Microtubule oscillations

Insights into Chemically Fueled Supramolecular Polymers

Supramolecular polymerization can be controlled in space and time by chemical fuels. A nonassembled monomer is activated by the fuel and subsequently self-assembles into a polymer. Deactivation of the molecule either in solution or inside the polymer leads to disassembly. Whereas biology has already mastered this approach, fully artificial examples have only appeared in the past decade. Here, we map the available literature examples into four distinct regimes depending on their activation/deactivation rates and the equivalents of deactivating fuel. We present increasingly complex mathematical models, first considering only the chemical activation/deactivation rates (i.e., transient activation) and later including the full details of the isodesmic or cooperative supramolecular processes (i.e., transient self-assembly). We finish by showing that sustained oscillations are possible in chemically fueled cooperative supramolecular polymerization and provide mechanistic insights. We hope our models encourage the quantification of activation, deactivation, assembly, and disassembly kinetics in future studies.

Oscillations, travelling fronts and patterns in a supramolecular system

Supramolecular polymers, such as microtubules, operate under non-equilibrium conditions to drive crucial functions in cells, such as motility, division and organelle transport¹. In vivo and in vitro size oscillations of individual microtubules^2,3 (dynamic instabilities) and collective oscillations⁴ have been observed. In addition, dynamic spatial structures, like waves and polygons, can form in non-stirred systems⁵. Here we describe an artificial supramolecular polymer made of a perylene diimide derivative that displays oscillations, travelling fronts and centimetre-scale self-organized patterns when pushed far from equilibrium by chemical fuels. Oscillations arise from a positive feedback due to nucleation-elongation-fragmentation, and a negative feedback due to size-dependent depolymerization. Travelling fronts and patterns form due to self-assembly induced density differences that cause system-wide convection. In our system, the species responsible for the nonlinear dynamics and those that self-assemble are one and the same. In contrast, other reported oscillating assemblies formed by vesicles⁶, micelles⁷ or particles⁸ rely on the combination of a known chemical oscillator and a stimuli-responsive system, either by communication through the solvent (for example, by changing pH^7-9), or by anchoring one of the species covalently (for example, a Belousov-Zhabotinsky catalyst^6,10). The design of self-oscillating supramolecular polymers and large-scale dissipative structures brings us closer to the creation of more life-like materials¹¹ that respond to external stimuli similarly to living cells, or to creating artificial autonomous chemical robots¹².

The Roles of β-Tubulin Mutations and Isotype Expression in Acquired Drug Resistance

The antitumor drug paclitaxel stabilizes microtubules and reduces their dynamicity, promoting mitotic arrest and eventually apoptosis. Upon assembly of the α/β-tubulin heterodimer, GTP becomes bound to both the α and β-tubulin monomers. During microtubule assembly, the GTP bound to β-tubulin is hydrolyzed to GDP, eventually reaching steady-state equilibrium between free tubulin dimers and those polymerized into microtubules. Tubulin-binding drugs such as paclitaxel interact with β-tubulin, resulting in the disruption of this equilibrium. In spite of several crystal structures of tubulin, there is little biochemical insight into the mechanism by which anti-tubulin drugs target microtubules and alter their normal behavior. The mechanism of drug action is further complicated, as the description of altered β-tubulin isotype expression and/or mutations in tubulin genes may lead to drug resistance as has been described in the literature. Because of the relationship between β-tubulin isotype expression and mutations within β-tubulin, both leading to resistance, we examined the properties of altered residues within the taxane, colchicine and Vinca binding sites. The amount of data now available, allows us to investigate common patterns that lead to microtubule disruption and may provide a guide to the rational design of novel compounds that can inhibit microtubule dynamics for specific tubulin isotypes or, indeed resistant cell lines. Because of the vast amount of data published to date, we will only provide a broad overview of the mutational results and how these correlate with differences between tubulin isotypes. We also note that clinical studies describe a number of predictive factors for the response to anti-tubulin drugs and attempt to develop an understanding of the features within tubulin that may help explain how they may affect both microtubule assembly and stability.

Effects of aging in catastrophe on the steady state and dynamics of a microtubule population

Several independent observations have suggested that the catastrophe transition in microtubules is not a first-order process, as is usually assumed. Recent in vitro observations by Gardner et al. [M. K. Gardner et al., Cell 147, 1092 (2011)] showed that microtubule catastrophe takes place via multiple steps and the frequency increases with the age of the filament. Here we investigate, via numerical simulations and mathematical calculations, some of the consequences of the age dependence of catastrophe on the dynamics of microtubules as a function of the aging rate, for two different models of aging: exponential growth, but saturating asymptotically, and purely linear growth. The boundary demarcating the steady-state and non-steady-state regimes in the dynamics is derived analytically in both cases. Numerical simulations, supported by analytical calculations in the linear model, show that aging leads to nonexponential length distributions in steady state. More importantly, oscillations ensue in microtubule length and velocity. The regularity of oscillations, as characterized by the negative dip in the autocorrelation function, is reduced by increasing the frequency of rescue events. Our study shows that the age dependence of catastrophe could function as an intrinsic mechanism to generate oscillatory dynamics in a microtubule population, distinct from hitherto identified ones.

