Determination of reaction volumes and polymer distribution characteristics of tobacco mosaic virus coat protein

ANALYTICALBIOCHEMISTRY

161,70-79(1987)

Determination of Reaction Volumes and Polymer Distribution Characteristics of Tobacco Mosaic Virus Coat Protein MARTIN POTSCHKA’ AND TODD M. SCHUSTER Department of Molecular and Cell Biology, University of Connecticut, Storm, Connecticut 06268 Received July 28, 1986 A method that allows the quantitative determination of reaction volumes from sedimentation velocity experiments in an analytical ultracentrifuge is presented. Combined with a second method for detecting pressure-induced depolymerization, general characteristics of polymer distributions may be probed. We show that it is possible to determine if a sample is in an equilibrium or metastable state of subunit association. Our approach to probe macromolecular aggregation systems by small pressure perturbations is not restricted to the use of centrifuges. This method has been applied to characterize certain aspects of the polymerization of tobacco mosaic virus coat protein (TMVP). There are at least two helical polymer conformations in RNA-free coat protein rods. The smaller, helix I. polymers are limited to sizes below about 70 subunits (four to five helical turns) and undergo some kind of cooperative conformational change before further subunits may be added indefinitely. In contrast to helix I, the larger helix II polymers occur as broader and skewed size distributions. Under moderately strong polymerization conditions, the equilibrium state can contain both types of helical rods. The reaction volume for the addition of trimers is -220 ml/mol for both types of helical polymers. These results are compared with the results of previous thermodynamic analyses of TMVP polymerization.

0 1987 Academic

Press, Inc.

tobacco mosaic virus; ultracentrifugation; pressure effects; partial specific volume: polymer distribution; nucleaction kinetics metastability. KEY WORDS:

As biology becomes increasingly concerned with aspects of supermolecular organization, improved means of characterizing quantitatively the association state and history of such samples are in demand. Methods based on small perturbations are particularly well suited for this purpose as they yield data that are simple to interpret and can be expected to reflect reversible properties. In recent years there has been increasing interest in the effects of pressure on the association properties of extended subunit assembly systems such as actin, myosin, tubulin, hemoglobin S, and ribosomes as well as subunit enzymes. Questions about the effects of pressure on association equilibria, enzyme activity, kinetics of subunit interaction, con-

formational changes, and the molecular mechanism of these pressure-induced changes have been investigated through measurements of reaction volumes and volumes of activation. The central theme in these studies has been to gain further understanding of protein stability and conformational mobility. The subject has been reviewed by Jaenicke (l), Heremans (2), and Weber and Drickamer (3). Recent studies by Ring and Weber (4) have employed pressure-induced dissociation of lactate dehydrogenase to investigate dissociation-dependent conformational changes of enzyme subunits. Following the early sedimentation studies of Josephs and Harrington (5) on the pressure dependence of myosin association, methods and analyses were developed to deal with pressure-dependent macromolecular interactions in the analytical ultracentrifuge (6). We present here a novel approach to the

’ Present address: Max Planck Institut fur biophysikalische Chemie, Am Fassberg, D-3400 Gottingen, Germany. 0003-2697187 $3.00 Copyright 0 1987 by Academic Press, Inc. All rights of reproduction in any form reserved.

