Anisotropic elastic network modeling of entire microtubules

Mechanical communication within the microtubule through network-based analysis of tubulin dynamics

The identification of the mechanisms underlying the transfer of mechanical vibrations in protein complexes is crucial to understand how these super-assemblies are stabilized to perform specific functions within the cell. In this context, the study of the structural communication and the propagation of mechanical stimuli within the microtubule (MT) is important given the pivotal role of the latter in cell viability. In this study, we employed molecular modelling and the dynamical network analysis approaches to analyse the MT. The results highlight that β -tubulin drives the transfer of mechanical information between protofilaments (PFs), which is altered at the seam due to a different interaction pattern. Moreover, while the key residues involved in the structural communication along the PF are generally conserved, a higher diversity was observed for amino acids mediating the lateral communication. Taken together, these results might explain why MTs with different PF numbers are formed in different organisms or with different β -tubulin isotypes.

Biomechanics of cells and subcellular components: A comprehensive review of computational models and applications

Cells are a fundamental structural, functional and biological unit for all living organisms. Up till now, considerable efforts have been made to study the responses of single cells and subcellular components to an external load, and understand the biophysics underlying cell rheology, mechanotransduction and cell functions using experimental and in silico approaches. In the last decade, computational simulation has become increasingly attractive due to its critical role in interpreting experimental data, analysing complex cellular/subcellular structures, facilitating diagnostic designs and therapeutic techniques, and developing biomimetic materials. Despite the significant progress, developing comprehensive and accurate models of living cells remains a grand challenge in the 21st century. To understand current state of the art, this review summarises and classifies the vast array of computational biomechanical models for cells. The article covers the cellular components at multi-spatial levels, that is, protein polymers, subcellular components, whole cells and the systems with scale beyond a cell. In addition to the comprehensive review of the topic, this article also provides new insights into the future prospects of developing integrated, active and high-fidelity cell models that are multiscale, multi-physics and multi-disciplinary in nature. This review will be beneficial for the researchers in modelling the biomechanics of subcellular components, cells and multiple cell systems and understanding the cell functions and biological processes from the perspective of cell mechanics.

Atomistic molecular dynamics simulations of tubulin heterodimers explain the motion of a microtubule

Microtubules are essential parts of the cytoskeleton that are built by polymerization of tubulin heterodimers into a hollow tube. Regardless that their structures and functions have been comprehensively investigated in a modern soft matter, it is unclear how properties of tubulin heterodimer influence and promote the self-assembly. A detailed knowledge of such structural mechanisms would be helpful in drug design against neurodegenerative diseases, cancer, diabetes etc. In this work atomistic molecular dynamics simulations were used to investigate the fundamental dynamics of tubulin heterodimers in a sheet and a short microtubule utilizing well-equilibrated structures. The breathing motions of the tubulin heterodimers during assembly show that the movement at the lateral interface between heterodimers (wobbling) dominates in the lattice. The simulations of the protofilament curvature agrees well with recently published experimental data, showing curved protofilaments at polymerization of the microtubule plus end. The tubulin heterodimers exposed at the microtubule minus end were less curved and displayed altered interactions at the site of sheet closure around the outmost heterodimers, which may slow heterodimer binding and polymerization, providing a potential explanation for the limited dynamics observed at the minus end.

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.

Revealing and Attenuating the Electrostatic Properties of Tubulin and Its Polymers

Tubulin is an electrostatically negative protein that forms cylindrical polymers termed microtubules, which are crucial for a variety of intracellular roles. Exploiting the electrostatic behavior of tubulin and microtubules within functional microfluidic and optoelectronic devices is limited due to the lack of understanding of tubulin behavior as a function of solvent composition. This work displays the tunability of tubulin surface charge using dimethyl sulfoxide (DMSO) for the first time. Increasing the DMSO volume fractions leads to the lowering of tubulin's negative surface charge, eventually causing it to become positive in solutions >80% DMSO. As determined by electrophoretic mobility measurements, this change in surface charge is directionally reversible, i.e., permitting control between -1.5 and + 0.2 cm²  (V s)^-1 . When usually negative microtubules are exposed to these conditions, the positively charged tubulin forms tubulin sheets and aggregates, as revealed by an electrophoretic transport assay. Fluorescence-based experiments also indicate that tubulin sheets and aggregates colocalize with negatively charged g-C₃ N₄ sheets while microtubules do not, further verifying the presence of a positive surface charge. This study illustrates that tubulin and its polymers, in addition to being mechanically robust, are also electrically tunable.

