A reassessment of the factors affecting microtubule assembly and disassembly in vitro

Current models of microtubule assembly from pure tubulin involve a nucleation phase followed by microtubule elongation at a constant polymer number. Both the rate of microtubule nucleation and elongation are thought to be tightly influenced by the free GTP-tubulin concentration, in a law of mass action-dependent manner. However, these basic hypotheses have remained largely untested due to a lack of data reporting actual measurements of the microtubule length and number concentration during microtubule assembly.Here, we performed simultaneous measurements of the polymeric tubulin concentration, of the free GTP-tubulin concentration, and of the microtubule length and number concentration in both polymerizing and depolymerizing conditions. In agreement with previous work we find that the microtubule nucleation rate is strongly dependent on the initial GTP-tubulin concentration. But we find that microtubule nucleation persists during microtubule elongation. At any given initial tubulin-GTP concentration, the microtubule nucleation rate remains constant during polymer assembly, despite the wide variation in free GTP-tubulin concentration. We also find a remarkable constancy of the rate of microtubule elongation during assembly. Apparently, the rate of microtubule elongation is intrinsic to the polymers, insensitive to large variations of the free GTP-tubulin concentration. Finally we observe that when, following assembly, microtubules depolymerize below the free GTP-tubulin critical concentration, the rate-limiting factor for disassembly is the frequency of microtubule catastrophe. At all time-points during disassembly, the microtubule catastrophe frequency is independent of the free GTP-tubulin concentration but, as the microtubule nucleation rate, is strongly dependent on the initial free GTP-tubulin concentration. We conclude that the dynamics of both microtubule assembly and disassembly depend largely on factors other than the free GTP-tubulin concentration. We propose that intrinsic structural factors and endogenous regulators, whose concentration varies with the initial conditions, are also major determinants of these dynamics.     

Allosteric models for cooperative polymerization of linear polymers

In the cytoskeleton, unfavorable nucleation steps allow cells to regulate where, when, and how many polymers assemble. Nucleated polymerization is traditionally explained by a model in which multistranded polymers assemble cooperatively, whereas linear, single-stranded polymers do not. Recent data on the assembly of FtsZ, the bacterial homolog of tubulin, do not fit either category. FtsZ can polymerize into single-stranded protofilaments that are stable in the absence of lateral interactions, but that assemble cooperatively. We developed a model for cooperative polymerization that does not require polymers to be multistranded. Instead, a conformational change allows subunits in oligomers to associate with high affinity, whereas a lower-affinity conformation is favored in monomers. We derive equations for calculating polymer concentrations, subunit conformations, and the apparent affinity of subunits for polymer ends. Certain combinations of equilibrium constants produce the sharp critical concentrations characteristic of cooperative polymerization. In these cases, the low-affinity conformation predominates in monomers, whereas virtually all polymers are composed of high-affinity subunits. Our model predicts that the three routes to forming HH dimers all involve unstable intermediates, limiting nucleation. The mathematical framework developed here can represent allosteric assembly systems with a variety of biochemical interpretations, some of which can show cooperativity, and others of which cannot.     

Nucleation and growth phases in the polymerization of coat and scaffolding subunits into icosahedral procapsid shells.

The polymerization of protein subunits into precursor shells empty of DNA is a critical process in the assembly of double-stranded DNA viruses. For the well-characterized icosahedral procapsid of phage P22, coat and scaffolding protein subunits do not assemble separately but, upon mixing, copolymerize into double-shelled procapsids in vitro. The polymerization reaction displays the characteristics of a nucleation limited reaction: a paucity of intermediate assembly states, a critical concentration, and kinetics displaying a lag phase. Partially formed shell intermediates were directly visualized during the growth phase by electron microscopy of the reaction mixture. The morphology of these intermediates suggests that assembly is a highly directed process. The initial rate of this reaction depends on the fifth power of the coat subunit concentration and the second or third power of the scaffolding concentration, suggesting that pentamer of coat protein and dimers or trimers of scaffolding protein, respectively, participate in the rate-limiting step.     