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study of an extended subunit assembly system, tobacco mosaic virus coat protein (TMVP).* Systems exhibiting nucleation-controlled aggregation are notoriously difficult to study due to their inherent tendency to form polymorphic and me&table states (78). A good share of the confusion that systems like TMVP have created during the past 50 years can be attributed to the neglect of controlling and reporting the history of the sample. Two assemblies of TMVP have been analyzed by X-ray studies at high resolution, namely fibers of helical virus (9) and crystals of twolayered cylindrical disks grown from high concentrations of ammonium sulfate solutions ( 10). In solution, RNA-free coat protein polymerizes in a number of ways. Three principal states have been recognized at 100 mM ionic strength: oligomers of less than 16 subunits, long helical rodlike polymers of more than a few hundred subunits, and intermediate size polymers. The intermediate size polymers at pH 7.0 and 20°C are actually variable size helical aggregates which increase continuously in length as the pH is reduced, forming short helical rods ( 1 l- 16). We refer to these intermediate size polymers as helix I and to the large ones as helix II. We have applied the methods described in this paper to obtain a better understanding of the physical properties of these helical polymers since the subunit packing arrangement in the long RNA-free TMVP rod is the same as that in native virus (17,18). In addition, one of the intermediate size polymers, the 20s boundary, has been shown to be essential for efficient self-assembly of the virus ( 19). METHODS

Analytical ultracentrijiigation. tion velocity ultracentrifugation

Sedimentawas per-

’ Abbreviations used: TMVP, tobacco mosaic virus coat protein; TMV, tobacco mosaic virus; p, density; ra, radial position of the meniscus between air and solution in centrifuge cell; Ar, distance from the meniscus (cm); [Xl and c,, molecular and weight concentration of species x; SDS, sodium dodecylsulfate; PAGE, polyacrylamide gel electrophoresis,

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VIRUS COAT PROTEIN

71

formed with a Model E Spinco centrifuge (Beckman Instruments), equipped with electronic speed control, schlieren optics, uvscanner, and RTIC-temperature control. Twelve-millimeter carbon-filled epon double-sector centerpieces were used in AnD or AnH-Ti rotors. Samples were loaded in a thermostated glovebox (+-05°C) and rotors were mounted using insulating gloves. Schlieren-image photographic plates were analyzed on a Nikon Model 6C shadowgraph comparator. Concentrations were calculated using a refractive index increment of TMVP of 0.1856 x 1O-3 (mg/ml)-’ at 546 nm. In the centrifuge scanner 1.30 (mg/ml)-’ was used as the TMVP extinction coefficient at 282 nm (20). All sedimentation coefficients are reported as s20.wvalues, that is, corrected for viscosity and density but not extrapolated to infinite dilution. Great care was taken to avoid proteolysis of TMVP through the use of filtered buffers and specially cleaned glassware and centrifuge cells. Sample preparations and characterization. TMV (common strain), kindly supplied as infected tobacco leaves by Dr. C. A. Knight, was isolated and TMVP was prepared by the acetic acid method as described previously (21). After 48 h of repeated dialysis to the final buffer conditions at 5°C the samples were centrifuged for 1 h at 145Kg in a Beckman Type 50 Ti rotor to remove particles larger than TMVP 4 S oligomers. Final sample conditions were 5 mg/ml TMVP in a buffer of 20 mM cacodylic acid with the ionic strength adjusted to 100 mM by the addition of KCl. The final pH values were either 6.40 or 6.60, at 20°C. Samples were warmed slowly from 0 to 20°C over a period of 41 h as described previously at a rate of O.O17’C/min (22). The final equilibration at 20°C was monitored for at least 8 days by drawing aliquots for velocity sedimentation analysis at 40K rpm before starting the actual experiments. Protein concentrations were measured to about 1% reproducibility by uv-absorption and schlieren optics and the results of the two methods were in fair agreement. Samples at

72

POTSCHKA

AND SCHUSTER

5 mg/ml total protein concentration at 1 atm and 20°C contained 5% 4 S oligomers at pH 6.40 and 8% 4 S oligomers at pH 6.60, irrespective of the pathway of aggregation. The pH 6.40 samples changed composition measurably only during the first 24 h of equilibrium at 20°C. During this time the bimodal polymer distribution changed from an initial composition of 20% 25 S and 30% 37 S to a final composition of 35% 25 S and 25% 37 S. Less than 1% pelleted rapidly (>200 S). The balance of the TMVP sedimented as a broad

