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1.
Microtubules are dynamic polymers with central roles in the mitotic checkpoint, mitotic spindle assembly, and chromosome segregation. Agents that block mitotic progression and cell proliferation by interfering with microtubule dynamics (microtubule-targeted tubulin-polymerizing agents (MTPAs)) are powerful antitumor agents. Effects of MTPAs (e.g. paclitaxel) on microtubule dynamics have not yet been directly demonstrated in intact animals, however. Here we describe a method that measures microtubule dynamics as an exchange of tubulin dimers into microtubules in vivo. The incorporation of deuterium ((2)H(2)) from heavy water ((2)H(2)O) into tubulin dimers and polymers is measured by gas chromatography/mass spectrometry. In cultured human lung and breast cancer cell lines, or in tumors implanted into nude mice, tubulin dimers and polymerized microtubules exhibited nearly identical label incorporation rates, reflecting their rapid exchange. Administration of paclitaxel during 24 h of (2)H(2)O labeling in vivo reduced (2)H labeling in polymers while increasing (2)H in dimers, indicating diminished flux of dimers into polymers (i.e. inhibition of microtubule dynamic equilibrium). In vivo inhibition of microtubule dynamics was dose-dependent and correlated with inhibition of DNA replication, a stable isotopic measure of tumor cell growth. In contrast, microtubule polymers from sciatic nerve of untreated mice were not in dynamic equilibrium with tubulin dimers, and paclitaxel increased label incorporation into polymers. Our results directly demonstrate altered microtubule dynamics as an important action of MTPAs in vivo. This sensitive and quantitative in vivo assay of microtubule dynamics may prove useful for pre-clinical and clinical development of the next generation of MTPAs as anticancer drugs.  相似文献   

2.
R H Himes  H W Detrich 《Biochemistry》1989,28(12):5089-5095
The tubulins of Antarctic fishes, purified from brain tissue and depleted of microtubule-associated proteins (MAPs), polymerized efficiently in vitro to yield microtubules at near-physiological and supraphysiological temperatures (5, 10, and 20 degrees C). The dynamics of the microtubules at these temperatures were examined through the use of labeled guanosine 5'-triphosphate (GTP) as a marker for the incorporation, retention, and loss of tubulin dimers. Following attainment of a steady state in microtubule mass at 20 degrees C, the rate of incorporation of [3H]GTP (i.e., tubulin dimers) during pulses of constant duration decreased asymptotically toward a constant, nonzero value as the interval prior to label addition to the microtubule solution increased. Concomitant with the decreasing rate of label incorporation, the average length of the microtubules increased, and the number concentration of microtubules decreased. Thus, redistribution of microtubule lengths (probably via dynamic instability and/or microtubule annealing) appears to be responsible for the time-dependent decrease in the rate of tubulin uptake. When the microtubules had attained both a steady state in mass and a constant length distribution, linear incorporation of labeled tubulin dimers over time occurred at rates of 1.45 s-1 at 5 degrees C, 0.48 s-1 at 10 degrees C, and 0.18 s-1 at 20 degrees C. Thus, the microtubules displayed greater rates of subunit flux, or treadmilling, at lower, near-physiological temperatures. At each temperature, most of the incorporated label was retained by the microtubules during a subsequent chase with excess unlabeled GTP.(ABSTRACT TRUNCATED AT 250 WORDS)  相似文献   

