Phosphate release during microtubule assembly: what stabilizes growing microtubules?

The molecular mechanism underlying microtubule dynamic instability depends on the relationship between the addition of tubulin-GTP to a growing microtubule and its hydrolysis in the microtubule lattice to tubulin-GDP, with release of inorganic phosphate (Pi). Since this relationship remains controversial, we have re-examined the release of Pi upon microtubule assembly using a fluorometric assay for Pi, based on the phosphate-binding protein of Escherichia coli [Brune M., Hunter, J. L., Corrie, J. E. T., and Webb, M. R. (1994) Biochemistry 33, 8262-8271]. Microtubule assembly and Pi release were monitored simultaneously in a standard fluorimeter as an increase in the turbidity and fluorescence, respectively, in tubulin-GTP solutions assembled under conditions supporting dynamic instability. At the steady state of assembly, Pi release is nonlinear with respect to time, proceeding at a rate determined by the following: (a) the intrinsic GTPase activity of the nonpolymerized tubulin-GTP, and (b) the microtubule number concentration, which decreases progressively. Direct observation of the time course of nucleated microtubule assembly indicates that Pi release is closely coupled to microtubule elongation, even during the initial stages of assembly when uncoupling of tubulin-GTP addition and GTP hydrolysis would be most evident. Studies of the inhibition and reversal of the growth phase by cytostatic drugs show no evidence of a burst of Pi release. We conclude that nucleotide hydrolysis can keep pace with tubulin-GTP addition rates of 200 molecules per second per microtubule and that extended caps of tubulin-GTP or tubulin-GDP-Pi are not generated in normal assembly, nor are they required to stabilize growing microtubules or to support the phenomenon of dynamic instability of microtubules at the steady state.     

Kinetics and mechanism of microtubule length changes by dynamic instability

Microtubules at steady state were found to undergo dramatic changes in length, with only very little change in number concentration and mean length. This result is accounted for by a mechanism in which microtubules are capped at ends by tubulin-GTP subunits; loss of the tubulin-GTP cap at one end results in disassembly of all the tubulin-GDP subunits, so that the medial edge of the distal tubulin-GTP cap is exposed; the exposed tubulin-GTP cap is sufficiently stable, so that microtubule regrowth from the cap rather than loss of the cap occurs. This mechanism predicts that a bell-shaped length distribution of sheared microtubules will be transiently bimodal, with peaks of short and moderate length microtubules, in rearranging to an exponential length distribution. We have observed the predicted transient bimodal length distribution experimentally and in a Monte Carlo simulation. Dynamic instability has recently been accounted for by assuming that microtubule ends are capped with only a single tubulin-GTP subunit at each end of the five helices that serve as elongation sites. Such a minimal tubulin-GTP cap is apparently ruled out by our observations, which require that the remnant tubulin-GTP cap generated from disassembly be able to serve as nucleating site; we do not expect that a stable nucleating site can be generated from five tubulin-GTP subunits, oriented as the five helices that serve as elongation sites.     

Mechanism of the microtubule GTPase reaction

The rate of GTP hydrolysis by microtubules has been measured at tubulin subunit concentrations where microtubules undergo net disassembly. This was made possible by using microtubules stabilized against disassembly by reaction with ethylene glycol bis-(succinimidylsuccinate) (EGS) as sites for the addition of tubulin-GTP subunits. The tubulin subunit concentration was varied from 25 to 90% of the steady state concentration, and there was no net elongation of stabilized microtubule seeds. The GTPase rate with EGS microtubules was linearly proportional to the tubulin-GTP subunit concentration when this concentration was varied by dilution and by using GDP to compete with GTP for the tubulin E-site. The linear dependence of the rate is consistent with a GTP mechanism in which hydrolysis is coupled to the tubulin-GTP subunit addition to microtubule ends. It is inconsistent with reaction schemes in which: microtubules are capped by a single tubulin-GTP subunit, which hydrolyzes GTP when a tubulin-GTP subunit adds to the end; hydrolysis occurs primarily in subunits at the interface of a tubulin-GTP cap and the tubulin-GDP microtubule core; hydrolysis is not coupled to subunit addition and occurs randomly in subunits in a tubulin-GTP cap. It was also found that GDP inhibition of the microtubule GTPase rate results from GDP competition for GTP at the tubulin subunit E-site. There is no additional effect of GDP on the GTPase rate resulting from exchange into tubulin subunits at microtubule ends.     

