How Taxol Modulates Microtubule Disassembly*

Measurement of the affinity of microtubules for the anti-cancer drug taxol is problematic, because microtubules are not stable at the very low concentrations re- quired to detect taxol dissociation. the GTP analogue microtubules nonsaturating A

(2). These results indicate a Kd value of taxol substantially less than 0.2 VM, by some factor that remains to be determined. Binding experiments at lower taxol and microtubule concentrations are rendered problematic by the fact that microtubules are not stable when diluted to 0.2 p~ tubulin in microtubules.' GM46773. The costs of publication of this article were defrayed in part * This work was supported by National Institutes of Health Grant by the payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Microtubules are stable at any concentration if they are diluted into a solution containing tubulin at the critical Concentration, but it would In contrast, microtubules assembled with GMPCPP' are extremely stable, and have a significant lifetime even after extreme dilution (3). In the present study, GMPCPP-microtubules were found to be sufficiently stable at m concentrations to allow equilibrium for taxol binding to tubulin subunits, including those at microtubule ends. The effect of taxol concentration on the dilution-induced disassembly rate and on the extent of binding of [3H]taxol allowed us to estimate a Kd value of about 10 n~. Taxol binding to the tubulin-GDP subunits that form the core of microtubules assembled with GTP is apparently comparable to that with GMPCPP-microtubules. However, taxol is not at equilibrium with terminal tubulin-GDP subunits, because taxol-free subunits dissociate from ends faster than taxol (at concentrations near K d ) is bound by these subunits. The escape of taxol-free tubulin subunits from ends of microtubules whose tubulin-GDP core is saturated with taxol can be suppressed by using taxol concentrations that are 1000 times greater than Kd. From these results, we infer that in chemotherapy a maximal effect is to be expected when the taxol concentration is sufficient both to saturate the core of the microtubule and to provide enough free taxol to capture taxol-free subunits efficiently at microtubule ends. The observed inhibition of disassembly by very high taxol concentrations can account for the observation that intracellular taxol concentrations that exceed the tubulin concentration are required to increase the amount of tubulin in polymer in HeLa cells (4). The assay described here for study of taxol binding with GMP-CPP-microtubules may prove useful in developing improved taxol derivatives.
EXPERIMENTAL PROCEDURES Materials-Beef brain tubulin, GMPCPP, and [y-32PlGMPCPP were prepared as described (3,5). [3HlTaxol was obtained from Morevic Biochemical; 99% of the tritium was shown to be in taxol by an analysis based on the Gibbs phase rule (6). This is a highly sensitive method and the most accurate method for determining taxol purity.
Methods-All reactions were at 37 "C in BRB80 buffer (80 m M Na-Pipes, 1 m MgCl,, 1 m M EGTA, pH 6.8); reaction mixtures with microtubules were made up and handled in a room at 37 "C. GMPCPPmicrotubules were prepared by two cycles of thermal induced assembly and disassembly with 10 VM tubulin, using 1 m M GMPCPP in the first cycle and 100 p~ [Y-~~PIGMPCPP in the second cycle. Microtubules were isolated using a Beckman Airfuge (3-10 min, 30 p.s.i.).
In studies of the effect of taxol on the rate of dilution-induced disassembly of GTP-microtubules, these were formed by a 30-min incubation of 50 PM tubulin, 44 nm acetyl phosphate, 0.36 unit/ml acetate kinase, and a trace amount of [a-32PlGTP. A 2 0 4 aliquot of this mixture that had been diluted with 1 ml of 5 VM tax01 was layered on a 4-ml cushion of 40% glycerol in BRB80 buffer. After microtubules were isolated by centrifugation (50,000 rpm, Ti50 rotor, 37 "C), the pellet was resuspended in 2 ml of buffer containing alkaline phosphatase (1 unit/ml) and taxol, which was transferred to a siliconized glass tube.
The kinetics for dilution-induced disassembly were measured from the rate of release of [32PlPi formed in Reactions 1 and 2. The abbreviations used are: GMPCPP, guanylyl a,P-methylenediphosphonate; Pipes, 1,4-piperazinediethanesulfonic acid.