Limitations on electromagnetic communication by vibrational resonances in biological systems

Previous research in biology and physics speculates that high-frequency electromagnetic fields may be an unexplored method of cellular and subcellular communication. The predominant theory for generating electric fields in the cell is mechanical vibration of charged or polar biomolecules such as cell membranes or microtubules. The challenge to this theory is explaining how high-frequency vibrations would not be overdamped by surrounding biological media. As many of these suspected resonators are too large for atomistic molecular dynamics simulations, accurately modeling biological resonators remains an ongoing challenge. While many resonators have been studied and simulated, the general limitations on communication imposed by energy transfer arguments have not been considered. Starting with energy transfer expressions from coupled-mode theory, we derive expressions for the minimum quality factor (Q factor) required to sustain communication for both near- and far-field interactions. We compare previous simulation studies and our theory. We determine the flexing mode of microtubules as an identified resonance in the literature which meets our criteria. Our results suggest the major obstacle to meeting our criteria for effective electromagnetic communication is the trade-off between the Q factor and the plasma frequency: Resonators must be large enough to have a large Q factor, but small enough to resonate at frequencies greater than the plasma frequency.

When Stiffness Matters: Mechanosensing in Heart Development and Disease

During embryonic morphogenesis, the heart undergoes a complex series of cellular phenotypic maturations (e.g., transition of myocytes from proliferative to quiescent or maturation of the contractile apparatus), and this involves stiffening of the extracellular matrix (ECM) acting in concert with morphogenetic signals. The maladaptive remodeling of the myocardium, one of the processes involved in determination of heart failure, also involves mechanical cues, with a progressive stiffening of the tissue that produces cellular mechanical damage, inflammation, and ultimately myocardial fibrosis. The assessment of the biomechanical dependence of the molecular machinery (in myocardial and non-myocardial cells) is therefore essential to contextualize the maturation of the cardiac tissue at early stages and understand its pathologic evolution in aging. Because systems to perform multiscale modeling of cellular and tissue mechanics have been developed, it appears particularly novel to design integrated mechano-molecular models of heart development and disease to be tested in ex vivo reconstituted cells/tissue-mimicking conditions. In the present contribution, we will discuss the latest implication of mechanosensing in heart development and pathology, describe the most recent models of cell/tissue mechanics, and delineate novel strategies to target the consequences of heart failure with personalized approaches based on tissue engineering and induced pluripotent stem cell (iPSC) technologies.

Mechanics and kinetics of dynamic instability

During dynamic instability, self-assembling microtubules (MTs) stochastically alternate between phases of growth and shrinkage. This process is driven by the presence of two distinct states of MT subunits, GTP- and GDP-bound tubulin dimers, that have different structural properties. Here, we use a combination of analysis and computer simulations to study the mechanical and kinetic regulation of dynamic instability in three-dimensional (3D) self-assembling MTs. Our model quantifies how the 3D structure and kinetics of the distinct states of tubulin dimers determine the mechanical stability of MTs. We further show that dynamic instability is influenced by the presence of quenched disorder in the state of the tubulin subunit as reflected in the fraction of non-hydrolysed tubulin. Our results connect the 3D geometry, kinetics and statistical mechanics of these tubular assemblies within a single framework, and may be applicable to other self-assembled systems where these same processes are at play.

Microtubule Simulations Provide Insight into the Molecular Mechanism Underlying Dynamic Instability

The dynamic instability of microtubules (MTs), which refers to their ability to switch between polymerization and depolymerization states, is crucial for their function. It has been proposed that the growing MT ends are protected by a "GTP cap" that consists of GTP-bound tubulin dimers. When the speed of GTP hydrolysis is faster than dimer recruitment, the loss of this GTP cap will lead the MT to undergo rapid disassembly. However, the underlying atomistic mechanistic details of the dynamic instability remains unclear. In this study, we have performed long-time atomistic molecular dynamics simulations (1 μs for each system) for MT patches as well as a short segment of a closed MT in both GTP- and GDP-bound states. Our results confirmed that MTs in the GDP state generally have weaker lateral interactions between neighboring protofilaments (PFs) and less cooperative outward bending conformational change, where the difference between bending angles of neighboring PFs tends to be larger compared with GTP ones. As a result, when the GDP state tubulin dimer is exposed at the growing MT end, these factors will be more likely to cause the MT to undergo rapid disassembly. We also compared simulation results between the special MT seam region and the remaining material and found that the lateral interactions between MT PFs at the seam region were comparatively much weaker. This finding is consistent with the experimental suggestion that the seam region tends to separate during the disassembly process of an MT.

