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Gel permeation chromatography of asymmetric proteins
ANALYTICAL
BIOCHEMISTRY
121, 234-243 (1982)
Gel Permeation STEPHEN Departments
of Biochemistry
Chromatography C.
MEREDITH
and Pathology,
of Asymmetric R. NATHANS~
AND GENE The University
Proteins’
of Chicago,
Chicago,
Illinois
60637
Received August 10, 198 1 The gel permeation chromatographic behavior of three asymmetric proteins-collagen, fibrinogen, and the prolate ellipsoid Iysozyme-was investigated using a variety of gel and highperformance liquid chromatographic media of various pore sizes and a wide range of flow rates. The time dependency of the elution patterns for columns and the partitioning of proteins between solvent and gel phases in batch experiments show that the “anomalous” behavior of asymmetric proteins is explicable by the mechanism proposed by Y. Nozaki, N. M. Schechter, J. A. Reynolds, and C. Tanford (1976, Biochemistry 15, 3884); i.e., that these proteins penetrate pores of a size comparable to the minor semiaxis of the protein by end-on insertion. Thus, native type I collagen behaves as if it were a spherical protein of radius 8.2 A, fibrinogen has an apparent radius of 32.4 A, and lysozyme has an apparent radius of 14.6 A. The rate at which asymmetric proteins penetrate the gel interior, however, is slow compared to the rate of gel penetration by globular proteins. The end-on insertion mechanism predicts that given infinite time, asymmetric proteins will be included into that portion of the internal volume of the gel which their smallest projectional cross sections allow them to penetrate. A method is presented for extrapolating the elution volume of asymmetric proteins to infinitely slow flow rate; from this extrapolation, one can calculate the minor semiaxis of the protein.
Gel permeation chromatography partitions molecules between a stationary gel phase and a mobile phase according to molecular dimensions. For globular proteins, the elution volume in gel permeation chromatography is exponentially related to the molecular weight, and hence to the radius of the hydrated molecule (1,2). On the other hand, asymmetric proteins elute anomalously late in gel permeation chromatography by this criterion, yielding low apparent molecular weights (3). It was proposed (3) that such behavior could be due to “end-on insertion” of asymmetric proteins into gel pores from which globular proteins of similar molecular weight would be excluded. We ’ This investigation was supported in part by U. S. Public Health Service Grant 5 T32 HL07237-03 0071, and by National Institutes of Health Research Grant GM-18939. 2 Present address: Hematology Division, Department of Medicine, The Johns Hopkins Medical Institutions, 601 N. Broadway, Baltimore, Maryland 21205. 0003-2697/82/060234-10$02.00/O Copyright Q 1982 by Academic Press. Inc. All rights of reproduction in any form reserved.
234
sought to test this hypothesis, and to determine what the partition coefficient, K,,, of asymmetric proteins actually measures, since it does not measure the Stokes’ radius. We present experimental evidence that the elution of asymmetric proteins in gel permeation chromatography is consistent with end-on insertion. If the end-on insertion mechanism is operative, then only a small proportion of the total number of possible collisions between the asymmetric protein molecules and the gel pores can result in endon insertion, and the penetration into the gel matrix should be slower than for globular proteins. The partition coefficient, K,,, should then be flow rate dependent even at moderate flow rates. This was confirmed experimentally. At infinitely slow flow rates, asymmetric proteins are included into that portion of the internal volume of the gel which their smallest projectional cross sections allow them to penetrate. That is, at infinitely slow flow rate, K,, should measure
GEL
PERMEATION
CHROMATOGRAPHY
the minor semiaxis of the hydrated molecule. In the present paper, we show that this is the case for the highly asymmetric proteins collagen and fibrinogen for which the molecular cross section measured by this method agrees well with the known dimensions of these molecules. MATERIALS
OF
ASYMMETRIC
PROTEINS
235
with a measured volume of protein solution of a given concentration. Stirring is continued until the system reaches equilibrium; the gel is then allowed to settle by gravity or by low-speed centrifugation, and the supernatant liquid is reassayed for protein content. The partition coefficient is given by the equation
AND METHODS
Chemicals. Sephadexes, Sepharoses, and crosslinked Sepharoses were from Pharmacia Fine Chemicals. Bio-Gel P-30 and P-300 were from Bio-Rad, Inc. Reagents were the purest grade commercially available. Rat skin type I collagen was prepared as previously described (4); crude calf skin soluble collagen was from Worthington Biochemicals, Corporation. Horse heart cytochrome c, sperm whale myoglobin, human (fraction II) gamma globulin, and hen egg ovalbumin were from Schwarz-Mann, Inc. Bovine serum albumin (fatty acid free, fraction V) was from Pentex Laboratories. Bovine pancreatic chymotrypsinogen and chicken egg white lysozyme were from Worthington Biochemicals Inc. Horse spleen ferritin, beef liver catalase, and rabbit muscle aldolase were from Boehringer-Mannheim. Mandutin was a gift of Dr. John H. Law, Department of Biochemistry, The University of Chicago. Human low-density lipoprotein was a gift of Dr. Robert L. Heinrikson, Department of Biochemistry, The University of Chicago. Column chromatography. Column eluants were monitored continuously at 230 nm using a Perkin-Elmer SP-55 spectrophotometer. Protein concentrations were estimated from absorbance at 230 nm unless otherwise specified. Column void and total volumes were estimated from the elution volumes of Blue Dextran 2000 and acetate ion, respectively. Batch partitioning. Batch partition experiments were performed according to the method of Warshaw and Ackers (5) in which a known quantity of swollen gel is mixed
where Q, = weight of protein added to the mixture; Csnal = concentration in grams per liter of the protein in the supernatant at equilibrium; Y0 = void volume of the swollen gel; V,, = volume of the protein solution which is added to the swollen gel; and V, = volume of the swollen gel. Weights of protein samples were measured using a Cahn RG electronic microbalance. Kinetics of penetration into the gel. A known quantity of swollen gel was rapidly stirred into a measured volume of a protein solution of a given concentration. At various time intervals, the mixture was placed on a Buchner funnel and filtered through a Whatman No. 1 paper. (It was previously determined that recovery of protein when passed through this paper is quantitative.) The first few drops of filtrate were assayed for protein concentration. High-performance liquid chromatography. High-performance liquid chromatog-
raphy of proteins was performed using two columns: Toyo-Soda TSK 3000 (300 mm length and 7.5 mm internal diameter) and Synchropak GPC 100 (250 mm length and 4.1 mm internal diameter). Both of these media are hydrophilic silica-based gels. The recovery of protein from the former column was quantitative for all proteins tested. The latter column adsorbed a variable amount of protein, but all of the adsorption sites could be eliminated by passing a small amount (of the order of 50 pg) of bovine serum albumin through the column at the start of each series of experiments. The high-
236
MEREDITH
Elution
Volume
AND NATHANS
(ml )
FIG. 1. Elution of a mixture of rat skin type I collagen and gelatin from Sepharose CL-6B. The column (2.6 X 95.0 cm) is equilibrated with 0.05 M sodium acetate, 0.3 M sucrose, pH 4.50; the same elution pattern is observed with a variety of other buffers, as described in the text.
