End-to-end joining of taxol-stabilized GDP-containing microtubules

By the use of the drug taxol, microtubules were assembled from tubulin that had GDP at its exchangeable nucleotide binding site. By means of dilution experiments and measurements of exchange of labeled subunits, it was determined that the rate of interchange of subunits between these microtubules and the solution is very slow: the upper limit of the dissociation rate constant was measured to be 0.2 subunit s-1 end-1. When they were broken into short pieces by gentle shearing, these microtubules were found to undergo a rapid subsequent spontaneous increase in length. This increase was attributed to end-to-end joining (also called annealing), because dynamic instability and other mechanisms involving either nucleotide hydrolysis or subunit interchange at the ends could be ruled out. To characterize the process, a diffusion-controlled joining mechanism was hypothesized, and a length-independent bimolecular rate constant, gamma, was defined. Length distributions were measured at a series of times after the initial shearing. By means of a novel iterative calculation, the best-fitting value of gamma was determined from the time-dependent changes in the length distributions. Fitting was carried out at each of three concentrations of microtubules. The resulting values show that end-to-end joining of microtubules is remarkably efficient and that gamma is concentration-dependent.     

Dynamics of Antarctic fish microtubules at low temperatures

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)     

Rapid rate of tubulin dissociation from microtubules in the mitotic spindle in vivo measured by blocking polymerization with colchicine

At metaphase, the amount of tubulin assembled into spindle microtubules is relatively constant; the rate of tubulin association equals the rate of dissociation. To measure the intrinsic rate of dissociation, we microinjected high concentrations of colchicine, or its derivative colcemid, into sea urchin embryos at metaphase to bind the free tubulin, thereby rapidly blocking polymerization. The rate of microtubule disassembly was measured from a calibrated video signal by the change in birefringent retardation (BR). After an initial delay after injection of colchicine or colcemid at final intracellular concentrations of 0.1-3.0 mM, BR decreased rapidly and simultaneously throughout the central spindle and aster. Measured BR in the central half-spindle decreased exponentially to 10% of its initial value within a characteristic period of approximately 20 s; the rate constant, k = 0.11 +/- 0.023 s-1, and the corresponding half-time, t 1/2, of BR decay was approximately 6.5 +/- 1.1 s in this concentration range. Below 0.1 mM colchicine or colcemid, the rate at which BR decreased was concentration dependent. Electron micrographs showed that the rapid decrease in BR corresponded to the disappearance of nonkinetochore microtubules; kinetochore fiber microtubules were differentially stable. As a control, lumicolchicine, which does not bind to tubulin with high affinity, was shown to have no effect on spindle BR at intracellular concentrations of 0.5 mM. If colchicine and colcemid block only polymerization, then the initial rate of tubulin dissociation from nonkinetochore spindle microtubules is in the range of 180-992 dimers per second. This range of rates is based on k = 11% of the initial polymer per second and an estimate from electron micrographs that the average length of a half-spindle microtubule is 1- 5.5 micron. Much slower rates of tubulin association are predicted from the characteristics of end-dependent microtubule assembly measured previously in vitro when the association rate constant is corrected for the lower rate of tubulin diffusion in the embryo cytoplasm. Various possibilities for this discrepancy are discussed.     

Redistribution of fluorescently labeled tubulin in the mitotic apparatus of sand dollar eggs and the effects of taxol