Mechanical properties of tubulin intra- and inter-dimer interfaces and their implications for microtubule dynamic instability

Thirteen tubulin protofilaments, made of αβ-tubulin heterodimers, interact laterally to produce cytoskeletal microtubules. Microtubules exhibit the striking property of dynamic instability, manifested in their intermittent growth and shrinkage at both ends. This behavior is key to many cellular processes, such as cell division, migration, maintenance of cell shape, etc. Although assembly and disassembly of microtubules is known to be linked to hydrolysis of a guanosine triphosphate molecule in the pocket of β-tubulin, detailed mechanistic understanding of corresponding conformational changes is still lacking. Here we take advantage of the recent generation of in-microtubule structures of tubulin to examine the properties of protofilaments, which serve as important microtubule assembly and disassembly intermediates. We find that initially straight tubulin protofilaments, relax to similar non-radially curved and slightly twisted conformations. Our analysis further suggests that guanosine triphosphate hydrolysis primarily affects the flexibility and conformation of the inter-dimer interface, without a strong impact on the shape or flexibility of αβ-heterodimer. Inter-dimer interfaces are significantly more flexible compared to intra-dimer interfaces. We argue that such a difference in flexibility could be key for distinct stability of the plus and minus microtubule ends. The higher flexibility of the inter-dimer interface may have implications for development of pulling force by curving tubulin protofilaments during microtubule disassembly, a process of major importance for chromosome motions in mitosis.

Simulation of electric fields generated from microtubule vibrations

Microtubules are tubular proteins that form part of the cytoskeleton in eukaryotic cells. Because of their unique mechanical properties, many studies have theorized microtubules could show high-frequency mechanical vibrations. Others have further suggested these vibrations of the electrically polar microtubules could be a source of electric fields inside the cell that could serve some biological function, such as a role in organizing mitosis or also possibly in cell-to-cell communication. In this work, we use a transient method to simulate the electric fields that would be generated from a single microtubule supposing they could sustain vibrations. We evaluate the biological significance of the electric fields and the potential energy microtubules might exert on one another. Our simulation method allows us to evaluate vibrational modes that have not previously been studied. The simulations suggest the acoustic branch flexing mode would actually be the most electrically active. Our results suggest a single vibrating microtubule could potentially exert significant forces (those that exceed thermal energy) on biological dipoles or charges at distances larger then the Debye length, on the order of 10nm from the surface of the microtubule, but interaction is not likely at greater distances.

Insights into the flexibility of the T3 loop and GTPase activating protein (GAP) domain of dimeric α and β tubulins from a molecular dynamics perspective

Tubulin protein is the fundamental unit of microtubules, and comprises of α and β subunits arranged in an alternate manner forming protofilaments. These longitudinal protofilaments are made up of intra- (α-β) and inter-dimer (β-α) interactions. Literature review confirms that GTP hydrolysis results in considerable structural rearrangement within GTP binding site of β-α dimer interface after the release of γ phosphate. In addition to this, the intra-dimer interface exhibits structural rigidity which needs further investigation. In this study, we explored the reasons for the flexibility and the rigidity of the β-α dimer and the α-β dimer respectively through molecular simulation and Anisotropic Normal Mode based analysis. As per the sequence alignment report, two glycine residues (Gly⁹⁶ and Gly⁹⁸) were observed in the T3 loop of the β subunit which get substituted by Asp⁹⁸ and Ala¹⁰⁰ in the T3 loop of the α subunit. The higher mobility of glycine residues contributes to the flexibility of the T3 loop of inter-dimer when they come in direct contact with the GTPase Activating Protein (GAP) domain of the subunit. This was confirmed through RMSD, RMSF and Radius of Gyration based studies. Conversely, the intra-dimer exhibited a lower mobility in the absence of glycine residues. As per ANM based analysis, positive domain correlations were observed between T3 loop and GAP domain of intra- and inter- dimeric contact regions. However, these correlation motions were higher in the intra-dimer as compared to the inter-dimer interface. Thus on the basis of our findings, we hypothesize that the higher flexibility of T3 loop and the GAP domain of the inter-dimer is required for structural rearrangement and protofilament stability during hydrolysis. Furthermore, the slightly rigid nature of the T3 loop and the GAP domain of the intra-dimer assists in enhancing the monomer-monomer interaction through the higher positive domain correlation.

