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THE JOURNAL OP BIOLOGKXL CHEMISTRY 0 1990 by The American Society for Biochemistry and Molecular Biology, Inc. Vol. 265, No. 8, Issue of March 15, pp. 438%43&3,1990 Printed in IJ. S. A. Microtubule Oscillations ROLE OF NUCLEATION AND MICROTUBULE NUMBER CONCENTRATION* (Received for publication, July 21, 1989) Heike Obermann, Eva-Maria Mandelkow, Gudrun Lange, and Eckhard MandelkowS From the Man-Planck-Unit for Structural Molecular Biology, % DESY, Notkestrasse 85, D-2000 Hamburg 52, Federal Republic of Germany Microtubules are capable of performing synchro- nized oscillations of assembly and disassembly which has been explained by reaction mechanisms involving tubulin subunits, oligomers, microtubules, and GTP. Here we address the question of how microtubule nu- cleation or their number concentration affects the os- cillations. Assembly itself requires a critical protein concentration (C,), but oscillations require in addition a critical microtubule number concentration (CM,). In spontaneous assembly this can be achieved with pro- tein concentrations C,. well above the critical concen- tration C!, because this enhances the efficiency of nu- cleation. Seeding with microtubules can either gener- ate oscillations or suppress them, depending on how the seeds alter the effective microtubule number con- centration. The relative influence of microtubule num- ber and total protein concentrations can be varied by the rate at which assembly conditions are induced (e.g. by a temperature rise): Fast T-jumps induce oscilla- tions because of efficient nucleation, slow ones do not. Oscillations become damped for several reasons. One is the consumption of GTP, the second is a decrease in microtubule number, and the third is that the ratio of microtubules in the two phases (growth-competent and shrinkage-competent) approach a steady state value. This ratio can be perturbed, and the oscillations re- started, by a cold shock, addition of seeds, addition of GTP, or fragmentation. Each of these is equivalent to a change in the effective microtubule number concen- tration. The self-assembly of biological polymers is traditionally described in terms of two main stages, nucleation and elon- gation (reviewed in Oosawa and Asakura, 1975). Nucleation tends to be slow, showing up as a lag in assays sensitive to overall polymerization. Because of the cooperative nature of nucleation its rate depends strongly on the protein concentra- tion; this in turn influences the apparent assembly rate which depends on polymer ends (Gaskin et al., 1974; Engelborghs et al., 1976; Bryan, 1976; Johnson and Borisy, 1977). The model implies that the polymer number concentration stays roughly constant after the nucleation phase, leading to pseudo-first order elongation kinetics. The final state is given by the equilibrium between subunits associating to the polymer ends *This work was supported by the Bundesministerium fiir For- schung und Technologie and the Deutsche Forschungsgemeinschaft. The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked “aduertisement” in accordance with 18 U.S.C. Section 1734 solely to indicate this fact. $ To whom correspondence should be addressed. and dissociating from them, such that a critical concentration of subunits remains in solution. The above description is only a first approximation; sec- ondary effects may include polymer fragmentation (Wegner and Savko, 1982), annealing (Rothwell et al., 1987), hetero- geneous nucleation (Voter and Erickson, 1974; Ferrone et al., 1985), and others. In particular, assembly may be coupled to nucleotide hydrolysis (ATP for actin, GTP for microtubules). This leads to treadmilling (Wegner, 1976; Margolis and Wil- son, 1978) or, in the case of microtubules, to dynamic insta- bility (Mitchison and Kirschner, 1984). In the latter case the polymers can fluctuate between phases of growth and shrink- age (Horio and Hotani, 1986; Walker et al., 1988). The “final state” equilibrium is now replaced by a steady state, deter- mined mainly by the association of protein with bound XTP and dissociation with bound XDP. The steady state concen- tration of unpolymerized protein is no longer independent of the polymer number concentration (Pantaloni et al., 1984). In the case of microtubules the dynamics of growth and shrinkage can be synchronized, leading to oscillations in bulk solution that can be observed by turbidity, x-ray scattering, or electron microscopy (Carlier et al., 1987; Pirollet et al., 1987; Chen and Hill, 1987; Mandelkow et al., 1988; Lange et al., 1988; Melki et al., 1988; Wade et al., 1989). Several models have been proposed to explain the phenomenon. One is based on the interactions between subunits and polymers and re- quires a slow (rate-limiting) exchange of GTP on subunits (Chen and Hill, 1987); the other is based on subunits, poly- mers, and oligomers (Mandelkow et al., 1988). In the model illustrated, microtubules are formed from assembly-competent subunits (tubulin. GTP); oligomers with bound GDP must dissociate before their subunits can be utilized for assembly (Spann et al., 1987); microtubules be- come intrinsically unstable after GTP hydrolysis and when the supply of tubulin. GTP becomes too low; they disassemble into oligomers (Mandelkow and Mandelkow, 1985); and the slow release of subunits from oligomers is an important factor for the oscillations. Several features were left open in the model below. In particular, computer modeling suggested that the microtubule number concentration played a key role in the oscillations. In other words, while the synchronization of the whole popula- tion and certain buffer conditions (affecting the intrinsic rate constants) are prerequisites, they fail to induce oscillations unless the polymer concentration is sufficiently high. The experiments reported here were designed to test this hypoth- esis. We show that oscillations can be influenced in three ways, all of which alter the effective number concentration: 1) variation of the rate of nucleation, 2) addition of polymer seeds, and 3) chemical or physical perturbation of an oscillat- ing solution. The data suggest that the control of the micro- 4382 by guest on June 29, 2020 http://www.jbc.org/ Downloaded from
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  • THE JOURNAL OP BIOLOGKXL CHEMISTRY 0 1990 by The American Society for Biochemistry and Molecular Biology, Inc.

