtubules are some micrometers long, it is difficult to simulate such a large system using an all-atom model. In this work, we use the newly developed convolutional and K-means coarse-graining (CK-CG) method to establish an ultra-coarse-grained (UCG) model of a single microtubule, on the basis of the low electron microscopy density data of microtubules. We discuss the rationale of the micro-coarse-grained microtubule models of different resolutions and explore microtubule models up to 12-micron length. We use the devised microtubule model to quantify mechanical properties of microtubules of different lengths. Our model allows mesoscopic simulations of micrometer-level biomaterials and can be further used to study important biological processes related to microtubule function.

Dynamic Instability from Non-equilibrium Structural Transitions on the Energy Landscape of Microtubule

Microtubules are the backbone of the cytoskeleton and vital to numerous cellular processes. The central dogma of microtubules is that all their functions are driven by dynamic instability, but its mechanism has remained unresolved for over 30 years because of conceptual difficulties inherent in the dominant GTP-cap framework. We present a physically rigorous structural mechanochemical model: dynamic instability is driven by non-equilibrium transitions between the bent (B), straight (S), and curved (C) forms of tubulin monomers and longitudinal interfaces in the two-dimensional lattice of microtubule. All the different phenomena (growth, shortening, catastrophe, rescue, and pausing) are controlled by the kinetic pathways for B↔S↔C transitions and corresponding energy landscapes. Different kinetics at minus end are due to different B↔S↔C pathways imposed by the polarity of microtubule lattice. This model enables us to reproduce all the observed phenomena of dynamic instability of purified tubulins in kinetic simulations.

Potent Small-Molecule Inhibitors Targeting Acetylated Microtubules as Anticancer Agents Against Triple-Negative Breast Cancer

Microtubules are one of the major targets for anticancer drugs because of their role in cell proliferation and migration. However, as anticancer drugs targeting microtubules have side effects, including the death of normal cells, it is necessary to develop anticancer agents that can target microtubules by specifically acting on cancer cells only. In this study, we identified chemicals that can act as anticancer agents by specifically binding to acetylated microtubules, which are predominant in triple-negative breast cancer (TNBC). The chemical compounds disrupted acetylated microtubule lattices by interfering with microtubule access to alpha-tubulin acetyltransferase 1 (αTAT1), a major acetyltransferase of microtubules, resulting in the increased apoptotic cell death of MDA-MB-231 cells (a TNBC cell line) compared with other cells, such as MCF-10A and MCF-7, which lack microtubule acetylation. Moreover, mouse xenograft experiments showed that treatment with the chemical compounds markedly reduced tumor growth progression. Taken together, the newly identified chemical compounds can be selective for acetylated microtubules and act as potential therapeutic agents against microtubule acetylation enrichment in TNBC.

The application of atomic force microscopy for viruses and protein shells: Imaging and spectroscopy

Atomic force microscopy (AFM) probes surface-adsorbed samples at the nanoscale by using a sharp stylus of nanometric size located at the end of a micro-cantilever. This technique can also work in a liquid environment and offers unique possibilities to study individual protein assemblies, such as viruses, under conditions that resemble their natural liquid milieu. Here, I show how AFM can be used to explore the topography of viruses and protein cages, including that of structures lacking a well-defined symmetry. AFM is not limited for imaging and allows the manipulation of individual viruses with force spectroscopy approaches, such as single indentation and mechanical fatigue assays. These pushing experiments deform the protein cages to obtain their mechanical information and can be used to monitor the structural changes induced by maturation or the exposure to different biochemical environments, such as pH variation. We discuss how studying capsid rupture and self-healing events offers insight into virus uncoating pathways. On the other hand, pulling tests can provide information about the virus-host interaction established between the viral fibers and the cell membrane.