performance liquid chromatography system was from ISCO. Buffer was 0.05 M TrisHCl, pH 7.40,0.4 M NaCI. Eluant was monitored continuously using a Perkin-Elmer LC-55 spectrophotometer; generally absorbance was measured at 230 nm, and occasionally at 280 nm. SDS3-polyacrylamide six SDS-polyacrylamide
gel electrophore-
gel electrophoresis was performed to assay intactness of collagen alpha chains, according to a previously described method (4). RESULTS
To test the hypothesis of end-on insertion, we have used two of the most asymmetric proteins, collagen and fibrinogen, which are readily available in pure form, and for which the molecular dimensions have been determined by a variety of independent methods. In addition, we have studied the prolate ellipsoid enzyme lysozyme. Chromatographic behavior of collagen and gelatin. A mixture of rat skin type I ’ Abbreviation used: SDS, sodium dodecyl sulfate.
collagen and gelatin elutes from Sepharose CL-6B as shown in Fig. 1. Gelatin was resolved into alpha chain monomers, dimers, trimers, and higher oligomers (peaks a-6). On the other hand, collagen (peak II) was totally included, indicating an apparent molecular weight of 5 104. The same elution pattern was observed for all of the following buffers: 0.05 M sodium acetate, pH 4.50, 0.3 M sucrose; 0.05 M sodium acetate, pH 4.50, 0.05 M NaCl; 0.16 M sodium phosphate, pH 7.40 or 7.60; 0.05 M Tris-HCl, pH 7.40, 0.4 M NaCl; 0.05 M Tris-HCl, pH 7.40, 1.0 M NaCl. Collagen eluted in the included volume from several homologous gel permeation media of differing fractionation ranges, such as Sepharose 2B and CL-2B, Sepharose 4B and CL-4B, Sepharose 6B, and Sephadex G-200. In addition, collagen eluted in the included volume from Bio-Gel P-300, using 0.05 M sodium acetate, pH 4.50, 0.3 M sucrose as the eluant. We have previously shown that collagen eluting from Sepharose CL-6B is in the native state in these buffers, as ascertained by several physical and chemical criteria (4): the collagen has [LY]$,“~ = -361.5” and [n]2’0c = 11.4 dl/g. After incubation with trypsin or pepsin under nondenaturing conditions, SDS-polyacrylamide gel electrophoresis shows that the collagen alpha chain still has an apparent molecular weight of 9.5 X 104. The chromatographed collagen precipitates from solution in 0.05 M Tris-HCl, pH 7.60, 0.4 M NaCl when NaCl is added to a concentration of 2.4 M. TABLE
1
BATCH PARTITIONING OF COLLAGEN INTO SEPHADEX G-50
Initial concentration b-e/ml)
Final concentration hidml)
L
0.336 0.069 0.030
0.181 0.038 0.016
0.773 0.751 0.807
GEL
PERMEATION
CHROMATOGRAPHY
OF ASYMMETRIC
Batch partitioning of collagen into Sephadex G-50. In order to demonstrate that the native collagen penetrates into small-pore gel permeation media, we determined the equilibrium concentration of collagen into Sephadex G-50. Table 1 lists the initial and final concentrations of collagen obtained when collagen solutions were mixed with equal volume of swollen Sephadex G-50 (fine) and incubated until no further changes in concentration occurred. At three different protein concentrations, over a lo-fold range, the ratios of the concentrations of collagen in the supernatant and in the gel yield a mean K,, of 0.78 k 0.03. These data indicate that the partitioning of collagen into Sephadex G-50 was independent of the protein concentration.
237
PROTEINS
The time course of the penetration of collagen into the Sephadex G-50 (fine) is shown in Fig. 2. The shape of the experimental curve was that of a simple exponential, and the data could be analyzed according to the scheme where both the entrance and exit of the collagen obey a first-order rate law, v = _ 4Collag40ut dt = k,( Collagen),,, Integrating ln
- k2( Collagen)i,.
[ 1]
this equation yields
(Coh3enhut - (Collagenh,t,t=, (Coh3en),,t,,=o - (CollagenLt,,=, = -kt.
The time course of the penetration
[2] of col-
0.
0.
_1 9
E g 0. 6-
TIME
(seconds)
2
0. 6-
0. .Q L 30 TIME
40
SO
t 60
(Seconds)
FIG. 2. Time dependence of penetration of collagen into Sephadex G-50 (fine). A solution of rat skin type I collagen (0.3 mg/ml in 0.16 M sodium phosphate, pH 7.40) is mixed with an equal volume of Sephadex G-50 (tine) equilibrated with the same buffer in which the collagen is dissolved. At various time intervals, remaining protein in the supernatant is measured as absorbance at 230 nm.
238
MEREDITH
AND
lagen into Sephadex G-50 (fine) obeys this simple scheme (Fig. 2, inset). The first-order rate constant, k, was approximately 9.9 X lo-* s-r. This behavior was compared to that of a globular protein, cytochrome c, which has a molecular weight of 1.3 1 X 104, and hence a K,, value of approximately 0.6 with Sephadex G-50. We found that the penetration of cytochrome c, into Sephadex G50 was maximal at the earliest measurable time point (i.e., the half-life was less than 2 s), and thus the rate of penetration is too fast to be measured using this technique. We infer that the rate of penetration of cytochrome c was at least 3.5 times faster than that of collagen (for which the half-life of penetration was approximately 7 s), despite the fact that the former protein has a somewhat lower K,, value than collagen, and thus occupies at equilibrium less of the internal volume of the gel. Flow
rate dependence of Km of collagen.