Microtubule oscillations. Role of nucleation and microtubule number concentration

Microtubules are capable of performing synchronized oscillations of assembly and disassembly which has been explained by reaction mechanisms involving tubulin subunits, oligomers, microtubules, and GTP. Here we address the question of how microtubule nucleation or their number concentration affects the oscillations. Assembly itself requires a critical protein concentration (Cc), but oscillations require in addition a critical microtubule number concentration (CMT). In spontaneous assembly this can be achieved with protein concentrations Cos well above the critical concentration Cc because this enhances the efficiency of nucleation. Seeding with microtubules can either generate oscillations or suppress them, depending on how the seeds alter the effective microtubule number concentration. The relative influence of microtubule number and total protein concentrations can be varied by the rate at which assembly conditions are induced (e.g. by a temperature rise): Fast T-jumps induce oscillations because of efficient nucleation, slow ones do not. Oscillations become damped for several reasons. One is the consumption of GTP, the second is a decrease in microtubule number, and the third is that the ratio of microtubules in the two phases (growth-competent and shrinkage-competent) approach a steady state value. This ratio can be perturbed, and the oscillations restarted, by a cold shock, addition of seeds, addition of GTP, or fragmentation. Each of these is equivalent to a change in the effective microtubule number concentration.     

Tubulin oligomers and microtubule assembly studied by time-resolved X-ray scattering: separation of prenucleation and nucleation events

This paper describes a time-resolved X-ray scattering study of microtubule assembly by synchrotron radiation. The method is complementary to light scattering but allows a better distinction between oligomeric and polymeric assembly states. With an improved rapid temperature jump device, it is shown that temperature-induced microtubule assembly is preceded by prenucleation and nucleation events involving oligomers of tubulin, in analogy with earlier results from near-equilibrium temperature scans. In general, the two phases closely overlap, but in certain conditions they can be observed separately. The prenucleation events seen by X-rays can be described as a rapid temperature-dependent equilibrium, with ring oligomers dissociating into smaller oligomers and subunits at elevated temperature. Different solution conditions affect mainly the time lag between the prenucleation and nucleation phases; this in turn determines the apparent magnitude of the prenucleation steps. By contrast, the temperature dependence of the equilibrium between the prenucleation oligomers shows little influence on solution conditions. The results suggest that the ring-forming and tubule-forming assembly modes of tubulin are governed by different interactions between subunits, although they may be based on a pool of similar intermediates.     

The kinetics of microtubule assembly. Evidence for a two-stage nucleation mechanism

A model describing the nucleation and assembly of purified tubulin has been developed. The novel feature of this model is a two stage nucleation process to allow the explicit inclusion of the two-dimensional nature of the early stages of microtubule assembly. In actin assembly the small starting nucleus has only one site for subunit addition as the two-stranded helix is formed. In contrast, microtubule assembly begins with the formation of a small two-dimensional section of microtubule wall. The model we propose is a modification of the work of Wegner and Engel (Wegner, A., and Engel, J. (1975) Biophys. Chem. 3, 215-225) wherein we add a second stage of nucleation to directly account for lateral growth, i.e. the addition of a small number of subunits to the side of an existing sheet structure. Subsequent elongation of the sheets is treated in the usual way. The experimental system used to test this model was the Mg2+/glycerol induced assembly of purified tubulin. The computer simulation of the polymerization time courses gave a fairly good fit to experimental kinetics for our model, where the primary nucleus comprises two protofilaments, of four and three subunits, and lateral growth requires a three-subunit nucleus to initiate a new protofilament.     

Rapid microtubule self-assembly kinetics

Microtubule assembly is vital for many fundamental cellular processes. Current models for microtubule assembly kinetics assume that the subunit dissociation rate from a microtubule tip is independent of free subunit concentration. Total-Internal-Reflection-Fluorescence (TIRF) microscopy experiments and data from a laser tweezers assay that measures in vitro microtubule assembly with nanometer resolution, provides evidence that the subunit dissociation rate from a microtubule tip increases as the free subunit concentration increases. These data are consistent with a two-dimensional model for microtubule assembly, and are explained by a shift in microtubule tip structure from a relatively blunt shape at low free concentrations to relatively tapered at high free concentrations. We find that because both the association and the dissociation rates increase at higher free subunit concentrations, the kinetics of microtubule assembly are an order-of-magnitude higher than currently estimated in the literature.     

