Mechanism of Microtubule Depolymerization by liaoqinmei


Vol. 255, No. 18, Issue of September 25, pp. 8560-8566. 19.84
Prrnled in U.S.A.

Mechanism of Microtubule Depolymerization

                                                                (Received for publication, December 18, 1979, and in revised form, May 16, 1980)

                  Timothy L. Karr, David Kristofferson, and Daniel L. PurichS
                  From the Departmentof Chemistry, University of California, Santa Barbara, California93106

  Microtubule disassembly has been studied using a                         Recently (3), we have developed an isothermal rapid dilution
rapid dilution technique (Karr, T. L., and Purich, D. L.                   technique which quickly drops the free monomer concentra-
(1979) J. BioL Chem. 254,10885-10888). Disassembly                         tion to well below the critical concentration, therebyallowing
curves, generated by computer from the solution of                         study of the depolymerization reaction without the interfering
series first order differential equations (see following                   effects of initiation orassembly. Earlier work on temperature-
paper), were fit to experimental data with excellent                       induced depolymerization kinetics   encountered inherent prob-
agreement when the diluted microtubules contained no                       lems (41, and it was desirable to further develop the rapid
microtubule-associated proteins. The rate constant for                     dilution method to characterize the  disassembly process. This
dimer release from microtubules was found to be 154                        requiredthe parallel development of akinetic theory for
s-’. Assuming a critical tubulin concentration of 8 to 9                   microtubule disassembly that includes the dependenceof the
X lo-‘ M, the apparent bimolecular rate constant (2 X
                                                                           disassembly process on the length distribution   (see miniprint
lo’ M” 5-l) for assembly is near the diffusion limit. It                   supplement’andthe        following paper). It was possible to
was also possible to use the rapid dilution technique
for quantitatively correlating the disassembly rate to                     correlate the computer-generateddepolymerization curves to
the number concentration of microtubule ends. These                        the experimental data. We report here on the application of
findings suggest that the dynamics of tubulin interac-                     our theory to study the   dynamics of microtubule disassembly.
tions with microtubules may be characterized in terms
of an endwise depolymerization model. A re-evaluation
of cold induced depolymerization kinetics (see mini-                                                    Materials
print supplement) is also fully consistent with our anal-
                                                                              GTP, Mes,’ and EGTA were obtained from Sigma. Phosphocellu-
ysis of disassembly dynamics.                                              lose was purchased from Whatman and all other chemicals used were
                                                                           reagent grade. The assembly/disassembly assay medium contained
                                                                           0.1 M Mes, 1 mM magnesium sulfate, and 1 mM EGTA and the pH
                                                                           was adjusted to 6.8 with KOH (designated ME medium). In experi-
  The end products of self-assembling systems (e.g. actin,                 ments involving phosphocellulose-purified microtubule protein, the
tubulin, viruses, and nucleosomes) result from an organized                ME medium contained 3.4 M glycerol and 16 m~ magnesium chloride
and deliberate packing of proteins and/or DNA into highly                  (5).
ordered and regulated structures. Many of these polymeric
structures have been studied in great detail and much has                                                Methods
been learned about their molecular dynamics and cellular                      Preparation of Microtubule Protein-Experiments involving the
behavior. Among these, the microtubule system has     received             dilution of whole microtubule protein (MTP) utilized protein pre-
much attentionfollowing the discovery by Weisenberg in 1972                pared by the method of Karr et al. (6), and experiments involving
                                                                           dilution of PC-tubulin used protein purified by the method of Shelan-
(1) of conditions for the self-assembly of tubulin into micro-             ski et al. (7). Atypicaldilution-induceddisassembly       experiment
tubules. Althoughmicrotubules have been studied avariety                   consisted of preparing the protein from a frozen pellet by thawing,
of methods(see Ref. 2 and references therein), the basic                   dissolving in ME medium a t 4”C, and centrifuging the protein a t
molecular mechanisms determining microtubule assembly/                     48,000 X g for 15 min after a 30-min incubation a t 4OC. The super-
disassembly behavior are only poorlyunderstood. Elucidation                natant from this procedure was used for subsequent assembly/disas-
of these mechanismsis complicated by the highly cooperative                sembly assays. Protein prepared as described above was also used to
                                                                           obtain phosphocellulose-purified microtubule protein. The microtu-
nature exhibited by the assembly process in addition to the                bule protein (75 mg) was loaded onto a      column    (1.6 X 10 cm)
complex nucleation events which have been postulated to                    containing phosphocellulose as previously described (8). The protein
occur at theinitiation of microtubule formation.
               of                            an
   In the study any kinetic system, it is obvious advantage
to be able to isolate and examine the individual elementary
                                                                              ’This discussion (including three additional figures) is presented
                                                                           in miniprintat the end this paper. Miniprintis easily read with the
processes from the obscuringeffects of other steps in the                  aid of a standard magnifying glass. Full size photocopies are available
mechanism, The process of microtubule formation appears     to             from the Journal of Biological Chemistry, 9650 Rockville Pike, Be-
be theresult of sequentialinitiation, polymerization, and                  thesda, Maryland 20014. Request Document No. 79M-2531, cite au-
depolymerization reactions which are not well time resolved.               thor(s), and includea check or money order for $1.00 per set of
                                                                           photocopies. Full size photocopies are also included in the microfilm
   * This research was supported in part by National Institutes of         edition of the Journal thatis available from Waverly Press.
Health Research Grant GM-24958. The costs of publication of this               Theabbreviations       used are: Mes, 2-(N-morpholino)ethane-
article were defrayed in part by the payment of page charges. This         sulfonic acidEGTA, ethylene         glycol bis(P-aminoethy1 ether)-
article must therefore be hereby marked “advertisement” in accord-         N,N,N’,N’,-tetraacetic acid; MAPS, microtubule-associated proteins;
ance with 18 U.S.C. Section 1734 solely to indicate this fact.             PC-tubulin, tubulin purified by phosphoceUulose chromatography;
   4 Recipient of a National Institutes of Health Research Career          MTP, whole microtubuleprotein; ME medium, 0.1 M Mes, 1 mM
Development Award and an Alfred P. Sloan Foundation Fellowship.            magnesium sulfate, 1 mM EGTA, pH 6.8.