Collagen solutions was chromatographed at various flow rate using Sephadex G-50 (medium) in a column with a volume of 207 ml. The K,, value of collagen was observed to be inversely related to the flow rate. The K,, value increased substantially as the flow rate decreased and appeared to approach a limiting value of approximately 0.81 at flow rates slower than 25 min/ml. For the analysis of the flow rate dependency of the elution volume, we needed the elution volume extrapolated to infinitely slow flow rate, and this value was obtained by the method described in the Appendix. Once this value is known, then the time dependency of the elution volume (or K,, value) can be analyzed assuming that a separate penetration process occurs at each theoretical plate of the column. For one theoretical plate, the volume into which a protein will penetrate after a time, t, is given by the equation V, = V, + ( Vem- V,)( 1 - eP) = Vem- (Vem - Vo)eek’,
[3]
where V, is the gel volume into which the
NATHANS
protein has penetrated at time, t, V0 is the void volume, and Vem is the volume into which the protein will penetrate given infinite time. For an entire column composed of n theoretical plates, V, = Vem- ( Vem- Vo)e-k’t~tdl”,
[41
where V, is the elution volume of the protein, and ttotal is the total retention time of the protein on the column. Therefore (see Appendix), ln (V,, - V,> = -kttOt,Jn
+ In (V, - V,).
[5]
Alternatively, this equation may be expressed in terms of K,, values,
ln[l -21
= - kt,,&,
161
where K,,, is the K,, value at infinitely slow flow rate. As shown in Fig. 3, the elution volume of collagen obeys the rate law given in Eqs. [ 51 and [6]. The K,, value at infinitely slow rate (0.81) agrees well with the K,, of 0.77 obtained in batch partitioning experiments and corresponds to the K,, value of a globular protein with an apparent molecular weight of 2.0 X 103. The radius of a spherical protein of molecular weight 2.0 X lo3 and V = 0.695 cm3/g (the value obtained for collagen by Boedtker and Doty, (6)) is 8.2 A. Th is radius of 8.2 A is the same, within experimental error, as the known minor semiaxis of collagen of 7.5 A (7). Flow rate dependence of the K,, value of fibrinogen. The recent availability of high-
performance liquid chromatography media of the appropriate pore size for the estimated size of fibrinogen allowed us to perform the gel permeation chromatography of fibrinogen with this most expedient method. Fibrinogen was chromatographed using two high-performance liquid chromatographic gel permeation columns, at a variety of flow rates. The calibration of these columns was
GEL PERMEATION
CHROMATOGRAPHY
FLOW
OF ASYMMETRIC
RATE
239
PROTEINS
(mirdml)
FIG. 3. Flow-rate dependence of K., values of rate skin type I collagen chromatographed using Sephadex G-50 (medium). The collagen is in 0.16 M sodium phosphate, pH 7.40, at a concentration of approximately 0.5 mg/ml. Points are experimentally obtained, the theoretical curves represent the fit of data to Eq. [4] (main figure) and Eq. [ 51 ( inset) using a linear regression analysis computer program.
performed using the globular protein standards listed under Materials and Methods (data not shown). In both cases the eluting buffer was 0.05 M Tris-HCl, pH 7.40, 0.4 M NaCl. The Synchropak GPClOO and Toyo Soda TSK 3000 columns had theoretical plate counts of 800 and 3200, respectively. We observed that the elution volumes of the globular proteins used for the calibration of the columns were independent of the flow rate, whereas the elution volumes of fibrinogen were markedly flow-rate dependent. As shown in Figs. 4 and 5, the elution volume of fibrinogen, like the elution volume of collagen from Sephadex G-50, obeys the rate law given in Eq. [5]. At infinitely slow flow rate, the apparent molecular weight of fibrinogen is 1.18 X lo’, whereas the true molecular weight of fibrinogen is 3.45 X 10’. The radius of a spherical protein with a molecular weight of 1.18 X 10’ and 0 = 0.73 cm3/g is 32.4 A. This value is in good agree-
ment with the published value of the minor semiaxis of fibrinogen (i.e., approximately 30 A) as measured by electron microscopy (8). Gel permeation chromatography
of ly-
sozyme. Lysozyme (molecular weight = 1.44 X 104) elutes anomalously late from Sephadex media (9, lo), yielding an apparent molecular weight of 1.14 X 104. This behavior has been explained as being due, in part, to the binding of lysozyme to Sephadex which, consisting of carbohydrate, might resemble a substrate of lysozyme. Diffusion ( 11) and X-ray crystallographic studies ( 12), however, have shown that lysozyme is a prolate ellipsoid with a minor semiaxis of 14.6 A. Lysozyme and three other proteins were chromatographed using Bio-Gel P-30, a gel permeation chromatography medium made of polyacrylamide, using 0.05 M Tris-HCl, pH 7.4, 0.4 M NaCl as the eluant. As shown in Fig. 6, lysozyme elutes late even though the gel medium is not made of carbohydrate.
240
MEREDITH
AND NATHANS
FLOW
RATE
(min/ml)
FIG. 4. Flow-rate dependence of elution volume, V,, of human fibrinogen chromatographed using a Synchropak GPC 100 column in a high-performance liquid chromatography system. The fibrinogen was dissolved in 0.05 M Tris-HCl, 0.4 M NaCl, pH 7.40, to a concentration of approximately 1 mg/ml. Points are experimentally obtained; the theoretical curves represent the fit of data to Eq. [4] (main figure) and Eq. [ 51 (inset) using a linear regression analysis computer program.
5.
5. C E 5
5.1
4.
I
I
2.0
6.0
4.0 FLOW
RATE
6.0
(minlml)
FIG. 5. Flow-rate dependence of elution volume, V., of human fibrinogen chromatographed using a Toyo Soda TSK 3000 column in a high-performance liquid chromatography system. The fibrinogen was dissolved in 0.05 M Tris-HCl, 0.4 M NaCl, pH 7.40, to a concentration of approximately 1 mg/ml. Points are experimentally obtained; the theoretical curves represent the fit of data to Eq, [4] (main figure) and Eq. [5] (inset) using a linear regression analysis computer program.
GEL PERMEATION
CHROMATOGRAPHY
OF ASYMMETRIC
4.20 log
PROTEINS
241
430 Molecular
Weight
FIG. 6. Chromatography of lysozyme and other proteins using Bio-Gel P-30. The proteins chromatographed are as follows: (3) cytochrome c; (4) myoglobin; (5) chymotrypsinogen; (1) and (2) lysozyme, plotted as having its true molecular weight (2) and as having a molecular weight of 1.14 X 104, i.e., the molecular weight calculated for a protein with a radius equal to the minor semiaxis of lysozyme determined by X-ray crystallography (14.6 A) and ti = 0.688 cm’/g.