A quantitative analysis of microtubule elongation

Methods have been developed for differentially inhibiting microtubule nucleation and elongation in vitro. By use of polyanions, assembly- competent tubulin solutions of several milligrams/milliliter can be prepared which do not exhibit appreciable spontaneous assembly during the time-course of an experiment. Microtubule elongation can be initiated by the addition of known numbers of microtubule fragments. A detailed analysis of the resulting process demonstrates that: (a) rings are not obligatory intermediates in the nucleation sequence, and neither rings nor protofilament sheets are obligatory intermediates in the elongation reaction. (b) The end of an elongating microtubule often has a short region of open protofilament sheet or "C-microtubule" similar to that observed in vivo. (c) The development of turbidity follows a simple exponential approach to an equilibrium value. (d) The final equilibrium values are independent of the number of added nucleating fragments, while the initial growth rates and half-times to reach equilibrium are dependent on the number of added nuclei. (e) The final lengths of the microtubules at equilibrium are inversely proportional to the number of added fragments. (f) The equilibrium constants are independent of microtubule length. (g) The number of assembly and disassembly sites per microtubule is not a function of microtubule length. (h) The forward rate constants, the final polymer concentrations, and growth rates of microtubules are dependent upon the concentration of polyanion present. These results are strongly supportive of the idea that microtubule assembly is a "condensation- polymerization" and provide basic information on the kinetics and length distributions of the elongation in vitro.     

Erythrocyte microtubule assembly in vitro. Tubulin oligomers limit the rate of microtubule self-assembly

Chicken erythrocyte tubulin containing a unique beta tubulin variant polymerizes with greater efficiency (lower critical concentration) but at a slower rate than chicken brain tubulin. In a previous study we demonstrated that the low net rate of assembly is partly due to the presence of large oligomers and rings which reduce the initial rate of subunit elongation on microtubule seeds (Murphy, D.B., and Wallis, K.T. (1985) J. Biol. Chem. 260, 12293-12301). In this study we show that erythrocyte tubulin oligomers also retard the rate of microtubule nucleation and the net rate of self-assembly. The inhibitory effect is most likely to be due to the increased stability of erythrocyte tubulin oligomers, including a novel polymer of coiled rings that forms during the rapid phase of microtubule polymerization. The slow rate of dissociation of rings and coils into dimers and small oligomers appears to limit both the nucleation and elongation steps in the self-assembly of erythrocyte microtubules.     

The sequence of a region of bacteriophage phiX174 DNA coding for parts of genes A and B

The kinetics of microtubule assembly were investigated by monitoring changes in turbidity which result from the scattering of incident light by the polymer. These studies indicated that assembly occurred by a pathway involving a nucleation phase, followed by an elongation phase as evidenced by a lag in the polymerization kinetics, followed by a psuedo-first-order exponential increase in turbidity. Analytical ultracentrifugation of solutions polymerized to equilibrium showed that 6 S tubulin was the only species detectable in equilibrium with microtubules. Investigation of the elongation reaction in mixtures of 6 S tubulin and microtubule fragments demonstrated that: (1) the net rate of assembly was the sum of the rates of polymerization and depolymerization; (2) the rate of polymerization was proportional to the product of the microtubule number concentration and the 6 S tubulin concentration; and (3) the rate of depolymerization was proportional to the number concentration of microtubules. These results demonstrate that microtubule assembly occurs by a condensation polymerization mechanism consisting of distinct nucleation and elongation steps. Microtubules are initiated in a series of protein association reactions in a pathway that has not been fully elucidated. Elongation proceeds by the consecutive association of 6 S tubulin subunits onto the ends of existing microtubules. Similarly, depolymerization occurs by dissociation of 6 S subunits from the ends of microtubules. The rate constants measured for polymerization and depolymerization at 30 °C were 4 × 10⁶m^?1 s^?1 and 7 s^?1, respectively.     

