Brownian Dynamics of Subunit Addition-Loss Kinetics and Thermodynamics in Linear Polymer Self-Assembly

The structure and free energy of multistranded linear polymer ends evolves as individual subunits are added and lost. Thus, the energetic state of the polymer end is not constant, as assembly theory has assumed. Here we utilize a Brownian dynamics approach to simulate the addition and loss of individual subunits at the polymer tip. Using the microtubule as a primary example, we examined how the structure of the polymer tip dictates the rate at which units are added to and lost from individual protofilaments. We find that freely diffusing subunits arrive less frequently to lagging protofilaments but bind more efficiently, such that there is no kinetic difference between leading and lagging protofilaments within a tapered tip. However, local structure at the nanoscale has up to an order-of-magnitude effect on the rate of addition. Thus, the kinetic on-rate constant, integrated across the microtubule tip (k_on,MT), is an ensemble average of the varying individual protofilament on-rate constants (k_on,PF). Our findings have implications for both catastrophe and rescue of the dynamic microtubule end, and provide a subnanoscale framework for understanding the mechanism of action of microtubule-associated proteins and microtubule-directed drugs. Although we utilize the specific example of the microtubule here, the findings are applicable to multistranded polymers generally.     

The minimum GTP cap required to stabilize microtubules

Background: Microtubules polymerized from pure tubulin show the unusual property of dynamic instability, in which both growing and shrinking polymers coexist at steady state. Shortly after its addition to a microtubule end, a tubulin subunit hydrolyzes its bound GTP. Studies with non-hydrolyzable analogs have shown that GTP hydrolysis is not required for microtubule assembly, but is essential for generating a dynamic polymer, in which the subunits at the growing tip have bound GTP and those in the bulk of the polymer have bound GDP. It has been suggested that loss of the ‘GTP cap’ through dissociation or hydrolysis exposes the unstable GDP core, leading to rapid depolymerization. However, evidence for a stabilizing cap has been very difficult to obtain.Results We developed an assay to determine the minimum GTP cap necessary to stabilize a microtubule from shrinking. Assembly of a small number of subunits containing a slowly hydrolyzed GTP analog (GMPCPP) onto the end of dynamic microtubules stabilized the polymer to dilution. By labeling the subunits with rhodamine, we measured the size of the cap and found that as few as 40 subunits were sufficient to stabilize a microtubule.Conclusion On the basis of statistical arguments, in which the proportion of stabilized microtubules is compared to the probability that when 40 GMPCPP-tubulin subunits have polymerized onto a microtubule end, all protofilaments have added at least one GMPCPP-tubulin subunit, our measurements of cap size support a model in which a single GTP subunit at the end of each of the 13 protofilaments of a microtubule is sufficient for stabilization. Depolymerization of a microtubule may be initiated by an exposed tubulin–GDP subunit at even a single position. These results have implications for the structure of microtubules and their means of regulation.     

Structure of the tubulin dimer in zinc-induced sheets

The structure of tubulin has been studied in projection by minimum beam electron microscopy and image processing of negatively stained zinc-induced sheets. The reconstructed images include data to 15 Å resolution.We report here a clear and reproducible 82 Å repeat arising from the arrangement of heterodimers in sheet aggregates of tubulin. This repeat is only observed in diffraction patterns from images recorded by minimum beam methods (10 to 20 e/Ų) and arises from small, but consistent, structural differences between two similar subunits believed to represent the two chemical species of tubulin monomer (M_r, 55,000). At higher electron doses (100 to 200 e/Ų), the additional information is lost or very much reduced, and only a repeat of 41 Å is observed, owing to the loss of distinction between monomers in the tubulin heterodimer.The sheets are composed of 49 Å wide, polar protofilaments, similar to those observed in microtubules; however, the interprotofilament packing is completely different in the two structures. In these sheets, adjacent protofilaments point and face in opposite directions; i.e. they are related by dyad-screw axes normal to the protofilament axes and in the plane of the sheet. Thus, the zinc-induced sheets are crystals of space group P2₁, with cell dimensions of about 97 Å × 82 Å, containing one tubulin heterodimer per asymmetric unit.Reconstructed images of four individual sheets, and their average, show the arrangement and shapes of the two heterodimers contained in each unit cell. The structure and packing of heterodimers in sheets are compared to those in opened out microtubules where all protofilaments point and face in the same direction.     