    Vol. 265, No. 8, Issue of March 15, pp. 438%43&3,1990 Printed in IJ. S. A.

    Microtubule Oscillations ROLE OF NUCLEATION AND MICROTUBULE NUMBER CONCENTRATION*

    (Received for publication, July 21, 1989)

    Heike Obermann, Eva-Maria Mandelkow, Gudrun Lange, and Eckhard MandelkowS From the Man-Planck-Unit for Structural Molecular Biology, % DESY, Notkestrasse 85, D-2000 Hamburg 52, Federal Republic of Germany

    Microtubules are capable of performing synchro- nized oscillations of assembly and disassembly which has been explained by reaction mechanisms involving tubulin subunits, oligomers, microtubules, and GTP. Here we address the question of how microtubule nu- cleation or their number concentration affects the os- cillations. Assembly itself requires a critical protein concentration (C,), but oscillations require in addition a critical microtubule number concentration (CM,). In spontaneous assembly this can be achieved with pro- tein concentrations C,. well above the critical concen- tration C!, because this enhances the efficiency of nu- cleation. Seeding with microtubules can either gener- ate oscillations or suppress them, depending on how the seeds alter the effective microtubule number con- centration. The relative influence of microtubule num- ber and total protein concentrations can be varied by the rate at which assembly conditions are induced (e.g. by a temperature rise): Fast T-jumps induce oscilla- tions because of efficient nucleation, slow ones do not. Oscillations become damped for several reasons. One is the consumption of GTP, the second is a decrease in microtubule number, and the third is that the ratio of microtubules in the two phases (growth-competent and shrinkage-competent) approach a steady state value. This ratio can be perturbed, and the oscillations re- started, by a cold shock, addition of seeds, addition of GTP, or fragmentation. Each of these is equivalent to a change in the effective microtubule number concen- tration.

    The self-assembly of biological polymers is traditionally described in terms of two main stages, nucleation and elon- gation (reviewed in Oosawa and Asakura, 1975). Nucleation tends to be slow, showing up as a lag in assays sensitive to overall polymerization. Because of the cooperative nature of nucleation its rate depends strongly on the protein concentra- tion; this in turn influences the apparent assembly rate which depends on polymer ends (Gaskin et al., 1974; Engelborghs et al., 1976; Bryan, 1976; Johnson and Borisy, 1977). The model implies that the polymer number concentration stays roughly constant after the nucleation phase, leading to pseudo-first order elongation kinetics. The final state is given by the equilibrium between subunits associating to the polymer ends

    *This work was supported by the Bundesministerium fiir For- schung und Technologie and the Deutsche Forschungsgemeinschaft. The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked “aduertisement” in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

    $ To whom correspondence should be addressed.

    and dissociating from them, such that a critical concentration of subunits remains in solution.

    The above description is only a first approximation; sec- ondary effects may include polymer fragmentation (Wegner and Savko, 1982), annealing (Rothwell et al., 1987), hetero- geneous nucleation (Voter and Erickson, 1974; Ferrone et al., 1985), and others. In particular, assembly may be coupled to nucleotide hydrolysis (ATP for actin, GTP for microtubules). This leads to treadmilling (Wegner, 1976; Margolis and Wil- son, 1978) or, in the case of microtubules, to dynamic insta- bility (Mitchison and Kirschner, 1984). In the latter case the polymers can fluctuate between phases of growth and shrink- age (Horio and Hotani, 1986; Walker et al., 1988). The “final state” equilibrium is now replaced by a steady state, deter- mined mainly by the association of protein with bound XTP and dissociation with bound XDP. The steady state concen- tration of unpolymerized protein is no longer independent of the polymer number concentration (Pantaloni et al., 1984).

    In the case of microtubules the dynamics of growth and shrinkage can be synchronized, leading to oscillations in bulk solution that can be observed by turbidity, x-ray scattering, or electron microscopy (Carlier et al., 1987; Pirollet et al., 1987; Chen and Hill, 1987; Mandelkow et al., 1988; Lange et al., 1988; Melki et al., 1988; Wade et al., 1989). Several models have been proposed to explain the phenomenon. One is based on the interactions between subunits and polymers and re- quires a slow (rate-limiting) exchange of GTP on subunits (Chen and Hill, 1987); the other is based on subunits, poly- mers, and oligomers (Mandelkow et al., 1988).

    In the model illustrated, microtubules are formed from assembly-competent subunits (tubulin. GTP); oligomers with bound GDP must dissociate before their subunits can be utilized for assembly (Spann et al., 1987); microtubules be- come intrinsically unstable after GTP hydrolysis and when the supply of tubulin. GTP becomes too low; they disassemble into oligomers (Mandelkow and Mandelkow, 1985); and the slow release of subunits from oligomers is an important factor for the oscillations.