Temperature-jump studies of microtubule dynamic instability

Evidence for a slowly dissociating tubulin-GTP cap at microtubule ends was derived from observation of a delay for attaining a maximum disassembly rate, after the temperature of steady state microtubules was rapidly decreased from 36 to 34 degrees C. The possibility that the microtubules were capped by a single tubulin-GTP subunit on each subhelix was ruled out, by comparison of the disassembly kinetics following a temperature decrease and dilution. The existence of a subpopulation of microtubules that underwent irreversible or near irreversible disassembly was demonstrated by a 30-s lag for attainment of a maximum assembly rate, after steady state microtubules were shifted from 34 to 36 degrees C. A dynamic instability model predicts that a maximum assembly rate will be delayed until disappearance of a subpopulation of microtubules that disassemble before being recapped. Analysis indicates that the 30-s lag resulted because approximately 2% of the mass in the steady state microtubule population was uncapped and disassembling and not readily recapped. The half-time for recapping of disassembling microtubules, by addition of tubulin-GTP subunits to ends, was equal to or greater than 20 s. Since tubulin-GDP dissociated from microtubules at a rate of about 4500 s-1, slow recapping resulted in dramatic shortening of disassembling microtubules.     

Interrelationships of tubulin-GDP and tubulin-GTP in microtubule assembly

We previously reported that direct incorporation of GDP (i.e., without an initial hydrolysis of GTP) into microtubules occurs throughout an assembly cycle in a constant proportion. The exact proportion varied with reaction conditions, becoming greater under all conditions in which tubulin-GDP increased relative to tubulin-GTP (low Mg2+ and GTP concentrations, high tubulin concentrations, and in the presence of exogenous GDP). These findings led us to explore further interrelationships of tubulin-GDP and tubulin-GTP in microtubule assembly. We have now determined the minimum amount of tubulin-GTP required for the initiation of microtubule assembly and the relative efficiency with which tubulin-GDP participates in microtubule elongation. When GTP, GDP, and tubulin concentrations were varied at a constant Mg2+ concentration (0.2 mM), initiation of assembly required that 35% of the nucleotide-bearing tubulin be in the form of tubulin-GTP, and incorporation of tubulin-GDP into microtubules during elongation was only 60% as efficient as would be predicted on the basis of its proportional concentration in the reaction mixtures. Very different results were obtained when the Mg2+ concentration was varied. Even though Mg2+ enhances the binding of GTP to tubulin (the equilibrium constant for the exchange of GTP for GDP was 0.2 in the absence of exogenous Mg2+, 3 with 0.2 mM Mg2+, 5 with 0.5 mM Mg2+, and 11 with 2 and 4 mM Mg2+), as Mg2+ was increased the proportion of tubulin-GTP required for the initiation of microtubule assembly rose greatly, and the direct incorporation of tubulin-GDP into microtubules during elongation became progressively more efficient. In the absence of exogenous Mg2+, only 20% tubulin-GTP was required for initiation, and tubulin-GDP was directly incorporated into microtubules half as efficiently as would be predicted on the basis of its concentration in the reaction mixture. At the highest Mg2+ concentration examined (4 mM), 80% tubulin-GTP was required for initiation of assembly, and tubulin-GDP was incorporated into microtubules as efficiently as tubulin-GTP.     

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.     