Evidence for a mixed lattice in microtubules reassembled in vitro

An extensive structural analysis of microtubules assembled in vitro has been carried out using electron microscopy in conjunction with computer analysis based on Fourier transforms and helical diffraction theory. Microtubules assembled in vitro displayed a range of numbers of protofilaments from 12 to 16, with 14 the most abundant (84% in one large sampling). In almost all structures observed protofilaments are staggered to form a characteristic 3-start shallow helix. The presence of the 3-start helix was confirmed by fiber tilting experiments to correct the effects of microtubule flattening. Since α and β tubulin subunits alternate along the protofilaments, continuous helical lattices can be constructed with interactions between adjacent protofilaments involving unlike subunits (type A lattice) or like subunits (type B lattice). However, the 14-protofilament, 3-start microtubules are incompatible with either the A or B-type continuous helical lattice. Evidence is presented which indicates that lattice discontinuities are present which generate features of both the A and B-types, with the latter predominating.     

Distribution of substituents in O-(2-hydroxyethyl)cellulose: A 13C-N.M.R. approach

O-(2-Hydroxyethyl)cellulose was converted into a mixture of the corresponding d-glucitol derivatives by hydrolysis followed by reduction of the sugars with NaBH₄. On the basis of the spectra of individual O-(2-hydroxyethyl)-d-glucitols, the ¹³C-n.m.r. spectrum of this mixture was assigned to the extent that permitted quantitative analysis in terms of monomer composition of the polymer. The monomer mole-fractions conform to a statistical, kinetic model that assumes that the reactivity of the 3-hydroxyl group of the d-glucosyl residues of cellulose depends on the state of substitution at O-2. The relative rate-constants of the hydroxyl groups in the (hydroxyethyl)ation reaction are k₂:k₃:k₃′:k₆:k_x = 6.0:1.0:4.0:11.1:34.6, indicating that the reactivity of OH-3 increases fourfold upon (hydroxyethyl)ation of OH-2.     

Diameters of microtubules change during rotation of the lipotubuloids of Ornithogalum umbellatum stipule epidermis as a result of varying protofilament monomers sizes and distance between them

Microtubules in lipotubuloids of the Ornithogalum umbellatum stipule epidermis cells change their diameters depending on the motion of the cytoplasmic domains rich in microtubules and lipid bodies. Microtubules fixed during rotary and progressive motion of the lipotubuloids composed of the same number of protofilaments fall into two populations – wide (43–58 nm) and narrow (24–39 nm) in size. Following blockage of the motion with 2,4-dinitrophenol (DNP), the range of this diversity is smaller, microtubules become a medium-sized population (34–48 nm). When DNP is removed and the motion reactivated, 2 populations of microtubules reappear. Analysis of the structure of the microtubule wall revealed that changes in the microtubule diameters resulted from varying distances between the adjacent protofilaments, and stretching and compression of tubulin subunits in the protofilaments.A supposition has been put forward that the changes in the sizes of O. umbellatum microtubule diameters: 1) are connected with the interactions between microtubules and actin microfilaments lying along these microtubules; 2) can be the driving force of the rotary motion of lipotubuloids.     

Resolving the molecular structure of microtubules under physiological conditions with scanning force microscopy

We have imaged microtubules, essential structural elements of the cytoskeleton in eukaryotic cells, in physiological conditions by scanning force microscopy. We have achieved molecular resolution without the use of cross-linking and chemical fixation methods. With tip forces below 0.3 nN, protofilaments with ~6 nm separation could be clearly distinguished. Lattice defects in the microtubule wall were directly visible, including point defects and protofilament separations. Higher tip forces destroyed the top half of the microtubules, revealing the inner surface of the substrate-attached protofilaments. Monomers could be resolved on these inner surfaces.Abbreviations APTS (3-aminopropyl)triethoxysilane - DETA N¹-[3-(trimethoxysilyl)propyl]diethylenetriamine - EM electron microscopy - MT microtubule - SFM scanning force microscopy     