Electromechanical vibration of microtubules and its application in biosensors

An electric field (EF) has the potential to excite the vibration of polarized microtubules (MTs) and thus enable their use as a biosensor for the biophysical properties of MTs or cells. To facilitate the development, this paper aims to capture the EF-induced vibration modes and the associated frequency for MTs. The analyses were carried out based on a molecular structural mechanics model accounting for the structural details of MTs. Transverse vibration, radial breathing vibration and axial vibration were achieved for MTs subject to a transverse or an axial EF. The frequency shift and stiffness alteration of MTs were also examined due to the possible changes of the tubulin interactions in physiological or pathological processes. The strong correlation achieved between the tubulin interaction and MT vibration excited by EF provides a new avenue to a non-contacting technique for the structural or property changes in MTs, where frequency shift is used as a biomarker. This technique can be used for individual MTs and is possible for those in cells when the cytosol damping on MT vibrations is largely reduced by the unique features of MT-cytosol interface.

Destabilizing the AXH Tetramer by Mutations: Mechanisms and Potential Antiaggregation Strategies

The AXH domain of protein Ataxin 1 is thought to play a key role in the misfolding and aggregation pathway responsible for Spinocerebellar ataxia 1. For this reason, a molecular level understanding of AXH oligomerization pathway is crucial to elucidate the aggregation mechanism, which is thought to trigger the disease. This study employs classical and enhanced molecular dynamics to identify the structural and energetic basis of AXH tetramer stability. Results of this work elucidate molecular mechanisms behind the destabilizing effect of protein mutations, which consequently affect the AXH tetramer assembly. Moreover, results of the study draw attention for the first time, to our knowledge, to the R638 protein residue, which is shown to play a key role in AXH tetramer stability. Therefore, R638 might be also implicated in the AXH oligomerization pathway and stands out as a target for future experimental studies focused on self-association mechanisms and fibril formation of full-length ATX1.

The long persistence length of model tubules

Young's elastic modulus and the persistence length are calculated for a coarse-grained model of tubule forming polymers. The model uses a wedge shaped composite of particles that previously has been shown to self-assemble into tubules. These calculations demonstrate that the model yields very large persistence lengths (corresponding to 78-126 μm) that are comparable to that observed in experiments for the microtubule lengths accessible to the calculations. The source for the stiffness is the restricted rotation of the monomer due to the excluded volume interactions between bonded macromolecular monomers as well as the binding between monomers. For this reason, large persistence lengths are common in tubule systems with a macromolecule as the monomer. The persistence length increases linearly with increased binding strength in the filament direction. No dependence in the persistence length is found for varying the tubule pitch for geometries with the protofilaments remaining straight.

Effect of Nucleotide State on the Protofilament Conformation of Tubulin Octamers

At the molecular level, the dynamic instability (random growth and shrinkage) of the microtubule (MT) is driven by the nucleotide state (GTP vs GDP) in the β subunit of the tubulin dimers at the MT cap. Here, we use large-scale molecular dynamics (MD) simulations and normal-mode analysis (NMA) to characterize the effect of a single GTP cap layer on tubulin octamers composed of two neighboring protofilaments (PFs). We utilize recently reported high-resolution structures of dynamic MTs to simulate a GDP octamer both with and without a single GTP cap layer. We perform multiple replicas of long-time atomistic MD simulations (3 replicas, 0.3 μs for each replica, 0.9 μs for each octamer system, and 1.8 μs total) of both octamers. We observe that a single GTP cap layer induces structural differences in neighboring PFs, finding that one PF possesses a gradual curvature, compared to the second PF which possesses a kinked conformation. This results in either curling or splaying between these PFs. We suggest that this is due to asymmetric strengths of longitudinal contacts between the two PFs. Furthermore, using NMA, we calculate mechanical properties of these octamer systems and find that octamer system with a single GTP cap layer possesses a lower flexural rigidity.

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.

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.