                                                   Microtubule Depolymerization                                                         8561
peakwascollected,pooled        together, and glycerol and magnesium      val to the next smaller interval. Consequently, k , , the conversion rate
chloride added to 3.4 M and 16 mM, respectively. The protein Solution between intervals, is slower than the rate constant for dimer        release
was adjusted to 1.0 mM in GTP and incubated at 37°C to induce by the number of dimers per interval, 1600 X L. Alternatively, the
assembly. Themicrotubules were harvested by centrifugation at experimental rate constant can befound from Equation 2, assuming
N, x
I )m g for 2% h and the resulting pellets were frozen in liquid one reacting end permicrotubule. One first converts the experimental
nitrogen. This pelleted material was then subsequently prepared as rate in absorbance/s to dimers/s by assuming a direct proportionality
described above and then used for assembly/disassembly assays as between absorbance and polymer weight (9). The rate in dimersh is
described below.                                                                                                             get
                                                                         then divided by the number concentration, n, to the rate of dimer
   Microtubule Assembly/Disassembly Assay-Microtubule assem- release/end.
bly/disassembly assays were performed as follows: microtubule pro-
                                                                                                         N,, (Cu - C )
tein,preparedasabove,       wasinduced toassemble by raising the                     n=                                                         (2)
temperature to30°C or 37°C. The assembly and      disassembly reactions                   (110,OOOg/mol) (1,600 dimerdpm) . <l>
were monitored turbidimetrically in a thermally regulated chamber        Where C,, is the total protein concentration, C, is the tubulin critical
of a Cary 118 recording spectrophotometer a t 350 nm(9). After           concentration, N,, is Avogadro’s number,and < I > is the average
assembly plateau was attained, the sample diluted approximately microtubule length in micrometers. The polymer concentration
20- to 50-fold. The exact dilution of the sample was later determined - Cc) must be corrected for the presence of nontubulin protein if
by the Bradford method (10). The design and application of a rapid       necessary. The averagemicrotubule length is determined by the
dilution mixing cell have been described (3, 11). Samples were pre- method given above.
pared for electron microscopic examination asdescribed below. Data          Comparing the two methods, one finds that the computer simula-
analysis of the kinetics of disassembly is also described below.         tion method is more accurate. Although both methods entail doing
   Preparation of Microtubules for Electron MicroscopicAnalysis-         length distribution measurements and extrapolating the experimental
Microtubulesamples for lengthdistributiondeterminations            were curves back to time zero, the computer simulation avoids any errors
prepared by standard procedures using cytochrome c, uranyl acetate, introduced by measuring protein concentrations which are only re-
andParlodion-coated 75 mesh grids. Inordertoobtainaccurate
                                                                         quired in the initial rate method.
length measurements, the samples       were first diluted 1:lO into iso-
thermal 50% sucrose (w/v) in ME medium and then fixed on grids.
This procedure lowered the microtubule density on the grids to a
level which allowed for accurate tracings of individual microtubules.       Kinetics of Microtubule Disassembly after Rapid Dilu-
A control experiment, done at low microtubule protein concentra-         tion-In an earlier report (3), it was possible to demonstrate
tions, showed that the average length of microtubules prepared with
                                                                         the celerity of microtubule depolymerization by using a rapid
or without the sucrose dilution was the same within experimental
error.Thisresult      is similar tothosereported      previously in the dilution technique. We encountered several minor experimen-
literature (12).                                                         tal difficulties inadapting the rapid dilution method quan-    for
   Determination of Microtubule Length Distributions a n d Compu- titative work on microtubule disassembly. The rapid dilution
tation of Theoretical Depolymerization Curues-Electron photomi- cuvette required refinement to                   minimize bubble formation
crographs a t a final magnificationof 4000 times were used to generate during the initial     mixing step. We also foundthat itis essential
the length distribution histograms. Using either a Hewlett-Packard
9825 calculator or adigitalDigital       Equipment Corp. P D P 11/03
                                                                         to remove gas and dust the buffer to eliminatenoise and
microprocessor equipped with a bomb site digitizer (15), the histo-      bubbles which can be a problem in            terms of the amplitude