Tax01 Reaction with Microtubules
A 80.  [32P]GMPCPP-tubulin subunit == alkaline phosphatase [32P]GMPCPP [32p1p, REACTION 2 The same assay was used with [c~-~~PIGTP-microtubules. Alkaline phosphatase cleavage of GMPCPP is rapid (0.56 s-' with GMPCPP and faster with GDP) under these conditions, so that the observed rate of Pi release closely tracked the rate of disassembly. The molecular rate constant for disassembly was obtained by multiplying the percent of microtubule disassembledhecond by the mean number of tubulin subunitdmicrotubule, with the latter value determined with electron microscopy to measure the length of 300 negatively stained microtubules.
The X, for dissociation of [3Hltaxol from GMPCPP-microtubuIes was determined from measurement of the radioactivity that remained in the supernatant when an excess of tubulin in microtubules was reacted with 5 n M [3H]taxol and polymer was isolated by centrifugation. The microtubules used here had been assembled by two assembly/ disassembly cycles with GMPCPP as described above, and the pellet from the second assembly step was gently mixed with warm buffer and then diluted into 5 n M [3Hltaxol. Reactions were incubated for approximately 2 min in siliconized polyethylene Airfuge tubes before centrifugation (5 min, 30 psi., 37 "C); three Airfuges were used so that all reactions could be run within about 20 min.

Reaction of Taxol with GMPCPP-Microtubules-Interaction
of taxol with GMPCPP-microtubules was detected by its effect on the rate of disassembly after a 10,000-fold dilution (Fig. 1). Reactions were run with both 5 and 10 m tubulin. C3HlTaxol was incubated with microtubules for 10 min, and the protein and radioactivity were determined in triplicate in the supernatant and pellet aRer centrifugation in an Airfuge.
Microtubules assembled with 1 m GTP and 50 tubulin were made 50 in taxol and incubated for 10 min. This mixture was diluted were then added to [3Hltaxol contained in either a 5% volume or a 9-fold 10-fold into 5 taxol and incubated an additional 10 min. Aliquots greater volume; after 90 s microtubules were isolated with an Airfuge. Radioactivity and protein were measured in the resultant pellet.
The resultant concentration of tubulin in microtubules was only 0.73 m, so that saturation was possible with low concentrations of taxol. The observed disassembly rate could be accounted for by assuming that the dissociation rate is 0.65 s-' for taxol-free tubulin subunits3 and 0.03 s-l for taxol-tubulin subunits, with taxol binding to a site with a Kd equal to 5 nM (Fig.   1). The 0.03 s-l rate for taxol-tubulin subunits was determined from measurements with 0.5 1.1~ taxol. That the rate can be accounted for by assuming that this is influenced by a single dissociation constant is consistent with a mechanism in which taxol is a t equilibrium with tubulin subunits in the microtubule, including those at microtubule ends.
Evidence consistent with the kinetically determined Kd was obtained from equilibrium measurements of [3H]taxol binding. The stoichiometry for taxol binding with both GTP-and GMP-CPP-microtubules was approximately 0.7, measured under conditions where taxol was in excess of the number of binding sites (experiment A in Table I). The Kd was measured with tubulin in GMPCPP-microtubules in excess (7.3-146 nM) of the 5 nM r3H]taxol. Under these conditions, the concentration of tubulin for half-maximal binding corresponds to Kd; this was equal to approximately 20 nM tubulin in microtubules (Fig. 2). 4 It is noted that about 15% of the [3Hltaxol did not pellet with microtubules, even with 1310 nM tubulin in microtubules. Incomplete binding of [3H]taxol did not result from contamination with nonbinding impurities, since 90% of the apparently unbound radiolabel in the supernatant was found to be [3Hltaxol, by an analysis based on the Gibbs phase rule. This 90% value is consistent with the fact that about 90% of the radioactive material was pelleted, and the starting [3H]taxol was 99% pure. The less than 100% pelleting of [3Hltaxol did not result because of binding to unpolymerized tubulin subunits, since the amount of radiolabel that was not pelleted remained a t 10-12% when 2 p~ GMPCPP-microtubules was added to 5 m r3H1taxol in a solution containing either 0 or 10 tubulin subunits. We are M. Caplow  formly distributed along the microtubule, the end subunit usually has equilibrium with tubulin subunits in the microtubule so that it is unibound taxol. Taxol-tubulin subunits predominate at ends because subunits without taxol dissociate rapidly. IB, the path for disassembly of taxol-microtubules involves dissociation of taxol (rather than a taxoltubulin subunit). This slow, rate-limiting dissociation of taxol is followed by very rapid loss of underlying taxol-free subunits. 11, at high taxol concentrations taxol rebinds to terminal tubulin subunits before they dissociate from the microtubule end. The recapture of the end before tubulin subunit dissociation reduces the rate; under these conditions, the rate-limiting step for disassembly is loss of taxol-free subunits.