Molecular mechanisms underlying the impact of mutations in SOD1 on its conformational properties associated with amyotrophic lateral sclerosis as revealed with molecular modelling

Background

So far, little is known about the molecular mechanisms of amyotrophic lateral sclerosis onset and progression caused by SOD1 mutations. One of the hypotheses is based on SOD1 misfolding resulting from mutations and subsequent deposition of its cytotoxic aggregates. This hypothesis is complicated by the fact that known SOD1 mutations of similar clinical effect could be distributed over the whole protein structure.

Results

In this work, a measure of hydrogen bond stability in conformational states was studied with elastic network analysis of 35 SOD1 mutants. Twenty-eight hydrogen bonds were detected in nine of 35 mutants with their stability being significantly different from that with the wild-type. These hydrogen bonds were formed by the amino acid residues known from the literature to be located in contact between SOD1 aggregates. Additionally, residues disposed between copper binding sites of both protein subunits were found from the models to form a stiff core, which can be involved in mechanical impulse transduction between these active centres.

Conclusions

The modelling highlights that both stability of the copper binding site and stability of the dimer can play an important role in ALS progression.

Electronic supplementary material

The online version of this article (10.1186/s12900-018-0080-9) contains supplementary material, which is available to authorized users.

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.

Data-driven reduced-order model of microtubule mechanics

A beam element is constructed for microtubules based upon data reduction of the results from atomistic simulation of the carbon backbone chain of αβ-tubulin dimers. The database of mechanical responses to various types of loads from atomistic simulation is reduced to dominant modes. The dominant modes are subsequently used to construct the stiffness matrix of a beam element that captures the anisotropic behavior and deformation mode coupling that arises from a microtubule's spiral structure. In contrast to standard Euler-Bernoulli or Timoshenko beam elements, the link between forces and node displacements results not from hypothesized deformation behavior, but directly from the data obtained by molecular scale simulation. Differences between the resulting microtubule data-driven beam model (MTDDBM) and standard beam elements are presented, with a focus on coupling of bending, stretch, shear deformations. The MTDDBM is just as economical to use as a standard beam element, and allows accurate reconstruction of the mechanical behavior of structures within a cell as exemplified in a simple model of a component element of the mitotic spindle.

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.

Explaining the Microtubule Energy Balance: Contributions Due to Dipole Moments, Charges, van der Waals and Solvation Energy

Microtubules are the main components of mitotic spindles, and are the pillars of the cellular cytoskeleton. They perform most of their cellular functions by virtue of their unique dynamic instability processes which alternate between polymerization and depolymerization phases. This in turn is driven by a precise balance between attraction and repulsion forces between the constituents of microtubules (MTs)—tubulin dimers. Therefore, it is critically important to know what contributions result in a balance of the interaction energy among tubulin dimers that make up microtubules and what interactions may tip this balance toward or away from a stable polymerized state of tubulin. In this paper, we calculate the dipole–dipole interaction energy between tubulin dimers in a microtubule as part of the various contributions to the energy balance. We also compare the remaining contributions to the interaction energies between tubulin dimers and establish a balance between stabilizing and destabilizing components, including the van der Waals, electrostatic, and solvent-accessible surface area energies. The energy balance shows that the GTP-capped tip of the seam at the plus end of microtubules is stabilized only by −9 kcal/mol, which can be completely reversed by the hydrolysis of a single GTP molecule, which releases +14 kcal/mol and destabilizes the seam by an excess of +5 kcal/mol. This triggers the breakdown of microtubules and initiates a disassembly phase which is aptly called a catastrophe.

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.

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.

Thermodynamic and kinetic stability of the Josephin Domain closed arrangement: evidences from replica exchange molecular dynamics

BACKGROUND

Molecular phenomena driving pathological aggregation in neurodegenerative diseases are not completely understood yet. Peculiar is the case of Spinocerebellar Ataxia 3 (SCA3) where the conformational properties of the AT-3 N-terminal region, also called Josephin Domain (JD), play a key role in the first step of aggregation, having the JD an amyloidogenic propensity itself. For this reason, unraveling the intimate relationship between JD structural features and aggregation tendency may lead to a step forward in understanding the pathology and rationally design a cure. In this connection, computational modeling has demonstrated to be helpful in exploring the protein molecular dynamics and mechanism of action.