Organization of early frog embryos by chemical waves emanating from centrosomes

The large cells in early vertebrate development face an extreme physical challenge in organizing their cytoplasm. For example, amphibian embryos have to divide cytoplasm that spans hundreds of micrometres every 30 min according to a precise geometry, a remarkable accomplishment given the extreme difference between molecular and cellular scales in this system. How do the biochemical reactions occurring at the molecular scale lead to this emergent behaviour of the cell as a whole? Based on recent findings, we propose that the centrosome plays a crucial role by initiating two autocatalytic reactions that travel across the large cytoplasm as chemical waves. Waves of mitotic entry and exit propagate out from centrosomes using the Cdk1 oscillator to coordinate the timing of cell division. Waves of microtubule-stimulated microtubule nucleation propagate out to assemble large asters that position spindles for the following mitosis and establish cleavage plane geometry. By initiating these chemical waves, the centrosome rapidly organizes the large cytoplasm during the short embryonic cell cycle, which would be impossible using more conventional mechanisms such as diffusion or nucleation by structural templating. Large embryo cells provide valuable insights to how cells control chemical waves, which may be a general principle for cytoplasmic organization.

Function of metabolic and organelle networks in crowded and organized media

(Macro)molecular crowding and the ability of the ubiquitous cytoskeleton to dynamically polymerize–depolymerize are prevalent cytoplasmic conditions in prokaryotic and eukaryotic cells. Protein interactions, enzymatic or signaling reactions - single, sequential or in complexes - whole metabolic pathways and organelles can be affected by crowding, the type and polymeric status of cytoskeletal proteins (e.g., tubulin, actin), and their imparted organization. The self-organizing capability of the cytoskeleton can orchestrate metabolic fluxes through entire pathways while its fractal organization can frame the scaling of activities in several levels of organization. The intracellular environment dynamics (e.g., biochemical reactions) is dominated by the orderly cytoskeleton and the intrinsic randomness of molecular crowding. Existing evidence underscores the inherent capacity of intracellular organization to generate emergent global behavior. Yet unknown is the relative impact on cell function provided by organelle or functional compartmentation based on transient proteins association driven by weak interactions (quinary structures) under specific environmental challenges or functional conditions (e.g., hypoxia, division, differentiation). We propose a qualitative, integrated structural–functional model of cytoplasmic organization based on a modified version of the Sierspinsky–Menger–Mandelbrot sponge, a 3D representation of a percolation cluster, and examine its capacity to accommodate established experimental facts.

Heuristic consequences of a load of oxygen in microtubules

The current cell oxygen paradigm shows some major gaps that have not yet been resolved. Something seems to be lacking for the comprehensive statement of the oxygen distribution in the cell, especially the low cytoplasmic oxygen level. The entrapment of oxygen in microtubules (MTs) resolves the latter observation, as well as the occurrence of an extensive cytoplasmic foam formation. It leads to a novel oxygen paradigm for cells. During the steady-state treadmilling, the mobile cavity would absorb oxygenated cytoplasm forward, entrap gas nuclei and concentrate them. A fluorescence method is described to confirm the in vitro load of oxygen in MTs during their periodic growths and shrinkages. The latter operating mechanism is called the gas dynamic instability (GDI) of MTs. Several known biosystems could rest on the GDI. (1) The GTP-cap is linked with the gas meniscus encountered in a tube filled with gas. The GTP hydrolysis is linked to the conformational change of the GTPase domain according to the bubble pressure, and to the shaking of protofilaments with gas particles (soliton-like waves). (2) The GDI provides a free energy water pump because water molecules have to escape from MT pores when foam concentrates within the MT. Beside ATP hydrolysis in motor proteins, the GDI provides an additional driving force in intracellular transport of cargo. The water streams flowing from the MT through slits organize themselves as water layers between the cargo and the MT surface, and break ionic bridges. It makes the cargo glide over a water rail. (3) The GDI provides a universal motor for chromosome segregation because the depolymerization of kinetochorial MTs is expected to generate a strong cytoplasmic foam. Chromosomes are sucked up according to the pressure difference (or density difference) applied to opposite sides of the kinetochore, which is in agreement with Archimedes' principle of buoyancy. Non-kinetochorial MTs reabsorb foam during GDI. Last, the mitotic spindle is imagined as a gas recycler. (4) The luminal particles within MTs (called MIPs) are imagined as a foam organizer, the luminal proteins being part of the borders and edges of identical bubbles. (5) Last, volatile anesthetics could destabilize MTs through anesthetic-induced bubble nucleation between protofilaments, and therefore causing shear stress and the opening of MT. The load of oxygen in MTs might provide a major advance in this area of research.