    Several features were left open in the model below. In particular, computer modeling suggested that the microtubule number concentration played a key role in the oscillations. In other words, while the synchronization of the whole popula- tion and certain buffer conditions (affecting the intrinsic rate constants) are prerequisites, they fail to induce oscillations unless the polymer concentration is sufficiently high. The experiments reported here were designed to test this hypoth- esis. We show that oscillations can be influenced in three ways, all of which alter the effective number concentration: 1) variation of the rate of nucleation, 2) addition of polymer seeds, and 3) chemical or physical perturbation of an oscillat- ing solution. The data suggest that the control of the micro-

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  • Microtubule Nucleation and Oscillations

    f (Rings)\

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    MATERIALS AND METHODS

    Protein Preparations-Microtubule protein (containing microtu- bule-associated protein) and phosphocellulose-purified tubulin (PC’- tubulin) was prepared at concentration up to 50 mg/ml as described (Mandelkow et al., 1985). The buffer used for standard microtubule assembly was 0.1 M PIPES, pH 6.9, with 1 mM each of MgSO,, EGTA, DTT, and GTP. Oscillations can be induced by various buffer modifications, for example by raising mono- and divalent salts and GTP (see figure legends).

    Preparation of Microtubule Fragments-Tubulin was polymerized in standard buffer conditions for 10 min and then sonicated for various times. The number concentration and length distribution of the seeds was checked by electron microscopy. Seeding was done by adding a few microliters of seed solution to 100 ~1 of sample solution.

    Time-resolued X-ray Scattering-The x-ray experiments were per- formed on instrument X33 of the EMBL Outstation at the DESY synchrot.ron laboratory, Hamburg (Koch and Bordas, 1983). The protein was filled into the chamber (depth 1 mm, covered with 50. pm mica windows on both sides) at O-4 “C, and the reaction was started by raising the temperature (typically to 37 “C) with defined heating rates (minimum half-time 4 s). Scattering patterns were recorded in 2-6-s intervals on a position-sensitive detector integrating azimuthally over 90 “C and analyzed as described (Bordas et al., 1983; Spann et al., 1987).

    Light Scattering-The turbidity was monitored in a Beckman DU 40 spectrophotometer by absorption at 350 nm. The sample holder and temperature jump device were the same as in the x-ray experi- ments.

    Electron Microscopy-Samples were checked by negative stain electron microscopy, using 400 mesh collodion-carbon coated grids and l-2’% uranyl acetate. For measuring number concentrations and length distributions, aliquots of an oscillating sample were fixed in 0.1% glutaraldehyde and 50% sucrose and then diluted 50,000 times into the same buffer. 20 ~1 of this solution was spun down in a Beckman Airfuge (EM-90 rotor) onto Movital-coated grids and ex- amined by negative stain electron microscopy. At the high protein concentrations used for the oscillations, the microtubules showed a tendency for lateral association which complicated the assessment of number concentrations and length distributions. In particular, be- cause of the bundling the apparent length distribution did not always reflect the true microtubule number concentration. We therefore used only those samples where the microtubules were well dispersed and where the observed microtubule mass agreed with the polymerized protein.

    RESULTS

    Influence of Spontaneous Nucleation on Oscillations-Fig. 1 shows an overview of oscillations observed by x-ray scattering. The assembly maxima are dominated by microtubules, the minima by oligomers which in this example are largely closed into rings, as seen from the subsidiary peaks. Their sizes are similar to the rings normally observed only at low temperature (about 35 nm). The oligomers are microtubule disassembly products (Mandelkow and Mandelkow, 1985), they contain bound GDP (Zeeberg et al., 1980; Mandelkow et al., 1988) and are in fact stabilized by it (Howard and Timasheff, 1986), their breakdown is a prerequisite for another round of assem- bly (Spann et al., 1987), and in oscillatory conditions the

    ’ The abbreviations used are: PC, phosphocellulose-purified tubu- lin; PIPES, 1,4-piperazinediethanesulfonic acid; EGTA, [ethylene- bis(oxyethylenenitrilo)]tetraacetic acid; DTT, dithiothreitol; AMP- PNP, adenosine 5’-(P,y-imino)triphosphate.

    FIG. 1. Projection plot of x-ray scattering traces of an os- cillating sample. X axis, scattering vector S = 2sin0Jambda; y axis, time; z axis, scattering intensity weighted by scattering vector, S. I(S). The curves shown are in 3-s intervals; the periodicity of the oscillations is about 150 s. PC-tubulin, 54 mg/ml, 0.1 M PIPES, pH 6.9, with 4 mM GTP, 20 mM MgCl?, 60 mM NaCl, 1 mM DTT. The temperature was raised from 0 to 37°C at time 0 (arrow) and kept constant thereafter. The degree of assembly is shown by the “central scatter” (left). The type of structure formed can be deduced from the scattering traces, e.g. the positions and heights of the subsidiary maxima (the side maxima of ring oligomers are labeled R, those of microtubules Mt). The sample shows the alternation between micro- tubules (maxima of overall assembly, see central scatter) and oligo- mers (minima of overall assembly) which in this case largely associate into tubulin rings (note the shift of the subsidiary peaks; for details of the interpretation see Bordas et al., 1983; Spann et al., 1987). At the first assembly minimum microtubules have disappeared com- pletely. The curves shown in some figures below correspond to the time course of the intensity at selected scattering angles (e.g. central scatter, S = 0.02 nm-‘, or “microtubule scatter at first side maximum of microtubules, S = 0.05 nm-‘).

