Biomechanics of actin filaments: a computational multi-level study

The actin microfilament (F-actin) is a structural and functional component of the cell cytoskeleton. Notwithstanding the primary role it plays for the mechanics of the cell, the mechanical behaviour of F-actin is still not totally explored. In particular, the relationship between the mechanics of F-actin and its molecular architecture is not completely understood. In this study, the mechanical properties of F-actin were related to the molecular topology of its building monomers (G-actin) by employing a computational multi-level approach. F-actins with lengths up to 500 nm were modelled and characterized, using a combination of equilibrium molecular dynamics (MD) simulations and normal mode analysis (NMA). MD simulations were performed to analyze the molecular rearrangements of G-actin in physiological conditions; NMA was applied to compute the macroscopic properties of F-actin from its vibrational modes of motion. Results from this multi-level approach showed that bending stiffness, bending modulus and persistence length are independent from the length of F-actin. On the contrary, the orientations and motions of selected groups of residues of G-actin play a primary role in determining the filament flexibility. In conclusion, this study (i) demonstrated that a combined computational approach of MD and NMA allows to investigate the biomechanics of F-actin taking into account the molecular topology of the filament (i.e., the molecular conformations of G-actin) and (ii) that this can be done using only crystallographic G-actin, without the need of introducing experimental parameters nor of reducing the number of residues.     

Regulation of microtubule dynamics by TOG-domain proteins XMAP215/Dis1 and CLASP

The molecular mechanisms by which microtubule-associated proteins (MAPs) regulate the dynamic properties of microtubules (MTs) are still poorly understood. We review recent advances in our understanding of two conserved families of MAPs, the XMAP215/Dis1 and CLASP family of proteins. In vivo and in vitro studies show that XMAP215 proteins act as microtubule polymerases at MT plus ends to accelerate MT assembly, and CLASP proteins promote MT rescue and suppress MT catastrophe events. These are structurally related proteins that use conserved TOG domains to recruit tubulin dimers to MTs. We discuss models for how these proteins might use these individual tubulin dimers to regulate dynamic behavior of MT plus ends.     

Modulating Microtubules: A Molecular Perspective on the Effects of Tail Modifications

Microtubules (MTs), an essential component of the eukaryotic cytoskeleton, are a lattice of polymerized tubulin dimers and are crucial for various cellular processes. The genetic and chemical diversity of tubulin and their disordered tails gives rise to a “tubulin code”. The functional role of tubulin post-translational modifications (PTMs), which contribute to the chemical diversity of the tubulin code, is gradually being unraveled. However, variation in the length and spatial organization of tubulin poly-modifications leads to an enormous combinatorial PTM space, which is difficult to study experimentally. Hence, the impact of the combinatorial tubulin PTM space on the biophysical properties of tubulin tails and their interactions with other proteins remains elusive.Here, we combine all-atom and coarse-grained molecular dynamics simulations to elucidate the biophysical implications of the large combinatorial tubulin PTM space in the context of an MT lattice. We find that tail–body interactions are more dominant in the tubulin dimer than in an MT lattice, and are more significant for the tails of α compared with β tubulin. In addition, polyglutamylation, but not polyglycylation, expands the dimensions of the tubulin tails. Polyglutamylation also leads to a decrease in the diffusion rate of MT-associated protein EB1 on MTs, while polyglycylation often increases diffusion rate. These observations are generally not sensitive to the organization of the polymodifications. The effect of PTMs on MT charge density and tail dynamics are also discussed. Overall, this study presents a molecular quantification of the biophysical properties of tubulin tails and their polymodifications, and provides predictions on the functional importance of tubulin PTMs.     

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. © 2012 Wiley Periodicals, Inc. Biopolymers 99: 282–291, 2013.     

Tubulin Dimers Oligomerize before Their Incorporation into Microtubules

In the presence of GTP, purified dimers of α- and β-tubulin will interact longitudinally and laterally to self-assemble into microtubules (MTs). This property provides a powerful in vitro experimental system to describe MT dynamic behavior at the micrometer scale and to study effects and functioning of a large variety of microtubule associated proteins (MAPs). Despite the plethora of such data produced, the molecular mechanisms of MT assembly remain disputed. Electron microscopy (EM) studies suggested that tubulin dimers interact longitudinally to form short oligomers which form a tube by lateral interaction and which contribute to MT elongation. This idea is however challenged: Based on estimated association constants it was proposed that single dimers represent the major fraction of free tubulin. This view was recently supported by measurements suggesting that MTs elongate by addition of single tubulin dimers. To solve this discrepancy, we performed a direct measurement of the longitudinal interaction energy for tubulin dimers. We quantified the size distribution of tubulin oligomers using EM and fluorescence correlation spectroscopy (FCS). From the distribution we derived the longitudinal interaction energy in the presence of GDP and the non-hydrolysable GTP analog GMPCPP. Our data suggest that MT elongation and nucleation involves interactions of short tubulin oligomers rather than dimers. Our approach provides a solid experimental framework to better understand the role of MAPs in MT nucleation and growth.     