Models of the collective behavior of proteins in cells: tubulin, actin and motor proteins

One of the most important issues of molecular biophysics is the complex and multifunctional behavior of the cell's cytoskeleton. Interiors of living cells are structurally organized by the cytoskeleton networks of filamentous protein polymers: microtubules, actin and intermediate filaments with motor proteins providing force and directionality needed for transport processes. Microtubules (MT's) take active part in material transport within the cell, constitute the most rigid elements of the cell and hence found many uses in cell motility (e.g. flagella andcilia). At present there is, however, no quantitatively predictable explanation of how these important phenomena are orchestrated at a molecular level. Moreover, microtubules have been demonstrated to self-organize leading to pattern formation. We discuss here several models which attempt to shed light on the assembly of microtubules and their interactions with motor proteins. Subsequently, an overview of actin filaments and their properties isgiven with particular emphasis on actin assembly processes. The lengths of actin filaments have been reported that were formed by spontaneous polymerization of highly purified actin monomers after labeling with rhodamine-phalloidin. The length distributions are exponential with a mean of about 7 μm. This length is independent of the initial concentration of actin monomer, an observation inconsistent with a simple nucleation-elongation mechanism. However, with the addition of physically reasonable rates of filament annealing and fragmenting, a nucleation-elongation mechanism can reproduce the observed average length of filaments in two types of experiments: (1) filaments formed from a wide range of highly purified actin monomer concentrations, and (2) filaments formed from 24 mM actin over a range of CapZ concentrations. In the final part of the paper we briefly review the stochastic models used to describe the motion of motor proteins on protein filaments. The vast majority of these models are based on ratchet potentials with the presence of thermal noise and forcing due to ATP binding and a subsequent hydrolysis. Many outstanding questions remain to be quantitatively addressed on a molecular level in order to explain the structure-to-function relationship for the key elements of the cytoskeleton discussed in this review.

Microtubule-like properties of the bacterial actin homolog ParM-R1

In preparation for mammalian cell division, microtubules repeatedly probe the cytoplasm to capture chromosomes and assemble the mitotic spindle. Critical features of this microtubule system are the formation of radial arrays centered at the centrosomes and dynamic instability, leading to persistent cycles of polymerization and depolymerization. Here, we show that actin homolog, ParM-R1 that drives segregation of the R1 multidrug resistance plasmid from Escherichia coli, can also self-organize in vitro into asters, which resemble astral microtubules. ParM-R1 asters grow from centrosome-like structures consisting of interconnected nodes related by a pseudo 8-fold symmetry. In addition, we show that ParM-R1 is able to perform persistent microtubule-like oscillations of assembly and disassembly. In vitro, a whole population of ParM-R1 filaments is synchronized between phases of growth and shrinkage, leading to prolonged synchronous oscillations even at physiological ParM-R1 concentrations. These results imply that the selection pressure to reliably segregate DNA during cell division has led to common mechanisms within diverse segregation machineries.

Novel actin-like filament structure from Clostridium tetani

Eukaryotic F-actin is constructed from two protofilaments that gently wind around each other to form a helical polymer. Several bacterial actin-like proteins (Alps) are also known to form F-actin-like helical arrangements from two protofilaments, yet with varied helical geometries. Here, we report a unique filament architecture of Alp12 from Clostridium tetani that is constructed from four protofilaments. Through fitting of an Alp12 monomer homology model into the electron microscopy data, the filament was determined to be constructed from two antiparallel strands, each composed of two parallel protofilaments. These four protofilaments form an open helical cylinder separated by a wide cleft. The molecular interactions within single protofilaments are similar to F-actin, yet interactions between protofilaments differ from those in F-actin. The filament structure and assembly and disassembly kinetics suggest Alp12 to be a dynamically unstable force-generating motor involved in segregating the pE88 plasmid, which encodes the lethal tetanus toxin, and thus a potential target for drug design. Alp12 can be repeatedly cycled between states of polymerization and dissociation, making it a novel candidate for incorporation into fuel-propelled nanobiopolymer machines.

Microtubule assembly of isotypically purified tubulin and its mixtures

Numerous isotypes of the structural protein tubulin have now been characterized in various organisms and their expression offers a plausible explanation for observed differences affecting microtubule function in vivo. While this is an attractive hypothesis, there are only a handful of studies demonstrating a direct influence of tubulin isotype composition on the dynamic properties of microtubules. Here, we present the results of experimental assays on the assembly of microtubules from bovine brain tubulin using purified isotypes at various controlled relative concentrations. A novel data analysis is developed using recursive maps which are shown to be related to the master equation formalism. We have found striking similarities between the three isotypes of bovine tubulin studied in regard to their dynamic instability properties, except for subtle differences in their catastrophe frequencies. When mixtures of tubulin isotypes are analyzed, their nonlinear concentration dependence is modeled and interpreted in terms of lower affinities of tubulin dimers belonging to the same isotype than those that represent different isotypes indicating hitherto unsuspected influences of tubulin dimers on each other within a microtubule. Finally, we investigate the fluctuations in microtubule assembly and disassembly rates and conclude that the inherent rate variability may signify differences in the guanosine-5'-triphosphate composition of the growing and shortening microtubule tips. It is the main objective of this article to develop a quantitative model of tubulin polymerization for individual isotypes and their mixtures. The possible biological significance of the observed differences is addressed.