Furthermore, the apparent molecular weight of lysozyme in this system is 1.14 X 104, which corresponds to a sphere with a radius of 14.6 A and 3 = 0.688 cm3/g (12) in excellent agreement with the minor semiaxis of lysozyme (i.e., 14.6 A). DISCUSSION
In agreement with earlier observations (3) we found that collagen and fibrinogen elute later from gel permeation chromatography columns than globular proteins of the same molecular weight. The late elution was shown to be independent of buffer ionic strength, chemical composition of the buffer, pH, and chemical composition of the chromatographic medium. In addition, the lack of protein concentration dependence of the K,, values argues strongly against adsorption. Finally, in the batch partitioning experiments, the independence of V,=, from the initial protein concentration is inconsistent with protein adsorption. The Kay values of these proteins are not determined by their Stokes’ radii. The Stokes’
radius of collagen, for example, is 830 A (6); a spherical protein of this radius would have a molecular weight of 1.88 X 109. A protein of this size should elute in the middle of the fractionation range of Sepharose 2B or CL2B; clearly this is not the case. All our observations are consistent with the hypothesis proposed by Nozaki et al. (3) that the cause of the late elution of asymmetric proteins in gel permeation chromatography is the end-on insertion of the protein into gel pores from which globular proteins of the same or comparable molecular weight would be excluded. Since only a small proportion of the total number of possible collisions between asymmetric protein molecules and gel pores can be favorable for end-on insertion, the rate of penetration by these molecules must be slower than that of globular proteins. Thus, the K,, value for these proteins in gel permeation chromatography was predicted to be flow-rate dependent. Similarly, in batch partitioning experiments, the time required to reach equilibrium should be longer than for globular proteins. Both of these predictions were
242
MEREDITH
AND
confirmed experimentally. Furthermore, the end-on insertion mechanism requires that given infinite time, asymmetric proteins would be included into that portion of the internal volume of the gel into which their smallest cross sections allow them to penetrate. Thus, at infinitely slow flow rate, K,, would measure the minor semiaxis. This has been confirmed in the cases of the proteins tested (collagen, fibrinogen, and the prolate ellipsoid enzyme, lysozyme). The end-on insertion mechanism accounts for the simple first-order rate law observed in the batch partitioning experiments. Were diffusion within the gel rate limiting, the rate of penetration would depend upon the internal volume of the gel, whereas experimentally we observed that it is proportional to the surface. Thus, while batch partitioning of collagen into Sephadex G-50 (fine) had a half-life of approximately 9 s, the rate of partitioning of collagen into Sephadex G-50 (medium) was too rapid to measure by this method. Thus, once the energy barrier of the penetration is overcome, the asymmetric protein molecules diffuse rapidly along their longitudinal axis. The occurrence of the end-on insertion mechanism of asymmetric proteins should also influence the behavior of these molecules in analogous processes involving the penetration of pores comparable in size to the molecular dimensions. In particular, asymmetric macromolecules should readily cross dialysis and ultrafiltration membranes which retain globular macromolecules of the same molecular weight, and should migrate further in pore gradient electrophoresis gels than globular molecules of comparable molecular weight. Indeed, Felgenhauer ( 13) has observed such behavior of asymmetric proteins using pore gradient electrophoresis, and we have observed such behavior during dialysis and ultrafiltration of collagen (4) and during ultrafiltration of xanthine oxidase ( 14). Finally, the experimental measurement of a K,, value of an asymmetric protein by gel
NATHANS
permeation chromatography at infinitely slow flow rate may provide a general method for the direct measurement of the minimal molecular cross section of the hydrated macromolecule. APPENDIX For a column containing n theoretical plates, the elution volume, V,, may be expressed as
where Vem is the elution volume at infinitely slow flow rate, and ttotal is the total retention time of the protein on the column. This equation may be expressed in terms of K,, values K
a”
= -zz V, - V. v, - vo
( Vem- Vo)[ 1 - eCkrlMadn] v, - v, ’
where V, is the total volume of the column. One may define the Kav value at infinitely slow flow rate, Kaym, as
- vo L, = K, v, - v, . Thus, K,, = Kaym[ 1 - e-kftotal’n] .
Rearranging
and integrating
yields,
(Ve- Vo) = InLl - (Vem - V(J) I. This equation may be linearized ical analysis as follows: In ( Vem - V,) = -ktt,,Jn
for graph-
+ In ( Vem - Vo) .
This form of the equation was useful for studies using the Toyo Soda TSK 3000 column, since the estimation of the void volume proved difficult; this form of the equation circumvents this problem.’ The elution volume of a protein at infinitely slow flow rate may be estimated by
GEL PERMEATION
differentiating
CHROMATOGRAPHY
Eq. [4] (see text) as follows:
OF ASYMMETRIC
n dVe
v, = V& - ___
k dttota, .
Thus, Vemmay be obtained graphically as the intercept of a plot of V, as a function of dVe/&,ta,. ACKNOWLEDGMENTS We are grateful to Dr. Ferenc J. KBzdy and Dr. John Westley of the Department of Biochemistry, The University of Chicago, for many helpful suggestions and informative discussions.
REFERENCES 1. Whitaker, J. R. (1963) Science 35, 1950-1953. 2. Ackers, G. K. (1975) in The Proteins (Neurath, H.,
243
and Hill, R. L., eds.), Vol. 1, pp. l-94, Academic Press, New York. 3. Nozaki, Y., Schechter, N. M., Reynolds, J. A., and Tanford, C. (1976) Biochemistry 15,3884-3890. 4. Meredith, S. C., and KBzdy, F. J. ( 198 1) Biochim. Biophys.
Thus,
PROTEINS
Acta
526, 357-369.
5. Warshaw, H. S., and Ackers, G. K. ( 197 1) Anal. Biochem. 42, 405-421. 6. Boedtker, H., and Doty, P. (1956) J. Amer. Chem. Sot. 78, 4267-4280. 7. Bornstein, P., and Traub, W. (1979) in The Proteins (Neurath, H., and Hill, R. L., eds.), Vol. 4, pp. 41 l-632, Academic Press, New York. 8. Hall, C. E., and Slayter, H. S. (1959) J. Biophys. Biochem. Cyfol. 5, 1 l-16. 9. Fernandez-Sousa, J. M., and Rodriguez, R. (1977) Biochem. Biophys. Res. Commun. 74, 14261431. 10. Fernandez-Sousa, J. M., Perez-Castells, R., and Rodriguez, R. (1978) Biochim. Biophys. Acta 523,430-437. 11. Phillips, D. C. (1967) Proc. Natl. Acad. Sci USA 57,484-495. 12. Colvin, J. R. (1952) Canad. J. Chem. 30,831-834. 13. Felgenhauer, K. (1974) Hoppe Seyler Z. Physiol. Chem. 355, 1281-1290. 14. Nathans, G. R., and Hade, E. P. (1978) Biochim. Biophys.