    release of tubulin subunits from them is slow. In previous reports we showed that up to 80% of the microtubules present at an oscillation maximum can disassemble at a minimum. This suggested that the remaining microtubules could serve as seeds for the next round of assembly, i.e. that no new nucleation was required. Here we show a case where diassem- bly is almost lOO%, i.e. no microtubules can be detected at the minimum, as judged by x-ray scattering. This could be considered as synchronized catastrophic disassembly; new microtubule assembly must be initiated by new nucleation rather than simply by regrowth of existing microtubules.

    To introduce the rationale for the following experiments, let us consider the initiation of spontaneous assembly. In the usual theoretical treatment (e.g. Oosawa and Asakura, 1975), the trigger for assembly is set at time 0, allowing the system to develop without further perturbation. In practice any trig- ger requires a finite time (e.g. mixing with salts or nucleotides, temperature jump). In most cases studied earlier the protein concentration was low so that nucleation was slow. This means that the initial perturbation was instantaneous relative to assembly, compatible with the theoretical assumptions. Thus, nucleation and elongation depended only on protein

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  • 4384 Microtubule Nucleation and Oscillations

    concentration and intrinsic rate constants. Consider the con- verse case where the perturbation is slow compared with nucleation; in this case the time course of the perturbation influences that of assembly (an example of a low T-scan is described in Bordas et al., 1983). Since microtubule assembly is entropy driven, nucleation is favored by increasing both the temperature and the protein concentration. Thus, the micro- tubule number concentration can be varied by adjusting the rate at which the temperature is raised. Nucleation is ineffi- cient below 20 “C but increases rapidly above that tempera- ture. Thus, if the critical range (say, 20-25 “C) is traversed slowly, few nuclei are formed spontaneously which then grow into long microtubules. Conversely, if the T-jump is rapid, many nuclei form before the elongation phase takes over, resulting in many short microtubules.

    Fig. 2A shows the behavior of tubulin in oscillation buffer after T-jumps to different final temperatures between 25 and 37”C, each with a half-time of 4 s. The higher the final temperature, the faster the critical temperature range is passed. This correlates with an increase in the microtubule number concentration (more than 3-fold, Fig. 2B), a shorter lag time, faster initial assembly rate (rising from about 90 to 560 subunits/microtubule/s), and higher maximum assembly, in keeping with earlier studies in standard assembly buffer (Gaskin et al., 1974; Engelborghs et al., 1976, Johnson and Borisy, 1977). However, the most striking difference is that of the oscillatory behavior. The higher the final temperature,

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    the more pronounced are the oscillations (rising from 20 to 85% of the maximum, Fig. 2B). Conversely, the oscillations induced at 37 “C can be suppressed by slowing the temperature rise (Fig. 2C).

    Fig. 3A illustrates the dependence of oscillations on protein concentration after rapid T-jumps to 37 “C. If the concentra- tion is too low, the protein will neither assemble nor oscillate (not shown). In oscillation buffer the critical concentration C, required for assembly is rather high, about 5 mg/ml in this case (obtained by back extrapolation of the assembly maxima, Fig. 323). In order to observe pronounced oscillations, the concentration must be raised to an even higher concentration, C,., well above C,. Back extrapolation of the amplitude of oscillations yields C,, = 8 mg/ml (Fig. 3B). A key difference between the experiments is the greater microtubule number generated by self-nucleation at higher protein concentrations (rising from about 1 to 8 nM, Fig. 8B). This suggests that oscillations require a minimum microtubule concentration which is generated above a protein concentration of C,.. In other words, the dependence of oscillations on protein con- centration appears to be mediated by the efficiency of nuclea- tion and the resulting microtubule number concentration.

    Influence of Seeding with Microtubule Fragments on Oscil- lations-If the above interpretation is correct it should be possible to influence the oscillations by the addition of micro- tubule fragments, i.e. by changing the microtubule number concentration. Fig. 44 (bottom trace) was obtained with a

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    FIG. 2. A, turbidity traces (A& of experiments with temperature jumps from 0 ‘C to different final temperatures (25,28, 37 “C) but similar rise times (half-time about 4 s). Thus, the period needed to traverse the nucleation range (above about 20 ‘C) was different (shortest at the highest final temperature, top trace). As a result the maximum assembly, extent of oscillation, and nucleation efficiency varied (see Fig. 2B). Conditions: PC-tubulin, 21 mg/ml, 0.1 M PIPES, pH 6.9, with 4 mM GTP, 20 mM MgCl,, 60 mM NaCl, 1 mM DTT. B, data derived from the experiments of A. Filled circles (dotted line), the number concentrations of microtubules increase from 1.8 nM at 25 ‘C to 6.2 nM at 37 “C (scale on right, inside box). Crosses (solid line), the lag time between the temperature jump and the onset of assembly decreases from 46 min to 1.4 min (scale on left, inside box). Asterisks (long dashes), the period of the oscillations decreases from 10 min to 1.8 min (scale on left, outside box). Filled squares (short dashes), the amplitude of the oscillations increases from 20% of the maximum at 25 ‘C to 85% at 37 “C (scale on right, outside box). C, time dependence of the x-ray scatter at S = 0.05 nm-’ in two experiments with identical final temperatures (37 “C) but different rise times (half-times, 4 and 17 s). The oscillations are most pronounced when the nucleation is most efficient (shortest half-time, top trace), other conditions being equal. Microtubule protein, 29 mg/ml, 0.1 M PIPES, pH 6.9, with 2 mM GTP, 20 mM MgCl*, 40 mM KCl, 1 mM DTT. The arrow indicates the beginning of the temperature jump.