Opposite-end behaviour of dynamic microtubules

Microtubules are dynamic polar structures with different kinetic properties at the two ends. The inherent asymmetry of the microtubule lattice determines that the relationship between the addition reaction of tubulin-GTP and the associated hydrolysis of a tubulin-GTP on the polymer is different at the two ends of the microtubule. We present a unified treatment for both ends of the microtubule, using the principles of the Lateral Cap formulation for microtubule dynamic instability. This shows that the two ends can exhibit significantly different dynamic properties in terms of amplitudes and lifetimes of growth and shrinking, depending on the relative importance of longitudinal and lateral contacts in the coupling of tubulin-GTP hydrolysis. These predictions are readily amenable to experimental verification. This modelling suggests that fine details of the subunit-subunit interactions at the microtubule end can determine the characteristic differences in kinetic behaviour of the opposite ends of dynamic microtubules. Variation of these interactions would provide a potentially sensitive general mechanism for the control of such dynamics, both in vitro and in vivo.     

The effect of podophyllotoxin on microtubule dynamics

We have investigated the effects of podophyllotoxin on the dynamic properties of microtubules assembled from pure tubulin dimer. Excess podophyllotoxin causes the complete disassembly of microtubules, through formation of a tubulin-GTP-podophyllotoxin ternary complex with a dissociation rate constant of 160 s-1 at 37 degrees C, similar to that found upon extensive isothermal dilution in this buffer system. Addition of substoichiometric concentrations of podophyllotoxin causes partial disassembly of microtubules through production of an equivalent amount of the ternary complex. Microtubule length measurements and incorporation of [3H]GTP-tubulin dimer show that podophyllotoxin can suppress the dynamic instability of tubulin dimer microtubules and that it acts substoichiometrically in so doing. We interpret the action of substoichiometric podophyllotoxin on microtubule ends in terms of effects on interconversion of growing and shrinking microtubules in a dynamic system in which tubulin-GTP-podophyllotoxin is kinetically analogous to tubulin-GTP in addition and to tubulin-GDP in dissociation. The ability to suppress dynamic instability may be one way in which drugs such as podophyllotoxin, acting at relatively low concentrations, are able to arrest cell growth and development in a selective way, without necessarily affecting the integrity of the major part of the cytoskeletal microtubule network.     

Microtubule dynamics.

Although compelling evidence has been obtained for heterogeneity in the structure of subunits in microtubules, it has not been possible to prove that this results from the presence of tubulin-GDP and tubulin-GTP in polymers. There are reasons to exclude the existence of even a monolayer of tubulin-GTP subunits at microtubule ends. Dynamic behavior appears to be best accounted for by a mechanism in which tubulin-GDP in microtubules exists in two conformations. The mechanism of microtubule-associated protein binding to microtubules and the role of phosphorylation on this reaction are discussed.     

Microtubules cut and run

There is broad agreement that cells reconfigure their microtubules through rapid bouts of assembly and disassembly, as described by the mechanism known as dynamic instability. However, many cell types have complex patterns of microtubule organization that are not entirely explicable by dynamic instability. There is growing evidence that microtubules can be moved into new patterns of organization by forces generated by molecular motor proteins. Studies on several cell types support a model called 'cut and run' in which long microtubules are stationary, but relatively short microtubules are mobile. In this model, cells mobilize their microtubules by severing them into short pieces, using enzymes such as katanin and spastin that break the lattice of the microtubule polymer. After being reorganized, the short microtubules can once again elongate and lose their mobility. Microtubule severing is also crucial for a variation of 'cut and run' in which the severed microtubules are reorganized by means of treadmilling.     

Mechanochemical model of microtubule structure and self-assembly kinetics

Microtubule self-assembly is largely governed by the chemical kinetics and thermodynamics of tubulin-tubulin interactions. An important aspect of microtubule assembly is that hydrolysis of the beta-tubulin-associated GTP promotes protofilament curling. Protofilament curling presumably drives the transition from tip structures associated with growth (sheetlike projections and blunt ends) to those associated with shortening (rams' horns and frayed ends), and transitions between these structures have been proposed to be important for growth-shortening transitions. However, previous models for microtubule dynamic instability have not considered such structures or mechanics explicitly. Here we present a three-dimensional model that explicitly incorporates mechanical stress and strain within the microtubule lattice. First, we found that the model recapitulates three-dimensional tip structures and rates of assembly and disassembly for microtubules grown under standard conditions, and we propose that taxol may stabilize microtubule growth by reducing flexural rigidity. Second, in contrast to recent suggestions, it was determined that sheetlike tips are more likely to undergo catastrophe than blunt tips. Third, partial uncapping of the tubulin-GTP cap provides a possible mechanism for microtubule pause events. Finally, simulations of the binding and structural effects of XMAP215 produced the experimentally observed growth and shortening rates, and tip structure.     