Identification and function of the centrosome centromatrix

Centrosomes direct the organization of microtubules in animal cells. However, in the absence of centrosomes, cytoplasm has the potential to organize microtubules and assemble complex structures such as anastral spindles. During cell replication or following fertilization, centrioles that are incapable of organizing microtubules into astral arrays are introduced into this complex cytoplasmic environment. These centrioles become associated with pericentriolar material responsible for centrosome-dependent microtubule nucleation, and thus the centrosome matures to ultimately become a dominant microtubule organizing center that serves as a central organizer of cell cytoplasm. We describe the identification of a novel structure within the pericentriolar material of centrosomes called the centromatrix. The centromatrix is a salt-insoluble filamentous scaffold to which subunit structures that are necessary for microtubule nucleation and abundant in the cytoplasm bind. We propose that the centromatrix serves to concentrate and focus these subunits to form the microtubule organizing center. Since binding of these subunits to the centromatrix does not require nucleotides, we propose a model for centrosome assembly which predicts that the assembly of the centromatrix is a rate-limiting step in centrosome assembly and maturation.     

Nucleation of protein crystals

This paper introduces nucleation theory applied to crystallizing protein solutions. It is shown that the classical approach explains the available nucleation data under most conditions used for growing protein crystals for structural studies and for industrial crystallization. However, it fails to explain most experimental data on the structure of the critical clusters. It is also shown that for open systems working out of equilibrium, such as hanging-drop and counterdiffusion techniques, the geometry of the Ostwald-Myers protein solubility diagram and the number, size, and quality of the forming crystals depend not only on supersaturation but also on the rate of development of supersaturation.     

The free energy for hydrolysis of a microtubule-bound nucleotide triphosphate is near zero: all of the free energy for hydrolysis is stored in the microtubule lattice [published erratum appears in J Cell Biol 1995 Apr;129(2):549]

The standard free energy for hydrolysis of the GTP analogue guanylyl- (a,b)-methylene-diphosphonate (GMPCPP), which is -5.18 kcal in solution, was found to be -3.79 kcal in tubulin dimers, and only -0.90 kcal in tubulin subunits in microtubules. The near-zero change in standard free energy for GMPCPP hydrolysis in the microtubule indicates that the majority of the free energy potentially available from this reaction is stored in the microtubule lattice; this energy is available to do work, as in chromosome movement. The equilibrium constants described here were obtained from video microscopy measurements of the kinetics of assembly and disassembly of GMPCPP-microtubules and GMPCP- microtubules. It was possible to study GMPCPP-microtubules since GMPCPP is not hydrolyzed during assembly. Microtubules containing GMPCP were obtained by assembly of high concentrations of tubulin-GMPCP subunits, as well as by treating tubulin-GMPCPP-microtubules in sodium (but not potassium) Pipes buffer with glycerol, which reduced the half-time for GMPCPP hydrolysis from > 10 h to approximately 10 min. The rate for tubulin-GMPCPP and tubulin-GMPCP subunit dissociation from microtubule ends were found to be about 0.65 and 128 s-1, respectively. The much faster rate for tubulin-GMPCP subunit dissociation provides direct evidence that microtubule dynamics can be regulated by nucleotide triphosphate hydrolysis.     

Microtubule nucleation from stable tubulin oligomers

Microtubule assembly from purified tubulin preparations involves both microtubule nucleation and elongation. Whereas elongation is well documented, microtubule nucleation remains poorly understood because of difficulties in isolating molecular intermediates between tubulin dimers and microtubules. Based on kinetic studies, we have previously proposed that the basic building blocks of microtubule nuclei are persistent tubulin oligomers, present at the onset of tubulin assembly. Here we have tested this model directly by isolating nucleation-competent cross-linked tubulin oligomers. We show that such oligomers are composed of 10-15 laterally associated tubulin dimers. In the presence of added free tubulin dimers, several oligomers combine to form microtubule nuclei competent for elongation. We provide evidence that these nuclei have heterogeneous structures, indicating unexpected flexibility in nucleation pathways. Our results suggest that microtubule nucleation in purified tubulin solution is mechanistically similar to that templated by gamma-tubulin ring complexes with the exception that in the absence of gamma-tubulin complexes the production of productive microtubule seeds from tubulin oligomers involves trial and error and a selection process.     