B

meniscus O’1

bottom

’ m

meniscus

bottom

FIG. 1. Sedimentation velocity experiment using the uv scanner and schlieren optics. Five milligrams per milliliter TMVP at pH 6.40 was slowly warmed from 0 to 20°C in cacodylate/KCl buffer (I = 100 mM) and then equilibrated for 8 days at 20°C. (A) Absorption at 282 nm as a function of radial distance 17 min (-), 22 min (- - -), and 33 min (* . .) after reaching 52K rpm. Total plateau o.d. - 8; only the beginning of the polymer gradient is observed under these conditions. (B) Turbidity at 313 nm as a function of radial distance 15 min after reaching speed (52K rpm). The polymer gradient resolves into a sharp 25 S boundary and a distribution of polymer sedimenting at 37 S on average. The schlieren image of the same sample after 30 min sedimentation at 40K rpm is inserted for comparison. The turbidity ofthe 4 S oligomers is less than noise.

weakly discernible trailing boundary with s values from 40 to 200 S. At pH 6.60 samples prepared by slow heating rates did not change composition or s values at all during the 8-day equilibration period at 20°C. They contained a single narrow and symmetric polymer distribution of 23 S. Samples warmed rapidly at pH 6.60 passed transiently within a few hours through a large polymerization overshoot (7,23). Over a period of 8 days at 20°C these samples re-equilibrated markedly from 40% 26 S and 50% 37 S to a single strongly skewed boundary of 23 S. The differences in the polymer distributions for the two heating rates clearly demonstrate that under these otherwise identical conditions the true equilibrium state of rapidly warmed samples is not attained even after 8 days (23). However, the fact that the rapidly warmed samples relaxed measurably toward equilibrium places a lower limit on the true number of polymers at equilibrium. The number at equilibrium must be at least as large as that observed in rapidly warmed samples. All samples were subjected to both experimental procedures reported below in order to eliminate the risk of variation resulting from metastable polymerization histories. At the end of the experiments samples were cooled to 0°C to verify reversibility by repolymerization. No proteolytic fragments were detected by sodium dodecylsulfate-polyacrylamide gel electrophoresis analysis ( 16). RESULTS

Verification of a Pressure-Induced Depolymerization During Sedimentation Figure 1 shows the results of a typical sedimentation velocity experiment with TMVP. Oligomers, mostly trimers, sediment at 4 S and are referred to as A-protein. This 4 S boundary hardly depletes the meniscus and never reaches a plateau concentration in these experiments. At pH 6.40 a bimodal distribution of polymers is observed (Fig. lb). The 25 S boundary is narrow and sym-

POLYMERIZATION

OF TOBACCO

metric, whereas the 37 S boundary is broad and skewed and a large portion of its high molecular weight tail is not easily detected by schlieren optics. At pH 6.60 a single narrow polymer distribution sedimenting at 23 S is observed (data not shown). Measurable turbidity is observed only for the polymers having a sedimentation coefficient greater than about 20 S. The apparent absorbance in the sloping boundary between oligomer and polymer gradients in Fig. IA continuously increases as polymer is depleted with time. Since the gradients observed at various times superimpose within experimental error, it can be assumed that significant sedimentation or diffusion of this boundary does not take place during the time of the experiment. These observations demonstrate that this sloping boundary is not due to larger sized oligomers. Rather it originates from pressure-induced rapid kinetics of subunit exchange in which equilibrium is always established at every point in the cell, on the time scale of the sedimentation. From kinetic analysis of the polymerization of TMVP it is known that the nucleation rate for new polymer (helical rod) formation is very slow once the mass distribution between oligomers and polymers approaches equilibrium (7,16). On the time scale of the centrifuge experiment only rapid polymer elongation reactions take place: A + PAi * PA;+*. Formally this is similar to the cases where there is cosedimentation of protein with ions or bound dyes. For the latter case it has been verified experimentally that unbound dye establishes a plateau region (24). The lack of such a plateau in the case of TMVP implies effects beyond a simple, pressure-independent, interactive boundary. Taken together these data suggest a pressure-induced dissociation of polymers to small subunits, probably no larger than trimers. Determination of the Apparent Reaction Volume The hydrostatic pressure during centrifugation (25) is given by

MOSAIC

P=$

73

VIRUS COAT PROTEIN

(r’ - r$ = p(rpm)2(2r&

+ (Ar)2).