PACSIN proteins bind tubulin and promote microtubule assembly

PACSINs are intracellular adapter proteins involved in vesicle transport, membrane dynamics and actin reorganisation. In this study, we report a novel role for PACSIN proteins as components of the centrosome involved in microtubule dynamics. Glutathione S-transferase (GST)-tagged PACSIN proteins interacted with protein complexes containing alpha- and gamma-tubulin in brain homogenate. Analysis of cell lysates showed that all three endogenous PACSINs co-immunoprecipitated dynamin, alpha-tubulin and gamma-tubulin. Furthermore, PACSINs bound only to unpolymerised tubulin, not to microtubules purified from brain. In agreement, the cellular localisation of endogenous PACSIN 2 was not affected by the microtubule depolymerising reagent nocodazole. By light microscopy, endogenous PACSIN 2 localised next to gamma-tubulin at purified centrosomes from NIH 3T3 cells. Finally, reduction of PACSIN 2 protein levels with small-interfering RNA (siRNA) resulted in impaired microtubule nucleation from centrosomes, whereas microtubule centrosome splitting was not affected, suggesting a role for PACSIN 2 in the regulation of tubulin polymerisation. These findings suggest a novel function for PACSIN proteins in dynamic microtubuli nucleation.

Collision induced spatial organization of microtubules

The dynamic behavior of microtubules in solution can be strongly modified by interactions with walls or other structures. We examine here a microtubule growth model where the increase in size of the plus-end is perturbed by collisions with other microtubules. We show that such a simple mechanism of constrained growth can induce ordered structures and patterns from an initially isotropic and homogeneous suspension. We find that microtubules self-organize locally in randomly oriented domains that grow and compete with each other. A weak orientation bias, similar to the one induced by gravity or cellular boundaries is enough to influence the domain growth direction, eventually leading to a macroscopic sample orientation.

Homology modeling of tubulin: influence predictions for microtubule's biophysical properties

Using comparative modeling, we have generated structural models of 475 alpha and beta tubulins. Using these models, we observed a global, structural similarity between the tubulin isotypes. However, a number of subtle differences in the isotypes physical properties, including net electric charges, solvent accessible surface areas, and electric dipole moments were also apparent. In order to examine the roles that these properties may play in microtubule (MT) assembly and stability, we have created a model to evaluate the dipole-dipole interaction energies of varying MT lattice conformations, using human tubulin isotypes as particularly important examples. We conclude that the dipole moments of each tubulin isotype may influence their functional characteristics within the cell, resulting in differences for MT assembly kinetics and stability.

Comparative modelling of human β tubulin isotypes and implications for drug binding

The protein tubulin is a target for several anti-mitotic drugs, which affect microtubule dynamics, ultimately leading to cell cycle arrest and apoptosis. Many of these drugs, including the taxanes and Vinca alkaloids, are currently used clinically in the treatment of several types of cancer. Another tubulin binding drug, colchicine, although too toxic to be used as a chemotherapeutic agent, is commonly used for the treatment of gout. The main disadvantage that all of these drugs share is that they bind tubulin indiscriminately, leading to the death of both cancerous and healthy cells. However, the broad cellular distribution of several tubulin isotypes provides a platform upon which to construct novel chemotherapeutic drugs that could differentiate between different cell types, reducing the undesirable side effects associated with current chemotherapeutic treatments. Here, we report an analysis of ten human β tubulin isotypes and discuss differences within each of the previously characterized paclitaxel, colchicine and vinblastine binding sites.

Heptaspanning membrane receptors and cytoskeletal/scaffolding proteins: focus on adenosine, dopamine, and metabotropic glutamate receptor function

Most cellular functions are mediated by multiprotein complexes. In neurons, these complexes are directly involved in the proper neuronal transmission, which is responsible for phenomena like learning, memory, and development. In recent years studies based on two-hybrid screens and proteomic, biochemical, and cell biology approaches have shown that intracellular domains of G protein-coupled receptors (GPCRs) or heptaspanning membrane receptors (HSMRs) interact with intracellular proteins. These interactions are the basis of a protein network associated with these receptors, which includes scaffolding proteins containing one or several PDZ (postsynaptic-density-95/discs-large/zona occludens-1) domains, signaling proteins, and proteins of the cytoskeleton. The present article is focused on the emerging evidence for interactions of adenosine, dopamine, and metabotropic glutamate receptors, with scaffolding and cytoskeletal proteins that play a role in the targeting and anchoring of these receptors to the plasma membrane, thus contributing to neuronal development and plasticity. Finally, given the complexity of neurological disorders such as ischemic stroke, Alzheimer's disease, and epilepsy, exploitation of these HSMR-associated interactions might prove to be efficient in the treatment of such disorders.