Quantitative analysis of multi-component spherical virus assembly: scaffolding protein contributes to the global stability of phage P22 procapsids

Assembly of the hundreds of subunits required to form an icosahedral virus must proceed with exquisite fidelity, and is a paradigm for the self-organization of complex macromolecular structures. However, the mechanism for capsid assembly is not completely understood for any virus. Here we have investigated the in vitro assembly of phage P22 procapsids using a quantitative model specifically developed to analyze assembly of spherical viruses. Phage P22 procapsids are the product of the co-assembly of 420 molecules of coat protein and approximately 100-300 molecules of scaffolding protein. Scaffolding protein serves as an assembly chaperone and is not part of the final mature capsid, but is essential for proper procapsid assembly. Here we show that scaffolding protein also affects the thermodynamics of assembly, and for the first time this quantitative analysis has been performed on a virus composed of more than one type of protein subunit. Purified coat and scaffolding proteins were mixed in varying ratios in vitro to form procapsids. The reactions were allowed to reach equilibrium and the proportion of the input protein assembled into procapsids or remaining as free subunits was determined by size exclusion chromatography and SDS-PAGE. The results were used to calculate the free energy contributions for individual coat and scaffolding proteins. Each coat protein subunit was found to contribute -7.2(+/-0.1)kcal/mol and each scaffolding protein -6.1(+/-0.2)kcal/mol to the stability of the procapsid. Because each protein interacts with two or more neighbors, the pair-wise energies are even less. The weak protein interactions observed in the assembly of procapsids are likely important in the control of nucleation, since an increase in affinity between coat and scaffolding proteins can lead to kinetic traps caused by the formation of too many nuclei. In addition, we find that adjusting the molar ratio of scaffolding to coat protein can alter the assembly product. When the scaffolding protein concentration is low relative to coat protein, there is a correspondingly low yield of proper procapsids. When the relative concentration is very high, too many nuclei form, leading to kinetically trapped assembly intermediates.     

Isolation of microtubule protein from chicken erythrocytes and determination of the critical concentration for tubulin polymerization in vitro and in vivo

Microtubule protein isolated from nucleated chicken erythrocytes was examined with respect to composition and assembly properties to determine its significance in a microtubule bundle called the marginal band. 1) The protein contains greater than 95% tubulin with small amounts of tau polypeptides and no high molecular weight polypeptides. 2) Microtubule assembly in vitro at 37 degrees C is characterized by low levels of nucleation, despite an abundance of ring oligomers at 5 degrees C, as indicated by long lag times, slow assembly rates, and microtubules that are twice as long as brain microtubules assembled under the same conditions. 3) By radioimmunoassay and sodium dodecyl sulfate gel analysis we determined that 0.6% of erythrocyte protein is tubulin of which three-quarters is in a nonextractable form and is associated with the microtubule bundle and the cell cortex. From these values the in vivo concentrations of total tubulin and tubulin dimer subunits are 2.4 and 0.7 mg/ml, respectively. The value of 0.7 mg/ml is close to the range of values of 0.1-0.6 mg/ml for the critical concentration of erythrocyte microtubule protein in vitro, suggesting that the assembly properties of tubulin in vitro and in vivo are similar.     

Assembly of GMPCPP-Bound Tubulin into Helical Ribbons and Tubes and Effect of Colchicine

Microtubule assembly and disassembly is a complex structural process that doesnot proceed by simple addition and subtraction of individual subunits to and from ahelical polymer, as would be the case for actin and other helical assemblies. Thedynamic process of microtubule growth and shrinking involves short-lasting polymerforms that differ substantially from the microtubule itself and constitute crucial assemblyand disassembly intermediates. Structural characterization thus depends on thestabilization of these brief intermediates and their preservation as polymericassemblies. This paper gives experimental details on the polymerization of GMPCPPtubulininto low-temperature stable polymers that we propose to correspond to the earlystages in microtubule assembly and includes new data on the effect of colchicine onGMPCPP-tubulin polymerization. Finally, we include our thoughts on the possiblebiological meaning of tubulin polymerization versatility.     