RESULTS

Conformational dynamics of the JD is here finely investigated by replica exchange molecular dynamics simulations able to sample the microsecond time scale and to provide both a thermodynamic and kinetic description of the protein conformational changes. Accessible structural conformations of the JD have been identified in: open, intermediate and closed like arrangement. Data indicated the closed JD arrangement as the most likely protein arrangement. The protein transition from closed toward intermediate/open states was characterized by a rate constant higher than 700 ns. This result also explains the inability of classical molecular dynamics to explore transitions from closed to open JD configuration on a time scale of hundreds of nanoseconds.

CONCLUSION

This work provides the first kinetic estimation of the JD transition pathway from open-like to closed-like arrangement and vice-versa, indicating the closed-like arrangement as the most likely configuration for a JD in water environment. More widely, the importance of our results is also underscored considering that the ability to provide a kinetic description of the protein conformational changes is a scientific challenge for both experimental and theoretical approaches to date.

REVIEWERS

This article was reviewed by Oliviero Carugo, Bojan Zagrovic.

Effect of amino acid mutations on intra-dimer tubulin–tubulin binding strength of microtubules

Binding strength inside αβ-tubulin dimers of a microtubule (MT) with atomic resolutions are of importance in determining the structural stability of the MT as well as designing self-assembled functional structures from it. Through simulations, this study proposes a new strategy to tune the binding strength inside microtubules through point mutations of amino acids on the intra-dimer interface.

Electromagnetic tweezers with independent force and torque control

Magnetic tweezers are powerful tools to manipulate and study the mechanical properties of biological molecules and living cells. In this paper we present a novel, bona fide electromagnetic tweezer (EMT) setup that allows independent control of the force and torque applied via micrometer-sized magnetic beads to a molecule under study. We implemented this EMT by combining a single solenoid that generates force (f-EMT) with a set of four solenoids arranged into a symmetric quadrupole to generate torque (τ-EMT). To demonstrate the capability of the tweezers, we attached optically asymmetric Janus beads to single, tethered DNA molecules. We show that tension in the piconewton force range can be applied to single DNA molecules and the molecule can simultaneously be twisted with torques in the piconewton-nanometer range. Furthermore, the EMT allows the two components to be independently controlled. At various force levels applied to the Janus bead, the trap torsional stiffness can be continuously changed simply by varying the current magnitude applied to the τ-EMT. The flexible and independent control of force and torque by the EMT makes it an ideal tool for a range of measurements where tensional and torsional properties need to be studied simultaneously on a molecular or cellular level.

Relating nucleotide-dependent conformational changes in free tubulin dimers to tubulin assembly

The complex dynamic behavior of microtubules (MTs) is believed to be primarily due to the αβ-tubulin dimer architecture and its intrinsic GTPase activity. Hence, a detailed knowledge of the conformational variations of isolated α-GTP-β-GTP- and α-GTP-β-GDP-tubulin dimers in solution and their implications to interdimer interactions and stability is directly relevant to understand the MT dynamics. An attempt has been made here by combining molecular dynamics (MD) simulations and protein-protein docking studies that unravels key structural features of tubulin dimer in different nucleotide states and correlates their association to tubulin assembly. Results from simulations suggest that tubulin dimers and oligomers attain curved conformations in both GTP and GDP states. Results also indicate that the tubulin C-terminal domain and the nucleotide state are closely linked. Protein-protein docking in combination with MD simulations suggest that the GTP-tubulin dimers engage in relatively stronger interdimer interactions even though the interdimer interfaces are bent in both GTP and GDP tubulin complexes, providing valuable insights on in vitro finding that GTP-tubulin is a better assembly candidate than GDP-tubulin during the MT nucleation and elongation processes.

Radiofrequency and microwave interactions between biomolecular systems

The knowledge of mechanisms underlying interactions between biological systems, be they biomacromolecules or living cells, is crucial for understanding physiology, as well as for possible prevention, diagnostics and therapy of pathological states. Apart from known chemical and direct contact electrical signaling pathways, electromagnetic phenomena were proposed by some authors to mediate non-chemical interactions on both intracellular and intercellular levels. Here, we discuss perspectives in the research of nanoscale electromagnetic interactions between biosystems on radiofrequency and microwave wavelengths. Based on our analysis, the main perspectives are in (i) the micro and nanoscale characterization of both passive and active radiofrequency properties of biomacromolecules and cells, (ii) experimental determination of viscous damping of biomacromolecule structural vibrations and (iii) detailed analysis of energetic circumstances of electromagnetic interactions between oscillating polar biomacromolecules. Current cutting-edge nanotechnology and computational techniques start to enable such studies so we can expect new interesting insights into electromagnetic aspects of molecular biophysics of cell signaling.