Functional analysis of microtubule-binding domain of bovine MAP4

Bovine microtubule-associated protein 4 (MAP4) consists of an amino-terminal projection domain and a carboxyl-terminal microtubule-binding domain. The carboxyl-terminal domain of MAP4 is further divided into three subdomains: a region rich in proline and basic residues (Pro-rich region), a region containing four repeats of an assembly-promoting (AP) sequence, which consists of 22 amino acid residues (AP sequence region), and a hydrophobic tail region (Tail region). The subdomain structure of MAP4 microtubule binding domain is similar to those of other MAPs (MAP2 and tau). In order to study the function of each subdomain per se of bovine MAP4 microtubule-binding domain, we purified a series of truncated fragments of MAP4, expressed in Escherichia coil. Binding affinity of the PA4T fragment (containing the Pro-rich region, the AP sequence region and the Tail region) is only four times higher than that of the A4T fragment (containing the AP sequence region and the Tail region), while the microtubule nucleating activity of the PA4T fragment is far greater. We propose that the Pro-rich region promotes the nucleation of microtubule assembly. The A4 fragment (corresponding to the AP sequence region) stimulated the assembly of tubulin into coldstable amorphous aggregates. The AP sequence region of MAP4 failed to promote microtubule assembly. On the other hand, the fragment has an activity to stimulate microtubule elongation. The function of the MAP4 Tail region is not clear at present. The A4T fragment (containing the AP sequence region and the Tail region) promote both microtubule nucleation and elongation step, but the A4 fragment only promotes microtubule elongation, suggesting that the Tail region is indispensable for the nucleation step. However, the fragment containing only the Tail region could not bind to microtubule. Although MAP4 was considered to be long, thin and flexible molecule, never the Tail region may contribute to be the proper folding of MAP4, and/or may interact with other molecules. We concluded that both the Pro-rich region and the AP sequence region take part in the promotion of tubulin polymerization, and that the former is important for the lateral protofilament-protofilament interaction, and the latter is important for the longitudinal affinity between each tubulin dimer in a protofilament.

Microtubule Dynamics may Embody a Stationary Bipolarity Forming Mechanism Related to the Prokaryotic Division Site Mechanism (Pole-to-Pole Oscillations)

Cell division mechanisms in eukaryotes and prokaryotes have until recently been seen as being widely different. However, pole-to-pole oscillations of proteins like MinE in prokaryotes are now known to determine the division plane. These protein waves arise through spontaneous pattern forming reaction-diffusion mechanisms, based on cooperative binding of the proteins to a quasistationary matrix (like the cell membrane or DNA). Rather than waves, stationary bipolar pattern formation may arise as well. Some of the involved proteins have eukaryotic homologs (e.g. FtsZ and tubulin), pointing to a possible ancient shared mechanism. Tubulin polymerizes to microtubules in the spindle. Mitotic microtubules are in a highly dynamical state, frequently undergoing rapid shortening (catastrophe), and fragments formed from the microtubule ends are inferred to enhance the destabilization. Here, we show that cooperative binding of such fragments to microtubules may set up a similar pattern forming mechanism as seen in prokaryotes. The result is a spontaneously formed, well controllable, bipolar state of microtubule dynamics in the cell, which may contribute to defining the bipolar spindle.

Large fluctuations in the disassembly rate of microtubules revealed by atomic force microscopy

Atomic force microscopy (AFM) in situ has been used to observe the cold disassembly dynamics of microtubules at a previously unrealised spatial resolution. Microtubules either electrostatically or covalently bound to aminosilane surfaces disassembled at room temperature under buffer solutions with no free tubulin present. This process was followed by taking sequential tapping-mode AFM images and measuring the change in the microtubule end position as a function of time, with an spatial accuracy down to +/-20nm and a temporal accuracy of +/-1s. As well as giving average disassembly rates on the order of 1-10 tubulin monomers per second, large fluctuations in the disassembly rate were revealed, indicating that the process is far from smooth and linear under these experimental conditions. The surface bound rates measured here are comparable to the rates for GMPCPP-tubulin microtubules free in solution, suggesting that inhibition of tubulin curvature through steric hindrance controls the average, relatively low disassembly rate. The large fluctuations in this rate are thought to be due to multiple pathways in the kinetics of disassembly with differing rate constants and/or stalling due to defects in the microtubule lattice. Microtubules that were covalently bound to the surface left behind the protofilaments covalently cross-linked to the aminosilane via glutaraldehyde during the disassembly process. Further work is needed to quantitatively assess the effects of surface binding on protofibril disassembly rates, reveal any differences in disassembly rates between the plus and minus ends and to enable assembly as well as disassembly to be imaged in the microscope fluid cell in real-time.

