THE JOURNAL OF Brouxrc~~ CHEMISTRY Vol. 253, No. 8, Issue of April 25, pp. 2852-2851, 19’78 Printed in U.S A. Sedimentation Velocity Analyses of the Effect of Hydrostatic Pressure on the 30 S Microtubule Protein Oligomer* (Received for publication, July 27, 1977) J. MICHAEL MARCUM~ AND GARY G. BORISY~ From the Laboratory of Molecular Biology, University of Wisconsin, Madison, Wisconsin 53706 Increasing hydrostatic pressure in the analytical ultra- centrifuge by increasing rotor velocity and overlayering protein samples with oil caused a depolymerization of the 30 S oligomer of microtubule protein. This result indicates that the reaction of 6 S microtubule protein to form the oligomer was accompanied by a positive volume change. The effect of hydrostatic pressure on the 6 S to 30 S transition was employed to demonstrate the presence of a rapidly reversible equilibrium between these components by showing polymerization or depolymerization of the oligo- mer during the course of ultracentrifugation. The magni- tude of the partial specific volume change accompanying this reaction was estimated from mass fraction measure- ments of microtubule protein solutions at a variety of hydrostatic pressures to be about 9 x 10m4 ml g-l. In another report (Marcum and Borisy, 1978), we described the results of sedimentation velocity studies on the effects of several physical and solution parameters on the formation of ring-shaped 30 S oligomers from microtubule protein.’ This reaction was characterized in relation to protein concentra- tion, pH, and ionic strength. Additionally, the results of several of these experiments suggested the presence of an equilibrium between the 6 S species and the 30 S oligomer. Although these results were consistent with an equilibrium model of 30 S formation, the existence of this equilibrium was not unequivocally established. Here we report the results of experiments on the effect of hydrostatic pressure on the 6 S to 30 S transition which allowed a direct demonstration of the equilibrium nature of this interaction. When an ultracentrifuge cell is spun at high rotor velocities a pressure gradient is generated throughout the cell which * This work was supported by Grant GB-36454 from the National Science Foundation and Grant GM-21963 from the National Insti- tutes of Health. 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. j. Recipient of a National Institutes of Health predoctoral trainee- ship. Present address, Department of Cell Biology, Baylor College of Medicine, Houston, Tex. 77025. 0 To whom correspondence should be addressed. ’ Microtubule protein refers to tubulin and associated proteins which are co-purified by the temperature-dependent assembly-disas- sembly procedure (Borisy et al., 1975). ranges from approximately 1 atm of pressure at the meniscus to upwards of several hundred atmospheres at the base of the cell. The theoretical considerations of Kegeles et al. (1967) and the demonstration of the highly pressure-dependent sedimen- tation of polymeric myosin by Josephs and Harrington (1967) have led to an appreciation of the magnitude and importance of the effects of pressure gradients developed in the ultracen- trifuge on the sedimentation behavior of interacting systems of macromolecules. In general, aggregation reactions such as myosin polymeri- zation are accompanied by positive volume changes (Josephs and Harrington, 1967; Harrington and Kegeles, 19731, and often these changes are of sufficient magnitude that the apparent association constant for the aggregation reaction can be drastically altered by the pressure gradient generated in an ultracentrifuge cell. Harrington and Kegeles (1973) have described methods by which such pressure effects can be utilized to demonstrate the presence of a rapidly reversible equilibrium in an associating system. Since Salmon (1975a, 1975b) has shown that microtubule assembly both in viuo and in vitro is a pressure-sensitive reaction accompanied by a positive volume change of approximately 90 ml/mol of poly- merizing subunit (6 S tubulin), it was not unreasonable to expect that the reaction of 6 S subunits to form the oligomers might also be accompanied by a similar positive volume change. The results of previous experiments (Marcurn and Borisy, 1978) indicated that the 30 S oligomer was favored under solution conditions that have been demonstrated to support rapid and extensive microtubule polymerization in vitro, while the 18 S species was increasingly favored under condi- tions which led to significantly reduced rates and extents of polymerization (Olmsted and Borisy, 1975). Because the 30 S species seemed to be more closely related to microtubule formation and since the analysis of the effects of pressure on a three-component system (6 S, 18 S, and 30 S) would be formidably complex, we decided to restrict the study of the effects of hydrostatic pressure to the 6 S and 30 S components. Thus the experiments reported below were designed to detect the presence of a pressure effect on the 6 S to 30 S transition and to utilize this effect to determine whether the reaction met the criteria for a rapidly reversible associating system. EXPERIMENTAL PROCEDURES Microtubule protein was prepared by two cycles of assembly- disassembly and stored as frozen pellets (Borisy et al., 1975). Except 2852 by guest on May 8, 2020 http://www.jbc.org/ Downloaded from
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THE JOURNAL OF Brouxrc~~ CHEMISTRY Vol. 253, No. 8, Issue of April 25, pp. 2852-2851, 19’78
Printed in U.S A.