Molecular modeling study on the differential microtubule-stabilizing effect in singly- and doubly-bonded complexes with peloruside A and paclitaxel

Microtubules (MT) are dynamic cytoskeletal components that play a crucial role in cell division. Disrupting MT dynamics by MT stabilizers is a widely employed strategy to control cell proliferation in cancer therapy. Most MT stabilizers bind to the taxol (TX) site located at the luminal interface between protofilaments, except laulimalide and peloruside A (PLA), which bind to an interfacial pocket on outer MT surface. Cryo-electron microscopy MTs reconstructions have shown differential structural effects on the MT lattice in singly- and doubly-bonded complexes with PLA, TX, and PLA/TX, as PLA is able to revert the lattice heterogeneity induced by TX association leading to more regular MT assemblies. In this work, fully-atomistic molecular dynamics simulations were employed to examine the single and double association of MT stabilizers to reduced MT models in the search for structural and energetic evidence that could be related to the differential regularization and stabilization effects exerted by PLA and TX on the MT lattice. Our results revealed that the double association of PLA/TX (a) strengthens the lateral contact between tubulin dimers compared to singly-bonded complexes, (b) favors a more parallel arrangement between tubulin dimers, and (c) induces a larger restriction in the interdimeric conformational motion increasing the probability of finding structures consistent with 13-protofilaments arrangements. These results and are valuable to increase understanding about the molecular mechanism of action of MT stabilizers, and could account for an overstabilization of MTs in doubly-bonded complexes compared to singly-bonded systems.     

CLAMP, a novel microtubule-associated protein with EB-type calponin homology

Microtubules (MTs) are polymers of alpha and beta tubulin dimers that mediate many cellular functions, including the establishment and maintenance of cell shape. The dynamic properties of MTs may be influenced by tubulin isotype, posttranslational modifications of tubulin, and interaction with microtubule-associated proteins (MAPs). End-binding (EB) family proteins affect MT dynamics by stabilizing MTs, and are the only MAPs reported that bind MTs via a calponin-homology (CH) domain (J Biol Chem 278 (2003) 49721-49731; J Cell Biol 149 (2000) 761-766). Here, we describe a novel 27 kDa protein identified from an inner ear organ of Corti library. Structural homology modeling demonstrates a CH domain in this protein similar to EB proteins. Northern and Western blottings confirmed expression of this gene in other tissues, including brain, lung, and testis. In the organ of Corti, this protein localized throughout distinctively large and well-ordered MT bundles that support the elongated body of mechanically stiff pillar cells of the auditory sensory epithelium. When ectopically expressed in Cos-7 cells, this protein localized along cytoplasmic MTs, promoted MT bundling, and efficiently stabilized MTs against depolymerization in response to high concentration of nocodazole and cold temperature. We propose that this protein, designated CLAMP, is a novel MAP and represents a new member of the CH domain protein family.     

A novel acetylation of β-tubulin by San modulates microtubule polymerization via down-regulating tubulin incorporation

Dynamic instability is a critical property of microtubules (MTs). By regulating the rate of tubulin polymerization and depolymerization, cells organize the MT cytoskeleton to accommodate their specific functions. Among many processes, posttranslational modifications of tubulin are implicated in regulating MT functions. Here we report a novel tubulin acetylation catalyzed by acetyltransferase San at lysine 252 (K252) of β-tubulin. This acetylation, which is also detected in vivo, is added to soluble tubulin heterodimers but not tubulins in MTs. The acetylation-mimicking K252A/Q mutants were incorporated into the MT cytoskeleton in HeLa cells without causing any obvious MT defect. However, after cold-induced catastrophe, MT regrowth is accelerated in San-siRNA cells while the incorporation of acetylation-mimicking mutant tubulins is severely impeded. K252 of β-tubulin localizes at the interface of α-/β-tubulins and interacts with the phosphate group of the α-tubulin-bound GTP. We propose that the acetylation slows down tubulin incorporation into MTs by neutralizing the positive charge on K252 and allowing tubulin heterodimers to adopt a conformation that disfavors tubulin incorporation.     