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.

Aldolases Utilize Different Oligomeric States To Preserve Their Functional Dynamics

Aldolases are essential enzymes in the glycolysis pathway and catalyze the reaction cleaving fructose/tagatose 1,6-bisphosphate into dihydroxyacetone phosphate and glyceraldehyde 3-phosphate. To determine how the aldolase motions relate to its catalytic process, we studied the dynamics of three different class II aldolase structures through simulations. We employed coarse-grained elastic network normal-mode analyses to investigate the dynamics of Escherichia coli fructose 1,6-bisphosphate aldolase, E. coli tagatose 1,6-bisphosphate aldolase, and Thermus aquaticus fructose 1,6-bisphosphate aldolase and compared their motions in different oligomeric states. The first one is a dimer, and the second and third are tetramers. Our analyses suggest that oligomerization not only stabilizes the aldolase structures, showing fewer fluctuations at the subunit interfaces, but also allows the enzyme to achieve the required dynamics for its functional loops. The essential mobility of these loops in the functional oligomeric states can facilitate the enzymatic mechanism, substrate recruitment in the open state, bringing the catalytic residues into their required configuration in the closed bound state, and moving back to the open state to release the catalytic products and repositioning the enzyme for its next catalytic cycle. These findings suggest that the aldolase global motions are conserved among aldolases having different oligomeric states to preserve its catalytic mechanism. The coarse-grained approaches taken permit an unprecedented view of the changes in the structural dynamics and how these relate to the critical structural stabilities essential for catalysis. The results are supported by experimental findings from many previous studies.

The molecular mechanism of conformational changes of the triplet prion fibrils for pH

The HET-s prion fibril, which is found in the filamentous fungus Podospora anserina, exhibits conformational changes due to variations in pH.

Tubulin bond energies and microtubule biomechanics determined from nanoindentation in silico

Microtubules, the primary components of the chromosome segregation machinery, are stabilized by longitudinal and lateral noncovalent bonds between the tubulin subunits. However, the thermodynamics of these bonds and the microtubule physicochemical properties are poorly understood. Here, we explore the biomechanics of microtubule polymers using multiscale computational modeling and nanoindentations in silico of a contiguous microtubule fragment. A close match between the simulated and experimental force–deformation spectra enabled us to correlate the microtubule biomechanics with dynamic structural transitions at the nanoscale. Our mechanical testing revealed that the compressed MT behaves as a system of rigid elements interconnected through a network of lateral and longitudinal elastic bonds. The initial regime of continuous elastic deformation of the microtubule is followed by the transition regime, during which the microtubule lattice undergoes discrete structural changes, which include first the reversible dissociation of lateral bonds followed by irreversible dissociation of the longitudinal bonds. We have determined the free energies of dissociation of the lateral (6.9 ± 0.4 kcal/mol) and longitudinal (14.9 ± 1.5 kcal/mol) tubulin–tubulin bonds. These values in conjunction with the large flexural rigidity of tubulin protofilaments obtained (18,000–26,000 pN·nm²) support the idea that the disassembling microtubule is capable of generating a large mechanical force to move chromosomes during cell division. Our computational modeling offers a comprehensive quantitative platform to link molecular tubulin characteristics with the physiological behavior of microtubules. The developed in silico nanoindentation method provides a powerful tool for the exploration of biomechanical properties of other cytoskeletal and multiprotein assemblies.

Investigation of the Josephin Domain protein-protein interaction by molecular dynamics

Spinocerebellar ataxia (SCA) 3, the most common form of SCA, is a neurodegenerative rare disease characterized by polyglutamine tract expansion and self-assembly of Ataxin3 (At3) misfolded proteins into highly organized fibrillar aggregates. The At3 N-terminal Josephin Domain (JD) has been suggested as being responsible for mediating the initial phase of the At3 double-step fibrillogenesis. Several issues concerning the residues involved in the JD's aggregation and, more generally, the JD clumping mechanism have not been clarified yet. In this paper we present an investigation focusing on the JD protein-protein interaction by means of molecular modeling. Our results suggest possible aminoacids involved in JD contact together with local and non-local effects following JD dimerization. Surprisingly, JD conformational changes following the binding may involve ubiquitin binding sites and hairpin region even though they do not pertain to the JD interaction surfaces. Moreover, the JD binding event has been found to alter the hairpin open-like conformation toward a closed-like arrangement over the simulated timescale. Finally, our results suggest that the JD aggregation might be a multi-step process, with an initial fast JD-JD binding mainly driven by Arg101, followed by slower structural global rearrangements involving the exposure to the solvent of Leu84-Trp87, which might play a role in a second step of JD aggregation.