Sedimentation Velocity Analyses of the Effect of Hydrostatic Pressure on the 30 S Microtubule Protein Oligomer*
(Received for publication, July 27, 1977)
J. MICHAEL MARCUM~ AND GARY G. BORISY~
From the Laboratory of Molecular Biology, University of Wisconsin, Madison, Wisconsin 53706
Increasing hydrostatic pressure in the analytical ultra- centrifuge by increasing rotor velocity and overlayering protein samples with oil caused a depolymerization of the 30 S oligomer of microtubule protein. This result indicates that the reaction of 6 S microtubule protein to form the oligomer was accompanied by a positive volume change. The effect of hydrostatic pressure on the 6 S to 30 S transition was employed to demonstrate the presence of a rapidly reversible equilibrium between these components by showing polymerization or depolymerization of the oligo- mer during the course of ultracentrifugation. The magni- tude of the partial specific volume change accompanying this reaction was estimated from mass fraction measure- ments of microtubule protein solutions at a variety of hydrostatic pressures to be about 9 x 10m4 ml g-l.
In another report (Marcum and Borisy, 1978), we described the results of sedimentation velocity studies on the effects of several physical and solution parameters on the formation of ring-shaped 30 S oligomers from microtubule protein.’ This reaction was characterized in relation to protein concentra- tion, pH, and ionic strength. Additionally, the results of several of these experiments suggested the presence of an equilibrium between the 6 S species and the 30 S oligomer. Although these results were consistent with an equilibrium model of 30 S formation, the existence of this equilibrium was not unequivocally established. Here we report the results of
experiments on the effect of hydrostatic pressure on the 6 S to 30 S transition which allowed a direct demonstration of the equilibrium nature of this interaction.
When an ultracentrifuge cell is spun at high rotor velocities a pressure gradient is generated throughout the cell which
* This work was supported by Grant GB-36454 from the National Science Foundation and Grant GM-21963 from the National Insti- tutes of Health. 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.
j. Recipient of a National Institutes of Health predoctoral trainee- ship. Present address, Department of Cell Biology, Baylor College of Medicine, Houston, Tex. 77025.
0 To whom correspondence should be addressed. ’ Microtubule protein refers to tubulin and associated proteins
which are co-purified by the temperature-dependent assembly-disas- sembly procedure (Borisy et al., 1975).
ranges from approximately 1 atm of pressure at the meniscus to upwards of several hundred atmospheres at the base of the cell. The theoretical considerations of Kegeles et al. (1967) and the demonstration of the highly pressure-dependent sedimen-
tation of polymeric myosin by Josephs and Harrington (1967) have led to an appreciation of the magnitude and importance of the effects of pressure gradients developed in the ultracen- trifuge on the sedimentation behavior of interacting systems of macromolecules.
In general, aggregation reactions such as myosin polymeri- zation are accompanied by positive volume changes (Josephs and Harrington, 1967; Harrington and Kegeles, 19731, and often these changes are of sufficient magnitude that the apparent association constant for the aggregation reaction can be drastically altered by the pressure gradient generated in an ultracentrifuge cell. Harrington and Kegeles (1973) have described methods by which such pressure effects can be utilized to demonstrate the presence of a rapidly reversible equilibrium in an associating system. Since Salmon (1975a, 1975b) has shown that microtubule assembly both in viuo and in vitro is a pressure-sensitive reaction accompanied by a positive volume change of approximately 90 ml/mol of poly- merizing subunit (6 S tubulin), it was not unreasonable to expect that the reaction of 6 S subunits to form the oligomers might also be accompanied by a similar positive volume change.