Three-dimensional reconstruction of tubulin in zinc-induced sheets: II. Consequences of removal of microtubule associated proteins

The three-dimensional structure of zinc-induced tubulin sheets freed of microtubule associated proteins has been determined to 20 Å resolution by electron microscopy and image reconstruction. The determination was carried out with porcine brain tubulin separated from microtubule associated proteins by phosphocellulose chromatography. Negatively stained samples were tilted using the goniometer stage of the electron microscope to provide images of the tubulin sheets ranging in tilt from ?60 ° to +60 °. The micrographs were digitized and subjected to a cross-correlation analysis to compensate for smooth curvature of the lattice in the sheets. For each angle of tilt, an average unit cell was obtained from the cross-correlation analysis and subsequently a Fourier transform was computed for inclusion in the three-dimensional Fourier data set. The transforms of 47 tilted images plus the average of five untilted sheets were combined and an inverse Fourier transform was applied to give a threedimensional reconstruction of the microtubule associated protein-free tubulin sheets. Comparison of the protofilament structure in these sheets with the previously published protofilament structure of zinc-induced tubulin sheets containing microtubule associated proteins reveals a number of consequences of the removal of microtubule associated proteins. (1) The extensive internal contact along the protofilament observed in microtubule associated protein-containing tubulin sheets is maintained in microtubule associated protein-free tubulin sheets. (2) In projection, the protofilaments in microtubule associated protein-free tubulin sheets are 2.2 Å closer together than in microtubule associated protein-tubulin sheets. (3) The deviations of adjacent protofilaments from the plane of the sheets when viewed end-on are more pronounced in the absence of microtubule associated proteins. Differences are also observed at the level of individual tubulin subunits. In particular, the distinct cleft which was found in one class of subunits in tubulin sheets with microtubule associated proteins is absent in the microtubule associated protein-free tubulin sheets. The loss of this cleft and some changes in the shape of the tubulin subunits upon removal of microtubule associated proteins suggest a possible site for the interaction of tubulin with microtubule associated proteins.     

Microtubule structure at improved resolution.

Microtubule architecture can vary with eukaryotic species, with different cell types, and with the presence of stabilizing agents. For in vitro assembled microtubules, the average number of protofilaments is reduced by the presence of sarcodictyin A, epothilone B, and eleutherobin (similarly to taxol) but increased by taxotere. Assembly with a slowly hydrolyzable GTP analogue GMPCPP is known to give 96% 14 protofilament microtubules. We have used electron cryomicroscopy and helical reconstruction techniques to obtain three-dimensional maps of taxotere and GMPCPP microtubules incorporating data to 14 A resolution. The dimer packing within the microtubule wall is examined by docking the tubulin crystal structure into these improved microtubule maps. The docked tubulin and simulated images calculated from "atomic resolution" microtubule models show tubulin heterodimers are aligned head to tail along the protofilaments with the beta subunit capping the microtubule plus end. The relative positions of tubulin dimers in neighboring protofilaments are the same for both types of microtubule, confirming that conserved lateral interactions between tubulin subunits are responsible for the surface lattice accommodation observed for different microtubule architectures. Microtubules with unconventional protofilament numbers that exist in vivo are likely to have the same surface lattice organizations found in vitro. A curved "GDP" tubulin conformation induced by stathmin-like proteins appears to weaken lateral contacts between tubulin subunits and could block microtubule assembly or favor disassembly. We conclude that lateral contacts between tubulin subunits in neighboring protofilaments have a decisive role for microtubule stability, rigidity, and architecture.     