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.     

A Highlights from MBoC Selection: MAP65/Ase1 promote microtubule flexibility

Microtubules (MTs) are dynamic cytoskeletal elements involved in numerous cellular processes. Although they are highly rigid polymers with a persistence length of 1–8 mm, they may exhibit a curved shape at a scale of few micrometers within cells, depending on their biological functions. However, how MT flexural rigidity in cells is regulated remains poorly understood. Here we ask whether MT-associated proteins (MAPs) could locally control the mechanical properties of MTs. We show that two major cross-linkers of the conserved MAP65/PRC1/Ase1 family drastically decrease MT rigidity. Their MT-binding domain mediates this effect. Remarkably, the softening effect of MAP65 observed on single MTs is maintained when MTs are cross-linked. By reconstituting physical collisions between growing MTs/MT bundles, we further show that the decrease in MT stiffness induced by MAP65 proteins is responsible for the sharp bending deformations observed in cells when they coalign at a steep angle to create bundles. Taken together, these data provide new insights into how MAP65, by modifying MT mechanical properties, may regulate the formation of complex MT arrays.     

Anterograde Microtubule Transport Drives Microtubule Bending in LLC-PK1 Epithelial Cells

Microtubules (MTs) have been proposed to act mechanically as compressive struts that resist both actomyosin contractile forces and their own polymerization forces to mechanically stabilize cell shape. To identify the origin of MT bending, we directly observed MT bending and F-actin transport dynamics in the periphery of LLC-PK1 epithelial cells. We found that F-actin is nearly stationary in these cells even as MTs are deformed, demonstrating that MT bending is not driven by actomyosin contractility. Furthermore, the inhibition of myosin II activity through the use of blebbistatin results in microtubules that are still dynamically bending. In addition, as determined by fluorescent speckle microscopy, MT polymerization rarely results, if ever, in bending. We suppressed dynamic instability using nocodazole, and we observed no qualitative change in the MT bending dynamics. Bending most often results from anterograde transport of proximal portions of the MT toward a nearly stationary distal tip. Interestingly, we found that in an in vitro kinesin-MT gliding assay, MTs buckle in a similar manner. To make quantitative comparisons, we measured curvature distributions of observed MTs and found that the in vivo and in vitro curvature distributions agree quantitatively. In addition, the measured MT curvature distribution is not Gaussian, as expected for a thermally driven semiflexible polymer, indicating that thermal forces play a minor role in MT bending. We conclude that many of the known mechanisms of MT deformation, such as polymerization and acto-myosin contractility, play an inconsequential role in mediating MT bending in LLC-PK1 cells and that MT-based molecular motors likely generate most of the strain energy stored in the MT lattice. The results argue against models in which MTs play a major mechanical role in LLC-PK1 cells and instead favor a model in which mechanical forces control the spatial distribution of the MT array.     

Arp2/3 phosphorylation kickstarts cells

The kinesin-13 motor protein family members drive the removal of tubulin from microtubules (MTs) to promote MT turnover. A point mutation of the kinesin-13 family member mitotic centromere-associated kinesin/Kif2C (E491A) isolates the tubulin-removal conformation of the motor, and appears distinct from all previously described kinesin-13 conformations derived from nucleotide analogues. The E491A mutant removes tubulin dimers from stabilized MTs stoichiometrically in adenosine triphosphate (ATP) but is unable to efficiently release from detached tubulin dimers to recycle catalytically. Only in adenosine diphosphate (ADP) can the mutant catalytically remove tubulin dimers from stabilized MTs because the affinity of the mutant for detached tubulin dimers in ADP is low relative to lattice-bound tubulin. Thus, the motor can regenerate for further cycles of disassembly. Using the mutant, we show that release of tubulin by kinesin-13 motors occurs at the transition state for ATP hydrolysis, which illustrates a significant divergence in their coupling to ATP turnover relative to motile kinesins.     