Role of sequence and structural polymorphism on the mechanical properties of amyloid fibrils

Amyloid fibrils playing a critical role in disease expression, have recently been found to exhibit the excellent mechanical properties such as elastic modulus in the order of 10 GPa, which is comparable to that of other mechanical proteins such as microtubule, actin filament, and spider silk. These remarkable mechanical properties of amyloid fibrils are correlated with their functional role in disease expression. This suggests the importance in understanding how these excellent mechanical properties are originated through self-assembly process that may depend on the amino acid sequence. However, the sequence-structure-property relationship of amyloid fibrils has not been fully understood yet. In this work, we characterize the mechanical properties of human islet amyloid polypeptide (hIAPP) fibrils with respect to their molecular structures as well as their amino acid sequence by using all-atom explicit water molecular dynamics (MD) simulation. The simulation result suggests that the remarkable bending rigidity of amyloid fibrils can be achieved through a specific self-aggregation pattern such as antiparallel stacking of β strands (peptide chain). Moreover, we have shown that a single point mutation of hIAPP chain constituting a hIAPP fibril significantly affects the thermodynamic stability of hIAPP fibril formed by parallel stacking of peptide chain, and that a single point mutation results in a significant change in the bending rigidity of hIAPP fibrils formed by antiparallel stacking of β strands. This clearly elucidates the role of amino acid sequence on not only the equilibrium conformations of amyloid fibrils but also their mechanical properties. Our study sheds light on sequence-structure-property relationships of amyloid fibrils, which suggests that the mechanical properties of amyloid fibrils are encoded in their sequence-dependent molecular architecture.

Electro-acoustic behavior of the mitotic spindle: a semi-classical coarse-grained model

The regulation of chromosome separation during mitosis is not fully understood yet. Microtubules forming mitotic spindles are targets of treatment strategies which are aimed at (i) the triggering of the apoptosis or (ii) the interruption of uncontrolled cell division. Despite these facts, only few physical models relating to the dynamics of mitotic spindles exist up to now. In this paper, we present the first electromechanical model which enables calculation of the electromagnetic field coupled to acoustic vibrations of the mitotic spindle. This electromagnetic field originates from the electrical polarity of microtubules which form the mitotic spindle. The model is based on the approximation of resonantly vibrating microtubules by a network of oscillating electric dipoles. Our computational results predict the existence of a rapidly changing electric field which is generated by either driven or endogenous vibrations of the mitotic spindle. For certain values of parameters, the intensity of the electric field and its gradient reach values which may exert a not-inconsiderable force on chromosomes which are aligned in the spindle midzone. Our model may describe possible mechanisms of the effects of ultra-short electrical and mechanical pulses on dividing cells--a strategy used in novel methods for cancer treatment.

The interplay of structure and dynamics: insights from a survey of HIV-1 reverse transcriptase crystal structures

HIV-1 reverse transcriptase (RT) is a critical drug target for HIV treatment, and understanding the exact mechanisms of its function and inhibition would significantly accelerate the development of new anti-HIV drugs. It is well known that structure plays a critical role in protein function, but for RT, structural information has proven to be insufficient-despite enormous effort-to explain the mechanism of inhibition and drug resistance of non-nucleoside RT inhibitors. We hypothesize that the missing link is dynamics, information about the motions of the system. However, many of the techniques that give the best information about dynamics, such as solution nuclear magnetic resonance and molecular dynamics simulations, cannot be easily applied to a protein as large as RT. As an alternative, we combine elastic network modeling with simultaneous hierarchical clustering of structural and dynamic data. We present an extensive survey of the dynamics of RT bound to a variety of ligands and with a number of mutations, revealing a novel mechanism for drug resistance to non-nucleoside RT inhibitors. Hydrophobic core mutations restore active-state motion to multiple functionally significant regions of HIV-1 RT. This model arises out of a combination of structural and dynamic information, rather than exclusively from one or the other.