Towards an understanding of microtubule function and cell organization: an overview.

Microtubules exhibit dynamic instability, converting abruptly between assembly and disassembly with continued growth dependent on the presence of a tubulin-GTP cap at the plus end of the organelle. Tubulin, the main structural protein of microtubules, is a heterodimer composed of related polypeptides termed alpha-tubulin and beta-tubulin. Most eukaryotic cells possess several isoforms of the alpha- and beta-tubulins, as well as gamma-tubulin, an isoform restricted to the centrosome. The isoforms of tubulin arise either as the products of different genes or by posttranslational processes and their synthesis is subject to regulation. Tubulin isoforms coassemble with one another and isoform composition does not appear to determine whether a microtubule is able to carry out one particular activity or another. However, the posttranslational modification of polymerized tubulin may provide chemical signals which designate microtubules for a certain function. Microtubules interact with proteins called microtubule-associated proteins (MAPs) and they can be divided into two groups. The structural MAPs stimulate tubulin assembly, enhance microtubule stability, and influence the spatial distribution of microtubules within cells. The dynamic MAPs take advantage of microtubule polarity and organization to vectorially translocate cellular components. The interactions between microtubules and MAPs contribute to the structural-functional integration that characterizes eukaryotic cells.     

Effects of GDP on microtubules at steady state

We have re-examined the effect of varying GDP concentrations on the kinetics of GTP-induced assembly of microtubules from microtubule protein, and on the elongation of pre-existing microtubules subjected to a temperature jump relaxation from 21.5 to 37 degrees C. The assembly kinetics follow a simple model for assembly which involves a fast equilibrium of tubulin-GTP and tubulin-GDP coupled to the elongation process due to tubulin-GTP. The initial rate of the relaxation process is found to be dependent upon the GTP/GDP ratio, in confirmation of the results of Engelborghs and Van Houtte (Biophys. Chem. 14 (1981) 195). As an alternative to the interpretation previously advanced by them, involving modification of the reactivity of microtubule ENDs by GDP, we show that this result is consistent with the above model with one reasonable modification, namely, that the ratio of the affinities of tubulin for GTP and GDP should vary with temperature. The analysis shows that a decrease in this ratio of approx. 2-fold at 37 degrees C accounts for the observed effects. We conclude that more complex mechanisms involving consideration of modification of the reactivity of microtubule ENDs by GDP are not required to explain these results. This finding has important implications for current models of GDP-induced microtubule disassembly.     

Estimation of the diffusion-limited rate of microtubule assembly.

Microtubule assembly is a complex process with individual microtubules alternating stochastically between extended periods of assembly and disassembly, a phenomenon known as dynamic instability. Since the discovery of dynamic instability, molecular models of assembly have generally assumed that tubulin incorporation into the microtubule lattice is primarily reaction-limited. Recently this assumption has been challenged and the importance of diffusion in microtubule assembly dynamics asserted on the basis of scaling arguments, with tubulin gradients predicted to extend over length scales exceeding a cell diameter, approximately 50 microns. To assess whether individual microtubules in vivo assemble at diffusion-limited rates and to predict the theoretical upper limit on the assembly rate, a steady-state mean-field model for the concentration of tubulin about a growing microtubule tip was developed. Using published parameter values for microtubule assembly in vivo (growth rate = 7 microns/min, diffusivity = 6 x 10(-12) m2/s, tubulin concentration = 10 microM), the model predicted that the tubulin concentration at the microtubule tip was approximately 89% of the concentration far from the tip, indicating that microtubule self-assembly is not diffusion-limited. Furthermore, the gradients extended less than approximately 50 nm (the equivalent of about two microtubule diameters) from the microtubule tip, a distance much less than a cell diameter. In addition, a general relation was developed to predict the diffusion-limited assembly rate from the diffusivity and bulk tubulin concentration. Using this relation, it was estimated that the maximum theoretical assembly rate is approximately 65 microns/min, above which tubulin can no longer diffuse rapidly enough to support faster growth.     