The results of previous experiments (Marcurn and Borisy, 1978) indicated that the 30 S oligomer was favored under solution conditions that have been demonstrated to support
rapid and extensive microtubule polymerization in vitro, while the 18 S species was increasingly favored under condi- tions which led to significantly reduced rates and extents of polymerization (Olmsted and Borisy, 1975). Because the 30 S species seemed to be more closely related to microtubule formation and since the analysis of the effects of pressure on a three-component system (6 S, 18 S, and 30 S) would be formidably complex, we decided to restrict the study of the effects of hydrostatic pressure to the 6 S and 30 S components. Thus the experiments reported below were designed to detect the presence of a pressure effect on the 6 S to 30 S transition and to utilize this effect to determine whether the reaction met the criteria for a rapidly reversible associating system.
EXPERIMENTAL PROCEDURES
Microtubule protein was prepared by two cycles of assembly- disassembly and stored as frozen pellets (Borisy et al., 1975). Except
Pressure Effect on Microtubule Protein 30 S Oligomer 2853
where noted, the frozen pellets were resuspended in 0.05 M Pipes2 at pH 6.65 measured at 24” containing 0.1 mM MgSO, and 1 mM GTP (Buffer A) and carried through one additional cycle of assembly- disassembly just prior to use. The resulting solutions of microtubule protein had a pH of 6.70 at 24” and an ionic strength of 0.095. Protein concentrations were determined by the method of Lowry et al. (1951) using bovine serum albumin as a standard and, except where indicated, the concentrations of the solutions of microtubule protein were adjusted to 5.0 mglml.
Protein samples in 12-mm double sector cells were analyzed by sedimentation velocity as described previously (Marcum and Borisy, 1978), and for some runs up to four samples were analyzed simulta- neously by using wedge quarts windows (+2”, +1°, and -1”) in addition to flat windows. Pressure was varied in the ultracentrifuge by a combination of varying rotor velocity and overlayering samples with paraffin oil (Josephs and Harrington, 1968) which had been equilibrated with buffer. The pressure at the position of the 30 S boundary was calculated from the following relation:
P, = 9 (9 - xi) + P, (1)
where P, is the hydrostatic pressure at position x in the cell, PO is the pressure at the meniscus (x0), p is the density of the solution (the solvent density was used), and o is the angular velocity of the rotor. P, was assumed to have a value of 1 atm at the solution-air meniscus while its value at the solution-oil interface was calculated from Equation 1 using the density of the paraffin oil (p = 0.869 g/ml at 5”).
Mass fraction determinations for the pressure experiments were made in the following way. The area under a schlieren peak was first calibrated in terms of protein concentration by use of a synthetic boundary cell. At low rotor velocities (up to 21,740 rpm) where the 6 S species was not completely resolved from the meniscus, the area of the 6 S peak was determined by measuring the area of the 30 S peak and subtracting this value from the area of the peak in a synthetic boundary cell for an identical sample. At higher rotor velocities (above 21,740 rpm) where hypersharpening of the 30 S boundary sometimes made accurate area measurements of this peak difficult, the area of the 30 S peak was determined by measuring the area of the 6 S peak and subtracting this value from the area of the synthetic boundary run peak. All areas were corrected for radial dilution prior to calculation of mass fractions.
RESULTS
Detection of Pressure Effects -The initial indication of the effect of hydrostatic pressure on the 30 S oligomer arose from a consideration of the difference in the shape of the 30 S schlieren peak at low and high rotor velocities. Fig. 1 shows schlieren patterns of identical solutions of microtubule protein centrifuged at low (15,220 rpm) and high (63,650 rpm) rotor velocities. The 30 S peak observed in the low speed run was relatively symmetrical with a slightly extended leading edge (Fig. la). Although the height of the peak was observed to decrease during centrifugation due to radial dilution, the shape was essentially unchanged (Fig. lb). The 6 S material
did not form a discrete schlieren peak at this low rotor velocity primarily due to diffusion of this protein species. However, at a high rotor velocity (63,650 rpm) the 6 S species was observed as a discrete peak throughout the course of centrifugation. Unlike the 30 S boundary seen at low rotor velocity, this boundary at high rotor speed was observed to change shape during centrifugation. At early times during the run (Fig. lc) the shape of the 30 S peak was essentially similar to that observed at low rotor velocity except for the effect of hyper- sharpening. However, as the 30 S component migrated down the cell and experienced ever-increasing hydrostatic pres-
sures, the schlieren peak developed an exaggerated trailing edge (Fig. Id). This change in shape of the 30 S boundary suggested a progressive depolymerization of the oligomer as it
* The abbreviation used is: Pipes, 1,4-piperazinediethanesulfonic acid.