Microtubules and nucleoside diphosphate kinase. Comparison of kinetics of GTP- and CTP-induced assembly.

The kinetics of assembly of MAP2-tubulin microtubule protein were examined as a function of the GTP concentration in order to test the hypothesis that CTP-induced assembly results from the generation of GTP by nucleoside diphosphate kinase. These studies show that (a) there is no assembly below a minimum GTP concentration and that this represents a nucleation requirement, (b) the rate of elongation is inconsistent with a single assembly-species, and (c) the elongation rate increases markedly as the GTP concentration is raised, although GTP is not absolutely required for elongation. These assembly kinetics have been compared with those with increasing CTP concentrations, by using microtubule protein containing a very low nucleoside diphosphate kinase activity of known substrate specificity. Neither nucleation nor the observed rates of elongation can be attributed to the formation of GTP, either (a) in terms of the generation of free GTP and subsequent binding to tubulin or (b) by the direct charging of GDP bound to the tubulin exchangeable site. The results show that nucleoside diphosphate kinase is not required for CTP-induced microtubule assembly, and suggest that CTP directly effects microtubule assembly.     

Stages of tubulin assembly and disassembly studied by time-resolved synchrotron X-ray scattering

The structural transitions occurring during the assembly and disassembly of pig brain microtubule protein were investigated by time-resolved X-ray scattering using synchrotron radiation. The reactions were introduced by a slow temperature scan (2 deg.C/min) from 0 °C to 37 °C and back. Several structurally distinct states could be resolved during one cycle of assembly/disassembly. During the temperature rise, one observes four main phases: prenucleation events, microtubule nucleation, growth, and postassembly events.Heating from 0 °C to 22 °C results in a biphasic breakdown of rings and other aggregates, while the apparent mean diameter increases from 38 to 41 nm. Parallel time-resolved electron microscopic observations suggest that the initial solution contains several types of aggregates, mostly double concentric and single rings, but also rod-like particles, clusters of rings and other aggregates. All of these tend to break down with increasing temperature. Double concentric rings seem to dissociate into large and small single rings before both types of rings break down into protofilament fragments and tubulin subunits. From the breakdown products, associations of several protofilament fragments are formed, which are important for initiating microtubule nucleation. Assembly of nuclei begins around 22 °C. Microtubule elongation takes place between 25 and 30 °C. They grow mainly by addition of tubulin subunits but not via rings.During the reverse temperature scan, microtubules shorten by the release of subunits and/or small protofilament fragments from their ends. The degree of disassembly is strongly increased below 22 °C. Below about 10 °C rings are reformed, probably from the fragments, but their final number is much less than initially.Conditions that prevent microtubule nucleation such as GDP or Ca²⁺ also stabilize rings, even at 37 °C. Thus, rings are viewed as storage aggregates of tubulin and microtubule associated proteins, whose breakdown is a prerequisite for microtubule formation, and whose reformation is independent of microtubule breakdown.The midpoints of microtubule growth and breakdown differ by about 12 deg.C so that the system shows hysteresis-like behavior. It is dependent on microtubule formation and is not seen when the temperature is cycled below that required for nucleation. Thus, even during a slow temperature scan, microtubule assembly is kinetically limited by nucleation. By contrast, depolymerization proceeds close to equilibrium.The radius of gyration of the tubulin heterodimers is 3.1 nm. The weight average diameter of rings in cold solutions is 38 nm, that of microtubules is 24.5 nm.At radiation dose rates of about 100 rad/s. radiation damage is of minor importance, as judged by the criterion of polymerizability. Total doses of up to 500,000 rad can be applied.Some concepts of analyzing time-resolved X-ray scattering data are presented. They make use of the fact that the scattering intensities vary continuously both with scattering angle and time. Cross-correlation of different regions of the pattern, and comparison of their temperature derivatives, reveals structural transitions not seen by other techniques.