Acta
526, 328-344.
BIOCHEMISTRY
121, 234-243 (1982)
Gel Permeation STEPHEN Departments
of Biochemistry
Chromatography C.
MEREDITH
and Pathology,
of Asymmetric R. NATHANS~
AND GENE The University
Proteins’
of Chicago,
Chicago,
Illinois
60637
Received August 10, 198 1 The gel permeation chromatographic behavior of three asymmetric proteins-collagen, fibrinogen, and the prolate ellipsoid Iysozyme-was investigated using a variety of gel and highperformance liquid chromatographic media of various pore sizes and a wide range of flow rates. The time dependency of the elution patterns for columns and the partitioning of proteins between solvent and gel phases in batch experiments show that the “anomalous” behavior of asymmetric proteins is explicable by the mechanism proposed by Y. Nozaki, N. M. Schechter, J. A. Reynolds, and C. Tanford (1976, Biochemistry 15, 3884); i.e., that these proteins penetrate pores of a size comparable to the minor semiaxis of the protein by end-on insertion. Thus, native type I collagen behaves as if it were a spherical protein of radius 8.2 A, fibrinogen has an apparent radius of 32.4 A, and lysozyme has an apparent radius of 14.6 A. The rate at which asymmetric proteins penetrate the gel interior, however, is slow compared to the rate of gel penetration by globular proteins. The end-on insertion mechanism predicts that given infinite time, asymmetric proteins will be included into that portion of the internal volume of the gel which their smallest projectional cross sections allow them to penetrate. A method is presented for extrapolating the elution volume of asymmetric proteins to infinitely slow flow rate; from this extrapolation, one can calculate the minor semiaxis of the protein.
Gel permeation chromatography partitions molecules between a stationary gel phase and a mobile phase according to molecular dimensions. For globular proteins, the elution volume in gel permeation chromatography is exponentially related to the molecular weight, and hence to the radius of the hydrated molecule (1,2). On the other hand, asymmetric proteins elute anomalously late in gel permeation chromatography by this criterion, yielding low apparent molecular weights (3). It was proposed (3) that such behavior could be due to “end-on insertion” of asymmetric proteins into gel pores from which globular proteins of similar molecular weight would be excluded. We ’ This investigation was supported in part by U. S. Public Health Service Grant 5 T32 HL07237-03 0071, and by National Institutes of Health Research Grant GM-18939. 2 Present address: Hematology Division, Department of Medicine, The Johns Hopkins Medical Institutions, 601 N. Broadway, Baltimore, Maryland 21205. 0003-2697/82/060234-10$02.00/O Copyright Q 1982 by Academic Press. Inc. All rights of reproduction in any form reserved.
234
sought to test this hypothesis, and to determine what the partition coefficient, K,,, of asymmetric proteins actually measures, since it does not measure the Stokes’ radius. We present experimental evidence that the elution of asymmetric proteins in gel permeation chromatography is consistent with end-on insertion. If the end-on insertion mechanism is operative, then only a small proportion of the total number of possible collisions between the asymmetric protein molecules and the gel pores can result in endon insertion, and the penetration into the gel matrix should be slower than for globular proteins. The partition coefficient, K,,, should then be flow rate dependent even at moderate flow rates. This was confirmed experimentally. At infinitely slow flow rates, asymmetric proteins are included into that portion of the internal volume of the gel which their smallest projectional cross sections allow them to penetrate. That is, at infinitely slow flow rate, K,, should measure
GEL
PERMEATION
CHROMATOGRAPHY
the minor semiaxis of the hydrated molecule. In the present paper, we show that this is the case for the highly asymmetric proteins collagen and fibrinogen for which the molecular cross section measured by this method agrees well with the known dimensions of these molecules. MATERIALS
OF
ASYMMETRIC
PROTEINS
235
with a measured volume of protein solution of a given concentration. Stirring is continued until the system reaches equilibrium; the gel is then allowed to settle by gravity or by low-speed centrifugation, and the supernatant liquid is reassayed for protein content. The partition coefficient is given by the equation
AND METHODS
Chemicals. Sephadexes, Sepharoses, and crosslinked Sepharoses were from Pharmacia Fine Chemicals. Bio-Gel P-30 and P-300 were from Bio-Rad, Inc. Reagents were the purest grade commercially available. Rat skin type I collagen was prepared as previously described (4); crude calf skin soluble collagen was from Worthington Biochemicals, Corporation. Horse heart cytochrome c, sperm whale myoglobin, human (fraction II) gamma globulin, and hen egg ovalbumin were from Schwarz-Mann, Inc. Bovine serum albumin (fatty acid free, fraction V) was from Pentex Laboratories. Bovine pancreatic chymotrypsinogen and chicken egg white lysozyme were from Worthington Biochemicals Inc. Horse spleen ferritin, beef liver catalase, and rabbit muscle aldolase were from Boehringer-Mannheim. Mandutin was a gift of Dr. John H. Law, Department of Biochemistry, The University of Chicago. Human low-density lipoprotein was a gift of Dr. Robert L. Heinrikson, Department of Biochemistry, The University of Chicago. Column chromatography. Column eluants were monitored continuously at 230 nm using a Perkin-Elmer SP-55 spectrophotometer. Protein concentrations were estimated from absorbance at 230 nm unless otherwise specified. Column void and total volumes were estimated from the elution volumes of Blue Dextran 2000 and acetate ion, respectively. Batch partitioning. Batch partition experiments were performed according to the method of Warshaw and Ackers (5) in which a known quantity of swollen gel is mixed
where Q, = weight of protein added to the mixture; Csnal = concentration in grams per liter of the protein in the supernatant at equilibrium; Y0 = void volume of the swollen gel; V,, = volume of the protein solution which is added to the swollen gel; and V, = volume of the swollen gel. Weights of protein samples were measured using a Cahn RG electronic microbalance. Kinetics of penetration into the gel. A known quantity of swollen gel was rapidly stirred into a measured volume of a protein solution of a given concentration. At various time intervals, the mixture was placed on a Buchner funnel and filtered through a Whatman No. 1 paper. (It was previously determined that recovery of protein when passed through this paper is quantitative.) The first few drops of filtrate were assayed for protein concentration. High-performance liquid chromatography. High-performance liquid chromatog-
raphy of proteins was performed using two columns: Toyo-Soda TSK 3000 (300 mm length and 7.5 mm internal diameter) and Synchropak GPC 100 (250 mm length and 4.1 mm internal diameter). Both of these media are hydrophilic silica-based gels. The recovery of protein from the former column was quantitative for all proteins tested. The latter column adsorbed a variable amount of protein, but all of the adsorption sites could be eliminated by passing a small amount (of the order of 50 pg) of bovine serum albumin through the column at the start of each series of experiments. The high-
236
MEREDITH
Elution
Volume
AND NATHANS
(ml )
FIG. 1. Elution of a mixture of rat skin type I collagen and gelatin from Sepharose CL-6B. The column (2.6 X 95.0 cm) is equilibrated with 0.05 M sodium acetate, 0.3 M sucrose, pH 4.50; the same elution pattern is observed with a variety of other buffers, as described in the text.
