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Light scattering of isoionic conalbumin
ARCHIVES OF BIOCHEMISTRY AND BIOPHYSICS
66, 427-437 (1957)
Light Scattering of Isoionic Conalbumin I Serge N. Timasheff 2 and Ignaci0 Tinoco, Jr. 3 From the Department of Chemistry, Yale University, New Haven, Connecticut Received June 20, 1956 INTRODUCTION
The Kirkwood-Shumaker theory (1) of forces between protein molecules arising from charge fluctuations can be tested by light-scattering measurements. Such measurements have been made on isoionic ~ serum albumin in the absence and presence of salt (2-4). The interpretation of the serum albumin experiments is complicated by the net negative charge on the isoionic salt-free protein which is a function of the protein concentration; 5 also, the chloride binding of the protein (5) makes the experiments in salt more difficult to interpret. Conalbumin has an isoionic point in water which is very close to p H 7; therefore, the net charge of the isoionic protein will be nearly zero at all concentrations. Furthermore, the chloride binding is less extensive than with serum albumin (6). Light-scattering measurements on isoionic conalbumin can thus be used to provide a further and more unequivocal test of the Kirkwood-Shumaker theory. METHODS The electrophoresis-convection apparatus has been described previously (7). The electrophoresis experiments were done at 0°C. in a Perkin-Elmer model 38 i Contribution No. 1382 from the Sterling Chemistry Laboratory, Yale University. This work was supported in part by the Office of Naval Research, Contract No. Nonr 659 (00). Present address: Eastern Regional Research Laboratory, U. S. Dept. of Agriculture, Philadelphia, Pa. 3 Public Health Service Research Fellow of the National Cancer Institute. 4 An isoionie protein is defined as a protein which has been passed through an ion-exchange column so as to remove all ions except hydrogen or hydroxyl. 5 The net negative charge of salt-free bovine serum albumin varies from approximately 0.1 to 1 protonic unit as the concentration changes from 1 to 0.05% (3). 427
428
TIMASHEFF AND TINOCO~ JR.
apparatus. The electrophoretic patterns were enlarged and traced to determine the mobilities and measure the areas of the schlieren peaks. The sedimentation experiments were carried Out in a Spinco model E analytical ultracentrifuge at room temperature and a speed of 59,780 r.p.m.
Light Scattering The clarification of the solutions for light scattering was accomplished by filtration through a specially designed ultrafine sintered-glass filter (8). Concentrated, deionized protein stock solution in water was successively added to the weighed Solvent in a 3-ml. light-scattering cell using a microburet. If the solvent contained NaC1, concentrated (1 M) salt solution was added at the same time from a separate microburet to keep the salt concentration constant. Water redistilled from an M1-Pyrex glass still was used for the preparation of all solutions. The concentration of the stock solution was determined from a dry weight obtained by drying the proteins at 107 ° and atmospheric pressure. The scattering intensities at 90 ° at a wavelength of 436 m~ were measured with a modified Brice-Phoenix photometer. The opal diffuser supplied by the manufacturer was used as a primary standard in the determination of the turbidities. The refractive increment of isoionic conalbumin [dn/dc~ = 0.192(g./ml.) -1] was determined using a Brice-Phoenix differential refractometer. Further details of the light-scattering technique used can be found in other publications from this laboratory (2, 3). ~ViATERIALS The eonalbumin was prepared from fresh eggs using a modified Warner (9) method. The procedure of Warner was followed through the ethanol precipitation step; then, instead of crystallizing the conalbumin as the iron complex, and removing the iron on an ion-exchange column in the presence of citrate, a singlestage electrophoresis-eonvection fractionation was used for the final purification. The electrophoretic pattern at pH 5.76 of the ethanol precipitate (Fig. 1, top) shows that there are approximately equal amounts of components with mobilities greater and less than the isoelectric conalbumin. To remove the positively charged component (lysozyme, u = 5.9 X 10-5 sq. cm./see, v.) a 2% solution of deoxyribonucleic acid (DNA) (Schwarz Laboratories, Lot No. 4904) in pH 5.76, r / 2 = 0.1, phosphate buffer was added to the eonalbumin solution in the same buffer. A precipitate formed immediately. The amount of D N A needed to precipitate completely the lysozyme was determined by trim on a small portion; a slight excess of D N A was used as its presence would not interfere in the eleetrophoresis-conveetion purification. The electrophoretie pattern of the supernatant from the I ) N A precipitation is shown (Fig. 1, middle); the lysozyme is now absent, but the negatively charged ovalbumin (u = 6.2 X 10-~ sq. em./see, v.) remains. The eleetrophoresis-convection fractionation of this D N A - t r e a t e d solution was carried out in a pH 5.76, r / 2 = 0.1 phosphate buffer at a field strength of 2 v./cm, applied for 48 hr. at 3-4°C. The electrophoretie pattern of the solution removed from the top reservoir at the end of the fraetionation is shown in Fig. 1, bottom. The conalbumin is electrophoretieally pure. The pure eonalbumin solution was dialyzed against water; it then was pervapo-
LIGHT SCATTERING OF ISOIONIC CONALBUMIN
429
FIG. 1. Electrophoretic patterns of protein fractions obtained in the preparation of conalbumin : after ethanol precipitation (top) ; supernatant from DNA precipitation (middle); contents of upper reservoir of electrophoresis-convection cell (bottom). All photographs were taken after 30 min. at 13 v./cm. rated to approximately half its volume to give a 4% solution. This solution was deionized by passing through a column containing a mixed cation- and anionexchange resin (Amberlite MB-1) above a cation-exchange resin (Amberlite IRC-120) ; the resins were in the hydrogen or hydroxyl form (10). Electrophoretie and ultracentrifugal analyses of the conalbumin before and after deionization showed that no gross changes in the protein had occurred during passage through the resin. The pH of the deionized eonalbumin was 6.8. The optical density at 470 mg of a 1% conalbumin solution in a 1-cm. cell was approximately 0.01, showing that no appreciable iron complex was present (9). RESULTS
AND
DISCUSSION
Theory T h e excess t u r b i d i t y r (11) of a t h r e e - c o m p o n e n t s y s t e m (macromolecule, c o m p o n e n t 2; small molecule, c o m p o n e n t 1; solvent, com-
430
TIMASHEFF AND TINOCO, JR.