grams could easily be generated by tracing over the microtubules         changes measured in these experiments. We first attempted
with the bomb site and allowing the calculator to process the data. to fit experimental disassembly curves to a computer-gener-
The sample size for a typical histogram was between       500 and 1000. ated curve asdescribed under “Methods.” Despite numerous
The histogram data were then used in a computer program to gen- attempts, the two curves were nonsuperimposable, as shown
erate a theoretical depolymerization curve (see following paper for
                                                                         in Fig. 1. The two curves consistently correlated well for the
   Calculation of Depolymerization Rate Constant-The experimen- first 70%of the reaction and then the experimental curve
tal curve was fit to the same scale by matching the initial turbidity consistently deviated above the theoretical one. Since the
reading and computer polymer weight values and using this ratio to theoretical curve was generated using histograms of microtu-
convert the turbidity to computer      polymerweights. The polymer       bule length distributions,we wished to eliminate the            possibil-
weight units are arbitrary since the computer programcalculated the ity that these distributions          were biased by the counting tech-
total length in micrometers of microtubules present in the histogram
                                                                         nique used. As discussed in the inset to Fig. 1, the computed
sample. The total length is clearly directly proportional to polymer
weight. The time axes were matched by using the ratio of times a t curve changesvery little over the number range this study.       in
the fiist half-lives and can be converted to seconds by this ratio. A                                         of
                                                                            Another interesting feature the disassembly curve is that
rate constant of 5 reciprocal computer time units was employed in the first 70% follows an exponential decay with a correlation
the theoretical calculation. Having matched the experimental and         coefficient of 0.999 with the complete reaction correlation
theoretical curves, the next step is tocalculatethe         microscopic equal to 0.99. It was, therefore, possible to fit the curve to an
depolymerization rate constant, k,, from the rate constant k , in the
                                                                         exponential of the form f(t) = ae-k‘ and to extrapolate to       back
computer simulation.The calculation requires two conversion factors
as shown in the following formula:                                       zero time to determine accurately the         initial turbidity reading
                                                                             for the reaction. The initial rate of depolymerization could
                    k,   =   kc.: .(lMX)”).L
                                t        dimers                              also be determined by solving the first derivative at zero time
                                t,                                           as was done in the shearing experiments   described below.
                                                                                Kinetics of PC-purifiedMicrotubule Disassembly-We
where t,. and t , are the half-lives for the computer and experimental were still faced with thepoor fit of the theory to experimental
reactions, and L is the histogram interval length in micrometers. T o data at the latter part the reaction, and we reasoned that
explain the first factor, we note that since k,. is in reciprocal computer
time units, one converts it to s” by multiplying it by the ratio of the      the MAPs present could be perturbing the kinetics. To elim-
computer and experimental half-lives. This is the same method that inate thispossibility, microtubule proteinwas further purified
is used to match the time axes of the experimental and theoretical           by phosphocellulose chromatography which removes essen-
curves. The second conversion factor arises from the           necessity to tially all of the MAPs fraction Microtubules formed in the
limit the number of reacting species in the computer program. Since absence of MAPs were diluted as described above and the
microtubules contain approximately 1600 dimers/pm, our program               theoretical and experimental curves are  shown inFig. 2 A . The
would need 1600 reacting subunits to handlea microtubule of only 1
pm in length. T o circumventthis problem, we use the histogram               curves compareextremely well with each other for the entire
intervals as the reacting  species and the frequency values as      concen- reaction. An explanation for the divergence of progress curves
trations in the computer simulation. The computer rate constant, in Fig. 1 but not Fig. 2 is given under “Discussion.” Compar-
therefore, governs the depolymerization of microtubules in any inter- ison of the histograms in Figs. 1 and 2B shows that the only
                                                         Microtubule Depolymerization