The AP2 adaptor enhances clathrin coat stiffness

Deformation of the plasma membrane into clathrin-coated vesicles is a critical step in clathrin-mediated endocytosis and requires the orchestrated assembly of clathrin and endocytic adaptors into a membrane-associated protein coat. The individual role of these membrane-bending and curvature-stabilizing factors is subject to current debate. As such, it is unclear whether the clathrin coat itself is stiff enough to impose curvature and if so, whether this could be effectively transferred to the membrane by the linking adaptor proteins. We have recently demonstrated that clathrin alone is sufficient to form membrane buds in vitro. Here, we use atomic force microscopy to assess the contributions of clathrin and its membrane adaptor protein 2 (AP2) to clathrin coat stiffness, which determines the mechanics of vesicle formation. We found that clathrin coats are less than 10-fold stiffer than the membrane they enclose, suggesting a delicate balance between the forces harnessed from clathrin coat formation and those required for membrane bending. We observed that clathrin adaptor protein AP2 increased the stiffness of coats formed from native clathrin, but did not affect less-flexible coats formed from clathrin lacking the light chain subunits. We thus propose that clathrin light chains are important for clathrin coat flexibility and that AP2 facilitates efficient cargo sequestration during coated vesicle formation by modulating clathrin coat stiffness.

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.

An estimate to the first approximation of microtubule rupture force

Microtubule mechanical properties are essential for understanding basic cellular processes, including cell motility and division, but the forces that result in microtubule rupture or breakage have not yet been measured directly. These forces are essential to understand the mechanical properties of the cytoskeleton and responses by cells to both normal conditions and stress caused by injury or disease. Here we estimate the force required to rupture a microtubule by analyzing kinesin-14 Ncd motor-induced microtubule breakage in ensemble motility assays. We model the breakage events as caused by Ncd motors pulling or pushing on single microtubules that are clamped at one end by other motors attached to the glass surface. The number of pulling or pushing Ncd motors is approximated from the length of the microtubule bound to the surface and the forces produced by the pulling or pushing motors are estimated from forces produced by the Ncd motor in laser-trap assays, reported by others. Our analysis provides an estimate, to the first approximation, of ~ 500 pN for the minimal force required to rupture a 13-pf microtubule. The value we report is close to the forces estimated from microtubule stretching/fragmentation experiments and overlaps with the forces applied by AFM in microtubule indentation assays that destabilize microtubules and break microtubule protofilaments. It is also consistent with the forces required to disrupt protein noncovalent bonds in force spectroscopy experiments. These findings are relevant to microtubule deformation and breakage caused by cellular tension in vivo.

Atomic Force Microscopy of Viruses

Atomic force microscopy employs a nanometric tip located at the end of a micro-cantilever to probe surface-mounted samples at nanometer resolution. Because the technique can also work in a liquid environment it offers unique possibilities to study individual viruses under conditions that mimic their natural milieu. Here, we review how AFM imaging can be used to study the surface structure of viruses including that of viruses lacking a well-defined symmetry. Beyond imaging, AFM enables the manipulation of single viruses by force spectroscopy experiments. Pulling experiments can provide information about the early events of virus-host interaction between the viral fibers and the cell membrane receptors. Pushing experiments measure the mechanical response of the viral capsid and its contents and can be used to show how virus maturation and exposure to different pH values change the mechanical response of the viruses and the interaction between the capsid and genome. Finally, we discuss how studying capsid rupture and self-healing events offers insight in virus uncoating pathways.

Structural Changes in Tubulin Sheets Caused by Immobilization on Solid Supports

In the presence of zinc, the protein tubulin assembles into two-dimensional sheets that are a useful model system for the study of both tubulin and microtubule structure. Tubulin sheets present an ideal protein structure for study with atomic force microscopy because they contain a two-dimensional crystalline protein lattice and retain many of the structural features of tubulin and microtubules. However, high-resolution imaging requires nonperturbative immobilization onto an appropriate imaging substrate. In this report, several substrates commonly used for scanning probe microscopy are evaluated for their ability to effectively immobilize tubulin sheets: mica, gold, highly ordered pyrolytic graphite, and carbon-coated electron microscopy grids. We hypothesize that the different intermolecular interactions presented by these substrates will affect the morphology of adsorbed tubulin sheets as well as the amount of other contaminating adsorbates. Tubulin sheets were successfully imaged on all of these substrates and structural characterization is reported. The most consistent results were obtained on carbon-coated electron microscopy grids, which preserved fine structural features of the sheets and had the least amount of contamination from the adsorption of unpolymerized tubulin. Images of tubulin sheets obtained with atomic force microscopy also compare favorably with published electron micrographs of sheets produced using similar procedures. This work demonstrates the importance of assessing substrate effects when studying two-dimensional protein crystals and identifies suitable substrates for immobilizing tubulin sheets.