3.
In Arabidopsis thaliana, the microtubule-associated protein AtMAP65-1 shows various functions on microtubule dynamics and organizations. However, it is still an open question about whether AtMAP65-1 binds to tubulin dimers and how it regulates microtubule dynamics. In present study, the tubulin-binding activity of AtMAP65-1 was investigated. Pull-down and co-sedimentation experiments demonstrated that AtMAP65-1 bound to tubulin dimers, at a molar ratio of 1 : 1. Cross-linking experiments showed that AtMAP65-1 bound to tubulin dimers by interacting with alpha-tubulin of the tubulin heterodimer. Interfering the bundling effect of AtMAP65-1 by addition of salt and monitoring the tubulin assembly, the experiment results indicated that AtMAP65-1 promoted tubulin assembly by interacting with tubulin dimers. In addition, five truncated versions of AtMAP65-1, namely AtMAP65-1 deltaN339 (amino acids 340-587); AtMAP65-1 deltaN494 (amino acids 495-587); AtMAP65-1 340-494 (amino acids 340-494); AtMAP65-1 deltaC495 (amino acids 1-494) and AtMAP65-1 deltaC340 (amino acids 1-339), were tested for their binding activities and roles in tubulin polymerization in vitro. Four (AtMAP65-1 deltaN339, deltaN494, AtMAP65-1 340-494 and deltaC495) from the five truncated proteins were able to co-sediment with microtubules, and three (AtMAP65-1 deltaN339, deltaN494 and AtMAP65-1 340-494) of them could bind to tubulin dimers in vitro. Among the three truncated proteins, AtMAP65-1 deltaN339 showed the greatest activity to promote tubulin polymerization, AtMAP65-1 deltaN494 exhibited almost the same activity as the full length protein in promoting tubulin assembly, and AtMAP65-1 340-494 had minor activity to promote tubulin assembly. On the contrast, AtMAP65-1 deltaC495, which bound to microtubules but not to tubulin dimers, did not affect tubulin assembly. Our study suggested that AtMAP65-1 might promote tubulin assembly by binding to tubulin dimers in vivo.  相似文献   

4.
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.  相似文献   

5.
Almost 40 years since the discovery of microtubule dynamic instability, the molecular mechanisms underlying microtubule dynamics remain an area of intense research interest. The “standard model” of microtubule dynamics implicates a “cap” of GTP-bound tubulin dimers at the growing microtubule end as the main determinant of microtubule stability. Loss of the GTP-cap leads to microtubule “catastrophe,” a switch-like transition from microtubule growth to shrinkage. However, recent studies, using biochemical in vitro reconstitution, cryo-EM, and computational modeling approaches, challenge the simple GTP-cap model. Instead, a new perspective on the mechanisms of microtubule dynamics is emerging. In this view, highly dynamic transitions between different structural conformations of the growing microtubule end – which may or may not be directly linked to the nucleotide content at the microtubule end – ultimately drive microtubule catastrophe.  相似文献   

6.
Estimation of the diffusion-limited rate of microtubule assembly.   总被引:2,自引:0,他引:2       下载免费PDF全文
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.  相似文献   

7.
Microtubules have been in the focus of biophysical research for several decades. However, the confusing and mutually contradictory results regarding their elasticity and fluctuations have cast doubt on their present understanding. In this paper, we present the empirical evidence for the existence of discrete guanosine diphosphate (GDP)–tubulin fluctuations between a curved and a straight configuration at room temperature as well as for conformational tubulin cooperativity. Guided by a number of experimental findings, we build the case for a novel microtubule model, with the principal result that microtubules can spontaneously form micron-sized cooperative helical states with unique elastic and dynamic features. The polymorphic dynamics of the microtubule lattice resulting from the tubulin bistability quantitatively explains several experimental puzzles, including anomalous scaling of dynamic fluctuations of grafted microtubules, their apparent length–stiffness relation, and their remarkable curved–helical appearance in general. We point out that the multistability and cooperative switching of tubulin dimers could participate in important cellular processes, and could in particular lead to efficient mechanochemical signaling along single microtubules.  相似文献   

8.
SCG10 (superior cervical ganglia neural-specific 10 protein) is a neuron specific member of the stathmin family of microtubule regulatory proteins that like stathmin can bind to soluble tubulin and depolymerize microtubules. The direct actions of SCG10 on microtubules themselves and on their dynamics have not been investigated previously. Here, we analyzed the effects of SCG10 on the dynamic instability behavior of microtubules in vitro, both at steady state and early during microtubule polymerization. In contrast to stathmin, whose major action on dynamics is to destabilize microtubules by increasing the switching frequency from growth to shortening (the catastrophe frequency) at microtubule ends, SCG10 stabilized the plus ends both at steady state and early during polymerization by increasing the rate and extent of growth. For example, early during polymerization at high initial tubulin concentrations (20 microM), a low molar ratio of SCG10 to tubulin of 1:30 increased the growth rate by approximately 50%. In contrast to its effects at plus ends, SCG10 destabilized minus ends by increasing the shortening rate, the length shortened during shortening events, and the catastrophe frequency. Consistent with its ability to modulate microtubule dynamics at steady state, SCG10 bound to purified microtubules along their lengths. The dual activity of SCG10 at opposite microtubule ends may be important for its role in regulating growth cone microtubule dynamics. SCG10's ability to promote plus end growth may facilitate microtubule extension into filopodia, and its ability to destabilize minus ends could provide soluble tubulin for net plus end elongation.  相似文献   