Fluorescently labeled tubulin was quickly incorporated into the mitotic apparatus when injected into a live sand dollar egg. After a rectangular area (1.6 X 16 microns) of the mitotic spindle was photobleached at metaphase or anaphase by the irradiation of a laser microbeam, redistribution of fluorescence was almost complete within 30 sec. The photobleached area did not change in shape during the redistribution. During the period of redistribution, the bleached area moved slightly toward the near pole at metaphase and anaphase (means: 1.6 and 1.8 micron/min, respectively). These results indicate that redistribution was not due to the exchange of tubulin subunits only at the ends of microtubules but to their rapid exchange at sites along the microtubules in the bleached region. Furthermore, treadmilling of tubulin molecules along with the spindle microtubules possibly occurred at the rate of 1.6 micron/min at metaphase. Birefringence of the mitotic apparatus increased with a large increase in both the number and length of astral rays shortly after taxol was injected. However, the microtubules did not all seem to elongate at the same rate but appeared to become equalized in length. Chromosome movement stopped within 60 sec after the injection. Centrospheres became large and the labeled tubulin already incorporated into the centrospheres was excluded from the enlarged centrospheres. Shortly after the labeled tubulin was injected following the injection of taxol, it accumulated in the peripheral region of the centrospheres, suggesting that microtubules first assembled at this region. Fluorescently labeled tubulin in the mitotic apparatus in the egg after injection of taxol was redistributed much more slowly after photobleaching than in uninjected eggs.     

Taxol stabilization of microtubules in vitro: dynamics of tubulin addition and loss at opposite microtubule ends

We have investigated the effects of taxol on steady-state tubulin flux and on the apparent molecular rate constants for tubulin addition and loss at the two ends of bovine brain microtubules in vitro. These microtubules, which consist of a mixture of 70% tubulin and 30% microtubule-associated proteins (MAPs), undergo a net addition of tubulin at one end of each microtubule (A end) and a precisely balanced net loss of tubulin at the opposite end (D end) at steady state in vitro. They do not exhibit to a detectable extent the "dynamic instability" behavior described recently for MAP-free microtubules, which would be evident as an increase in the mean microtubule length and a decrease in the number of microtubules in the suspensions [Mitchison, T., & Kirschner, M. (1984) Nature (London) 312, 237-242]. We used a double-label procedure in which microtubules were labeled with tritium and carbon-14 at A ends and carbon-14 at D ends to distinguish the two ends, combined with a microtubule collection procedure that permitted rapid and accurate analysis of retention of the two labels in the microtubules. We found that taxol slowed the flux of tubulin in a concentration-dependent manner, with 50% inhibition occurring between 5 and 7 microM drug. The effects of taxol on the apparent molecular rate constants for tubulin addition and loss at the two microtubule ends were determined by dilution analysis at an intermediate taxol concentration. The results indicated that taxol decreased the magnitudes of the dissociation rate constants at the two ends to similar extents, while exerting little effect on the association rate constants.(ABSTRACT TRUNCATED AT 250 WORDS)     

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.     

Oscillations in microtubule polymerization: the rate of GTP regeneration on tubulin controls the period.

The essential reactions involved in the oscillatory kinetics of microtubule polymerization have been investigated. The rate of GDP dissociation from tubulin decreased cooperatively upon increasing tubulin concentration above 20 microM, consistent with the formation of GDP oligomers whose dissociation is rate limiting in nucleotide exchange. The apparent rate constant for nucleotide exchange at high tubulin concentration was 0.02 s-1 at 37 degrees C, which is the exact value needed in previous theoretical simulations to obtain oscillations with the real period of 70-80 s. A glass filter assay separating microtubules from oligomers and tubulin allowed nucleotide bound to non-microtubular tubulin during the oscillations to be monitored. In agreement with nucleotide exchange data, tubulin-bound GDP was found to oscillate in antiphase with microtubules. By varying the concentration of an enzymatic GTP-regenerating system, we could demonstrate that the period of the oscillations is directly controlled by the rate at which GTP is regenerated on tubulin, and oscillations can be observed under conditions where the dissociation of oligomers is no longer rate limiting. The possible physiological significance of GTP-regenerating systems in establishing synchrony in a microtubule population is evoked. The present data confirm and extend the model that we previously proposed to account for the oscillations.     