                                          Average Length; 6.5 p m

                                Microtubub Length~pm)


                                                                                                                    Average Length ~5.2m

                 2      4   6      8     10     12      14     16
  FIG. 1. Plot of theoretical   ()
                                 -   experimental (0)depo-
lymerization curves for whole microtubule protein. The theo-
retical curve was calculated from the frequencies in the inset. The
experimental curve was obtained by diluting 0.4 ml of a 0.92 mg/ml
microtubule solution at steady state into approximately 18.2 mlof
isothermal (30°C) buffer containing 0.5 mM GTP in the rapid dilution
mixing cell. Computer time units are used. One time unit = 12.7 s.                                      15                         45
Inset, condensed microtubule length distribution for whole microtu-                                    M~croiubulelength,lptn)
bule protein. Frequency values from an expanded version of this              FIG. 2. Plot of theoretical ()
                                                                                                          -     and experimental (0)depo-
histogram with twice as many intervals were used in the computer           lymerization curves for PC-purified tubulin. The theoretical
calculations. To test the effect of distribution size on the theoretical   curve was calculated from the frequencies in B. A rate constant of 5
curve, 500 and IO00 microtubule samples were also used to calculate        reciprocal computertimeunits        wasemployed inthetheoretical
curves. If one compares these curves to the theoretical curve in this      calculation. One computer time unit = 34.5 s. A , the experimental
figure, they arevirtually identical. The largest deviation betweentime     curve was obtained by diluting 0.5 ml of a 2.4 m g / d microtubule
zero and time 15 is only 8% of the Fig. 1 values.                          solution a t steady state into approximately   18.2 ml of isothermal
                                                                           (30°C) buffer containing 0.5 mM G T P in the rapid dilution cell. Inset,
                                                                           first order plot of the experimental data points in B , microtubule
obvious difference is in the average length the samples (6.5               length distribution for PC-purified tubulin used in the calculations
uersus 5.2 pm, respectively). Whether or not this difference               for A .
accounts for thedeviationsseen in MAP tubules will be
discussed below.                                                                        3
  Dependence of the Initial Disassembly on the Number
Concentration of Microtubule Ends-One of the better ways                                        "Sheared Sample"
to describe a mechanism for microtubule disassembly is to
observe its kinetic dependence on the number concentration
since it can be shown (Equation 3, below) that the initial rate
should be proportional to the number concentration micro-
tubule ends (4):