unable to account for the less than 100% recovery of [3Hltaxol in our binding reactions; perhaps a fraction of the microtubule pellet is lost because of turbulence during deceleration of the Airfuge rotor.
The agreement between the Kd values determined from kinetic and thermodynamic measurements proves that taxol is at equilibrium with tubulin subunits in the microtubule. For taxol in solution to be at equilibrium with terminal subunits, it is required that both taxol dissociation from and association with terminal subunits be faster than subunit dissociation. With regard to the taxol dissociation rate, since tubulin-GMPCPP rate on the taxol concentration. Note that at low taxol concentrations (Curve A, Region I), the rate is extremely sensitive to the taxol concentration because taxol is lost from terminal subunits relatively slowly, so that dissociation of underlying taxol-free subunits is impeded. The rate levels out at concentrations greater than Kd because virtually all subunits arriving at the end are bound to taxol, and the rate-limiting dissociation of taxol from terminal subunits is a first-order process. At higher taxol concentrations (Curve A, Region II), the rate decreases because taxol-free tubulin subunits at the microtubule end react with taxol faster than they dissociate from the end. The disassembly rate is reduced because addition of taxol consumes taxol-free tubulin subunits that had been generated in a rate-limiting step. Curve A was calculated from Equation 1, with k., the rate of dissociation of taxol-free subunits, equal to 1000 ~~( 5 ) .
The path fork, was assumed to involve loss of taxol (k.two,), followed by tubulin subunit dissociation from the microtubule (k-). For this sequence: k, = (k-taxo, x k_ll[k. + k+,,,,,(taxol)). For Curve A, k-,,,, was taken to be 30 s-', from the rate of disassembly with the taxol concentration between 25 and100 nM, and k,,,,, was taken to be 2 x 10' M-', to fit the data. Curve B was calculated for a mechanism in which taxol is at equilibrium with all subunits, including terminal subunits; the rate was calculated from the equation: rate = k. x f _ + k+ x f,. In this case, the curve resembles a simple titration curve with a half-maximal decrease in rate when 50% of the subunits have bound taxol. The data at high taxol concentrations rule out the mechanism described by Curve B. subunits dissociate from microtubule ends at a rate of only 0. 1-1 s" (3); maintaining equilibrium requires that taxol dissociate at a rate >10 SI. With regard to the taxol association rate, for this rate to exceed the subunit dissociation rate in the nM concentration range, the second-order rate constant for taxol addition must be on the order of 1 x lo9 s-', so that addition of taxol occurs at rates >10 s-', even at the lowest taxol concentration. Results described next prove that both the taxol dissociation and association rates with microtubules are sufflciently large to allow the taxo1:GMPCPP-microtubule reaction to be at equilibrium.