A Metastable Intermediate State of Microtubule Dynamic Instability That Differs Significantly between Plus and Minus Ends

The current two-state GTP cap model of microtubule dynamic instability proposes that a terminal crown of GTP-tubulin stabilizes the microtubule lattice and promotes elongation while loss of this GTP-tubulin cap converts the microtubule end to shortening. However, when this model was directly tested by using a UV microbeam to sever axoneme-nucleated microtubules and thereby remove the microtubule's GTP cap, severed plus ends rapidly shortened, but severed minus ends immediately resumed elongation (Walker, R.A., S. Inoué, and E.D. Salmon. 1989. J. Cell Biol. 108: 931–937).

To determine if these previous results were dependent on the use of axonemes as seeds or were due to UV damage, or if they instead indicate an intermediate state in cap dynamics, we performed UV cutting of self-assembled microtubules and mechanical cutting of axoneme-nucleated microtubules. These independent methods yielded results consistent with the original work: a significant percentage of severed minus ends are stable after cutting. In additional experiments, we found that the stability of both severed plus and minus ends could be increased by increasing the free tubulin concentration, the solution GTP concentration, or by assembling microtubules with guanylyl-(α,β)-methylene-diphosphonate (GMPCPP).

Our results show that stability of severed ends, particularly minus ends, is not an artifact, but instead reveals the existence of a metastable kinetic intermediate state between the elongation and shortening states of dynamic instability. The kinetic properties of this intermediate state differ between plus and minus ends. We propose a three-state conformational cap model of dynamic instability, which has three structural states and four transition rate constants, and which uses the asymmetry of the tubulin heterodimer to explain many of the differences in dynamic instability at plus and minus ends.

     

Stabilization of microtubules by tubulin-GDP-Pi subunits

Microtubule dynamic instability has been accounted for by assuming that tubulin subunits at microtubule ends differ from the tubulin-GDP subunits that constitute the bulk of the microtubule. It has been suggested that this heterogeneity results because ends contain tubulin subunits that have not yet hydrolyzed an associated GTP molecule. Alternatively, in a recent model it was proposed that ends contain tubulin-GDP-Pi subunits from which Pi has not yet dissociated. The models differ in their predicted response to added ligands: because GDP in subunits in microtubules does not exchange with nucleotide in solution, the heterogeneity from a tubulin-GTP cap will not be eliminated by added GTP; however, the dissociability of Pi in tubulin-GDP-Pi subunits will allow a heterogeneity resulting from a tubulin-GDP-Pi cap to be eliminated by added excess Pi. Elimination of the heterogeneity is expected to be manifested by an elimination of dynamic instability behavior. Using video microscopy to study the kinetic behavior of individual microtubules under reaction conditions where dynamic instability is the dominant mechanism for microtubule length changes, we have determined the effects of 0.167 M Pi on the rate of subunit addition in the elongation phase, the rate of subunit dissociation in the rapid shortening phase, and the rates of the phase transitions from elongation to rapid shortening and from rapid shortening to growing. Since 0.167 M Pi did not decrease the subunit dissociation rate in the rapid shortening phase or the rate of the phase transition from growing to rapid shortening, our results provide no support for the hypothesis that tubulin-GDP-Pi subunits are responsible for dynamic instability behavior of microtubules.(ABSTRACT TRUNCATED AT 250 WORDS)     

Mechanism of GTP hydrolysis at microtubule ends

The kinetics of tubulin subunits incorporation into microtubules and the kinetics of inorganic phosphate release have been measured in parallel. Correlation of the two measurements indicates that the tubulin GTPase activity is due to GTP hydrolysis and exchange at the end of the microtubules. In some cases where the free GTP available in the medium is in-sufficient the rate of GTP hydrolysis is limited by the rate of tubulin-GTP association at the end of the microtubules. The affinity constant of GTP for the microtubule end appears to be 100 times lower than the affinity constant of the tubulin-GTP complex.     