Microtubule self-healing and defect creation investigated by in-line force measurements during high-speed atomic force microscopy imaging

Microtubules are biopolymers composed of tubulin and play diverse roles in a wide variety of biological processes such as cell division, migration and intracellular transport in eukaryotic cells. To perform their functions, microtubules are mechanically stressed and, thereby, susceptible to structural defects. Local variations in mechanical properties caused by these defects modulate their biological functions, including binding and transportation of microtubule-associated proteins. Therefore, assessing the local mechanical properties of microtubules and analyzing their dynamic response to mechanical stimuli provide insight into fundamental processes. It is, however, not trivial to control defect formation, gather mechanical information at the same time, and subsequently image the result at a high temporal resolution at the molecular level with minimal delay. In this work, we describe the so-called in-line force curve mode based on high-speed atomic force microscopy. This method is directly applied to create defects in microtubules at the level of tubulin dimers and monitor the following dynamic processes around the defects. Furthermore, force curves obtained during defect formation provide quantitative mechanical information to estimate the bonding energy between tubulin dimers.

Causes and Consequences of Microtubule Acetylation

Among the different types of cytoskeletal components, microtubules arguably accumulate the greatest diversity of post-translational modifications (PTMs). Acetylation of lysine 40 (K40) of α-tubulin has received particular attention because it is the only tubulin PTM to be found in the lumen of microtubules: most other tubulin PTMs are found at the outer surface of the microtubule. As a consequence, the enzyme catalyzing K40 acetylation needs to penetrate the narrow microtubule lumen to find its substrate. Acetylated microtubules have been considered to be stable, long-lived microtubules; however, until recently, there was little information about whether the longevity of these microtubules is the cause or the consequence of acetylation. Current advances suggest that this PTM helps the microtubule lattice to cope with mechanical stress, thus facilitating microtubule self-repair. These observations now shed new light on the structural integrity of microtubules, as well as on the mechanisms and biological functions of tubulin acetylation. Here, we discuss recent insights into how acetylation is generated in the lumen of microtubules, and how this 'hidden' PTM can control the properties and functions of microtubules.

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.

Direct visualization of single virus restoration after damage in real time

We use the nano-dissection capabilities of atomic force microscopy to induce structural alterations on individual virus capsids in liquid milieu. We fracture the protein shells either with single nanoindentations or by increasing the tip-sample interaction force in amplitude modulation dynamic mode. The normal behavior is that these cracks persist in time. However, in very rare occasions they self-recuperate to retrieve apparently unaltered virus particles. In this work, we show the topographical evolution of three of these exceptional events occurring in T7 bacteriophage capsids. Our data show that single nanoindentation produces a local recoverable fracture that corresponds to the deepening of a capsomer. In contrast, imaging in dynamic mode induced cracks that separate the virus morphological subunits. In both cases, the breakage patterns follow intratrimeric loci.

Elastic, dipole-dipole interaction and viscosity impact on vibrational properties of anisotropic hexagonal microtubule lattice

The paper investigates microtubules lattice properties taking into consideration elastic, dipole-dipole interaction of tubulins and viscosity. A microtubule is modeled as a system of bound tubulins, forming a skewed hexagonal two-dimensional lattice. Wave frequencies and group velocities have been calculated. Calculations have been performed for various directions of wave front propagation: helix, along the protofilament, and anti-helix. Three different wave polarization directions have been considered. It has been shown that the direction of the wave polarization influences the frequency and wave group velocity values in the lattice considerably. The impact of dipole-dipole interaction greatly depends on the direction of the wave polarization; thus, it is only moderate for the longitudinally (LA) polarized waves while it is sufficient for the transversely (TA), and out-of-plane (ZA) polarized waves. Moreover dipole-dipole interaction may result in the waves which are able to cause the rupture of microtubules. With viscosity considered, lattice oscillations become harmonically damped only over a certain wavelength range when longitudinal polarization occurs. Out of this range as well as for the other polarization directions, lattice deviations from equilibrium are dampened exponentially. Taking viscosity into consideration also results in a noticeable decrease in frequency and increase in the group wave velocity when the waves are longitudinally polarized. Reverse wave domains which may be associated with a possible phenomenon of negative refraction have been determined for hexagonal microtubule lattice.