Reaction of Taxol with GTP-Microtubules-Because microtubules formed with GTP are more dynamic than GMPCPP-microtubules, there is an important difference in the mechanism for taxol inhibition of the disassembly rate. Unlike GMPCPPmicrotubules, where taxol-free subunits at the ends of microtubules wait around long enough before dissociating to rebind taxol from solution, taxol-free subunits at ends of GTP-microtubules are likely to dissociate before they rebind taxol. This rapid dissociation is expected to continue until a taxol-containing subunit is discovered at the microtubule end; as a result, terminal tubulin subunits will be enriched with tax01 compared to interior subunits (Fig. 3). Under these conditions, the observed rate constant for disassembly (kobs) is described by the relationship in Equation 1, where fand f+ are, respectively, the fraction of tubulin subunits in the microtubule without and with bound taxol ( f = (Kd)/(Kd + taxol) and f+ = (1f-)); Kis the rate of dissociation of taxol-free tubulin-GDP subunits (1000 s-'; Ref. 5) and K+ is the rate of dissociation of terminal subunits that arrive at microtubule ends with bound taxol. Substitution into Equation 1 reveals that if tubulin-taxol subunits dissociation is very slow, there is an enormous potential for taxol to retard disassembly. For example, if taxol reduces the rate of subunit dissociation loo-fold, then the disassembly rate is reduced 2-fold when only 1% of subunits contain taxol.
The disassembly rate with GTP-microtubules was too fast to study with taxol concentrations < 10 nM. The markedly reduced rate observed with 10 nM taxol was little changed by taxol concentrations up to 100 n~ (Fig. 4A). The invariance of the rate in this concentration range is consistent with the 5-20 nM Kd determined for taxol binding to GMPCPP-microtubules. It was, therefore, of interest that the disassembly rate decreased 10-fold when the taxol concentration was increased from 500 to 5000 nM (Fig. 4). This decrease apparently did not result from an increase in the amount of bound taxol, since the stoichiometry for taxol binding was constant when taxol was varied in the micromolar concentration range (experiment B in Table I).
The rate decrease at very high taxol concentrations would appear to result because the path for disassembly of taxolstabilized GDP-microtubules involves rate-limiting dissociation of taxol, followed by rapid loss of the resultant taxol-free subunit. The observed rate for microtubule disassembly when taxol dissociation is rate-limiting5 (ie. with 10-100 nM taxol) gives the rate constant for taxol dissociation; this is equal to 30 s-I.Akobs of d . 3 7 s-l was previously found for disassembly in 50 p~ taxol (7). This lower rate probably resulted from the inhibition by taxol concentrations > 0.5 PM, as described in Fig. 4. Fig. 4B shows that the rate is equal to k-,,, when k-> k,,,,(taxol). A different rate-limiting step holds at taxol concentrations sufficient that k _ < k+,,,(taxol). In this case, kabs = (Kd/(taxol)#. and loss of taxol-free subunits (k-) is rate-limiting.

Inspection of the equation describing k, in the legend to
It was possible to determine the rate constant for taxol binding to tubulin subunits at microtubule ends from the inhibition of the disassembly rate induced by 0.5-5 p~ taxol. Inhibition in this concentration range apparently results because the rate of taxol binding is sufficiently rapid so that taxol-free subunits are captured before they can dissociate; this corresponds to a change in rate-limiting step so that dissociation of taxol-free tubulin subunits becomes raCe-limiting.5 Since 0.5 VM taxol reduced kobs 2-fold, compared to the rate with taxol at 25-100 nM, the rate for taxol binding must be equal to that for subunit dissociation; the rate of taxol binding is therefore 1000 s-l. This rate with 0.5 VM taxol corresponds to a second-order rate constant equal to 2 x io9 M -~ s-'.
The Kd for reaction of taxol with GTP-microtubules can be calculated from the ratio of the constant for taxol binding and dissociation described above; this is equal to 30 s"I2 x lo9 = 15 nM. This value agrees with the 5-20 n~ value determined with GMPCPP microtubules (Figs. 1 and 2); however, these results differ dramatically from the 790-870 m value for Kd reported previously (2). In the earlier study, microtubules were titrated with [3Hltaxol under conditions where 100% of the added taxol bound to microtubules; the concentration of taxol sufficient to saturate half the active tubulin concentration was mistakenly taken to be the equilibrium constant. That is, microtubules assembled with microtubule protein containing 3.08 PM tubulin6 were found to bind 0.53 taxolhubulin dimer in microtubules at saturating concentrations of taxol, corresponding to binding of 1630 nM taxol. When 815 n~ taxol was added the concentration of tubulin subunits with and without bound taxol was equal. However, the concentration of free taxol was near zero, rather than equal to 815 m, as required if Kd is equal to 815 nM.