15,220 rpm (372 min)
63,650 rpm (3 min)
63,650 rpm (31 mid
FIG. 1. The effect of rotor velocity on the shape of the 30 S boundary. A microtubule protein solution (5 mg/ml) prepared in Buffer A was centrifuged at 15,220 rpm at 5” and schlieren photo- graphs were taken at a phase plate setting of 75” at 180 min (a) and 373 min (6) after reaching speed. An identical protein solution was centrifuged at 63,650 rpm at 5” and photographed as above at 3 min (c) and 31 min (d) after reaching speed.
migrated centrifugally into regions of higher pressure. At this rotor speed (63,650 rpm) the pressure at the 30 S boundary changed from approximately 35 atm at 3 min after attaining speed (Fig. lc) to approximately 180 atm after 30 min at speed (Fig. Id).
A more direct demonstration of the effect of increasing hydrostatic pressure on the 6 S and 30 S components was obtained by overlayering identical protein solutions with increasing amounts of paraffin oil followed by centrifugation at a constant rotor velocity. The effect of the overlayering with oil is equivalent to applying a pressure head at the position of the oil-solution meniscus before significant mass transfer occurs. Fig. 2 shows the results of such an overlayer- ing experiment for a solution prepared in 0.1 M Pipes buffer containing 0.1 mM MgCl, and 1 mM GTP at a protein concen- tration of 4 mglml. The increase in hydrostatic pressure brought about by the overlayering of oil caused a significant decrease in the mass fraction of the 30 S oligomer. As the
2854 Pressure Effect on Microtubule Protein 30 S Oligomer
FIG. 2. The effect of overlayering of oil on the mass fractions of the microtubule protein species. Purified microtubule protein solu- tions at 4 mglml were prepared in 0.1 M Pipes buffer containing 0.1 mM MgCl, and 1 mM GTP at pH 6.94 at 24”. Aliquots (0.2 ml) were loaded into one chamber of each of four 12-mm double sector centrifuge cells and overlavered with 0. 0.05. 0.10. and 0.20 ml of paraffin-oil and the other chamber of each of the cells was tilled to the level of the air-liquid interface with buffer. The cells were centrifuged at 29,500 rpm at 5” and photographed at a phase plate angle of 80” 55 min after attaining speed.
pressure at the position of the oligomer changed from approx- imately 25 atm for the upper pattern in Fig. 2 to greater than 53 atm for the lower pattern, the mass fraction of the 30 S species was reduced by more than 50%.
A similar pressure-induced depolymerization of the 30 S tubulin oligomer was observed when identical solutions of microtubule protein were overlayered with a constant volume of oil and subsequently centrifuged at a variety of rotor speeds as shown in Fig. 3. For this experiment 0.2-ml samples of purified microtubule protein in Buffer A were loaded into one chamber of each of four 12-mm double sector centrifuge cells and overlayered with 0.25 ml of paraffin oil. The other chamber of each of the cells was filled with buffer and the cells were centrifuged at the speeds indicated in Fig. 3. As the pressure was increased from 23 atm for the sample centrifuged at 19,160 rpm to 178 atm for the sample centrifuged at 52,640 rpm, the mass fraction of 30 S material decreased from 0.68 to 0.33. Thus, increasing hydrostatic pressure in the ultracentri- fuge by either overlayering of oil, or increasing rotor velocity, or a combination of methods caused a depolymerization of the 30 S ring oligmer of microtubule protein with a corresponding increase in 6 S tubulin concentration. This behavior indicated that the reaction of 6 S protein to form the 30 S oligomer was accompanied by a positive volume change which is character- istic of many protein polymerization reactions (Harrington and Kegeles, 1973).