Microtubules with different diameter, protofilament number and protofilament spacing in Ornithogalum umbellatum ovary epidermis cells

Microtubules present in the epidermis of Ornithogalum umbellatum ovary in the area of lipotubuloids (i.e. aggregates of lipid bodies surrounded by microtubules) are 25-51 nm in diameter. They consist mainly of 10 and 11, sometimes 9 and 12 protofilaments. An average diameter of microtubule consisting of 9 subunits is about 32 nm, of 10-35 nm, of 11-38 nm and of 12-43 nm, however, individual microtubules in each category significantly vary in size. These differences result from varying distance between protofilaments in microtubule walls and diameters of protofilaments: in thin microtubules they are densely packed and smaller while in thicker ones they are loosely arranged and bigger. A hypothesis has been put forward that changes in microtubule diameter depend on structural changes associated with their functional status and are executed by modifications of protofilament arrangement density and their diameters in microtubule wall. The above hypothesis seems to be in agreement with the opinion formed on the basis of in vitro image of microtubules, that lateral contact between tubulin subunits in neighboring protofilaments indicates some flexibility and changeability during microtubule function.     

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.     

HURP wraps microtubule ends with an additional tubulin sheet that has a novel conformation of tubulin

HURP is a newly discovered microtubule-associated protein (MAP) required for correct spindle formation both in vitro and in vivo. HURP protein is highly charged with few predicted secondary and tertiary folding domains. Here we explore the effect of HURP on pure tubulin, and describe its ability to induce a new conformation of tubulin sheets that wrap around the ends of intact microtubules, thereby forming two concentric tubes. The inner tube is a normal microtubule, while the outer one is a sheet composed of tubulin protofilaments that wind around the inner tube with a 42.5° inclination. We used cryo-electron microscopy and unidirectional surface shadowing to elucidate the structure and conformation of HURP-induced tubulin sheets and their interaction with the inner microtubule. These studies clarified that HURP-induced sheets are composed of anti-parallel protofilaments exhibiting P2 symmetry. HURP is a unique MAP that not only stabilizes and bundles microtubules, but also polymerizes free tubulin into a new configuration.     

Chromator is required for proper microtubule spindle formation and mitosis in Drosophila

The chromodomain protein, Chromator, has been shown to have multiple functions that include regulation of chromatin structure as well as coordination of muscle remodeling during metamorphosis depending on the developmental context. In this study we show that mitotic neuroblasts from brain squash preparations from larvae heteroallelic for the two Chromator loss-of-function alleles Chro⁷¹ and Chro⁶¹² have severe microtubule spindle and chromosome segregation defects that were associated with a reduction in brain size. The microtubule spindles formed were incomplete, unfocused, and/or without clear spindle poles and at anaphase chromosomes were lagging and scattered. Time-lapse analysis of mitosis in S2 cells depleted of Chromator by RNAi treatment suggested that the lagging and scattered chromosome phenotypes were caused by incomplete alignment of chromosomes at the metaphase plate, possibly due to a defective spindle-assembly checkpoint, as well as of frayed and unstable microtubule spindles during anaphase. Expression of full-length Chromator transgenes under endogenous promoter control restored both microtubule spindle morphology as well as brain size strongly indicating that the observed mutant defects were directly attributable to lack of Chromator function.     

Biochemical and Structural Analyses of Microtubules in the Pellicular Membrane of Leishmania tropica1

The structure of the major protein of the pellicular membrane of Leishmania tropica was investigated. This protein is composed of two polypeptides, of ca. 50,000 d molecular weight, that were found to cross-react immunologically with the α and β subunits of pig brain tubulin. The polypeptides and pig brain tubulin subunits were partially digested with S. aureus V8 protease, and the peptides obtained analysed by SDS-polyacrylamide gel electrophoresis. A comparison of the patterns showed that the β subunits of Leishmania and pig tubulin have very similar primary structures, while the α subunits have evolved divergently. These experiments demonstrate that the major polypeptides found in the pellicular membrane of L. tropica are α and β subunits of tubulin. Immuno-electron microscopy indicates that the tubulin is located in the microtubules associated with the pellicular membrane of Leishmania. Arrays of microtubules were prepared by nonionic detergent treatment of the cells and observed by electron microscopy after negative staining. Optical diffraction reveals a 5 nm spacing between protofilaments in the microtubule and a 4 nm axial periodicity corresponding to the tubulin subunits. The pitch of the shallow left-hand three-start helix is 12°. A distance of 47 nm separates each microtubule from the next. These data show that the dimensions and supramolecular organization of the tubulin subunits in the microtubules are identical in the pellicular membrane of L. tropica and in mammalian brain.     