where c , is the free monomer concentration and c, is the
microtubule number concentration. Under our experimental
conditions, the association reaction can be ignored and the                    0     20    40    60      80 100 120   '
rate is, therefore, directly proportional to c,~.The data pre-                             lime after Dilution,(secondr)
sented in Figs. 3 and 4 demonstrate the correlation between        FIG. 3. Microtubule shearing experiment. Upper curue, exper-
the disassembly kinetics and the histograms of sheared and imental depolymerization curve of sheared                          sample.
unsheared microtubules. Clearly, both the rate and total re- Lower curue, experimental depolymerization curve of unsheared mi-
action time are faster and shorter,respectively, for the sheared crotubule sample. In both the upper and lower curves, depolymeri-
                                                                 zation was initiated by injecting approximately 0.4 ml of a 1.5 mg/ml
sample as expected. Table I quantitates these results and        microtubule solution at steady state into approximately 18.2mlof
illustrates the very close agreement between the observed buffer a t 37°C containing 0.5 m GTP. Shearing was performed by
initial rates and the change in the average lengths. Earlier rapidly drawing a portion of the unsheared samplefrom the solution
studies ( 4 ) only provided a semiquantitative relationship be- used for the upper curve three times through 22-gauge needle.
                        Depolymerization                Microtubule                                                                    8563
tween initial rates and number concentration, as discussed                                 TABLE   I1
further in the miniprint supplement. Since average length Summary of rate constants measuredby computer simulation and
                                                                                     initial rate analyses
is directly related to thenumber of ends, we conclude that the
microtubules depolymerize from the ends.                        Values obtained from Equations I and 2 given in text.
   In Table we present the measured depolymerization rate
constants for PC-tubulin and whole microtubule protein. Uti-
lizing the fact that the critical concentration equals K,,, we
can then calculate the on-rate constant also shown in Table
                                            as                                                                    X IO' M " s"

1 . For PC-tubulin, the off-rate constant at 30" C is 105 s",
  1                                                            MTP               113" (la)*        113 (150)            lo'
corresponding to a 9.5 ms average lifetime for a dimer on ? Sheared MTP               (150)         (150)               10
microtubule end. This yields an on-rate constant of 1 X 10' PC-tubulin                             105 (210)             1
"1   s-l
                                                                  Values obtained at 30°C.
         using a criticd concentration of 8 to 10 X lod6M (5).             'I

A similar analysis for microtubule proteinyields values in the  * Values in parentheses were measured at 37°C.
range of 1 X 10' M" s-'. We should note here that the on-rate " Values obtained by using equilibrium constants given in text.
constants were estimated using a Keqvalue of approximately
 1X        M which is a lowest estimate because the MAPS are
also diluted in this process and, consequently, the critical
 concentration will be correspondingly higher. This is not a
 problem when PC-tubulin is used.
   Using Table 11, we may also compare the off-rate constants
 at 30°C and 37°C for whole microtubule protein. As expected,
 the rate constant sensitive to temperature, and this temper-
 ature dependence is being further studied in this laboratory.
   Careful inspection of the disassembly curve for the sheared
 sample in Fig. 3 reveals that the shape and the time course

                      (A)           Average L e n g t h z 7 9 5 ~ m
             40   n

                                                                           FIG.5. Theoretical (-)      and experimental (0)depolymeri-
                                                                         zation curves for the sheared microtubule sample (from Figs.
                                                                         3 and 4). The theoretical curve was calculated from the frequencies
                                                                         given in Fig. 4B. Theexperimental curve was fit to the computer data
                                                                         as explained under "Methods." One computer time unit = 9.8 s.