Effects of brain microtubule-associated proteins on microtubule dynamics and the nucleating activity of centrosomes

In this paper, we report on the effect of brain microtubule-associated proteins (MAPs) on the dynamic instability of microtubules as well as on the nucleation activity of purified centrosomes. Under our experimental conditions, tau and MAP2 have similar effects on microtubule nucleation and dynamic instability. Tau increases the apparent elongation rate of microtubules in proportion to its molar ratio to tubulin, and we present evidence indicating that this is due to a reduction of microtubule instability rather than to an increase of the on rate of tubulin subunits at the end of growing microtubules. Increasing the molar ratio of tau over tubulin leads also to an increase in the average number of microtubules nucleated per centrosome. This number remains constant with time. This suggests that the number of centrosome-nucleated microtubules at steady state can be determined by factors that are not necessarily irreversibly bound to centrosomes but, rather, affect the dynamic properties of microtubules.     

Dynamic instability of individual microtubules analyzed by video light microscopy: rate constants and transition frequencies

We have developed video microscopy methods to visualize the assembly and disassembly of individual microtubules at 33-ms intervals. Porcine brain tubulin, free of microtubule-associated proteins, was assembled onto axoneme fragments at 37 degrees C, and the dynamic behavior of the plus and minus ends of microtubules was analyzed for tubulin concentrations between 7 and 15.5 microM. Elongation and rapid shortening were distinctly different phases. At each end, the elongation phase was characterized by a second order association and a substantial first order dissociation reaction. Association rate constants were 8.9 and 4.3 microM-1 s-1 for the plus and minus ends, respectively; and the corresponding dissociation rate constants were 44 and 23 s-1. For both ends, the rate of tubulin dissociation equaled the rate of tubulin association at 5 microM. The rate of rapid shortening was similar at the two ends (plus = 733 s-1; minus = 915 s-1), and did not vary with tubulin concentration. Transitions between phases were abrupt and stochastic. As the tubulin concentration was increased, catastrophe frequency decreased at both ends, and rescue frequency increased dramatically at the minus end. This resulted in fewer rapid shortening phases at higher tubulin concentrations for both ends and shorter rapid shortening phases at the minus end. At each concentration, the frequency of catastrophe was slightly greater at the plus end, and the frequency of rescue was greater at the minus end. Our data demonstrate that microtubules assembled from pure tubulin undergo dynamic instability over a twofold range of tubulin concentrations, and that the dynamic instability of the plus and minus ends of microtubules can be significantly different. Our analysis indicates that this difference could produce treadmilling, and establishes general limits on the effectiveness of length redistribution as a measure of dynamic instability. Our results are consistent with the existence of a GTP cap during elongation, but are not consistent with existing GTP cap models.     

Kinetic analysis of tubulin exchange at microtubule ends at low vinblastine concentrations

We have investigated the effects of vinblastine at micromolar concentrations and below on the dynamics of tubulin exchange at the ends of microtubule-associated-protein-rich bovine brain microtubules. The predominant behavior of these microtubules at polymer-mass steady state under the conditions examined was tubulin flux, i.e., net addition of tubulin at one end of each microtubule, operationally defined as the assembly or A end, and balanced net loss at the opposite (disassembly or D) end. No dynamic instability behavior could be detected by video-enhanced dark-field microscopy. Addition of vinblastine to the microtubules at polymer-mass steady state resulted in an initial concentration-dependent depolymerization predominantly at the A ends, until a new steady-state plateau at an elevated critical concentration was established. Microtubules ultimately attained the same stable polymer-mass plateau when vinblastine was added prior to initiation of polymerization as when the drug was added to already polymerized microtubules. Vinblastine inhibited tubulin exchange at the ends of the microtubules at polymer-mass steady state, as determined by using microtubules differentially radiolabeled at their opposite ends. Inhibition of tubulin exchange occurred at concentrations of vinblastine that had very little effect on polymer mass. Both the initial burst of incorporation that occurs in control microtubule suspensions following a pulse of labeled GTP and the relatively slower linear incorporation of label that follows the initial burst were inhibited in a concentration-dependent manner by vinblastine. Both processes were inhibited to the same extent at all vinblastine concentrations examined. If the initial burst of label incorporation represents a low degree of dynamic instability (very short excursions of growth and shortening of the microtubules at one or both ends), then vinblastine inhibits both dynamic instability and flux to similar extents. The ability of vinblastine to inhibit tubulin exchange at microtubule ends in the micromolar concentration range appeared to be mediated by the reversible binding of vinblastine to tubulin binding sites exposed at the polymer ends. Determination by dilution analysis of the effects of vinblastine on the apparent dissociation rate constants for tubulin loss at opposite microtubule ends indicated that a principal effect of vinblastine is to decrease the dissociation rate constant at A ends (i.e., it produces a kinetic cap at A ends), whereas it has no effect on the D-end dissociation rate constant.     