It can be seen that pressure is an almost linear function of the depth in the solution column, exceeding 100 atm at the bottom of the cell, even at 40K rpm. The pressure dependence of a chemical equilibrium is described thermodynamically by the following expression where K, and I&, are equilibrium constants at some radial position (of elevated pressure) in the centrifuge cell and at 1 atm, respectively. PAV In K, = In K,, - RT or in terms of species weight concentrations In

[X31,

1 [XI pr AV*

PJV - -=+x7--

[X310

I

z[X,,]RT

*

The apparent reaction volume A V* is related to the true reaction volume by a proportionality constant: AV* =&-A, In the case of small perturbations, this proportionality constant is easily identified as the gamma function familiar from amplitude analysis in relaxation kinetics theory (26). Figure 2 gives a summary of sedimentation velocity scanner tracings resealed such that the slope in the region of pressure-induced polymer dissociation equals the apparent reaction volume AV*. Values for AL’* obtained by this simple graphical method are independent of the speed of centrifugation within the given error margin and are approximately equal to -200 f 15 ml/m01 of trimer for both samples studied. Characterization

of the Polymer

Distribution

Instead of depleting the polymer boundary and calculating the apparent reaction volume directly from the concentration gradient of dissociation products left behind, one may monitor the decrease in polymer

74

POTSCHKA

AND SCHUSTER

‘” OD282

FIG. 2. Pressure-induced dissociation of TMVP followed by the excessoligomer concentration observed after depletion of polymer. The data obtained from primary scanner traces at 282 nm in the ultracentrifuge are resealed by -= P RT

6.6 X 10-r’ 3 (rpm)’ (2r&

+

(Ar)‘)

to provide a convenient graphical means of determining the reaction volume AL’* [ml/mol reaction] = - slope. Five milligrams per milliliter TMVP at pH 6.60 (- - -) and at pH 6.40 (-), both equilibrated at 20°C for 8 days in cacodylate/KCl buffer of total ionic strength 100 mM. The numbers next to each trace are the centrifugation speeds in K rpm. Inset: Av* as a function of the speed of centrifugation at pH 6.60 (X) and pH 6.40 (0).

size (at constant protein mass) by following the turbidity of the plateau region as a function of radial distance and centrifugation speed since c3 ln

[X3lr

-

For equilibrium distributions Hill has derived a generalized quasi-isodesmic distribution that takes into account the loss of translational and rotational degrees of freedom upon polymerization (27). Here

+ c, 1-R 1 01. (

IX310

c3

The number average size (i) of the polymers, though difficult to measure directly, may be obtained from turbidity, which is proportional to the weight average size (i’) if the size distribution function is known, (8i2) = (i’)

- (i)‘.

Oosawa has shown that a nucleation-controlled polymerization reaction transiently leads to a Poisson distribution of polymer sizes (8). From (ai’) rolSSoN = (i) it follows that (i’) - (i)‘.