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  • Microtubule Nucleation and Oscillations 4385

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    a FIG. 3. Assembly and oscillations as function of protein concentration. A, turbidity traces (AzSO versus

    time). Top curve, 25 mg/ml; middle, 12.5 mg/ml; bottom, 8.5 mg/ml. Oscillations are most pronounced at the highest protein concentration (top). Conditions as in Fig. 2.4. B, data derived from the experiments of A. Filled circles (dotted line), the number concentrations of microtubules are 1.2, 3.4, 7.1, and 3.4 nM at C,,, = 8.5, 12.5, 17.0, and 25.0 mg/ml, respectively (scale on right, inside box). These values refer to the first assembly peak; at the 7th peak (about 18 min later) the values are about 50% lower (open circles, dotted line, 2.1, 3.2, and 4.3 nM for 12.5,17.0, and 25.0 mg/ml). Crosses (solid line), the maximum turbidity increases from 0.125 to 0.5; the extrapolated critical concentration for assembly C, is 5 mg/ml (scale on left, inside bon). Asterisks (long dashes), the period of the oscillations shows little variation between 12.5 and 25 mg/ml (around 3 min, scale on left, outside box). Filled squares (short dashes), the amplitude of the oscillations increases up to 92% with increasing protein concentration; the critical concentration for oscillations is about 6 mg/ml (scale on right, outside box).

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    FIG. 4. A, oscillations induced by addition of microtubule fragments (A 350 versus time). Bottom curue, sponta- neous assembly showing only slight oscillations. Top curue, addition of seeds (obtained by sonication of preformed microtubules for 60 s) immediately after initiating the T-jump. PC-tubulin, 8 mg/ml, 0.1 M PIPES, pH 6.9, with 3 mM GTP, 10 mM MgCl,, 30 mM NaCl, 1 mM DTT. B, oscillations suppressed by addition of microtubule fragments (ASa versus time). Top curue, spontaneous assembly showing pronounced oscillations (arrow, T-jump). Microtubule number concentration 10 nM in first peak. Bottom curue, addition of 0.6 nM seeds (obtained by sonication of preformed microtubules for 60 s, large arrow) immediately after initiating the T-jump (small arrow). After assembly the microtubule number concentration is 7 nM, showing that there is still substantial self-nucleation. PC-tubulin, 20 mg/ml, 0.1 M PIPES, pH 6.9, with 3 mM GTP, 10 mM MgC12, 1 mM DTT.

    tubulin solution which oscillates only marginally at 8 mg/ml. centration 10 nM). Surprisingly, when 0.6 nM seeds are added Addition of seeds induces this sample to oscillate (top curue). immediately after the T-jump, the oscillations are not en- In a parallel experiment the microtubule number concentra- hanced but suppressed, and one observes a slow approach to tion increased from 4.5 nM (no seeding ) to 10.7 nM after steady state (bottom curve). This behavior is simply explained seeding. This experiment is akin to previous studies using if the effective number concentration of microtubules is too tubulin that would not self-nucleate, but its assembly could low for supporting oscillations, yet sufficient for elongation. be induced by seeding (e.g. Gaskin et al., 1974; Bryan, 1976; In summary, we distinguish two types of seeding experi- Johnson and Borisy, 1977). Yet the difference is that we now ments. 1) In conditions where self-nucleation alone is not use seeds to trigger oscillations of a protein solution that is efficient enough for oscillations, addition of seeds can gener- otherwise perfectly capable of self-nucleation and assembly. ate oscillations. 2) In conditions where self-nucleation is

    There is however another possibility which was not en- efficient, addition of seeds can reduce the number concentra- countered in the earlier studies and effectively amounts to a tion and thus suppress oscillations. reduction of seeds. Fig. 4B (top curue) shows a sample capable Damping and Restart of Oscillations-Since GTP provides of oscillations after spontaneous nucleation (microtubule con- the fuel for oscillations they are expected to die out when

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  • 4386 Microtubule Nucleation and Oscillations

    GTP becomes too low or when the assembly inhibitor GDP becomes too high. However, oscillations usually stop earlier than expected from the GTP/GDP content which therefore cannot fully account for the damping. In seeking alternative explanations we considered the possibility of a decreasing microtubule number concentration. This was indeed observed, as shown in Fig. 3B. In oscillation conditions the number decreased by about 50% between the first and seventh assem- bly maximum. A decrease in number concentration would imply an increase in the average microtubule length. This is also observed, for example, in the experiment of Fig. 3 with Ctot = 17 mg/ml the mean length increases from 11.4 to 18.1 pm between the first and seventh assembly peak (the decrease in numbers is not necessarily compensated by an increase in length because the protein tends to accumulate in the oligomer state). The data suggests that the decreasing microtubule number concentration is a key factor in the damping, inde- pendently of how much GTP is available. This would be analogous to the damping of oscillations by microtubule seeds described above (Fig. 4B).