9.
In neurons, the regulation of microtubules plays an important role for neurite outgrowth, axonal elongation, and growth cone steering. SCG10 family proteins are the only known neuronal proteins that have a strong destabilizing effect, are highly enriched in growth cones and are thought to play an important role during axonal elongation. MAP1B, a microtubule-stabilizing protein, is found in growth cones as well, therefore it was important to test their effect on microtubules in the presence of both proteins. We used recombinant proteins in microtubule assembly assays and in transfected COS-7 cells to analyze their combined effects in vitro and in living cells, respectively. Individually, both proteins showed their expected activities in microtubule stabilization and destruction respectively. In MAP1B/SCG10 double-transfected cells, MAP1B could not protect microtubules from SCG10-induced disassembly in most cells, in particular not in cells that contained high levels of SCG10. This suggests that SCG10 is more potent to destabilize microtubules than MAP1B to rescue them. In microtubule assembly assays, MAP1B promoted microtubule formation at a ratio of 1 MAP1B per 70 tubulin dimers while a ratio of 1 SCG10 per two tubulin dimers was needed to destroy microtubules. In addition to its known binding to tubulin dimers, SCG10 binds also to purified microtubules in growth cones of dorsal root ganglion neurons in culture. In conclusion, neuronal microtubules are regulated by antagonistic effects of MAP1B and SCG10 and a fine tuning of the balance of these proteins may be critical for the regulation of microtubule dynamics in growth cones.  相似文献   

10.
BACKGROUND: CLIP-170 is a microtubule binding protein specifically located at microtubule plus ends, where it modulates their dynamic properties and their interactions with intracellular organelles. The mechanism by which CLIP-170 is targeted to microtubule ends remains unclear today, as well as its precise effect on microtubule dynamics. RESULTS: We used the N-terminal part of CLIP-170 (named H2), which contains the microtubule binding domains, to investigate how it modulates in vitro microtubule dynamics and structure. We found that H2 primarily promoted rescues (transitions from shrinkage to growth) of microtubules nucleated from pure tubulin and isolated centrosomes, and stimulated microtubule nucleation. Electron cryomicroscopy revealed that H2 induced the formation of tubulin rings in solution and curved oligomers at the extremities of microtubules in assembly conditions. CONCLUSIONS: These results suggest that CLIP-170 targets specifically at microtubule plus ends by copolymerizing with tubulin and modulates microtubule nucleation, polymerization, and rescues by the same basic mechanism with tubulin oligomers as intermediates.  相似文献   

11.
Microtubules are intrinsically dynamic polymers. Two kinds of dynamic behaviors, dynamic instability and treadmilling, are important for microtubule function in cells. Both dynamic behaviors appear to be tightly regulated, but the cellular molecules and the mechanisms responsible for the regulation remain largely unexplored. While microtubule dynamics can be modulated transiently by the interaction of regulatory molecules with soluble tubulin, the microtubule itself is likely to be the primary target of cellular molecules that regulate microtubule dynamics. The antimitotic drugs that modulate microtubule dynamics serve as excellent models for such cellular molecules. Our laboratory has been investigating the interactions of small drug molecules and stabilizing microtubule-associated proteins (MAPs) with microtubule surfaces and ends. We find that drugs such as colchicine, vinblastine, and taxol, and stabilizing MAPs such as tau, strongly modulate microtubule dynamics at extremely low concentrations under conditions in which the microtubule polymer mass is minimally affected. The powerful modulation of the dynamics is brought about by the binding of only a few drug or MAP molecules to distinct binding sites at the microtubule surface or end. Based upon our understanding of the well-studied drugs and stabilizing MAPs, it is clear that molecules that regulate dynamics such as Kin 1 and stathmin could bind to a large number of distinct tubulin sites on microtubules and employ an array of mechanisms to selectively and powerfully regulate microtubule dynamics and dynamics-dependent cellular functions.  相似文献   