performance liquid chromatography system was from ISCO. Buffer was 0.05 M TrisHCl, pH 7.40,0.4 M NaCI. Eluant was monitored continuously using a Perkin-Elmer LC-55 spectrophotometer; generally absorbance was measured at 230 nm, and occasionally at 280 nm. SDS3-polyacrylamide six SDS-polyacrylamide
gel electrophore-
gel electrophoresis was performed to assay intactness of collagen alpha chains, according to a previously described method (4). RESULTS
To test the hypothesis of end-on insertion, we have used two of the most asymmetric proteins, collagen and fibrinogen, which are readily available in pure form, and for which the molecular dimensions have been determined by a variety of independent methods. In addition, we have studied the prolate ellipsoid enzyme lysozyme. Chromatographic behavior of collagen and gelatin. A mixture of rat skin type I ’ Abbreviation used: SDS, sodium dodecyl sulfate.
collagen and gelatin elutes from Sepharose CL-6B as shown in Fig. 1. Gelatin was resolved into alpha chain monomers, dimers, trimers, and higher oligomers (peaks a-6). On the other hand, collagen (peak II) was totally included, indicating an apparent molecular weight of 5 104. The same elution pattern was observed for all of the following buffers: 0.05 M sodium acetate, pH 4.50, 0.3 M sucrose; 0.05 M sodium acetate, pH 4.50, 0.05 M NaCl; 0.16 M sodium phosphate, pH 7.40 or 7.60; 0.05 M Tris-HCl, pH 7.40, 0.4 M NaCl; 0.05 M Tris-HCl, pH 7.40, 1.0 M NaCl. Collagen eluted in the included volume from several homologous gel permeation media of differing fractionation ranges, such as Sepharose 2B and CL-2B, Sepharose 4B and CL-4B, Sepharose 6B, and Sephadex G-200. In addition, collagen eluted in the included volume from Bio-Gel P-300, using 0.05 M sodium acetate, pH 4.50, 0.3 M sucrose as the eluant. We have previously shown that collagen eluting from Sepharose CL-6B is in the native state in these buffers, as ascertained by several physical and chemical criteria (4): the collagen has [LY]$,“~ = -361.5” and [n]2’0c = 11.4 dl/g. After incubation with trypsin or pepsin under nondenaturing conditions, SDS-polyacrylamide gel electrophoresis shows that the collagen alpha chain still has an apparent molecular weight of 9.5 X 104. The chromatographed collagen precipitates from solution in 0.05 M Tris-HCl, pH 7.60, 0.4 M NaCl when NaCl is added to a concentration of 2.4 M. TABLE
1
BATCH PARTITIONING OF COLLAGEN INTO SEPHADEX G-50
Initial concentration b-e/ml)
Final concentration hidml)
L
0.336 0.069 0.030
0.181 0.038 0.016
0.773 0.751 0.807
GEL
PERMEATION
CHROMATOGRAPHY
OF ASYMMETRIC
Batch partitioning of collagen into Sephadex G-50. In order to demonstrate that the native collagen penetrates into small-pore gel permeation media, we determined the equilibrium concentration of collagen into Sephadex G-50. Table 1 lists the initial and final concentrations of collagen obtained when collagen solutions were mixed with equal volume of swollen Sephadex G-50 (fine) and incubated until no further changes in concentration occurred. At three different protein concentrations, over a lo-fold range, the ratios of the concentrations of collagen in the supernatant and in the gel yield a mean K,, of 0.78 k 0.03. These data indicate that the partitioning of collagen into Sephadex G-50 was independent of the protein concentration.
237
PROTEINS
The time course of the penetration of collagen into the Sephadex G-50 (fine) is shown in Fig. 2. The shape of the experimental curve was that of a simple exponential, and the data could be analyzed according to the scheme where both the entrance and exit of the collagen obey a first-order rate law, v = _ 4Collag40ut dt = k,( Collagen),,, Integrating ln
- k2( Collagen)i,.
[ 1]
this equation yields
(Coh3enhut - (Collagenh,t,t=, (Coh3en),,t,,=o - (CollagenLt,,=, = -kt.
The time course of the penetration
[2] of col-
0.
0.
_1 9
E g 0. 6-
TIME
(seconds)
2
0. 6-
0. .Q L 30 TIME
40
SO
t 60
(Seconds)
FIG. 2. Time dependence of penetration of collagen into Sephadex G-50 (fine). A solution of rat skin type I collagen (0.3 mg/ml in 0.16 M sodium phosphate, pH 7.40) is mixed with an equal volume of Sephadex G-50 (tine) equilibrated with the same buffer in which the collagen is dissolved. At various time intervals, remaining protein in the supernatant is measured as absorbance at 230 nm.
238
MEREDITH
AND
lagen into Sephadex G-50 (fine) obeys this simple scheme (Fig. 2, inset). The first-order rate constant, k, was approximately 9.9 X lo-* s-r. This behavior was compared to that of a globular protein, cytochrome c, which has a molecular weight of 1.3 1 X 104, and hence a K,, value of approximately 0.6 with Sephadex G-50. We found that the penetration of cytochrome c, into Sephadex G50 was maximal at the earliest measurable time point (i.e., the half-life was less than 2 s), and thus the rate of penetration is too fast to be measured using this technique. We infer that the rate of penetration of cytochrome c was at least 3.5 times faster than that of collagen (for which the half-life of penetration was approximately 7 s), despite the fact that the former protein has a somewhat lower K,, value than collagen, and thus occupies at equilibrium less of the internal volume of the gel. Flow
rate dependence of Km of collagen.