A role for epsin N-terminal homology/AP180 N-terminal homology (ENTH/ANTH) domains in tubulin binding

The epsin N-terminal homology (ENTH) domain is a protein module of approximately 150 amino acids found at the N terminus of a variety of proteins identified in yeast, plants, nematode, frog, and mammals. ENTH domains comprise multiple alpha-helices folded upon each other to form a compact globular structure that has been implicated in interactions with lipids and proteins. In characterizing this evolutionarily conserved domain, we isolated and identified tubulin as an ENTH domain-binding partner. The interaction, which is direct and has a dissociation constant of approximately 1 microm, was observed with ENTH domains of proteins present in various species. Tubulin is co-immunoprecipitated from rat brain extracts with the ENTH domain-containing proteins, epsins 1 and 2, and punctate epsin staining is observed along the microtubule cytoskeleton of dissociated cortical neurons. Consistent with a role in microtubule processes, the over-expression of epsin ENTH domain in PC12 cells stimulates neurite outgrowth. These data demonstrate an evolutionarily conserved property of ENTH domains to interact with tubulin and microtubules.

Modeling oscillatory microtubule polymerization

Polymerization of microtubules is ubiquitous in biological cells and under certain conditions it becomes oscillatory in time. Here, simple reaction models are analyzed that capture such oscillations as well as the length distribution of microtubules. We assume reaction conditions that are stationary over many oscillation periods, and it is a Hopf bifurcation that leads to a persistent oscillatory microtubule polymerization in these models. Analytical expressions are derived for the threshold of the bifurcation and the oscillation frequency in terms of reaction rates, and typical trends of their parameter dependence are presented. Both, a catastrophe rate that depends on the density of guanosine triphosphate liganded tubulin dimers and a delay reaction, such as the depolymerization of shrinking microtubules or the decay of oligomers, support oscillations. For a tubulin dimer concentration below the threshold, oscillatory microtubule polymerization occurs transiently on the route to a stationary state, as shown by numerical solutions of the model equations. Close to threshold, a so-called amplitude equation is derived and it is shown that the bifurcation to microtubule oscillations is supercritical.

Growth pulsations in symmetric dendritic crystallization in thin polymer blend films

The crystallization of polymeric and metallic materials normally occurs under conditions far from equilibrium, leading to patterns that grow as propagating waves into the surrounding unstable fluid medium. The Mullins-Sekerka instability causes these wave fronts to break up into dendritic arms, and we anticipate that the normal modes of the dendrite tips have a significant influence on pattern growth. To check this possibility, we focus on the dendritic growth of polyethylene oxide in a thin-film geometry. This crystalline polymer is mixed with an amorphous polymer (polymethyl-methacrylate) to "tune" the morphology and clay was added to nucleate the crystallization. The tips of the main dendrite trunks pulsate during growth and the sidebranches, which grow orthogonally to the trunk, pulsate out of phase so that the tip dynamics is governed by a limit cycle. The pulsation period P increases sharply with decreasing film thickness L and then vanishes below a critical value L(c) approximately 80 nm. A change of dendrite morphology accompanies this transition.

Metabotropic glutamate receptor type 1alpha and tubulin assemble into dynamic interacting complexes

Metabotropic glutamate receptors (mGlu receptors) are coupled to G-protein second messenger pathways and modulate glutamate neurotransmission in the brain, where they are targeted to specific synaptic locations. Very recently, we identified tubulin as an interacting partner of the mGlu(1alpha) receptor in rat brain. Using BHK-570 cells permanently expressing the receptor we have shown that this interaction occurs predominantly with soluble tubulin, following its translocation to the plasma membrane. In addition, treatment of the cells with the agonist quisqualic acid induce tubulin depolymerization and its translocation to the plasma membrane. Immunofluorescence detection of both the receptor and tubulin in agonist-treated cells reveals a disruption of the microtubule network and an increased clustering of the receptor. Collectively these data demonstrate that the mGlu(1alpha) receptor interacts with soluble tubulin and that this association can take place at the plasma membrane.

Binding and phosphorylation of tubulin by G protein-coupled receptor kinases

Although the beta-adrenergic receptor kinase (betaARK) mediates agonist-dependent phosphorylation and desensitization of G protein-coupled receptors, recent studies suggest additional cellular functions. During our attempts to identify novel betaARK interacting proteins, we found that the cytoskeletal protein tubulin could specifically bind to a betaARK-coupled affinity column. In vitro analysis demonstrated that betaARK and G protein-coupled receptor kinase-5 (GRK5) were able to stoichiometrically phosphorylate purified tubulin dimers with a preference for beta-tubulin and, under certain conditions, the betaIII-isotype. Examination of the GRK/tubulin binding characteristics revealed that tubulin dimers and assembled microtubules bind GRKs, whereas the catalytic domain of betaARK contains the primary tubulin binding determinants. In vivo interaction of GRK and tubulin was suggested by the following: (i) co-purification of betaARK with tubulin from brain tissue; (ii) co-immunoprecipitation of betaARK and tubulin from COS-1 cells; and (iii) co-localization of betaARK and GRK5 with microtubule structures in COS-1 cells. In addition, GRK-phosphorylated tubulin was found preferentially associated with the microtubule fraction during in vitro assembly assays suggesting potential functional significance. These results suggest a novel link between the cytoskeleton and GRKs that may be important for regulating GRK and/or tubulin function.