Computational modeling of single-cell mechanics and cytoskeletal mechanobiology

Cellular cytoskeletal mechanics plays a major role in many aspects of human health from organ development to wound healing, tissue homeostasis and cancer metastasis. We summarize the state-of-the-art techniques for mathematically modeling cellular stiffness and mechanics and the cytoskeletal components and factors that regulate them. We highlight key experiments that have assisted model parameterization and compare the advantages of different models that have been used to recapitulate these experiments. An overview of feed-forward mechanisms from signaling to cytoskeleton remodeling is provided, followed by a discussion of the rapidly growing niche of encapsulating feedback mechanisms from cytoskeletal and cell mechanics to signaling. We discuss broad areas of advancement that could accelerate research and understanding of cellular mechanobiology. A precise understanding of the molecular mechanisms that affect cell and tissue mechanics and function will underpin innovations in medical device technologies of the future. WIREs Syst Biol Med 2018, 10:e1407. doi: 10.1002/wsbm.1407 This article is categorized under: Models of Systems Properties and Processes > Mechanistic Models Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Cellular Models.

TensorCalculator: exploring the evolution of mechanical stress in the CCMV capsid

A new computational methodology for the accurate numerical calculation of the Cauchy stress tensor, stress invariants, principal stress components, von Mises and Tresca tensors is developed. The methodology is based on the atomic stress approach which permits the calculation of stress tensors, widely used in continuum mechanics modeling of materials properties, using the output from the MD simulations of discrete atomic and [Formula: see text]-based coarse-grained structural models of biological particles. The methodology mapped into the software package TensorCalculator was successfully applied to the empty cowpea chlorotic mottle virus (CCMV) shell to explore the evolution of mechanical stress in this mechanically-tested specific example of a soft virus capsid. We found an inhomogeneous stress distribution in various portions of the CCMV structure and stress transfer from one portion of the virus structure to another, which also points to the importance of entropic effects, often ignored in finite element analysis and elastic network modeling. We formulate a criterion for elastic deformation using the first principal stress components. Furthermore, we show that von Mises and Tresca stress tensors can be used to predict the onset of a viral capsid's mechanical failure, which leads to total structural collapse. TensorCalculator can be used to study stress evolution and dynamics of defects in viral capsids and other large-size protein assemblies.

Microtubules acquire resistance from mechanical breakage through intralumenal acetylation

Eukaryotic cells rely on long-lived microtubules for intracellular transport and as compression-bearing elements. We considered that long-lived microtubules are acetylated inside their lumen and that microtubule acetylation may modify microtubule mechanics. Here, we found that tubulin acetylation is required for the mechanical stabilization of long-lived microtubules in cells. Depletion of the tubulin acetyltransferase TAT1 led to a significant increase in the frequency of microtubule breakage. Nocodazole-resistant microtubules lost upon removal of acetylation were largely restored by either pharmacological or physical removal of compressive forces. In in vitro reconstitution experiments, acetylation was sufficient to protect microtubules from mechanical breakage. Thus, acetylation increases mechanical resilience to ensure the persistence of long-lived microtubules.

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.

Dynamics of microtubules: highlights of recent computational and experimental investigations

Microtubules are found in most eukaryotic cells, with homologs in eubacteria and archea, and they have functional roles in mitosis, cell motility, intracellular transport, and the maintenance of cell shape. Numerous efforts have been expended over the last two decades to characterize the interactions between microtubules and the wide variety of microtubule associated proteins that control their dynamic behavior in cells resulting in microtubules being assembled and disassembled where and when they are required by the cell. We present the main findings regarding microtubule polymerization and depolymerization and review recent work about the molecular motors that modulate microtubule dynamics by inducing either microtubule depolymerization or severing. We also discuss the main experimental and computational approaches used to quantify the thermodynamics and mechanics of microtubule filaments.