    In interpreting the results given so far we have tacitly assumed that every microtubule end is capable of elongating, in keeping with the traditional theory of nucleated assembly. This assumption obviously cannot always hold or else there would be no oscillations. We therefore have to distinguish between microtubule ends ready to grow (E,) and those ready to shrink (E,), the conversion between the two being akin to

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    FIG. 5. Restart of damped oscillations, observed by central x-ray scatter (A), turbidity (Asso) (B). A, top curue: oscillations were initially induced by a T-jump (left arrow). After damping to a steady level, a brief cold shock (from 37 to 20°C and back, arrows) was applied, leading to partial diassembly and then to renewed oscillations. Microtubule protein 32 mg/ml, 0.1 M PIPES pH 6.8, with 4 mM GTP, 3 mM AMP-PNP, 20 mM MgC12, 1 mM DTT, and 60 mM NaCl. Bottom curue: oscillations were initially induced by a T-jump (left arrow). After damping 7 mM GTP was added (arrow). PC-tubulin, 42 mg/ml, 0.1 M PIPES, pH 6.9, initially with 4 mM GTP, 20 mM MgCL, 1 mM DTT, and 60 mM NaCl. Dotted parts of curve indicate periods where the data collection was interrupted due to data transfer to the main computer. B, oscillations initially induced by a T-jump, and 7 mM GTP added after damping (arrow). Oscilla- tions are restarted (period 180 s); in this case they also show beating (super-period 26 min). PC-tubulin, 32 mg/ml, 0.1 M PIPES, pH 6.9, initially with 2 mM GTP, 20 mM MgC&, 60 mM NaCl. Note the longer time scale.

    a phase transition (Chen and Hill, 1985). Each of these have their own number concentration. It is intuitively clear that their ratio affects the oscillations, and a perturbation of that ratio should show up as a change of the oscillations. Computer simulations (not shown) suggest that the system starts with an unbalanced ratio of E, and E, ends and then oscillates until a critical value of E,/Es is reached, well before GTP is exhausted. If this is correct, then it should be possible to perturb the E,/EB ratio of a damped solution and thereby restart oscillations.

    The perturbation can be done in various ways. A simple method is to apply a brief cold shock after the damping of oscillations (Fig. 5A, top). This leads to transient microtubule disassembly, followed by regrowth and oscillations which can be explained by a temporary enrichment of E, ends. Another method is to add more GTP (Fig. 5A, bottom, and b). The E,/ E, ratio is linked to the ratio of tubulin-GTP and tubulin- GDP which in turn depends on GTP/GDP (Bayley and Martin, 1986). Thus, a change in GTP leads to more oscilla- tions. Fig. 5B also illustrates that oscillations can be more complicated than a simple damped wave. After restarting there is a basic periodicity of 180 s whose amplitude is modulated with a beat periodicity of 26 min (such effects can be due to spatial pattern formation, Mandelkow et al., 1989). Finally, oscillations can be restarted by fragmentation (Car- lier et al., 1987), presumably because this exposes new E, ends.

    DISCUSSION

    Microtubules are unique among the biopolymers in several respects. They show dynamic instability, i.e. growing and shrinking microtubules can coexist at steady state (Mitchison and Kirschner, 1984); the conversion between phases of growth and shrinkage occurs in uitro as well as in living cells (Horio and Hotani, 1986; Sammak et al., 1987); and a whole population of microtubules can be induced to oscillate syn- chronously (Carlier et al., 1987; Pirollet et al., 1987; Mandel- kow et al., 1988; Melki et al., 1988; Lange et al., 1988; Wade et al., 1989). Among the known biochemical oscillators the microtubule system is notable because the oscillations are coupled to the growth and decay of a structure and not just to the periodic change in enzyme activities. The oscillations represent the property of dynamic instability in an amplified form; this makes them suitable for studying the requirements for the dynamic behavior.

    Several reaction mechanisms have been proposed to explain the oscillations (see above references). They share certain basic features, for example that microtubules are formed from tubulin with bound GTP which is hydrolyzed upon assembly, that microtubules can undergo a phase transition from growth to shrinkage, and that there is a refractory state before tubulin can be reactivated for assembly by binding another GTP from the solution. There are differences with regard to the struc- tures involved (i.e. oligomers or no oligomers), the rate- limiting step in tubulin activation (slow exchange of nucleo- tide on tubulin or slow release of tubulin from oligomers), or the details of the phase change between growth and shrinkage (i.e. the problem of a GTP cap). The actual mechanism is likely to be more complicated than any of the models. Apart from the uncertainties in the reactions addressed explicitly (e.g. nucleation, phase transition, GTP, cap, nature of the oligomers), they do not deal with the difference between plus and minus ends of microtubules, microtubule breakage and annealing, microtubule bundling, spatial heterogeneity of the solution, and other effects that are known to exist but difficult to incorporate into a model. In the present study we have investigated one aspect, the role of nucleation and the micro-

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  • Microtubule Nucleation and Oscillations 4387

    tubule number concentration, because of its special impor- tance for generating oscillations. As a starting point for the interpretation, we have used the model proposed earlier (Man- delkow et al., 1988) which involves the breakdown of micro- tubules into oligomers as part of the cycle.