Use of Pressure Effect as Diagnostic Test for Rapidly Reversible Associating System -The existence of an experi- mentally detectable pressure effect on the mass distribution of the protein species was highly suggestive of a rapidly reversi- ble equilibrium between 6 S and 30 S species. However, in order to provide a more direct experimental demonstration of this equilibrium, it was desirable to show both polymerization and depolymerization of the 30 S oligomer during the course of an ultracentrifugation experiment. This was accomplished by changing the rotor velocity during centrifugation of protein
solutions overlayered with paraffin oil. The results of increas- ing rotor velocity during ultracentrifugation are shown in Fig. 4. For this experiment a solution of microtubule protein was sedimented at 10,589 rpm until the 30 S boundary was approx- imately one-third the distance between the meniscus and the cell bottom (Fig. 4a). The rotor velocity was then rapidly increased to 50,740 rpm with a corresponding increase in hydrostatic pressure from approximately 10 atm to greater than 190 atm. This increase in pressure caused a dissociation of the 30 S boundary into two schlieren peaks (Fig. 4, b to d). The faster of the two peaks corresponded to the 30 S oligomer, while the rather broad slower boundary sedimented at approx- imately 6 S and corresponded to the tubulin dimer. Thus the depolymerizing effect of increasing hydrostatic pressure was directly demonstrated during the course of a single ultracen- trifuge run.
If the tubulin oligomerization reaction represented a rapidly reversible associating system, then it would be predicted that a reduction of rotor velocity and consequently of the hydro- static pressure would lead to the reassociation of a portion of the 6 S species into the 30 S oligomer. This experiment is exactly the reverse of the one just described and the results are presented in Fig. 5. Under the conditions of high hydro- static pressure (205 atm) experienced by the solution centri- fuged at 50,740 rpm (Fig. 5a), a relatively small hypersharp oligomer peak and a large 6 S peak were observed. After the pressure was reduced to approximately 10 atm by rapid deceleration of the rotor to 10,589 rpm, the initially single 6 S boundary gradually resolved into two diffuse schlieren peaks (Fig. 5, b to d). The slower of these corresponded to the 6 S tubulin species, while the faster sedimented with an sZO, w value of 25.9 S appreciably larger than the value of 20.7 S displayed by the oligomer in this experiment. The larger observed sedimentation coefficient of this boundary is pre- dicted from the concentration dependence of the sedimentation coefficient of the 30 S species (Marcum and Borisy, 1978). Since the newly formed boundary is sedimenting through a region of reduced protein concentration relative to the pre- existing oligomer boundary, it will have a correspondingly larger sedimentation coefficient. Thus, we infer that the newly formed boundary represented 30 S tubulin oligomers which were formed after the reduction in pressure. The reassociation of 6 S microtubule protein into the oligomeric state brought about by a reduction in the hydrostatic pressure provides compelling evidence for the existence of a rapidly reversible equilibrium between 6 S and 30 S microtubule protein.
Estimate of Change in Partial Specific Volume -The mag- nitude of the hydrostatic pressure effect on the 6 S + 30 S equilibrium will be governed by the magnitude of the molar volume change of the reaction and the pressure gradient developed in the ultracentrifuge. If it is assumed that the species concentrations at any level in the centrifuge cell satisfy the local value of the equilibrium constant for the association reaction, then, as Josephs and Harrington (1967) have shown, the pressure dependence of the equilibrium constant is given by:
where Kc,, is the equilibrium constant at any position x in the centrifuging protein solution, and K, is the equilibrium con- stant at the meniscus position, x0. The symbol AV represents the volume change upon formation of 1 mol of oligomer, and
Pressure Effect on Microtubule Protein 30 S Oligomer 2855
19,160 rpm
10,589 rpm
50,740 rpm (4 min)
52,640 rpm
50,740 rpm (IO minl
50,740 rpm (16 min)
FIG. 3 (left). The effect of increasing rotor velocity on the mass distribution between the microtubule protein species. Aliquots (0.2 ml) of microtubule protein solutions at 5 mglml in Buffer A were overlayered with 0.25 ml of paraffin oil and centrifuged at 5” at the indicated rotor velocities. Schlieren photographs were taken at a phase plate setting of 75” at the following times after attaining rotor velbcity: a, 76 min; b, 62 min; c, 25 min; and d, 13 min.