(bi’) = --&

(i)‘;

(i)* = (i’) n+l. n+2

With n = 0 this reduces to the classical exponential distribution. The actual magnitude of n depends on the internal flexibility of the polymer. For real systems the true distribution functions are expected to deviate from the limiting cases above since proteins, especially homopolymers, are expected to exhibit electrostatic cooperativity. Furthermore minimum nucleus sizes and possible limitations of the maximum size to which a polymer can

POLYMERIZATION

OF TOBACCO

MOSAIC VIRUS COAT PROTEIN

75

If independent measurements of AI/* are available, f can be used to retrieve information about features of the polymer size distribution without having to specify a detailed molecular distribution function. f< 1 indicates that the sample was still in a metastable state and relaxed from a Poissonlike distribution toward an exponential one or that some kind of cooperativity limits the maximum size of polymers, provided the actual sizes are close to this limit.f> 1 will be However, if the distribution type changes we expected whenever polymer sizes approach write the minimum nucleus size and nucleation rates are too slow on the time scale of the ln w31r m=ln[z(l -f(sr2)+ 11, experiment. If the distribution character indeed where fin most cases can be expected to be changes, f is expected to vary strongly with the extent of perturbation. Since the different ( ;y2 Gf s (2)“? asymmetries of greatly different sized polymers will add additional unknown factors to the equation of turbidity with size average this analysis is only applicable for small perturbations. Figure 3 shows the data obtained for the two samples studied. From gel permeation chromatography under similar conditions it is known that at low concentrations A-protein contains mostly trimers, some monomenEcus bottom mer, and little dimer or other oligomers (28). The pressure-induced dissociation of polymers is therefore dominated by a trimerpolymer reaction. Monomer concentration is somewhat more than 1% at pH 6.40 and somewhat less than 2% at pH 6.60. Monomer subtraction from the measured oligomer menses bottom concentration tends to increase the comFIG. 3. Pressure-induced dissociation of TMVP monitored by a decrease in turbidity in the plateau region of a puted values of AV*, but the effect is neglisedimentation velocity run. Five milligrams per milligible. liter TMVP warmed slowly from 0 to 20°C for 41 h and The insert graph in Figure 3 shows that the then equilibrated for another 230 h at 20°C. Cacodyapparent reaction volumes obtained with f late/KC1 buffer (I = 100 mM) at pH 6.40 (A) and pH = 1 are independent of pressure with the pos6.60 (B). The numbers next to each trace are the centrifsible exception of the pH 6.60 sample at 64K ugation speeds in K rpm. Partial sedimentation was corrected by the law of radial dilution which aligns the rpm. At pH 6.40 AL’* = -195 (+25) ml/mol traces to a common point at the meniscus without af- reaction which is indistinguishable from the fecting slopes. Apparent reaction volumes Av* are cal- value obtained with the depletion method. culated from the slopes of these data as outlined in the Thus the character of the distribution does text. c, = 9590, c,,, = 4% at pH 6.40 and c,, = 92%, c,,, not change during limited rapid depolymer= 6% at pH 6.60 were used. Inset graphs AV* as a funcization. The polymer distribution at pH 6.40 tion of speed assuming that the polymer size distribution remains unchanged ( f= 1). as illustrated in Fig. 1 therefore represents an grow introduce further distortions of the distribution. As long as the polymer distribution function does not change its character during pressure-induced depolymerization, the ratio of number to weight average degree of polymerizations remains constant and cancels out:

$!l$=(pJ2,

76

FQTSCHKA

AND SCHUSTER

equilibrium state within the errors of measurement. At pH 6.60 AI’* = -100 (&lo) ml/mol reaction which is a factor of 2 less than the true value of AI’* determined from Fig. 2. It is therefore qualitatively obvious that the character of the distribution function changes strongly at pH 6.60. DISCUSSION