Taxol effect on tubulin polymerization and associated guanosine 5'-triphosphate hydrolysis

Taxol has been used as a tool to investigate the relationship between microtubule assembly and guanosine 5'-triphosphate (GTP) hydrolysis. The data support the model previously proposed [Carlier, M.-F., & Pantaloni, D. (1981) Biochemistry 20, 1918] that GTP hydrolysis is not tightly coupled to the polymerization process but takes place as a monomolecular process following polymerization. The results further indicate that the energy liberated by GTP hydrolysis is not responsible for the subsequent blockage of GDP on polymerized tubulin. When tubulin is polymerized in the presence of 10-100 microM taxol, the rapid formation of a large number of very short microtubules (l less than 1 micron) is accompanied by the development of turbidity to a lesser extent than what is observed when the same weight amount of longer microtubules (l = 5 microns) is formed. A slower subsequent turbidity increase corresponds to the length redistribution of these short microtubules into 3-5-fold longer ones without any change in the weight amount of polymer. The evolution of the rate of length redistribution with the concentration of taxol suggests a model within which taxol would bind to dimeric tubulin and to tubulin present at the ends of microtubules with a somewhat 10-fold lower affinity than to polymerized tubulin embedded in the bulk of microtubules. In agreement with this model, binding of taxol to the tubulin-colchicine complex in the dimeric form could be measured from the increase in the GTPase activity of the tubulin-colchicine complex accompanying taxol binding.     

Microtubule elongation and guanosine 5'-triphosphate hydrolysis. Role of guanine nucleotides in microtubule dynamics

The tubulin concentration dependence of the rates of microtubule elongation and accompanying GTP hydrolysis has been studied over a large range of tubulin concentration. GTP hydrolysis followed the elongation process closely at low tubulin concentration and became gradually uncoupled at higher concentrations, reaching a limiting rate of 35-40 s-1. The kinetic parameters for microtubule growth were different at low and high tubulin concentrations. Elongation of microtubules has also been studied in solutions containing GDP and GTP in variable proportions. Only traces of GTP present in GDP were necessary to confer a high stability (low critical concentration) to microtubules. Pure GDP-tubulin was found unable to elongate microtubules in the absence of GTP but blocked microtubule ends with an equilibrium dissociation constant of 5-6 microM. These data were accounted for by a model within which, in the presence of GTP-tubulin at high concentration, microtubules grow at a fast rate with a large GTP cap; the GTP cap may be quite short in the region of the critical concentration; microtubule stability is linked to the strong interaction between GTP and GDP subunits at the elongating site; dimeric GDP-tubulin does not have the appropriate conformation to undergo reversible polymerization. These results are discussed with regard to possible role of GDP and GTP and of GTP hydrolysis in microtubule dynamics.     

Erythrocyte microtubule assembly in vitro. Determination of the effects of erythrocyte tau, tubulin isoforms, and tubulin oligomers on erythrocyte tubulin assembly, and comparison with brain microtubule assembly

Two tubulin variants, isolated from chicken brain and erythrocytes and known to have different peptide maps and electrophoretic properties, are demonstrated to exhibit different assembly properties in vitro: 1) erythrocyte tubulin assembles with greater efficiency (lower critical concentration, greater elongation rate) but exhibits a lower nucleation rate than brain tubulin, and 2) erythrocyte tubulin readily forms oligomers whose presence significantly retards the rate of elongation, suggesting that tubulin oligomers may also be important for determining the rate of assembly and the length of microtubules in erythrocytes. Erythrocyte tubulin isolated by cycles of in vitro assembly-disassembly is also demonstrated to contain a 67-kDa tau factor that greatly enhances microtubule nucleation but has little effect on elongation rates or critical concentration. Immunofluorescence microscopy with tau antibody indicates that tau is specifically associated with marginal band microtubules, suggesting that it may be important for determining microtubule function in vivo.     