FIG. 4 (center). The effect of rotor acceleration on the microtubule protein species. An aliquot (0.2 ml) of microtubule protein solution at 5 mglml prepared in Buffer A was overlayered with 0.25 ml of paraffin oil. The sample was centrifuged at 5” at 10,589 rpm for 276 min (a) until the 30 S boundary was approximately one-third the distance between the meniscus and the cell bottom. The rotor
R, T, and P are the gas law constant, the absolute tempera- ture, and the pressure, respectively. If it is assumed that the solution is incompressible and the density increments of the solutes are invariant with pressure then the hydrostatic pressure at position x in the cell can be evaluated from Equation 1 and Equation 2 can be integrated to yield:
In K,,, = In K. - $$$ (2 - xf)
Thus the molar volume change can be evaluated from a plot of log K versus pressure.
In applying this analysis to the present system, a reaction mechanism and stoichiometry must be assumed in order to calculate the equilibrium constant for the 6 S + 30 S reaction. We assumed the general equation for associating systems of the nM a P type for which
where c,, is the polymer concentration (30 8, c,,~ is the monomer (6 S) concentration, both expressed as mglml, and n
50,740 rpm
10.589 ram (63 mid
10,589 rpm (143 mid
velocity was then rapidly increased to 50,740 rpm and photographs were taken at a phase plate setting of 75” at 4 (b), 10 (cl, and 16 min Cd) after reaching the higher rotor speed.
FIG. 5 (right). The effect of rotor deceleration on the microtubule protein species. A 0.2-ml aliquot of a microtubule protein solution (5 mg/ml prepared in Buffer A) was overlayered with 0.25 ml of paraffin oil. The sample was centrifuged at 5” at 50,470 rpm for 10 min (a) until the 30 S boundary was approximately one-third the distance between the oil-solution meniscus and the cell bottom. The rotor was then rapidly decelerated to 10,589 rpm and photographs were taken at a 75” phase plate angle at 63 (b), 95 Cc), and 143 min (d) after attaining the lower rotor velocity.
is the stoichiometry of the reaction. Electron microscopic observations (Olmstead et al ., 1974) indicated that the rings in our preparations of microtubule protein consisted of single- walled rings (or lock-washers) and short axial stacks of these rings (or lock-washers). Therefore we analyzed the data for choices of n = 13 or small multiples thereof; however, as will be shown, when n is a moderately large number, the calcu- lated value of AV per subunit is an insensitive function of n and hence would be approximately correct for choices of n other than those we have made. Plots of log K uersus pressure for values of n = 13 and n = 26 are shown in Fig. 6. The data used in this analysis were obtained from centrifugation of solutions of microtubule protein at 5 mg/ml where the pres- sure was varied by a combination of overlayering with oil and centrifugation at a variety of rotor velocities. When a value of n = 13 was chosen for the stoichiometry of the reaction we calculated a value of approximately 1300 ml/m01 for the volume change accompanying 30 S oligomer formation which corresponds to a molar volume change of 100 ml/m01 of 6 S tubulin, or on a mass basis, 9.1 x 10e4 ml/g. When the value of n was set equal to 26, the volume change for oligomer
2856 Pressure Effect on Microtubule Protein 30 S Oligomer
1 I 1 I I I 0 Jo 100 IS0 200 250 300
PRESSURE (otm) FIG. 6. The variation of the equilibrium constant with hydro-
static pressure. Experimental data were obtained from centrifuging microtubule protein solutions (5 mglml in Buffer A) at 5” at a variety of rotor velocities (10,589 rpm; 15,220 rpm; 21,740 rpm; 31,410 rpm; 44,770 rpm; and 63,650 rpm). Two 12.mm double sector cells were used for each run. One cell contained 0.2 ml of the protein solution balanced by 0.2 ml of buffer in the other chamber, and the second cell contained the same volume of protein solution overlayered with 0.25 ml of paraffin oil balanced by 0.45 ml of buffer in the second chamber. Mass fraction measurements were made from tracings of schlieren photographs taken at a phase plate angle of 75” as described under “Experimental Procedures” and values for log K were calculated as described under “Results.” n , log K values for n = 13; 0, log K values calculated using n = 26. The lines were derived from a least squares analysis of the experimental data.