Non-equilibrium assembly of microtubules: from molecules to autonomous chemical robots

Biological systems have evolved to harness non-equilibrium processes from the molecular to the macro scale. It is currently a grand challenge of chemistry, materials science, and engineering to understand and mimic biological systems that have the ability to autonomously sense stimuli, process these inputs, and respond by performing mechanical work. New chemical systems are responding to the challenge and form the basis for future responsive, adaptive, and active materials. In this article, we describe a particular biochemical-biomechanical network based on the microtubule cytoskeletal filament - itself a non-equilibrium chemical system. We trace the non-equilibrium aspects of the system from molecules to networks and describe how the cell uses this system to perform active work in essential processes. Finally, we discuss how microtubule-based engineered systems can serve as testbeds for autonomous chemical robots composed of biological and synthetic components.

Atomic force microscopy of virus shells

Microscopes are used to characterize small specimens with the help of probes, such as photons and electrons in optical and electron microscopies, respectively. In atomic force microscopy (AFM) the probe is a nanometric tip located at the end of a microcantilever which palpates the specimen under study as a blind person manages a white cane to explore the surrounding. In this way, AFM allows obtaining nanometric resolution images of individual protein shells, such as viruses, in liquid milieu. Beyond imaging, AFM also enables the manipulation of single protein cages, and the characterization of every physico-chemical property able of inducing any measurable mechanical perturbation to the microcantilever that holds the tip. Here we describe several AFM approaches to study individual protein cages, including imaging and spectroscopic methodologies for extracting mechanical and electrostatic properties. In addition, AFM allows discovering and testing the self-healing capabilities of protein cages because occasionally they may recover fractures induced by the AFM tip. Beyond the protein shells, AFM also is able of exploring the genome inside, obtaining, for instance, the condensation state of dsDNA and measuring its diffusion when the protein cage breaks.

Invited review: Microtubule severing enzymes couple atpase activity with tubulin GTPase spring loading

Microtubules are amazing filaments made of GTPase enzymes that store energy used for their own self-destruction to cause a stochastically driven dynamics called dynamic instability. Dynamic instability can be reproduced in vitro with purified tubulin, but the dynamics do not mimic that observed in cells. This is because stabilizers and destabilizers act to alter microtubule dynamics. One interesting and understudied class of destabilizers consists of the microtubule-severing enzymes from the ATPases Associated with various cellular Activities (AAA+) family of ATP-enzymes. Here we review current knowledge about GTP-driven microtubule dynamics and how that couples to ATP-driven destabilization by severing enzymes. We present a list of challenges regarding the mechanism of severing, which require development of experimental and modeling approaches to shed light as to how severing enzymes can act to regulate microtubule dynamics in cells. © 2016 Wiley Periodicals, Inc. Biopolymers 105: 547-556, 2016.

αTAT1 controls longitudinal spreading of acetylation marks from open microtubules extremities

Acetylation of the lysine 40 of α-tubulin (K40) is a post-translational modification occurring in the lumen of microtubules (MTs) and is controlled by the α-tubulin acetyl-transferase αTAT1. How αTAT1 accesses the lumen and acetylates α-tubulin there has been an open question. Here, we report that acetylation starts at open ends of MTs and progressively spreads longitudinally from there. We observed acetylation marks at the open ends of in vivo MTs re-growing after a Nocodazole block, and acetylated segments growing in length with time. Bias for MTs extremities was even more pronounced when using non-dynamic MTs extracted from HeLa cells. In contrast, K40 acetylation was mostly uniform along the length of MTs reconstituted from purified tubulin in vitro. Quantitative modelling of luminal diffusion of αTAT1 suggested that the uniform acetylation pattern observed in vitro is consistent with defects in the MT lattice providing lateral access to the lumen. Indeed, we observed that in vitro MTs are permeable to macromolecules along their shaft while cellular MTs are not. Our results demonstrate αTAT1 enters the lumen from open extremities and spreads K40 acetylation marks longitudinally along cellular MTs. This mode of tip-directed microtubule acetylation may allow for selective acetylation of subsets of microtubules.