Tubulin subunit sorting: Analysis of the mechanisms involved in the segregation of unique tubulin isotypes within microtubule copolymers

Summary Vertebrate cells contain biochemical and genetic isotypes of tubulin which are expressed in unique combinations in different tissues and cell types. To determine if mixtures of tubulin isotypes assemblein vitro to form different classes of microtubules, we analyzed the composition of microtubule copolymers assembled from mixtures of chicken brain and erythrocyte tubulin. During microtubule elongation brain tubulin assembled onto the ends of microtubules faster than erythrocyte tubulin, resulting in copolymers with continually changing ratios of isotypes along their lengths. Unlike examples of microtubule assembly where the rate of polymerization depends on the association rate constant (k⁺) and the subunit concentration, the rate and extent of sorting in copolymers appear to depend on the dissociation rate constant (k^–), which governs the rate at which subunits are released from tubulin oligomers and microtubules and thereby made available for reassembly into copolymers. The type of microtubule seed used to initiate elongation was also found to influence the composition of copolymers, indicating that polymerization favors association of subunits of the same isotype.     

Stathmin strongly increases the minus end catastrophe frequency and induces rapid treadmilling of bovine brain microtubules at steady state in vitro

Stathmin is a ubiquitous microtubule destabilizing protein that is believed to play an important role linking cell signaling to the regulation of microtubule dynamics. Here we show that stathmin strongly destabilizes microtubule minus ends in vitro at steady state, conditions in which the soluble tubulin and microtubule levels remain constant. Stathmin increased the minus end catastrophe frequency approximately 13-fold at a stathmin:tubulin molar ratio of 1:5. Stathmin steady-state catastrophe-promoting activity was considerably stronger at the minus ends than at the plus ends. Consistent with its ability to destabilize minus ends, stathmin strongly increased the treadmilling rate of bovine brain microtubules. By immunofluorescence microscopy, we also found that stathmin binds to purified microtubules along their lengths in vitro. Co-sedimentation of purified microtubules polymerized in the presence of a 1:5 initial molar ratio of stathmin to tubulin yielded a binding stoichiometry of 1 mol of stathmin per approximately 14.7 mol of tubulin in the microtubules. The results firmly establish that stathmin can increase the steady-state catastrophe frequency by a direct action on microtubules, and furthermore, they indicate that an important regulatory action of stathmin in cells may be to destabilize microtubule minus ends.     

Some thoughts on the partitioning of tubulin between monomer and polymer under conditions of dynamic instability

We have considered the partitioning of tubulin between monomer and polymer in the cell under conditions of dynamic instability. Dynamic instability adds to the on and off rate constant of steady-state dynamics’ new parameters: (1) the rate at which growing microtubules transit to a shrinking phase; and (2) the rate at which shrinking microtubules transit to the growing phase. Under these conditions the free-monomer concentration in the cell increases with total tubulin if the number of nucleating sites is fixed. If the number of nucleating sites increases at fixed total tubulin, subunits shift from the monomer to the polymer phase. These important properties deviate from the traditional equilibrium and steady-state theories and have important implications for the biosynthetic regulation of tubulin.     