Collagen solutions was chromatographed at various flow rate using Sephadex G-50 (medium) in a column with a volume of 207 ml. The K,, value of collagen was observed to be inversely related to the flow rate. The K,, value increased substantially as the flow rate decreased and appeared to approach a limiting value of approximately 0.81 at flow rates slower than 25 min/ml. For the analysis of the flow rate dependency of the elution volume, we needed the elution volume extrapolated to infinitely slow flow rate, and this value was obtained by the method described in the Appendix. Once this value is known, then the time dependency of the elution volume (or K,, value) can be analyzed assuming that a separate penetration process occurs at each theoretical plate of the column. For one theoretical plate, the volume into which a protein will penetrate after a time, t, is given by the equation V, = V, + ( Vem- V,)( 1 - eP) = Vem- (Vem - Vo)eek’,
[3]
where V, is the gel volume into which the
NATHANS
protein has penetrated at time, t, V0 is the void volume, and Vem is the volume into which the protein will penetrate given infinite time. For an entire column composed of n theoretical plates, V, = Vem- ( Vem- Vo)e-k’t~tdl”,
[41
where V, is the elution volume of the protein, and ttotal is the total retention time of the protein on the column. Therefore (see Appendix), ln (V,, - V,> = -kttOt,Jn
+ In (V, - V,).
[5]
Alternatively, this equation may be expressed in terms of K,, values,
ln[l -21
= - kt,,&,
161
where K,,, is the K,, value at infinitely slow flow rate. As shown in Fig. 3, the elution volume of collagen obeys the rate law given in Eqs. [ 51 and [6]. The K,, value at infinitely slow rate (0.81) agrees well with the K,, of 0.77 obtained in batch partitioning experiments and corresponds to the K,, value of a globular protein with an apparent molecular weight of 2.0 X 103. The radius of a spherical protein of molecular weight 2.0 X lo3 and V = 0.695 cm3/g (the value obtained for collagen by Boedtker and Doty, (6)) is 8.2 A. Th is radius of 8.2 A is the same, within experimental error, as the known minor semiaxis of collagen of 7.5 A (7). Flow rate dependence of the K,, value of fibrinogen. The recent availability of high-
performance liquid chromatography media of the appropriate pore size for the estimated size of fibrinogen allowed us to perform the gel permeation chromatography of fibrinogen with this most expedient method. Fibrinogen was chromatographed using two high-performance liquid chromatographic gel permeation columns, at a variety of flow rates. The calibration of these columns was
GEL PERMEATION
CHROMATOGRAPHY
FLOW
OF ASYMMETRIC
RATE
239
PROTEINS
(mirdml)
FIG. 3. Flow-rate dependence of K., values of rate skin type I collagen chromatographed using Sephadex G-50 (medium). The collagen is in 0.16 M sodium phosphate, pH 7.40, at a concentration of approximately 0.5 mg/ml. Points are experimentally obtained, the theoretical curves represent the fit of data to Eq. [4] (main figure) and Eq. [ 51 ( inset) using a linear regression analysis computer program.
performed using the globular protein standards listed under Materials and Methods (data not shown). In both cases the eluting buffer was 0.05 M Tris-HCl, pH 7.40, 0.4 M NaCl. The Synchropak GPClOO and Toyo Soda TSK 3000 columns had theoretical plate counts of 800 and 3200, respectively. We observed that the elution volumes of the globular proteins used for the calibration of the columns were independent of the flow rate, whereas the elution volumes of fibrinogen were markedly flow-rate dependent. As shown in Figs. 4 and 5, the elution volume of fibrinogen, like the elution volume of collagen from Sephadex G-50, obeys the rate law given in Eq. [5]. At infinitely slow flow rate, the apparent molecular weight of fibrinogen is 1.18 X lo’, whereas the true molecular weight of fibrinogen is 3.45 X 10’. The radius of a spherical protein with a molecular weight of 1.18 X 10’ and 0 = 0.73 cm3/g is 32.4 A. This value is in good agree-
ment with the published value of the minor semiaxis of fibrinogen (i.e., approximately 30 A) as measured by electron microscopy (8). Gel permeation chromatography
of ly-
sozyme. Lysozyme (molecular weight = 1.44 X 104) elutes anomalously late from Sephadex media (9, lo), yielding an apparent molecular weight of 1.14 X 104. This behavior has been explained as being due, in part, to the binding of lysozyme to Sephadex which, consisting of carbohydrate, might resemble a substrate of lysozyme. Diffusion ( 11) and X-ray crystallographic studies ( 12), however, have shown that lysozyme is a prolate ellipsoid with a minor semiaxis of 14.6 A. Lysozyme and three other proteins were chromatographed using Bio-Gel P-30, a gel permeation chromatography medium made of polyacrylamide, using 0.05 M Tris-HCl, pH 7.4, 0.4 M NaCl as the eluant. As shown in Fig. 6, lysozyme elutes late even though the gel medium is not made of carbohydrate.
240
MEREDITH
AND NATHANS
FLOW
RATE
(min/ml)
FIG. 4. Flow-rate dependence of elution volume, V,, of human fibrinogen chromatographed using a Synchropak GPC 100 column in a high-performance liquid chromatography system. The fibrinogen was dissolved in 0.05 M Tris-HCl, 0.4 M NaCl, pH 7.40, to a concentration of approximately 1 mg/ml. Points are experimentally obtained; the theoretical curves represent the fit of data to Eq. [4] (main figure) and Eq. [ 51 (inset) using a linear regression analysis computer program.
5.
5. C E 5
5.1
4.
I
I
2.0
6.0
4.0 FLOW
RATE
6.0
(minlml)
FIG. 5. Flow-rate dependence of elution volume, V., of human fibrinogen chromatographed using a Toyo Soda TSK 3000 column in a high-performance liquid chromatography system. The fibrinogen was dissolved in 0.05 M Tris-HCl, 0.4 M NaCl, pH 7.40, to a concentration of approximately 1 mg/ml. Points are experimentally obtained; the theoretical curves represent the fit of data to Eq, [4] (main figure) and Eq. [5] (inset) using a linear regression analysis computer program.
GEL PERMEATION
CHROMATOGRAPHY
OF ASYMMETRIC
4.20 log
PROTEINS
241
430 Molecular
Weight
FIG. 6. Chromatography of lysozyme and other proteins using Bio-Gel P-30. The proteins chromatographed are as follows: (3) cytochrome c; (4) myoglobin; (5) chymotrypsinogen; (1) and (2) lysozyme, plotted as having its true molecular weight (2) and as having a molecular weight of 1.14 X 104, i.e., the molecular weight calculated for a protein with a radius equal to the minor semiaxis of lysozyme determined by X-ray crystallography (14.6 A) and ti = 0.688 cm’/g.