0 50 100 IS0 200 250 300 350
PRESSURE (otm)
FIG. 7. The change in the mass fractions of the microtubule protein species with hydrostatic pressure. The mass fractions of the 6 S (0) and 30 S (W) components were determined at a variety of hydrostatic pressures as described under “Experimental Procedures” and the legend of Fig. 6. The lines represent a theoretical description of the variation of mass fraction with pressure and were derived as described under “Results.”
formation was correspondingly larger; however, the volume change per 6 S tubulin subunit was not greatly altered. The calculated volume change was 95 ml/m01 or 8.6 x 10ml ml/g of 6 S subunit. Thus for either ring model the partial specific volume changes were nearly identical indicating that when n is large, doubling its value has little effect on the calculated volume changes per polymerizing unit.
The data used in the preceding analysis (Fig. 6) can also be expressed as the variation in the mass fraction of the protein species with hydrostatic pressure as shown in Fig. 7. The points indicated in this figure represent the experimental results while the lines are theoretical curves which were
derived numerically from Equations 3 and 4 in the following way. First, a value for the stoichiometry, n = 13 was assumed. Values for the mass fractions of the species were then chosen and log K was calculated from Equation 4. This value of log K was then substituted into the least squares equation for log K uersus pressure in order to calculate the pressure correspond- ing to the assumed mass fraction values. Thus at constant protein concentration and known volume change, unique values of mass fractions for the 6 S and 30 S species could be assigned to each value of pressure. As Fig. 7 shows, the theoretical lines thus derived provide an adequate description of the experimental data. Calculations were also carried out assuming a stoichiometry of n = 26 for the reaction and slightly more sigmoidal curves were obtained which, however, still fitted the data, indicating again that when n is suff- ciently large the variation of mass fraction with pressure is not a sensitive function of the stoichiometry of the association reaction. From the data presented in Figs. 6 and 7, we estimate that microtubule protein solutions at 5 mg/ml in Buffer A will contain approximately 70% 30 S material at a pressure of 1 atm.
DISCUSSION
The existence of a pressure effect on the reaction of 6 S microtubule protein to form 30 S oligomers has been demon- strated in three ways. First, the elevation of the schlieren pattern off the base-line between the monomer and oligomer boundaries of schlieren patterns from centrifuge runs at high rotor velocity (Fig. 1) was indicative of the increased concen- tration gradient of 6 S microtubule protein due to the pressure- dependent depolymerization of the 30 S oligomer. The effect of pressure on the 30 S species was also demonstrated by the decrease in the mass fraction of the 30 S oligomer when identical samples were overlayered with increasing amounts of paraffin oil (Fig. 2). The effect of oil overlayering was simply to increase the hydrostatic pressure head at the oil- solution interface thus causing a depolymerization of the 30 S
oligomer. Finally, the effect of pressure on the 6 S to 30 S transition was demonstrated by the decrease in 30 S mass fraction when samples overlayered with identical amounts of oil were centrifuged at increasing rotor velocities (Fig. 3). The
observed depolymerization of the 30 S oligomer caused by increasing hydrostatic pressure in the ultracentrifuge indi- cated that a positive volume change accompanied the forma- tion of the oligomer.
Positive volume changes are charact,eristic of protein asso- ciation reactions such as microtubule assembly (Salmon, 1975a, 1975b), myosin polymerization (Josephs and Harring- ton, 1967) and tobacco mosaic virus protein assembly (Stevens and Lauffer, 1965). As Kauzmann (1959) has described, a positive volume change is predicted for reactions in which either ionic or hydrophobic interactions are involved. Both types of bonds are stabilized by entropic effects and the positive volume change which accompanies their formation results from a decrease in the structure of ordered water surrounding the groups involved in the interaction. In the case of microtubule protein oligomer formation it is likely that ionic bonding plays a more important role in the reaction since increasing salt concentration causes a destabilization of the oligomer (Marcurn and Borisy, 1978). Hydrophobic inter- actions are generally strengthened by increases in salt concen- tration due to the decreased solubility of nonpolar groups in an increasingly polar solvent (Josephs and Harrington, 1968).
The demonstration of the pressure-induced depolymeriza-
Pressure Effect on Microtubule Protein 30 S Oligomer 2857
tion of the 30 S oligomer suggested that, in addition to being accompanied by a positive volume change, the 6 S ti 30 S interaction was a rapidly reversible associating system. The results of other experiments on the effects of protein concen- tration, temperature, pH, and ionic strength (Marcum and Borisy, 1978) had indicated that equilibria existed among the tubulin subunit and oligomeric forms. However, by utilizing the pressure effect we were able to demonstrate directly polymerization and depolymerization of the 30 S oligomer during the course of ultracentrifugation (Figs. 4 and 5), and thus were able to provide unequivocal evidence for the rapidly reversible equilibrium nature of the 6 S + 30 S reaction.