12.
Electric birefringence has been used to examine the states of association of tubulin in phosphocellulose-purified tubulin or depolymerized microtubule protein solutions at low temperature. In a high electric field (1000-4000 V/cm), tubulin could be orientated (owing to the existence of a permanent and/or induced dipole) and exhibited a positive birefringence (delta n), related to its intrinsic optical anisotropy. The analysis of the relaxation process (depending on hydrodynamic properties of molecules), by measurement of the time decay of delta n, revealed the existence of a multicomponent or polydisperse system, whatever the tubulin solution. Two relaxation times, representative of the smallest and the largest orientated species, were obtained by computer-fitting analysis. The mean values of relaxation time for phosphocellulose-purified tubulin were 0.8 and 8 microseconds. In microtubule protein solutions, large-sized macromolecular species with relaxation time up to 450 microseconds were detected. The largest species (relaxation times ranging from 50 to 450 microseconds) could be eliminated by centrifugation at 3000000 X g for 1 h. Addition of microtubule-associated protein to either pure tubulin or high-speed centrifuged microtubule protein led to a rapid formation of large species analogous to those present in microtubule protein. Molecular dimensions of the relaxing structures were estimated using simple hydrodynamic models and values of rotational diffusion constants calculated from the relaxation times, and compared to those of the structures described in the literature. In conclusion, we have found that (a) phosphocellulose-purified tubulin is not only composed of elementary species (dimers) but also contains tubulin-associated forms of limited size (up to 7-10 dimers), (b) depolymerized microtubule protein solutions contain ring oligomers and structures very much larger, the formation of which is dependent on the presence of microtubule-associated protein.  相似文献   

13.
Erent M  Drummond DR  Cross RA 《PloS one》2012,7(2):e30738
The kinesins-8 were originally thought to be microtubule depolymerases, but are now emerging as more versatile catalysts of microtubule dynamics. We show here that S. pombe Klp5-436 and Klp6-440 are non-processive plus-end-directed motors whose in vitro velocities on S. pombe microtubules at 7 and 23 nm s(-1) are too slow to keep pace with the growing tips of dynamic interphase microtubules in living S. pombe. In vitro, Klp5 and 6 dimers exhibit a hitherto-undescribed combination of strong enhancement of microtubule nucleation with no effect on growth rate or catastrophe frequency. By contrast in vivo, both Klp5 and Klp6 promote microtubule catastrophe at cell ends whilst Klp6 also increases the number of interphase microtubule arrays (IMAs). Our data support a model in which Klp5/6 bind tightly to free tubulin heterodimers, strongly promoting the nucleation of new microtubules, and then continue to land as a tubulin-motor complex on the tips of growing microtubules, with the motors then dissociating after a few seconds residence on the lattice. In vivo, we predict that only at cell ends, when growing microtubule tips become lodged and their growth slows down, will Klp5/6 motor activity succeed in tracking growing microtubule tips. This mechanism would allow Klp5/6 to detect the arrival of microtubule tips at cells ends and to amplify the intrinsic tendency for microtubules to catastrophise in compression at cell ends. Our evidence identifies Klp5 and 6 as spatial regulators of microtubule dynamics that enhance both microtubule nucleation at the cell centre and microtubule catastrophe at the cell ends.  相似文献   

14.
We investigated how the self-association of isolated tubulin dimers affects the rate of GTP hydrolysis and the equilibrium of nucleotide exchange. Both reactions are relevant for microtubule (MT) dynamics. We used HPLC to determine the concentrations of GDP and GTP and thereby the GTPase activity of SEC-eluted tubulin dimers in assembly buffer solution, free of glycerol and tubulin aggregates. When GTP hydrolysis was negligible, the nucleotide exchange mechanism was studied by determining the concentrations of tubulin-free and tubulin-bound GTP and GDP. We observed no GTP hydrolysis below the critical conditions for MT assembly (either below the critical tubulin concentration and/or at low temperature), despite the assembly of tubulin 1D curved oligomers and single-rings, showing that their assembly did not involve GTP hydrolysis. Under conditions enabling spontaneous slow MT assembly, a slow pseudo-first-order GTP hydrolysis kinetics was detected, limited by the rate of MT assembly. Cryo-TEM images showed that GTP-tubulin 1D oligomers were curved also at 36 °C. Nucleotide exchange depended on the total tubulin concentration and the molar ratio between tubulin-free GDP and GTP. We used a thermodynamic model of isodesmic tubulin self-association, terminated by the formation of tubulin single-rings to determine the molar fractions of dimers with exposed and buried nucleotide exchangeable sites (E-sites). Our analysis shows that the GDP to GTP exchange reaction equilibrium constant was an order-of-magnitude larger for tubulin dimers with exposed E-sites than for assembled dimers with buried E-sites. This conclusion may have implications on the dynamics at the tip of the MT plus end.  相似文献   