                                                                       for the reaction were very similar to those obtained from PC-
                                                                       tubulin. We, therefore, analyzed the histogram and the exper-
                                                                       imental tracing in Fig. 3 for a possible correlation between the
                                                                       two. The results of this analysis are presented in      Fig. 5.
                                                                       Surprisingly, the correlation is as good if not better than the
                                                                       curves shown in Fig. 2. This would indicate that either the
                                                                       time course for the reaction or the shape of the histogram is
                                                                       important in determining the degree to which the experimen-
  FIG. 4. Histograms of sheared andunsheared microtubules. tal and theoretical analyses correspond. These possibilities
A, experimental length distribution of the unsheared microtubule
sample used in Fig. 3. B, experimental length distribution of the same will be examined under "Discussion."
microtubule solution as in A after shearing the tubules by three rapid
passes through a 22-gauge needle. Average lengths were calculated                                   DISCUSSION
using expanded versions of these two histograms which have been           The assembly/disassembly properties of microtubules ap-
condensed for the purpose of simpler illustration.                     pear to involve a complex series of interactions with accessory
                                                                       proteins (16,17), nucleotide binding and hydrolysis (18,191,
                             TABLE      1                              and subsequent elongation until an apparent equilibrium is
   Initial rate dependence on microtubule number concentration         reached. The assembly reaction is also characterized by its
  Results are for whole microtubule Protein.
                                                                    - high temperature dependence as would be expected for an
    Sample"         :
                   ?iy        Initial rate erage lengths Ratio of ini-
                                            Ratio of Av-
                                                          tial rate
                                                                       entropy-driven process (14). Prior work has focused on the
                                                                       assembly properties of microtubules, and many of the effectors
                     pm       X IO-^ A / ~
Unsheared            7.95       - 12.7                                 (e.g.colchicine) have been described in terms of the assembly
                                                                       inhibition of the reaction (20). Unfortunately, careful kinetic
                                               3.12         3.18       studies of assembly are complicated by these complex inter-
                                                                       actions, making mechanistic interpretations difficult.
Sheared             2.55          -4.0                                   These inherent difficulties in the analysis of microtubule
  " For experhental details see legends to Figs. 3 and 4 and "Re- assembly led us toattackthe             problem from the reverse
sults."                                                                direction by fist describing the disassembly properties of the
8564                 Depolymerization         Microtubule
system (3). Conceptually this should be the simplest process         attractive to explain the excellent fit‘ between theory and
to analyze kinetically because we can experimentally make            experiment in Fig. 5 as beingmainly due to the marked
 the process unidirectional and irreversible. We have success-       decrease in the total reaction time        (100 s uersus 460 s for
fully used the isothermal rapid   dilution technique to correlate    sheared and unsheared, respectively). Other differences be-
experimental results with theoretical predictions (for      a de-                                      as
                                                                     tween the two samples such the average length and distri-
tailed description of the theoreticalderivation, see thefollow-                                                in
                                                                     bution shape are taken into account the theory, and are       we
ing paper).                                                          led to conclude that the                           in
                                                                                                 longer reaction times the unsheared
   Theexperimentspresentedabovedeal              with isothermal     sample give the MAPs time to rebind to the microtubules,
microtubule disassembly upon rapid dilution. On the other            thereby attenuating the      dissociation rate. These observations
hand,Johnsonand         Borisy(4) havestudied cold induced           led us further to  conclude that MAP-free microtubules should
disassembly, and their conclusions were based in part upon           show no deviation in the correlation kinetics. The results of
the assumption that the microtubule length distribution              shape A and B, clearly showthis to be the
                                                                     Fig. 2,                                         case. Microtubules