By observing pressure-induced partial dissociation of TMV protein aggregates during normal ultracentrifugation, we have developed a combination of approaches that makes it possible to determine reaction volumes as well as to probe several aspects of the size distribution of the protein aggregates. In deriving the quantitative relationships for this pressure-dependent reaction advantage is taken of the fact that only small perturbations of the initial equilibrium states are considered. Higher pressures obtained by more specialized ultracentrifuge techniques, such as overlaying oil or pressurizing with nitrogen (6), could be counterproductive in some cases because of the departure from small perturbation conditions thereby precluding linearization in the gamma function. Compared with dilatometric determinations of reaction volumes our approach has the advantage of greater sensitivity and therefore requires orders of magnitude less sample and avoids nonideality effects in highly concentrated protein solutions. Since the method is relatively rapid and can be performed in the cold on very small volumes, i.e., 0.1 to 0.4 ml, it is applicable to unstable or rare proteins or nucleoprotein complexes. Furthermore it is possible to probe the protein sample under conditions normally used for other analytical ultracentrifuge studies. Since reaction volumes for polymer aggregation are quite similar in magnitude for most proteins (29), measurable fractions (more than 5%) of the total loading concentrations could be dissociated in long column centrifugation experiments at 40K rpm. The methodology described here provides a

means of testing quantitatively for such effects. To illustrate the general usefulness of our approach we have chosen two sample conditions for the polymerization of TMVP that are known to exhibit a variety of metastable states (23). Briefly stated, the principal source of metastability in any nucleationcontrolled polymerization network is as follows: A slow rate for the formation and disappearance of the number of polymers is paired with a rapid rate for the addition and removal of subunits. This combination of relative rates allows for mass equilibration between oligomers and polymers at the expense of the size of nonequilibrium polymers. In warming our samples very slowly from 0 to 20°C and permitting a week’s time for final relaxation we hoped to approach equilibrium states as closely as possible. Depending on the detailed properties of the states passed in the course of equilibration, the final samples may contain either too few or too many polymers, with respect to true equilibrium. Given the bimodal polymer distribution of the pH 6.40 TMVP sample, conventional means fail to allow us to judge whether or not this sample has reached equilibrium. Our new approach, on the other hand, qualitatively yields answers independent of a detailed knowledge of the polymer distribution itself. It demonstrates that the pH 6.40 sample, as characterized in Fig. 1, represents an equilibrium state within the errors of the measurement. The slowly warmed pH 6.60 sample, on the other hand, does relax toward a more exponential distribution upon pressure-induced dissociation. Thus it is either not at equilibrium or some kind of cooperativity limits the size to which polymers can grow. The existence of bimodal distributions of polymer sizes at equilibrium implies two different subunit conformations. Our data suggest that the smaller polymers (helix I) cannot grow beyond a certain size limit unless they undergo a cooperative transition to a

POLYMERIZATION

OF

TOBACCO

somewhat different subunit conformation (helix II) which leads to extended polymer growth (long helical II rods). Sedimentation velocity boundary analysis suggests that this size limit is between four and five turns of subunits in the helical rod (about 70 subunits). Circular dichroism spectra support this estimate (K. Raghavendra and T. Schuster, unpublished results). We have previously demonstrated that helix I polymers bind at most one proton per subunit whereas helix II subunits may bind up to two protons per subunit (1 I), but we are still far from understanding the cooperativity in terms of changes in the conformation of the constituent subunits. The observed coexistence of polymers having two conformations at equilibrium excludes the possibility that the phenomenon is related to the 16f or 174 subunits per turn helical packing polymorphism reported by Mandelkow et al, (30) and by Stubbs et al. (17) for very long TMVP helical rods. In order to extract thermodynamic information from the apparent reaction volume AI/* one must specify the amplitude function for the reaction believed to take place. This is only straightforward in the limit of small perturbations. Here the amplitude function is given by 2 r-l=

c&,

where [Xi] are molar reactant concentrations, Si are their respective stoichiometric coefficients, and summation is over all products and adducts involved. For the elongation of a polymer distribution containing (i) subunits on average with oligomers containing (x) subunits, one easily derives from relaxation kinetics theory that

p-w 1f G

CP

with 1 G f< i. fis a sensitive function of the polymer distribution shape and is expected to be less than 5 ( 13). That fis almost independent of size i at any pH is experimentally demonstrated by observing nearly identical