    Experimentally the variation in the microtubule number concentration was achieved in two ways. In the case of spon- taneous assembly the efficiency of nucleation was changed by exploiting its temperature and concentration dependence (Figs. 2 and 3). The faster a tubulin solution is brought into assembly conditions (i.e. by raising the temperature), the more nuclei will form simultaneously. Secondly, a tubulin solution can be seeded with a defined concentration of microtubule fragments obtained by sonication of preformed microtubules (Fig. 4).

    A key result is that oscillations occur only when the micro- tubule number concentration exceeds some threshold value. Appropriate buffer conditions and a critical protein concen- tration are necessary but not sufficient. If the protein concen- tration is just above this value there will be assembly but little oscillations since the nucleation is not efficient enough. If the protein concentration is high enough, but the temperature jump is too slow, oscillations are suppressed because the system’s behavior is dominated by the inefficient nucleation in the lower temperature range. Using seeds, oscillations can either be generated (in conditions where spontaneous nuclea- tion is inefficient) or suppressed (in conditions where spon- taneous nucleation would be more efficient than the seeding).

    Because of these features we have to consider two critical concentrations, that of the protein concentration, C,, and that of the microtubule number concentration, C&r. A critical protein concentration is required to support assembly in the first place. It is analogous to the C, encountered in many earlier assembly studies where an approach to a steady state was monitored. In the simplest case it is given by the equilib- rium between subunit addition and loss from the polymer ends; in the presence of nucleotide hydrolysis coupled to assembly it is a more complex function of several rate con- stants. In any case the critical protein concentration is defined within narrow limits for a given set of assembly conditions. Addition of seeds enhances assembly because it helps over- come the nucleation barrier, but seeding does not alter the final equilibrium between polymers and subunits. Seeding enhances assembly but does not suppress it.

    By contrast, the oscillations can be influenced by seeding in both directions, depending on the effective microtubule number concentration. The critical number concentration for oscillations can be generated by increasing the protein con- centration above C, in order to enhance the efficiency of nucleation, or by addition of seeds. However, seeding can also be used to suppress oscillations. The effect of seeds depends on how they perturb the relative weight of spontaneous nu- cleation and elongation. The critical number concentration does not have the all-or-nothing character of the critical protein concentration; that is, the transition from simple assembly to oscillations is more gradual, and there is a com- plex dependence on all the rate constants in the reaction cycle. In the case of self-nucleation, the critical number con- centration C& can be translated into a protein concentration C,, at which oscillations become noticeable (Fig. 3B).

    Considering that growing and shrinking microtubules can coexist in solution (“dynamic instability”) it is clear that bulk oscillations are observed only when growth-competent (E,) and shrinkage-competent microtubule ends (E.) are out of balance. Computer simulations suggest that the ratio E$Es oscillates but approaches a limiting value at which oscillations

    are damped out. Interestingly, this limit is usually achieved long before GTP is exhausted. Conversely, when the balance is perturbed the oscillations start again, provided GTP is still present. This can be achieved in several ways, e.g. by cold shock, addition of GTP, addition of seeds, fragmentation, etc. as in Fig. 4.

    Regarding the mechanism of damping one can broadly distinguish two causes, loss of energy or loss of synchrony between the particles. Since microtubule assembly requires GTP it is clear that oscillations stop at the latest when this is exhausted, or when the buildup of GDP becomes inhibitory (this results in a final state dominated by inactive oligomers). But damping usually occurs earlier than that (see Fig. 4). One obvious factor is the decrease in microtubule numbers (Fig. 3B), another one is the approach of the ratio E,/Es towards the limiting value, equivalent to the loss of synchrony in the strict sense.

    It is instructive to relate our data to the elegant observations of microtubule dynamics by video microscopy (Horio and Hotani, 1986; Walker et al., 1988). The advantage of these methods is that they reveal individual microtubules, including the rate constants of growth and shrinkage, and the different behavior of plus and minus ends. A notable feature was that the phase transitions appeared to be random. By contrast, the rates we observed in our present study represent averages over a large number of microtubules (several hundred million) so that the results do not suffer from statistical fluctuations, but we cannot distinguish between microtubule ends. The most striking difference is that the transitions are periodic, i.e. the microtubules oscillate. How could these apparent differences in behavior be reconciled?

    Part of the explanation is that the experimental conditions are different in several ways. (a) The video microscopy ex- periments were performed at low tubulin concentrations (around 7-15 pM) where synchronized oscillations do not occur, as shown above. Moreover, Walker et al. (1988) used a concentration of axoneme seeds around 0.5. lo-l3 M, about five orders of magnitude lower than the concentration re- quired for oscillations. If one raises these two parameters to the levels used in this study one can in fact observe oscillations in real time by video microscopy (Mandelkow et al., 1989). (b) The buffer conditions were different. In the conditions of Walker et al., the frequency of catastrophic disassembly be- comes zero around 17 pM tubulin concentration while in our conditions the protein remains dynamic up to 500 pM. More- over, our buffer conditions enhance the stability of oligomers whose slow dissolution is one of the factors contributing to oscillations. (c) Because of the low concentrations used by Walker et al. it is possible that spatial inhomogeneities con- tribute to the apparent randomness. Various types of inhom- ogeneities have been observed, particularly in thin layers of tubulin solution (Mandelkow et al., 1989).