Decrease in pH destabilizes individual vault nanocages by weakening the inter-protein lateral interaction

Vault particles are naturally occurring proteinaceous cages with promising application as molecular containers. The use of vaults as functional transporters requires a profound understanding of their structural stability to guarantee the protection and controlled payload delivery. Previous results performed with bulk techniques or at non-physiological conditions have suggested pH as a parameter to control vault dynamics. Here we use Atomic Force Microscopy (AFM) to monitor the structural evolution of individual vault particles while changing the pH in real time. Our experiments show that decreasing the pH of the solution destabilize the barrel region, the central part of vault particles, and leads to the aggregation of the cages. Additional analyses using Quartz-Crystal Microbalance (QCM) and Differential Scanning Fluorimetry (DSF) are consistent with our single molecule AFM experiments. The observed topographical defects suggest that low pH weakens the bonds between adjacent proteins. We hypothesize that the observed effects are related to the strong polar character of the protein-protein lateral interactions. Overall, our study unveils the mechanism for the influence of a biologically relevant range of pHs on the stability and dynamics of vault particles.

Ultradonut topology of the nuclear envelope

The nuclear envelope is a unique topological structure formed by lipid membranes in eukaryotic cells. Unlike other membrane structures, the nuclear envelope comprises two concentric membrane shells fused at numerous sites with toroid-shaped pores that impart a "geometric" genus on the order of thousands. Despite the intriguing architecture and vital biological functions of the nuclear membranes, how they achieve and maintain such a unique arrangement remains unknown. Here, we used the theory of elasticity and differential geometry to analyze the equilibrium shape and stability of this structure. Our results show that modest in- and out-of-plane stresses present in the membranes not only can define the pore geometry, but also provide a mechanism for destabilizing membranes beyond a critical size and set the stage for the formation of new pores. Our results suggest a mechanism wherein nanoscale buckling instabilities can define the global topology of a nuclear envelope-like structure.

Swelling and softening of the cowpea chlorotic mottle virus in response to pH shifts

Cowpea chlorotic mottle virus (CCMV) forms highly elastic icosahedral protein capsids that undergo a characteristic swelling transition when the pH is raised from 5 to 7. Here, we performed nano-indentation experiments using an atomic force microscope to track capsid swelling and measure the shells' Young's modulus at the same time. When we chelated Ca(2+) ions and raised the pH, we observed a gradual swelling of the RNA-filled capsids accompanied by a softening of the shell. Control experiments with empty wild-type virus and a salt-stable mutant revealed that the softening was not strictly coupled to the swelling of the protein shells. Our data suggest that a pH increase and Ca(2+) chelation lead primarily to a loosening of contacts within the protein shell, resulting in a softening of the capsid. This appears to render the shell metastable and make swelling possible when repulsive forces among the capsid proteins become large enough, which is known to be followed by capsid disassembly at even higher pH. Thus, softening and swelling are likely to play a role during inoculation.

Strong Resistance to Bending Observed for Nanoparticle Membranes

We demonstrate how gold nanoparticle monolayers can be curled up into hollow scrolls that make it possible to extract both bending and stretching moduli from indentation by atomic force microscopy. We find a bending modulus that is 2 orders of magnitude larger than predicted by standard continuum elasticity, an enhancement we associate with nonlocal microstructural constraints. This finding opens up new opportunities for independent control of resistance to bending and stretching at the nanoscale.

Computational mechanics of viral capsids

Viral capsids undergo significant mechanical deformations during their assembly, maturation, and infective life-span. In order to characterize the mechanics of viral capsids, their response to applied external forces is analyzed in several experimental studies using, for instance, Atomic Force Microscope (AFM) indentation experiments. In recent years, a broader approach to study the mechanics of viral capsids has leveraged the theoretical tools proper of continuum mechanics. Even though the theory of continuum elasticity is most commonly used to study deformable bodies at larger macroscopic length scales, it has been shown that this very rich theoretical field can still offer useful insights into the mechanics of viral structures at the nanometer scale. Here we show the construction of viral capsid continuum mechanics models starting from different forms of experimental data. We will discuss the kinematics assumptions, the issue of the reference configuration, the material constitutive laws, and the numerical discretization necessary to construct a complete Finite Element capsid mechanical model. Some examples in the second part of the chapter will show the predictive capabilities of the constructed models and underline useful practical aspects related to efficiency and accuracy. We conclude each example by collecting several key findings discovered by simulating AFM indentation experiments using the constructed numerical models.