G protein alpha subunits activate tubulin GTPase and modulate microtubule polymerization dynamics

G proteins serve many functions involving the transfer of signals from cell surface receptors to intracellular effector molecules. Considerable evidence suggests that there is an interaction between G proteins and the cytoskeleton. In this report, G protein alpha subunits Gi1alpha, Gsalpha, and Goalpha are shown to activate the GTPase activity of tubulin, inhibit microtubule assembly, and accelerate microtubule dynamics. Gialpha inhibited polymerization of tubulin-GTP into microtubules by 80-90% in the absence of exogenous GTP. Addition of exogenous GTP, but not guanylylimidodiphosphate, which is resistant to hydrolysis, overcame the inhibition. Analysis of the dynamics of individual microtubules by video microscopy demonstrated that Gi1alpha increases the catastrophe frequency, the frequency of transition from growth to shortening. Thus, Galpha may play a role in modulating microtubule dynamic instability, providing a mechanism for the modification of the cytoskeleton by extracellular signals.     

Insights into allosteric control of microtubule dynamics from a buried β‐tubulin mutation that causes faster growth and slower shrinkage

αβ‐tubulin subunits cycle through a series of different conformations in the polymer lattice during microtubule growing and shrinking. How these allosteric responses to different tubulin:tubulin contacts contribute to microtubule dynamics, and whether the contributions are evolutionarily conserved, remains poorly understood. Here, we sought to determine whether the microtubule‐stabilizing effects (slower shrinking) of the β:T238A mutation we previously observed using yeast αβ‐tubulin would generalize to mammalian microtubules. Using recombinant human microtubules as a model, we found that the mutation caused slow microtubule shrinking, indicating that this effect of the mutation is indeed conserved. However, unlike in yeast, β:T238A human microtubules grew faster than wild‐type and the mutation did not appear to attenuate the conformational change associated with guanosine 5′‐triphosphate (GTP) hydrolysis in the lattice. We conclude that the assembly‐dependent conformational change in αβ‐tubulin can contribute to determine the rates of microtubule growing as well as shrinking. Our results also suggest that an allosteric perturbation like the β:T238A mutation can alter the behavior of terminal subunits without accompanying changes in the conformation of fully surrounded subunits in the body of the microtubule.     

Differentiation between dynamic instability and end-to-end annealing models for length changes of steady-state microtubules

Short microtubules can be formed by shearing a sample at polymerization steady state of microtubules formed by glycerol-induced assembly of pure tubulin dimer. Such short microtubules show a rapid increase in mean length. The rate of this increase is too fast to be accounted for by statistical redistribution of subunits between microtubules. We propose that the fast length changes are a result of the end-to-end annealing of microtubules demonstrated by Rothwell et al. (Rothwell, S. W., Grasser, W. A., and Murphy, D. B. (1986) J. Cell Biol. 102, 619-627). This proposal has been tested by measuring the rate of annealing of free microtubules to Tetrahymena axonemes under conditions identical to those used for the lengthening of sheared microtubules. That free microtubules anneal to axonemal microtubules is indicated by the following observations. Axonemes elongate at both ends in the presence of steady state microtubules, as predicted for a symmetrical annealing process; under conditions where the microtubule number concentration is greater than that for axonemes, the initial rate of axoneme elongation is more rapid with a low concentration of long microtubules at steady state than with a high number concentration of short microtubules at steady state. These observations are inconsistent with the predictions of a model based on microtubule dynamic instability (Mitchison, T., and Kirschner, M. (1984) Nature 312, 237-242). The annealing rate observed with axonemes can account for the rate of elongation of sheared steady state microtubules.