remains constant throughout the disassembly process. Work            formed in the absenceof MAPs correlate extremely          well with
by Kristofferson et al. (13) suggests that this assumption is        the threotical predictions throughout the entire time course.
not strictly true, but there isa more significant experimental       We, therefore, conclude that microtubules disassemble from
limitation regarding the time required for the temperature           their ends in accordance with the models proposed (3,4, 13).
jump from 30°C to 5.4”C. Johnson and Borisy (4) predicted               Figs. 3 and 4 demonstrate in a qualitative fashion how the
that the shape the depolymerization curve shouldbe linear            shapes of the distribution canprofoundly alter thekinetics of
over the range in which the number concentration remained            the reaction. Shearing microtubules to approximately one-
unchanged, and curvature should result the polymer num-              third of their length resultedin a %fold increase in the initial
                               in                of
ber concentration is changed the late phase the disassem-                                                             was
                                                                     rate (see Table I). The total reaction time also substan-
bly. Indeed, they observed a linear depolymerization time                                                               of
                                                                     tially decreased andwe noted that the shape the disassem-
course for a substantial fraction of the entire process. This        bly curve for the sheared sample resembled that of the PC-
result is in disagreement with our findings, and it requires         tubulin curve. We, therefore, correlated the experimental re-
explanation. We reasoned that thecold depolymerization ex-           sults of the sheared sample to the theoretical curve, and as
periments were possibly misleading because their apparent            noted above, they correlated to a high degree (see Fig. 5).
cold induceddisassembly curves must be deconvoluted to                  Table I1 summarizes our results for the measured off-rate
eliminate the effects of the slow temperature jump and the           constants and the calculated on-rate constants.      One important
change in rate constant with temperature. Furthermore, the           result in Table I1 is that theoff-rate constant for the sheared
central region of their water-jacketed glass cuvette shouldbe        microtubule sample is very nearly the same as calculated by
the last to achieve thermal equilibration in the absence of          either Equations 1 or 2. This furthers our conviction that
mechanical mixing. For these reasons, we reinvestigated this         microtubules are disassembling from their ends in a manner
matter with the aid of a specially fabricated rapid heat ex-         consistent with the model proposed (13). The off-rate con-
changer capableof thermal equilibrationin less than 3 s. The         stants reported in Table I1 for PC-tubulin and whole micro-
results in the miniprint supplement areclearly in agreement          tubule protein cannot at thispoint be directly compared
with the mechanistic interpretations presentedin our study.          because of differences in the buffers used. Curiously, these
Most significantly,the theoretical and experimental    disassem-     reverse rates exceed those reported by Johnson and Borisy
bly kinetics is in remarkable agreement (see Fig. 3 of the           (4)by a factor of approximately 22. It is not clear to what
supplement). A rate constant of 166 s-’ was obtained in our          extentthese differencesreflectspecies          variationor buffer
cold depolymerization studies, and itis clear from these data        conditions since these investigators used porcine brains and
that the rate of polymer disappearance is changing continu-          no glycerol for their studies. Recently, the disassembly rate
ously as evidenced by the lack of any linear segment to the          constant has been revised upwards by work from Borisy’s
disassembly curve.                                                   laboratory (23) to approximately 24/s when one accounts for
   An interesting feature the disassembly curves is that they
                           of                                        theactivity at both ends. Thisleavesourrateconstants
are initially nearly first order. We have found that the shape       differing from each other by a factor of 5 to 10. We have
of the observed progress curve is influenced by the form of          shown in separate experiments (data not shown) that order   in
the length distribution and the microtubule number       concen-     to obtain a true off-rate constant, one must dilute to          well
tration changes during disassembly. A sound theoretical un-          below the critical concentration. Since the rate is -dS/dt =
derpinning for these statements and the data analysis    is given                                            -
                                                                     k+[M[q- k-[IMJ = [ M I (k+[S] k - ) , it is important that
in the accompanying report (13).                                          S remain muchless thank- to obtain an accurate off-rate
                                                                     k , [I
   Dilution of MAP-containing microtubles      gave experimental     constant. In previous work from Borisy’s laboratory, thefinal
tracings which consistently failed to correlatewith theoretical      concentrations of protein after dilution     were 0.08 and 0.32 mg/
predictions at latertimes,asshown          in Fig. 1. Wewere,        ml. Their microtubule preparation had       a criticalconcentration
therefore, intrigued by the very close agreement between the         of 0.2 mg/ml, consequently, in the latter case, the microtu-