Furthermore, the apparent molecular weight of lysozyme in this system is 1.14 X 104, which corresponds to a sphere with a radius of 14.6 A and 3 = 0.688 cm3/g (12) in excellent agreement with the minor semiaxis of lysozyme (i.e., 14.6 A). DISCUSSION
In agreement with earlier observations (3) we found that collagen and fibrinogen elute later from gel permeation chromatography columns than globular proteins of the same molecular weight. The late elution was shown to be independent of buffer ionic strength, chemical composition of the buffer, pH, and chemical composition of the chromatographic medium. In addition, the lack of protein concentration dependence of the K,, values argues strongly against adsorption. Finally, in the batch partitioning experiments, the independence of V,=, from the initial protein concentration is inconsistent with protein adsorption. The Kay values of these proteins are not determined by their Stokes’ radii. The Stokes’
radius of collagen, for example, is 830 A (6); a spherical protein of this radius would have a molecular weight of 1.88 X 109. A protein of this size should elute in the middle of the fractionation range of Sepharose 2B or CL2B; clearly this is not the case. All our observations are consistent with the hypothesis proposed by Nozaki et al. (3) that the cause of the late elution of asymmetric proteins in gel permeation chromatography is the end-on insertion of the protein into gel pores from which globular proteins of the same or comparable molecular weight would be excluded. Since only a small proportion of the total number of possible collisions between asymmetric protein molecules and gel pores can be favorable for end-on insertion, the rate of penetration by these molecules must be slower than that of globular proteins. Thus, the K,, value for these proteins in gel permeation chromatography was predicted to be flow-rate dependent. Similarly, in batch partitioning experiments, the time required to reach equilibrium should be longer than for globular proteins. Both of these predictions were
242
MEREDITH
AND
confirmed experimentally. Furthermore, the end-on insertion mechanism requires that given infinite time, asymmetric proteins would be included into that portion of the internal volume of the gel into which their smallest cross sections allow them to penetrate. Thus, at infinitely slow flow rate, K,, would measure the minor semiaxis. This has been confirmed in the cases of the proteins tested (collagen, fibrinogen, and the prolate ellipsoid enzyme, lysozyme). The end-on insertion mechanism accounts for the simple first-order rate law observed in the batch partitioning experiments. Were diffusion within the gel rate limiting, the rate of penetration would depend upon the internal volume of the gel, whereas experimentally we observed that it is proportional to the surface. Thus, while batch partitioning of collagen into Sephadex G-50 (fine) had a half-life of approximately 9 s, the rate of partitioning of collagen into Sephadex G-50 (medium) was too rapid to measure by this method. Thus, once the energy barrier of the penetration is overcome, the asymmetric protein molecules diffuse rapidly along their longitudinal axis. The occurrence of the end-on insertion mechanism of asymmetric proteins should also influence the behavior of these molecules in analogous processes involving the penetration of pores comparable in size to the molecular dimensions. In particular, asymmetric macromolecules should readily cross dialysis and ultrafiltration membranes which retain globular macromolecules of the same molecular weight, and should migrate further in pore gradient electrophoresis gels than globular molecules of comparable molecular weight. Indeed, Felgenhauer ( 13) has observed such behavior of asymmetric proteins using pore gradient electrophoresis, and we have observed such behavior during dialysis and ultrafiltration of collagen (4) and during ultrafiltration of xanthine oxidase ( 14). Finally, the experimental measurement of a K,, value of an asymmetric protein by gel
NATHANS
permeation chromatography at infinitely slow flow rate may provide a general method for the direct measurement of the minimal molecular cross section of the hydrated macromolecule. APPENDIX For a column containing n theoretical plates, the elution volume, V,, may be expressed as
where Vem is the elution volume at infinitely slow flow rate, and ttotal is the total retention time of the protein on the column. This equation may be expressed in terms of K,, values K
a”
= -zz V, - V. v, - vo
( Vem- Vo)[ 1 - eCkrlMadn] v, - v, ’
where V, is the total volume of the column. One may define the Kav value at infinitely slow flow rate, Kaym, as
- vo L, = K, v, - v, . Thus, K,, = Kaym[ 1 - e-kftotal’n] .
Rearranging
and integrating
yields,
(Ve- Vo) = InLl - (Vem - V(J) I. This equation may be linearized ical analysis as follows: In ( Vem - V,) = -ktt,,Jn
for graph-
+ In ( Vem - Vo) .
This form of the equation was useful for studies using the Toyo Soda TSK 3000 column, since the estimation of the void volume proved difficult; this form of the equation circumvents this problem.’ The elution volume of a protein at infinitely slow flow rate may be estimated by
GEL PERMEATION
differentiating
CHROMATOGRAPHY
Eq. [4] (see text) as follows:
OF ASYMMETRIC
n dVe
v, = V& - ___
k dttota, .
Thus, Vemmay be obtained graphically as the intercept of a plot of V, as a function of dVe/&,ta,. ACKNOWLEDGMENTS We are grateful to Dr. Ferenc J. KBzdy and Dr. John Westley of the Department of Biochemistry, The University of Chicago, for many helpful suggestions and informative discussions.
REFERENCES 1. Whitaker, J. R. (1963) Science 35, 1950-1953. 2. Ackers, G. K. (1975) in The Proteins (Neurath, H.,
243
and Hill, R. L., eds.), Vol. 1, pp. l-94, Academic Press, New York. 3. Nozaki, Y., Schechter, N. M., Reynolds, J. A., and Tanford, C. (1976) Biochemistry 15,3884-3890. 4. Meredith, S. C., and KBzdy, F. J. ( 198 1) Biochim. Biophys.
Thus,
PROTEINS
Acta
526, 357-369.
5. Warshaw, H. S., and Ackers, G. K. ( 197 1) Anal. Biochem. 42, 405-421. 6. Boedtker, H., and Doty, P. (1956) J. Amer. Chem. Sot. 78, 4267-4280. 7. Bornstein, P., and Traub, W. (1979) in The Proteins (Neurath, H., and Hill, R. L., eds.), Vol. 4, pp. 41 l-632, Academic Press, New York. 8. Hall, C. E., and Slayter, H. S. (1959) J. Biophys. Biochem. Cyfol. 5, 1 l-16. 9. Fernandez-Sousa, J. M., and Rodriguez, R. (1977) Biochem. Biophys. Res. Commun. 74, 14261431. 10. Fernandez-Sousa, J. M., Perez-Castells, R., and Rodriguez, R. (1978) Biochim. Biophys. Acta 523,430-437. 11. Phillips, D. C. (1967) Proc. Natl. Acad. Sci USA 57,484-495. 12. Colvin, J. R. (1952) Canad. J. Chem. 30,831-834. 13. Felgenhauer, K. (1974) Hoppe Seyler Z. Physiol. Chem. 355, 1281-1290. 14. Nathans, G. R., and Hade, E. P. (1978) Biochim. Biophys.
Acta
526, 328-344.