Proteins from morphologically differentiated neuroblastoma cells promote tubulin polymerization

Clonal cells (N18) of the mouse neuroblastoma C-1300 can be induced to undergo a morphological differentiation characterized by the outgrowth of very long neurites (> 150 microns) that contain many microtubules. Because the marked increase in the number and length of microtubules is apparently not due to an increase in the concentration of tubulin subunits, the possible role of additional macromolecules in the regulation of tubulin polymerization during neurite formation by N18 cells was examined. Using an in vitro system where the polymerization of low concentrations (< 4 mg/ml) of purified brain tubulin requires microtubule-associated proteins (MAPs), high-speed supernates (250,000 g) from neuroblastoma and glioma cells were assayed for their ability to replace MAPs in the polymerization of brain tubulin. Only the supernates from "differentiated" N18 cells were polymerization competent. Electron microscope observations of these supernates failed to demonstrate the presence of nucleation structures (rings or disks). The active factor(s) sedimented at approximately 7S on sucrose gradient centrifugation and eluted from 4B Sepharose in the region of 170,000 mol wt proteins. Furthermore, the inactive supernates from other cells did not inhibit polymerization when tested in the presence of limiting MAPs. Thus, microtubule formation accompanying neurite outgrowth in neuroblastoma cells appears to be regulated by the presence of additional macromolecular factor(s) that may be functionally equivalent to the MAPs found with brain microtubules.     

Dynamics of microtubules from erythrocyte marginal bands.

Microtubules can adjust their length by the mechanism of dynamic instability, that is by switching between phases of growth and shrinkage. Thus far this phenomenon has been studied with microtubules that contain several components, that is, a mixture of tubulin isoforms, with or without a mixture of microtubule-associated proteins (MAPs), which can act as regulators of dynamic instability. Here we concentrate on the influence of the tubulin component. We have studied MAP-free microtubules from the marginal band of avian erythrocytes and compared them with mammalian brain microtubules. The erythrocyte system was selected because it represents a naturally stable aggregate of microtubules; second, the tubulin is largely homogeneous, in contrast to brain tubulin. Qualitatively, erythrocyte microtubules show similar features as brain microtubules, but they were found to be much less dynamic. The critical concentration of elongation, and the rates of association and dissociation of tubulin are all lower than with brain microtubules. Catastrophes are rare, rescues frequent, and shrinkage slow. This means that dynamic instability can be controlled by the tubulin isotype, independently of MAPs. Moreover, the extent of dynamic behavior is highly dependent on buffer conditions. In particular, dynamic instability is strongly enhanced in phosphate buffer, both for erythrocyte marginal band and brain microtubules. The lower stability in phosphate buffer argues against the hypothesis that a cap of tubulin.GDP.Pi subunits stabilizes microtubules. The difference in dynamics between tubulin isotypes and between the two ends of microtubules is preserved in the different buffer systems.     

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.     

Effects of magnesium on the dynamic instability of individual microtubules

We investigated the effect of magnesium ion (Mg) on the parameters of dynamic instability of individual porcine brain microtubules. Rates of elongation and rapid shortening were measured by using video-enhanced DIC light microscopy and evaluated by using computer-generated plots of microtubule length vs time. Increasing [Mg] from 0.25 to 6 mM increased the second-order association rate constant for elongation about 25% at each end. At plus ends, this resulted in a 1.5-2-fold increase in elongation rates over the tubulin concentrations explored. Rapid shortening rates were more dramatically affected by Mg. As [Mg] was increased from 0.25 to 6 mM, the average rate of rapid shortening increased about 3-fold at plus ends and 4-5-fold at minus ends. The ends had roughly equivalent average rates at low [Mg], of 30-45 microns/min. At any Mg concentration, rates of disassembly varied from one microtubule to another, and often an individual microtubule would exhibit more than one rate during a single shortening phase. Individual rates at 6 mM Mg varied from 12 to 250 microns/min. Over the concentration range explored, Mg affected the frequencies of transition from elongation to shortening and back only at minus ends. Minus ends were relatively stable at low [Mg], having 4 times the frequency of rescue than at high [Mg], and a lower frequency of catastrophe (particularly evident at low tubulin concentrations). Plus ends, surprisingly, were highly unstable at all Mg concentrations investigated, having about the same transition frequencies as did the least stable (high Mg) minus ends. Our results have implications for models of the GTP cap, again emphasizing that GTP caps cannot build up in proportion to elongation rate, and must be constrained to the tips of growing microtubules.