Interaction of vinblastine with steady-state microtubules in vitro

At low concentrations, vinblastine binds rapidly and reversibly to a very limited number of high affinity sites on steady-state bovine brain microtubules (mean K_d, 1.9 × 10^?6m; 16.8 ± 4.3 vinblastine binding sites per microtubule) which appear to be located at one or both ends of the microtubules. At high concentrations, vinblastine binds to a high binding capacity class of sites of undetermined affinity, located on helical strands of protofilaments which form at the ends of depolymerizing microtubules, and/or along the surface of the microtubules. Substoichiometric inhibition of microtubule assembly, which occurs at low vinblastine concentrations, appears to be due to the binding of vinblastine to the high affinity class of sites. Fifty per cent inhibition of tubulin addition to the net assembly ends of steady-state microtubules occurred at 1.38 × 10^?7m-drug, and at this concentration, 1.16 ± 0.27 molecules of vinblastine were bound to the high affinity class of sites. Vinblastine appeared to bind directly to the microtubule ends, and our results indicate that vinblastine inhibits the assembly of steady-state bovine brain microtubules by binding rapidly and with high affinity to one or two molecules of tubulin at the net assembly ends. Splaying and peeling of protofilaments at microtubule ends and the active depolymerization of microtubules occurred only at vinblastine concentrations greater than 1 × 10^?6 to 2 × 10^?6m. This action of vinblastine is associated with and may be due to the binding of vinblastine to the high capacity class of sites. Both actions of vinblastine may be due to the binding of vinblastine to the same binding sites on the tubulin molecule, with the sites exhibiting either a high or low affinity depending upon the location in the microtubule.     

Head-to-tail polymerization of microtubules in vitro

The kinetics of microtubule polymerization to steady-state and the ability of tubulin subunits to exchange with polymer at steady-state were examined to determine the applicability of the head-to-tail polymerization mechanism (Wegner, 1976) to microtubule assembly in vitro. Under conditions where self-nucleation was a rare event, tubulin was induced to polymerize by the addition of short microtubule fragments, and the kinetics of elongation were analyzed as a pseudofirst-order reaction. At steady-state, a trace amount of [³H]tubulin, prepared by labeling in vivo of chick brain protein, was added to polymerized microtubules and the kinetics of label uptake into polymer were monitored by a rapid centrifugal assay. The isotope exchange kinetics were analyzed according to a theoretical model previously applied to actin polymerization (Wegner, 1976) and extended for the case of microtubule polymerization. The rate of head-to-tail polymerization, expressed as the steady-state subunit flux, was 27·6 ± 7·6 per second at 37 °C. The head-to-tail parameter s, a measure of the efficiency of subunit flux, was 0·26 ± 0·07, indicating that four association and four dissociation events resulted in the flux of one subunit through the polymer at steady-state.The role of GTP in this mechanism of microtubule polymerization was examined by replacement of the nucleotide occupying the exchangeable binding site of tubulin with the non-hydrolyzable GTP analog guanosine 5′-(β,γ-methylene)triphosphate. It was found that the rate of steady-state flux was reduced by two orders of magnitude compared to tubulin polymerized with GTP. The head-to-tail parameter approached its limiting value of zero, indicating greatly reduced efficiency of subunit flux through the polymer in the presence of this analog.In summary, this study demonstrates that microtubules exhibit significant headto-tail polymerization in the presence of GTP and, in keeping with theoretical considerations, provides evidence that nucleotide hydrolysis is required for subunit flux through the polymer.     

The accuracy of the rapid equilibrium assumption in steady-state enzyme kinetics in the case of a multipath arbitrary enzyme mechanism with a number of equilibrium segments

A quantitative evaluation of the accuracy of the rapid-equilibrium assumption in steady-state enzyme kinetics was obtained for a multipath arbitrary enzyme mechanism with a number of equilibrium segments. Explicit expressions for estimating the contribution of any equilibrium segment to the accuracy of the rapid-equilibrium assumption were obtained. This allowed us to determine the accuracy of the rapid-equilibrium assumption (Δ) in general: 1 + Δ = (1 + Δ₁)(1 + Δ₂)... (1 + Δ_k), where Δ₁, Δ₂,..., Δ_k is the contribution of each individual equilibrium segment. The accuracy depends only on the structure and properties of equilibrium segments, which have been accounted for in the rapid-equilibrium assumption, but it is independent of the number of paths in the mechanism of the enzymatic reaction and on the structure and properties of the remaining part (steady-state) of the kinetic scheme.     