15.
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.  相似文献   

16.
A combined morphometric and biochemical approach has been used to identify and quantitate microtubules and tubulin in isolated hepatocytes. The total soluble pool of microtubule protein was estimated by specific high affinity binding to radiolabeled colchicine. Scatchard analysis of the data identified two populations of binding sites: high affinity-low capacity sites resembling tubulin and low affinity-high capacity sites believed to represent nonspecific colchicine-binding sites. Data from these studies indicate that tubulin represents 1% of the soluble protein of the cell, that 9.0 X 10(-14) dimers of tubulin are present per microgram soluble hepatocyte protein, and that the average hepatocyte contains 3.1 X 10(7) tubulin dimers. Our calculations suggest that this amount of tubulin would form a microtubule 1.9 cm in length if totally assembled. However, stereological measurements indicate that the actual length of microtubules in the cytosolic compartment of the average hepatocyte is only 0.28 cm. Thus, these experiments suggest that only 15% of the available tubulin in hepatocytes of postabsorptive rats is assembled in the form of microtubules.  相似文献   

17.
The molecular mechanisms by which microtubule-associated proteins (MAPs) regulate the dynamic properties of microtubules (MTs) are still poorly understood. We review recent advances in our understanding of two conserved families of MAPs, the XMAP215/Dis1 and CLASP family of proteins. In vivo and in vitro studies show that XMAP215 proteins act as microtubule polymerases at MT plus ends to accelerate MT assembly, and CLASP proteins promote MT rescue and suppress MT catastrophe events. These are structurally related proteins that use conserved TOG domains to recruit tubulin dimers to MTs. We discuss models for how these proteins might use these individual tubulin dimers to regulate dynamic behavior of MT plus ends.  相似文献   

18.
Stathmin is a phosphorylation-regulated tubulin-binding protein. In vitro and in vivo studies using nonphosphorylatable and pseudophosphorylated mutants of stathmin have questioned the view that stathmin might act only as a tubulin-sequestering factor. Stathmin was proposed to effectively regulate microtubule dynamic instability by increasing the frequency of catastrophe (the transition from steady growth to rapid depolymerization), without interacting with tubulin. We have used a noninvasive method to measure the equilibrium dissociation constants of the T(2)S complexes of tubulin with stathmin, pseudophosphorylated (4E)-stathmin, and diphosphostathmin. At both pH 6.8 and pH 7.4, the relative sequestering efficiency of the different stathmin variants depends on the concentration of free tubulin, i.e. on the dynamic state of microtubules. This control is exerted in a narrow range of tubulin concentration due to the highly cooperative binding of tubulin to stathmin. Changes in pH affect the stability of tubulin-stathmin complexes but do not change stathmin function. The 4E-stathmin mutant mimics inactive phosphorylated stathmin at low tubulin concentration and sequesters tubulin almost as efficiently as stathmin at higher tubulin concentration. We propose that stathmin acts solely by sequestering tubulin, without affecting microtubule dynamics, and that the effect of stathmin phosphorylation on microtubule assembly depends on tubulin critical concentration.  相似文献   

19.
MCAK belongs to the Kin I subfamily of kinesin-related proteins, a unique group of motor proteins that are not motile but instead destabilize microtubules. We show that MCAK is an ATPase that catalytically depolymerizes microtubules by accelerating, 100-fold, the rate of dissociation of tubulin from microtubule ends. MCAK has one high-affinity binding site per protofilament end, which, when occupied, has both the depolymerase and ATPase activities. MCAK targets protofilament ends very rapidly (on-rate 54 micro M(-1).s(-1)), perhaps by diffusion along the microtubule lattice, and, once there, removes approximately 20 tubulin dimers at a rate of 1 s(-1). We propose that up to 14 MCAK dimers assemble at the end of a microtubule to form an ATP-hydrolyzing complex that processively depolymerizes the microtubule.  相似文献   

20.
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.  相似文献   

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