    Irrespective of the difficulties in making direct comparisons between the two types of experiment, we would favor the assumption that the basic modes of microtubule reactions are similar. If this is the case, the discrepancy between stochastic and synchronized behavior would have to be explained. We would argue that there is in fact no real discrepancy, for the following reasons: First, any reaction between diffusible mol- ecules becomes stochastic when it is viewed on a sufficiently small scale since it depends on the probability of successful encounters. This does not preclude synchronous behavior of a large number of molecules. As examples, consider the oscil- lations in yeast glycolysis or in the Belousov-Zhabotinskii reaction (see Hess, 1977). The subreactions are stochastic in detail, but the system as a whole acts in a correlated and

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  • 4388 Microtubule Nucleation and Oscillations

    predictable fashion. The key is that the subreactions are coupled to one another by the fact that the output of one serves as input to the next. If at least one of these steps is nonlinear, one can expect regular patterns and/or oscillations (the nonlinearity can be introduced via the dependence of the subunit association on the composition of the microtubule end). Secondly, if the microtubule number concentration is too low in our experiments, microtubules assemble but show no net oscillations. All other parameters being equal, the only explanation is that microtubules grow or shrink asynchro- nously, as in the video microscopy experiments. This means that the behavior of the individual microtubules must be very similar in the two cases.

    Several authors have modeled the mechanism of the phase change at a microtubule end (e.g. Chen and Hill, 1985, 1987; Bayley et al., 1989). Disregarding differences in detail, the common assumptions are that it depends on the association of tubulin. GTP (determined by diffusion, i.e. stochastic), followed by a step that tends to destabilize the microtubule (probably related to GTP hydrolysis), and that the stability and/or association depends on the composition or conforma- tion of the end. The consequence is that when the rate of stabilizing interactions becomes too low, the end will convert from growth to shrinkage. Consider an end with an average of N encounters of tubulin. GTP/s, with a standard deviation JN. The mean time between two encounters is T = l/N (S.D. = 7). If the conversion time from the growing to the shrinking conformation is to essentially no shrinkage is observed as long as the frequency of encounters is well above l/to and microtubules continue to grow. However, N decreases as tubulin . GTP becomes exhausted, and for statistical reasons some microtubules can convert to shrinkage while others still grow. Depending on how the frequency of encounters de- creases with time one will either observe an extended period of statistical fluctuations (as in the video microscopy experi- ments), or a conversion of a substantial fraction of microtu- bules to shrinkage within a short period (as in the oscilla- tions). Note that N depends both on the tubulin subunit concentration and on the microtubule number concentration. These arguments could be developed in more detail, but for the present purpose the main conclusion is that stochastic length fluctuations and synchronous oscillations can be ex- plained in terms of the same set of reactions and are therefore not contradictory.

    Analogous arguments can be invoked for the rescue from shrinkage to growth; in the case of oscillations, an important parameter is the refractory state of oligomers which inhibits the regeneration of assembly-competent tubulin. GTP (see Mandelkow et al., 1988; Lange et al., 1988).

    Do these results have implications for the behavior of microtubules in cells? Length fluctuations of individual mi- crotubules have been observed not only in vitro but also within cells (Sammak et al., 1987; Schulze & Kirschner, 1987; Cas- simeris et al., 1988), consistent with the concept of dynamic instability (Mitchison and Kirschner, 1984). However, the chemical basis of these reactions is not easily obtained at the level of single particles. By contrast, oscillations allow us to study the conditions for dynamic instability in detail because they represent this behavior in an amplified form, including even synchronized catastrophic disassembly and renucleation. As described above, oscillations in vitro depend on a high

    microtubule number concentration, leading to a rapid con- sumption of the active subunits (tubulin.GTP) which even- tually causes the synchronous conversion to the shrinking phase. In the cell, growing microtubules generally have their fast-growing (plus) ends exposed which therefore determine the dynamics. Rapid consumption of active subunits could take place either by the simultaneous growth of many micro- tubules, as in uitro, or by some other mechanism which limits the pool of tubulin or its assembly competence, such as restricted diffusion, availability of microtubule-associated proteins or their phosphorylation (known to affect oscilla- tions, Mandelkow et al., 1988), etc. In other words, the effects observed in vitro in bulk solution could take place in vitro in a local environment. This could lead to the length fluctuations of single microtubules whose mechanism would be analogous to the one described here.

    Ackrmuledgments-We are grateful to M. Koch and the staff of EMBL-Hamburg for use of their x-ray facilities, to P. Derr and C. Haas for skilled technical assistance, to A. Jagla for sharing unpub- lished data, and to A. Marx for help with computer programs. This work is part of the doctoral thesis of H. 0.

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    Microtubule oscillations. Role of nucleation and microtubule number

    1990, 265:4382-4388.J. Biol. Chem.

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