Role of tubulin-associated proteins in microtubule nucleation and elongation

Previous experiments have shown that a fraction of microtubule-associated proteins is essential for the self-assembly of microtubules in vitro. When tubulin was titrated with increasing concentrations of these non-tubulin accessory factors, both the rate and extent of polymerization increased in a sigmoidal as opposed to a stoichiometric fashion. The non-tubulin proteins promoted the nucleation of microtubules as determined from the analysis of the kinetics of tubulin selfassembly and the examination of the microtubule length distribution following polymerization. The effect of the non-tubulin factors on microtubule elongation was determined by kinetic experiments in which purified tubulin subunits were added to microtubule seeds and the initial rate of polymerization was measured under conditions where spontaneous self-assembly was below detectable levels. In addition, microtubule growth was also observed when isolated flagellar axonemes were incubated with purified tubulin subunits indicating that the non-tubulin factors were not an absolute requirement for elongation. Analysis of the data in terms of the condensation mechanism of microtubule assembly indicated that the non-tubulin proteins stimulated the growth of microtubules not by increasing the rate of polymerization but by decreasing the rate of depolyerization. The mechanism by which these accessory factors promote tubulin assembly may be summarized as follows: under the conditions employed, they are required for tubulin initiation but not for elongation; the factors affect the extent and net rate at which polymer is formed by binding to the polymer, thereby stabilizing the formed microtubules and consequently shifting the equilibrium to favor assembly.     

Kinetics of hydrolysis of type I,II, and III collagens by the class I and IIClostridium histolyticum collagenases

The kinetics of hydrolysis of rat tendon type I, bovine nasal septum type II, and human placental type III collagens by class I and class IIClostridium histolyticum collagenases (CHC) have been investigated. To facilitate this study, radioassays developed previously for the hydrolysis of these [³H]acetylated collagens by tissue collagenases have been adapted for use with the CHC. While the CHC are known to make multiple scissions in these collagens, the assays are shown to monitor the initial proteolytic events. The individual kinetic parametersk _cat andK _M have been determined for the hydrolysis of all three collagens by both class I and class II CHC. The specific activities of these CHC toward fibrillar type I and III collagens have also been measured. In contrast to human tissue collagenases, neither class of CHC exhibits a marked specificity toward any collagen type either in solution or in fibrillar form. The values of the kinetic parametersk _cat andK _M for the CHC are similar in magnitude to those of the human enzymes acting on their preferred substrates. Thus, the widely held view that the CHC are more potent collagenases is not strictly correct. As with the tissue collagenases, the local collagen structure at the cleavage sites is believed to play an important role in determining the rates of the reactions studied.     

Straight GDP-tubulin protofilaments form in the presence of taxol

Microtubules exist in dynamic equilibrium, growing and shrinking by the addition or loss of tubulin dimers from the ends of protofilaments. The hydrolysis of GTP in beta-tubulin destabilizes the microtubule lattice by increasing the curvature of protofilaments in the microtubule and putting strain on the lattice. The observation that protofilament curvature depends on GTP hydrolysis suggests that microtubule destabilizers and stabilizers work by modulating the curvature of the microtubule lattice itself. Indeed, the microtubule destabilizer MCAK has been shown to increase the curvature of protofilaments during depolymerization. Here, we show that the atomic force microscopy (AFM) of individual tubulin protofilaments provides sufficient resolution to allow the imaging of single protofilaments in their native environment. By using this assay, we confirm previous results for the effects of GTP hydrolysis and MCAK on the conformation of protofilaments. We go on to show that taxol stabilizes microtubules by straightening the GDP protofilament and slowing down the transition of protofilaments from straight to a curved configuration.