Microtubule polymerization dynamics

The polymerization dynamics of microtubules are central to their biological functions. Polymerization dynamics allow microtubules to adopt spatial arrangements that can change rapidly in response to cellular needs and, in some cases, to perform mechanical work. Microtubules utilize the energy of GTP hydrolysis to fuel a unique polymerization mechanism termed dynamic instability. In this review, we first describe progress toward understanding the mechanism of dynamic instability of pure tubulin and then discuss the function and regulation of microtubule dynamic instability in living cells.

How tubulin subunits are lost from the shortening ends of microtubules

Microtubules exhibit dynamic instability, switching between persistent states of growth and shortening at their ends. The switch between growth and shortening has been proposed to depend on end conformation where growing ends have "straight" tubulin protofilaments stabilized by a terminal cap of GTP-tubulin, while-shortening ends have lost their GTP-tubulin cap, allowing terminal GDP-tubulin dimers to curve inside-out and peel rapidly away from the microtubule lattice. This "conformational cap" model predicts that tubulin dissociation from shortening ends is a two-step process where the average lengths of curved GDP-tubulin protofilaments at a depolymerizing end will depend on the ratio of the rate of peeling to the rate of breakage of the longitudinal bonds between adjacent curved dimers. We have tested this model for the plus and minus ends of microtubules assembled with pure porcine tubulin off the ends of axoneme fragments in standard assembly buffer. Individual microtubule ends were imaged using video-enhanced differential interference contrast light microscopy. The rate of rapid shortening was systematically increased by isothermal dilution into assembly buffer containing various concentrations of Mg2+ or Ca2+ ions. At 1 mM Mg2+ and no Ca2+, shortening occurred at 20 (plus) and 45 (minus) microns/min. The ends appeared similar in contrast to growing ends and the core of the microtubule and the ends appeared blunt or slightly frayed by negative stain electron microscopy. Above 20 mM Mg2+ or above 5 mM Ca2+, microtubule shortening occurred at 60 (plus) and 115 (minus) microns/min or faster and "knobs" were distinctly visible at depolymerizing ends, particularly at the faster minus ends, and knob contrast remained constant during many micrometers of rapid shortening. Negative stain electron microscopy revealed that these knobs were "blossoms" of inside-out curved protofilaments, some extending for several helical turns (30 to 60 dimers in length) at constant curvature from the ends. At these high shortening velocities, the peeling of curved protofilaments was confined to within several dimers of the end of the microtubule cylinder, suggesting that dimer curling and protofilament peeling is constrained to the tip by interactions between adjacent straight protofilaments. Depolymerization is produced by conformational changes in GDP-tubulin since microtubules assembled with a slowly hydrolizable analog of GTP, GMPCPP, are stable even at 20 mM Mg2+ or 5 mM Ca2+. Monte Carlo simulations show that the ratio of the peeling to breakage rate constants can control the steady-state average length of curved GDP-tubulin protofilaments at the depolymerizing end.

Selected physical issues in the structure and function of microtubules

The cytoskeleton consists of networks of protein polymers which structurally and dynamically organize interiors of living cells. Microtubules exhibit a complex array of self-organization phenomena which are very sensitive to various laboratory conditions. In this paper we discuss the main features of microtubules focusing our attention on a selection of their physical properties, i.e., the questions of assembly dynamics and energy transfer along their protofilaments, the possible dipolar phases which we predict to exist, and, finally, the hypothesis of current flows associated with the electric field lines produced by cytoskeletal components.

Electrodynamics of microtubular motors: the building blocks of a new model

Microtubules are ubiquitous components of the cytoskeleton. They participate in many motility processes ranging from intracellular transport or chromosome movement during mitosis to ciliary and flagellar beating. The biophysical mechanism inherent in the generation and control of movement in all these motility phenomena has not yet been entirely elucidated. The authors propose a new model based on a charge transfer mechanism capable of shedding a new light on the molecular foundations of all motility processes. Electron transfer along the microtubular lattice is responsible for activation and control of all microtubule-associated ATPases (i.e. force generating enzymes). Microtubules are thus shown to be the basic motors of cell dynamics. The model is first applied to intracellular transport and ciliary and flagellar beating. Through two additional examples, the authors show the heuristic capabilities of the suggested hypothesis. The application of charge transfer control to the Protozoan Euglena gracilis leads to a plausible model capable of accounting for its phototactic response mechanism. Furthermore, the model allows a new interpretation of the electrophysiological response in vertebrate photoreceptors.