Microtubular Protofilament Analysis Based on Molecular Level Tubulin Interaction

Nonlinear microstructure of the microtubules (MTs) plays an important role in their mechanical properties. Despite the extensive efforts into the development of continuum models for microtubules, a mesoscale finite element model that can link the molecular level information to the overall performance of microtubules is still missing. The aim of this study is to develop a molecular dynamics model (MDM), finite element model (FEM) and structural mechanics beam model (SMBM) for tubulins of protofilament (PF). In MDM, the backbone atoms of α-tubulin were fixed while the backbone atoms of β-tubulin were attached to a molecular dynamics (MD) atom through a virtual spring. In FEM, both α and β tubulins are modeled as spherical shells and adjacent tubulins are connected by linear springs. The spherical shells were framed as beams in SMBM. Corresponding parameters such as the elasticity of tubulin-tubulin interaction (TTI) and the stiffness of springs and beam are derived from MD simulation. Marginal differences in the force-deflection curve among the FEM, the MDM and SMBM indicate the good accuracy in describing the mechanical properties of microtubules. Simulation results show that the protofilament behaves non-linearly under tension and torsion but linearly under bending. Deformation pattern of a PF from the SMBM frame bending can be well captured by the classical Euler-Bernouli beam theory and the flexural rigidity derived from FEM is in good agreement with SMBM. These findings lend compelling credence in our developed models of PF to deepen our understanding of the underlying mechanism of statics and dynamics of MTs. In perspective our approach provides a tool for the analysis of MTs mechanical behavior under different conditions.     

Root contraction in hyacinth. II. Changes in tubulin levels,microtubule number and orientation associated with differential cell expansion

Root contraction in hyacinth (Hyacinthus orientalis L.) is marked by reoriented cell growth in the cortex of the contractile region. Cellular volume of the inner cortex enlarges fourfold during root contraction. This is associated with large increases in the radial and tangential dimensions and decreases in the longitudinal dimension of the cells. In order to determine the possible role of microtubules (MTs) in these changes we compared tubulin levels and MT numbers and orientation in contracted and non-contracted regions of hyacinth roots. Tubulin content was analysed by a radioimmunoassay; MT numbers and orientation were analyzed by counting profiles in sectioned material using transmission electron microscopy. Contracted tissue was found to have significantly higher levels of tubulin on a per-cell basis than non-contracted tissue, and also increased tubulin levels relative to total protein. The spatial MT frequencies were the same in contracted and non-contracted tissues, indicating a proportional increase in MT numbers in the expanded cells. Although the absolute spatial frequency of MTs was constant, the orientation, as determined by morphometric analysis of MT profiles, was not. While in the longitudinal section plane 42% of the MTs in the non-contracted cells were oblique, in the contracted cells the percentage of MTs presenting oblique profiles increased to 87%. Additionally, a qualitative difference in MTs was observed in contracted cells; electron-opaque material was seen peripherally associated with the MTs of the inner cortex. The changes in tubulin levels and in MT numbers as well as the qualitative differences in the MTs of contracted and non-contracted root regions indicate that, in hyacinth, reoriented cellular enlargement associated with root contraction cannot be explained simply by shifts in the arrangement of preexisting cortical MT arrays, but involves more complex changes in the cytoskeleton.Abbreviations MT(s) microtubule(s) - TEM transmission electron microscopy - RIA radioimmunoassay - M_r apparent molecular mass I=Jernstedt (1984b)     

Mechanical Properties of a Complete Microtubule Revealed through Molecular Dynamics Simulation

Microtubules (MTs) are the largest type of cellular filament, essential in processes ranging from mitosis and meiosis to flagellar motility. Many of the processes depend critically on the mechanical properties of the MT, but the elastic moduli, notably the Young's modulus, are not directly revealed in experiment, which instead measures either flexural rigidity or response to radial deformation. Molecular dynamics (MD) is a method that allows the mechanical properties of single biomolecules to be investigated through computation. Typically, MD requires an atomic resolution structure of the molecule, which is unavailable for many systems, including MTs. By combining structural information from cryo-electron microscopy and electron crystallography, we have constructed an all-atom model of a complete MT and used MD to determine its mechanical properties. The simulations revealed nonlinear axial stress-strain behavior featuring a pronounced softening under extension, a possible plastic deformation transition under radial compression, and a distinct asymmetry in response to the two senses of twist. This work demonstrates the possibility of combining different levels of structural information to produce all-atom models suitable for quantitative MD simulations, which extends the range of systems amenable to the MD method and should enable exciting advances in our microscopic knowledge of biology.     

Template-free 13-protofilament microtubule-MAP assembly visualized at 8 A resolution

Microtubule-associated proteins (MAPs) are essential for regulating and organizing cellular microtubules (MTs). However, our mechanistic understanding of MAP function is limited by a lack of detailed structural information. Using cryo-electron microscopy and single particle algorithms, we solved the 8 Å structure of doublecortin (DCX)-stabilized MTs. Because of DCX’s unusual ability to specifically nucleate and stabilize 13-protofilament MTs, our reconstruction provides unprecedented insight into the structure of MTs with an in vivo architecture, and in the absence of a stabilizing drug. DCX specifically recognizes the corner of four tubulin dimers, a binding mode ideally suited to stabilizing both lateral and longitudinal lattice contacts. A striking consequence of this is that DCX does not bind the MT seam. DCX binding on the MT surface indirectly stabilizes conserved tubulin–tubulin lateral contacts in the MT lumen, operating independently of the nucleotide bound to tubulin. DCX’s exquisite binding selectivity uncovers important insights into regulation of cellular MTs.     