Throughout the pressure experiments, the convective dis- turbances that have been theoretically predicted for pressure- dependent association reactions (Johnson et al., 1973) were generally minor or not observed. This was documented not only by the absence of convective fringes from the schlieren
photographs, but also by the fact that the sum of the areas under the 6 S and 30 S boundaries, after correction for radial dilution, were approximately equal to the area of a synthetic boundary peak from an identical protein sample. This system thus satisfies the criteria for convection-free sedimentation in a pressure-dependent association reaction as described by Josephs and Harrington (1967). These criteria include: 1) the pressure favors the formation of the more slowly sedimenting species (monomer); 2) the polymer has a significantly greater sedimentation coefficient than the monomer; and 3) the stoi- chiometry of the reaction is large.
Frigon and Timasheff (1975) have studied the pressure dependence of formation of a 42 S oligomer from DEAE- Sephadex-purified tubulin and have estimated the partial specific volume change accompanying 42 S oligomer formation to he 2.5 x lo-’ ml/g. This value is 3- to 4-fold lower than the values reported here for the volume change accompanying 30 S oligomer formation. However, Frigon and Timasheff (1975) indicated that the value they reported might be an underesti- mate of Ati and could be low by as much as a factor of 2. In addition, our values of Au are overestimates since the contri- bution of nontubulin protein was not taken into account; thus, the disparity between our results and those of Frigon and Timasheff (1975) is probably quite small.
In the calculation of the equilibrium constant for oligomer formation, we approximated the oligomerization reaction as a simple nM e P type reaction. However, as discussed in an accompanying paper (Vallee and Borisy, 1978), a large amount of evidence has indicated that nontubulin proteins are directly involved as reactants in the 30 S oligomerization reaction and thus should be considered in the equilibrium constant calcu- lations. However, in order to include these nontubulin pro- teins in the analysis, knowledge of their stoichiometry of binding in the oligomer and their concentration in both bound and free states would be required. Since the nontubulin proteins in our preparations have an average sedimentation coefficient of approximately 4 S (Vallee and Borisy, 1978) they are obscured by the broad 6 S subunit boundary, and it would be difficult to evaluate independently the concentrations of free nontubulin proteins and 6 S components by sedimentation velocity ultracentrifugation. This difficulty introduces an er- ror into the calculation of the equilibrium constant, since the apparent monomer (6 S) concentration would be increased by the contribution of the unbound nontubulin protein. At lower
pressures where high oligomer concentrations and thus low free nontubulin protein concentrations occur, the error intro- duced would be small. However, at higher pressures the error introduced might be significantly increased, because the free nontubulin protein concentration would be larger. Since the monomer concentration is raised to the n”’ power in the
equilibrium constant calculations, the effect of approximating c, in Equation 4 as the sum of the free non-tubulin plus 6 S subunit concentrations would be a decrease in the value of log K, leading to an overestimate of the pressure-induced volume changes.
Additional refinements in our calculation of the volume change would come from explicitly including the nontubulin proteins in the reaction mechanism for oligomer formation. We have refrained from a detailed analysis using these refinements due to the uncertainties mentioned above; how- ever, we have estimated that with these corrections our value
for the volume change per subunit in oligomer formation would be revised downward by a factor of 2 and thus is in rough agreement with the upper limit for the values of Frigon and Timasheff (1975).
The values reported here for the volume change per mol of 6 S tubulin (100 ml/m01 when n = 13, and 95 ml/m01 when n = 26) are also similar to the value of 90 ml/m01 of 6 S subunit reported by Salmon (1975a, 1975b) for the volume change accompanying microtubule polymerization both in viuo and in vitro. Thus the association of 6 S dimers to form ring oligomers may be mediated by bonding domains similar to those in- volved in the formation of microtubles (Scheele and Borisy, 1978).
In conclusion, we have used ultracentrifugation analyses to demonstrate a rapid and reversible equilibrium between the
6 S tubulin dimer and the 30 S oligomer and have quantita- tively interpreted the pressure dependence in terms of a positive volume change upon oligomer formation.
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