theoretical and experimental tracings when sheared whole             bules did not completely depolymerize when added to buffer.
microtubule protein   was used for disassembly experiments
                                    the                              In experiments not shown, we have demonstrated that even
(see Fig. 5). One possible explanation for the kinetic behavior      at a final dilution of 4 times below the critical concentration,
in Fig. 1 could be that as microtubules depolymerize, the                                     by
                                                                     the rate has changed a factor of 2 over an identical sample
MAPs that arefreed can also rebind to still existing microtu-        diluted to the  critical concentration. InFig. 2, the microtubule
bules and stabilize them further, thereby    decreasing their off-   samples were diluted 12.5 times below the critical concentra-
rate constant. Alternatively, since dilution perturbs the equi-      tion, and these differences in dilution technique most likely
librium, MAPs may dissociate along the entire length of the          account for the discrepancy between the two reported rate
microtubule. As the microtubulesdepolymerize, the MAPs to            constants. Priorwork by Bryan (24) and Sternlicht and        Ringel
polymer ratio will increase, and by Le Chatelier’s principle,        (25) utilized experimental procedures similar to Johnson and
the MAPs may rebind and perturb the        kinetics.                 Borisy’s ( 4 ) and, therefore, differences in rate constants may
   The deviations from theory in Fig. 1 are most likely the          have a similar interpretation.
result of MAP-induced perturbations (21, 22). It, therefore, is         In conclusion, we should note that themolecular action of
                                                  Microtubule Depolymerization                                                          8565
many microtubule effectors remains relatively unclear. For       8. Weingarten, M. D., Lockwood, A. H., Hwo, S. Y., and Kirschner,
example, does calcium-induced depolymerization resultfrom             M. W. (1975) Proc. Natl. Acad. Sci. U. S. A. 72, 1858-1862
endwiserelease of dimersor destabilization of the overall        9. Gaskin, F., Cantor, C . R., and Shelanski, M. L. (1974) J. Mol.
microtubule structure?   The mechanistic implicationsare par-         Biol. 89,737-755
                                                                10. Bradford, M. M. (1976) Anal. Biochem. 72,248-254
ticularly important when viewed in terms       of the action of 11. Karr, T. L., and Purich, D.L. (1980) Anal. Biochem. 104, 311-
calmodulin,the calcium-dependent regulatory proteingreatof            314
abundance in brain  tissue. The methods outlined in this report 12. Margolis, R. L., and Wilson, L. (1978) Cell 13, 1-8
provide a theoretical and experimental basis for examining      13. Kristofferson, D., Karr, T. L., and Punch, D. L. (1980) J. Biol.
such processes. In this respect, it will also be of interest to       Chem. 255,8567-8572
probe other polymeric protein structures such as actin and 14. Lauffer, M. (1978) in Physical Aspects of Protein Interactions
                                                                      (Catsimpoolas, N., ed), pp. 115-170, Elsevier/North Holland
flagellin which also have assembly/disassembly properties.            Publishing Co., New York
                                                                15. Shindell, D. M., Magagnosc, C., and Purich, D.L. (1978) J.Chem.
  Acknolwedgments-We are pleased to acknowledge Mr. Me1 Ald-                  Ed. 55, 708-711
erman’s help in providing calf brain tissue. We are also grateful to    16. Murphy, D. B., and Borisy, G. G. (1975) Proc. Natl. Acad.Sei. U.
Dr. Hona Metiu for helpful discussions.                                       S. A . 72,2696-2700
                                                                        17. Sloboda,R. D., Dentler, W.    L., and Rosenbaum, J. L. (1976)
                                                                              Biochemistry 15,4497-4505
                         REFERENCES                                     18. Kobayashi, T . (1975) J . Biochem. (Tokyo) 77, 1193-1197
1. Weisenberg, R. (1972) Science 177, 1104-1105                         19. MacNeal, R. K., and Purich, D.L. (1978) J. B i d . Chem. 253,
2. Goldman, R., Pollard, T., and Rosenbaum, J., eds, Cold Spring              4683-4687
     Harbor Conference on Cell Proliferation 111. Cell Motility, pp.    20. Margolis, R. L., and Wilson, L. (1977) Proc. Natl. Acad. Sci. U.
     1065-1233, Cold Spring Harbor Laboratory,     New York                   S. A . 74,3466-3470
3. Karr, T. L., and Punch, D. L. (1979) J. Biol. Chem. 254, 10885-      21. Murphy, D. B., Johnson, K. A., and Borisy, G. G. (1977) J.Mol.
     10888                                                                    Biol. 117, 33-52
4. Johnson, K. A., and Borisy, G. G. (1977) J. Mol. Biol. 117, 1-31     22. Sloboda, R. D., and Rosenbaum, J . L. (1979) Biochemistry 18,
5. Lee, J. C., and Timasheff, S.N. (1975) Biochemistry 14, 5183-              48-55
     5187                                                               23. Bergen, L. G., and Borisy, G. G. (1980) J. Cell Biol. 84, 141-150
6. Karr, T. L., White, H. D., and Purich, D. L. (1979) J.Biol. Chem.    24. Bryan, J. (1976) J.Cell Biol. 71, 749-767
     254,6107-6111                                                      25. Sternlicht, H., and Ringel, I. (1979) J. B i d . Chem. 254, 10540-
7. Shelanski, M. L., Gaskin, F., and Cantor, R. C. (1973) Proc. Natl.         10550
     Acad. Sci. U. S. A. 70, 765-768                                    Additional references are found on p. 8566.
8566   Microtubule Depolymerization

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