Force generation by microtubule assembly/disassembly in mitosis and related movements

In this article, we review the dynamic nature of the filaments (microtubules) that make up the labile fibers of the mitotic spindle and asters, we discuss the roles that assembly and disassembly of microtubules play in mitosis, and we consider how such assembling and disassembling polymer filaments can generate forces that are utilized by the living cell in mitosis and related movements.

Interaction of tubulin with guanosine 5'-O-(1-thiotriphosphate) diastereoisomers: specificity of the alpha-phosphate binding region

The exchangeable nucleotide-binding site of tubulin has been studied using diastereoisomers A (Sp) and B (Rp) of guanosine 5'-O-(1-thiotriphosphate) (GTP alpha S) in which the phosphorus atom to which sulfur is attached is chiral. GTP alpha S(A) (10 microM) nucleated assembly of purified tubulin (20 microM) into microtubules in buffer containing 0.1 M 2-(N-morpholino)ethanesulfonic acid with 3 mM Mg2+ and 1 mM EGTA, pH 6.6 at 37 degrees C. With 0.2 mM GTP alpha S(A), the critical concentration (Cc; minimum protein concentration required for assembly) was 8 microM tubulin. Neither 0.2 mM GTP nor GTP alpha S(B) promoted microtubule assembly in buffer with 0.5-6.75 mM Mg2+ and 20-70 microM tubulin. The Cc values for GTP alpha S-(A)-induced assembly of tubulin in buffer with 30% glycerol and of microtubule protein (tubulin and microtubule-associated proteins) in buffer were lower than for GTP. GTP alpha S(A)-induced microtubules were more stable to the cold and to Ca2+. GTP alpha S(A) and GTP but not GTP alpha S(B) bound tightly to tubulin at 4 degrees C. Although GTP alpha S(B) did not nucleate assembly, it did bind to tubulin since it was incorporated into the growing microtubule. Both isomers were hydrolyzed in the microtubules. These studies show that GTP alpha S(A) promotes tubulin assembly better than GTP and GTP alpha S(B) and that there is stereoselectivity at the alpha-phosphate binding region of tubulin. The stereoselectivity may be due to different MgGTP alpha S(A) and -(B) interactions with tubulin.

A model of microtubule oscillations

Simulations of microtubule oscillations have been obtained by a kinetic model including nucleation of microtubules, elongation by addition of GTP-loaded tubulin dimers, disassembly into oligomers, and dissolution of oligomers followed by nucleotide exchange at the free dimers. Dynamic instability is described by the on and off rates for dimer association in the growth phase, the rate of rapid shortening, and the transition rates for catastrophe and rescue. The latter are assumed to be completely determined by the current state of the system ("short cap hypothesis"). Microtubule oscillations and normal polymerizations measured by time-resolved X-ray scattering were used to test the model. The model is able to produce oscillations without further assumptions. However, in order to obtain good fits to the experimental data one requires an additional mechanism which prevents rapid desynchronization of the microtubules. One of several possible mechanisms that will be discussed is the destabilization of microtubules by the products of disassembly.

Dynamic instability of microtubules: Monte Carlo simulation and application to different types of microtubule lattice

Dynamic instability is the term used to describe the transition of an individual microtubule, apparently at random, between extended periods of slow growth and brief periods of rapid shortening. The typical sawtooth growth and shortening transition behavior has been successfully simulated numerically for the 13-protofilament microtubule A-lattice by a lateral cap model (Bayley, P. M., M. J. Schilstra, and S. R. Martin. 1990. J. Cell Sci. 95:33-48). This kinetic model is now extended systematically to other related lattice geometries, namely the 13-protofilament B-lattice and the 14-protofilament A-lattice, which contain structural "seams". The treatment requires the assignment of the free energies of specific protein-protein interactions in terms of the basic microtubule lattice. It is seen that dynamic instability is not restricted to the helically symmetric 13-protofilament A-lattice but is potentially a feature of all A- and B-lattices, irrespective of protofilament number. The advantages of this general energetic approach are that it allows a consistent treatment to be made for both ends of any microtubule lattice. Important features are the predominance of longitudinal interactions between tubulin molecules within the same protofilament and the implication of a relatively favorable interaction of tubulin-GDP with the growing microtubule end. For the three lattices specifically considered, the treatment predicts the dependence of the transition behavior upon tubulin concentration as a cooperative process, in good agreement with recent experimental observations. The model rationalizes the dynamic properties in terms of a metastable microtubule lattice of tubulin-GDP, stabilized by the kinetic process of tubulin-GTP addition. It provides a quantitative basis for the consideration of in vitro microtubule behaviour under both steady-state and non-steady-state conditions, for comparison with experimental data on the dilution-induced disassembly of microtubules. Similarly, the effects of small tubulin-binding molecules such as GDP and nonhydrolyzable GTP analogues are readily treated. An extension of the model allows a detailed quantitative examination of possible modes of substoichiometric action of a number of antimitotic drugs relevant to cancer chemotherapy.