MOSAIC

VIRUS

COAT

PROTEIN

77

oligomer to polymer weight fractions regardless of the degree of size overshoot. Thus

which is an exact solution as opposed to the order of magnitude estimate A V - A I’* presented previously (5). With x = 3 for trimers andf = 5 one obtains AV = -220 (+20) ml for both pH values reported here for TMVP. The reaction volume difference between helix I and helix II is not considered to be significant. The average partial specific volume increment between oligomers and polymers is therefore AU = 0.0042 + 0.0003 ml/g. We shall now compare our results with the dilatometric data gathered by Lauffer (3 1). For the complete polymerization of oligomers at pH 7.6 to large helix II polymers at pH 5.5 he obtains Au = 0.0075 f 0.0003 ml/g. Lauffer actually reports several values obtained with different corrections which we simply averaged for this comparison. He also determined the difference between so-called polymerized protein samples at pH 6.8 and 25°C and large helix II polymers at pH 5.5, viz., Au = 0.0025 ml/g. From this, a value of Au = 0.0049 + 0.0003 ml/g was derived for the complete polymerization of oligomers at pH 6.8 and 25°C and used in a more recent high-pressure study of TMVP (32). From spring balance data a value of Au = 0.0041 + 0.0008 ml/g was obtained (33). These sample conditions are very similar to pH 6.60 at 20°C (unpublished observations) except that Lauffer’s samples probably contained large amounts of metastable helix II polymers as judged by the reported turbidity values (33). Thus our results agree well with Lauffer’s data in the same pH and temperature range.

78

POTSCHKA

AND

For helix I polymers (14,15), which Lauffer considers to be “double disks” (twolayer disks), he indirectly obtains a value of only Av = 0.00 18 ml/g relative to oligomers. If this value were correct one would expect large volume changes upon changing the conformation of helix II. However, our data clearly demonstrate that the cooperative conformational change between helix I and helix II is not accompanied by significant volume changes. The most conservative allowance for such a difference on the basis of a 10% uncertainty in our data is lbvl = &0.0005 ml/g. In pursuing a detailed interpretation, Lauffer determined the electrostriction of protonating the intact virus and found an average Av = 0.0004 ml/g for each proton added (3 1). This corresponds to AV = -7 ml/mol H+ and agrees well with the order of magnitude observed for the protonation of small model compounds. Thus polymerization-linked protonation contributes negligibly to the total volume difference observed for the polymerization of TMVP. On the other hand there is ample evidence that water of hydration is denser than bulk water such that most of the observed volume changes upon subunit association are expected to be due to water removed from the areas of contact between the subunits (29). It should be added that complete unfolding of proteins is paralleled by unexpectedly small volume changes (6,34), which suggests that reaction volumes of conformational changes can be small compared with the reaction volumes of subunit association (35). Even though it has become common practice to estimate partial specific volumes by calculations based upon amino acid composition, it should be recognized that such values may be too small for subunit aggregates, depending on the extent of polymerization. In the case of more asymmetric subunits with correspondingly larger contact areas than in TMVP, such underestimates of the partial specific volume might exceed 0.0 1 ml/g.

SCHUSTER

We have previously reported conformational differences of TMVP subunits in various states of aggregation up to 23 S as measured by ultraviolet absorption spectroscopy and have provided evidence that each of these average conformational states “temper” with small changes in temperature ( 11,12). However, if large perturbations had been employed in the present investigation, time-dependent conformational changes similar to those reported recently (36) might drift.” have occurred, i.e., “conformational Since long-lived metastable assembly states of TMVP which are larger than 23 S do occur when large perturbations are made, corresponding conformational metastability might also be expected to occur. Nevertheless, a principal advantage of the methodology described here is that it employs small perturbations thus minimizing nonequilibrium effects in the determinations of reaction volumes that can be obtained as a result of the linearization of the relaxation amplitude function. ACKNOWLEDGMENT This research has been supported by a grant from the National Institutes of Health (AI 11573).

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OF TOBACCO

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