Mechanical Regulation of Neurite Polarization and Growth: A Computational Study

The densely packed microtubule (MT) array found in neuronal cell projections (neurites) serves two fundamental functions simultaneously: it provides a mechanically stable track for molecular motor-based transport and produces forces that drive neurite growth. The local pattern of MT polarity along the neurite shaft has been found to differ between axons and dendrites. In axons, the neurons’ dominating long projections, roughly 90% of the MTs orient with their rapidly growing plus end away from the cell body, whereas in vertebrate dendrites, their orientations are locally mixed. Molecular motors are known to be responsible for cytoskeletal ordering and force generation, but their collective function in the dense MT cytoskeleton of neurites remains elusive. We here hypothesized that both the polarity pattern of MTs along the neurite shaft and the shaft’s global extension are simultaneously driven by molecular motor forces and should thus be regulated by the mechanical load acting on the MT array as a whole. To investigate this, we simulated cylindrical bundles of MTs that are cross-linked and powered by molecular motors by iteratively solving a set of force-balance equations. The bundles were subjected to a fixed load arising from actively generated tension in the actomyosin cortex enveloping the MTs. The magnitude of the load and the level of motor-induced connectivity between the MTs have been varied systematically. With an increasing load and decreasing motor-induced connectivity between MTs, the bundles became wider in cross section and extended more slowly, and the local MT orientational order was reduced. These results reveal two, to our knowledge, novel mechanical factors that may underlie the distinctive development of the MT cytoskeleton in axons and dendrites: the cross-linking level of MTs by motors and the load acting on this cytoskeleton during growth.     

Rapid assembly and collective behavior of microtubule bundles in the presence of polyamines

Microtubules (MTs) are cylindrical cytoskeleton polymers composed of α-β tubulin heterodimers whose dynamic properties are essential to fulfill their numerous cellular functions. In response to spatial confinement, dynamic MTs, even in the absence of protein partners, were shown to self-organize into higher order structures (spindle or striped structures) which lead to interesting dynamical properties (MT oscillations). In this study, we considered the assembly and sensitivity of dynamic MTs when in bundles. To perform this study, spermine, a natural tetravalent polyamine present at high concentrations in all eukaryote cells, was used to trigger MT bundling while preserving MT dynamics. Interestingly, we first show that, near physiological ionic strengths, spermine promotes the bundling of MTs whereas it does not lead to aggregation of free tubulin, which would have been detrimental to MT polymerization. Experimental and theoretical results also indicate that, to obtain a high rate of bundle assembly, bundling should take place at the beginning of assembly when rapid rotational movements of short and newly nucleated MTs are still possible. On the other hand, the bundling process is significantly slowed down for long MTs. Finally, we found that short MT bundles exhibit a higher sensitivity to cold exposure than do isolated MTs. To account for this phenomenon, we suggest that a collective behavior takes place within MT bundles because an MT entering into a phase of shortening could increase the probability of the other MTs in the same bundle to enter into shortening phase due to their close proximity. We then elaborate on some putative applications of our findings to in vivo conditions including neurons.     

Microinjection of fluorescent tubulin into plant cells provides a representative picture of the cortical microtubule array

By microinjecting rhodamine-labelled tubulin into living plant cells, it is possible to observe microtubules (MTs) directly and to see how the cortical array reorganizes itself. The validity of the conclusions drawn from such observations depends upon the assumption that most, if not all, of the native MTs are dynamic and incorporate labelled tubulin. However, if arrays also contain MTs that are not exchanging tubulin subunits, such MTs will remain unlabelled, and the labelled MT population will be under-representative of the whole array. To address this potential problem, we microinjected pea epidermal cells with rhodamine-labelled tubulin, then fixed the cells and used fluorescein-conjugated antibodies against tubulin to detect the entire MT array. The two fluorescent patterns corresponded well, confirming that the MTs labelled with exogenous tubulin were evenly distributed throughout the entire array. Also, by comparing the MT image before and after aldehyde fixation, we observed that, although some of the MTs were lost in the procedure, the fixation was able to preserve the arrangement of MTs seen in the living cell. We conclude that fluorescence analogue cytochemistry provides a valid representation of the entire cortical MT array.