ponent 0) may be written in terms of the molecular weights M~, and the 0 chemical potentials, gi = R T in ca ÷ g~e ÷ g~(T, P), of the solutes in the following manner. At constant temperature and pressure:
M~ \~$-~/o~\OC~/o~ + L M~ \~/o~ \-~-(/o~j ILl
32~%'~(an/OcD~
(~n/OcDo.
3X4N
(On~Oct)el
(1)
where c~ is the concentration in g./ml, of component i, n is the refractive index of the solution, X is the wavelength of the light, N is Avogadro's number, R is the gas constant, and T is the thermodynamic temperature. In the absence of strong interaction between components 1 and 2, Eq. (1) reduces to the usual two-component equation.
T
M~
k ~ \0-~-:/d
(2)
Kirkwood and Shumaker (1) give the following expression for the derivative of the excess chemical potential of a protein with an average charge of zero, but a non-zero mean square charge,
M2 ( 0 ~ = -~rNe4{z 2) 7vNa 3 R--T \O-c~/r,e (DkT)2~(1 -4- ~a) 2 + ~ -4- 2B' --
c~ D k T L500 ÷ M~
]
(3) = 4
-~g2
where (z2 is the mean square charge of the protein in protonic units e, D is the dielectric constant of the solvent, k is Boltzmann's constant, a is the radius of a protein molecule, and 1~/2 is the ionic strength of the added electrolyte. The first term on the right in Eq. (3) gives the fluctuating charge interaction; the second term is the excluded volume contribution; the last term, 2B', includes the effects of permanent and fluctuating multipoles and non-electrostatic forces. Binomial expansion of (1 ÷ Ka)-2 gives for the salt-free system:
C2 (Og~ R-T \0-~2]
=
-
-
7r,/2N,/2ea/ kz 2,a/2 ? c2,/2 2(DkT)a~2M~I 2
0
÷ B c~ ÷ . . . .
(4)
431
LIGHT SCATTERING OF ISOIONIC COXALBUMIi~
In the presence of excess salt, the equivalent expression is:
RT\O-~/c,
- L ( D k T ) ~
+
K0a)2 - B "
c2 + . . .
(5)
In the absence of added electrolyte, the limiting slope of Hc2/r is linear in c~/2 and the only unknown parameter in the slope is the mean square charge (z2}. When the ionic strength of the solution is governed solely by the added electrolyte, the limiting slope of Hc2/r is linear in c2, but the slope now also depends on the intermolecular forces other than those due to the fluctuating charges. The terms B ° and B", contain the contribution of multipolar attractive forces and both attractive and repulsive non-electrostatic forces. B" also coniains the contribution of the net charge resulting fl'om the bound chloride. At low concentrations of added electrolyte, neither term contributing to K2 will be negligible and Hc2/r will not be linear in any simple function of c2.
Salt-Free System Light-scattering results for the isoionic salt-free conalbumin in water are shown in Fig. 2. It is seen that Hc2/r approaches linearity in c~/2 at high dilution as predicted by the Kirkwood-Shumaker theory. The data can be represented by the least-squares equation:
Hc2/r = (1.36-4-.01) X 10-5 _
o
(2.8±0.2)
o
X
1 ~u- 5
Light
c21/2
Scattering
--
Data
(42.2±0.4)
X
10-5c~
of
-o_ × Q]lz
0'90.0
01.5
I'.O
I,Sr
2r.O
2.5
(Protein C0ncantralion, graml/litar) I/z
FIG. 2. Light scattering of iseionic salt-free conalbumin plotted against the s q u a r e r o o t of c o n c e n t r a t i o n .
432
TIMASHEFF
AND
TINOCO,
JR.
This leads to a molecular weight of M: = 73,600 and a root-mean-square charge (z2)1/2 - 3.53 q- 0.25 protonic unit. The data show also that over the concentration range studied, the constant B ° in Eq. (4) has a negative value, indicating a net attractive force. As shown recently (12), the interpretation of light-scattering data obtained with isoionic salt-free protein solutions is complicated by the fact that with dilution the protein becomes progressively ionized. This gives rise to an additional positive term in the first power of c2, the magnitude of which increases with dilution of the protein solution. Thus, data obtained on such a solution has to be corrected for this term prior to its interpretation by the theory of Kirkwood and Shumaker (1). In conalbumin, however, as its isoionic point is very close to pH 7.0, the contribution of progressive ionization with dilution remains negligibly small down to the lowest concentrations used in the present measurements.
Added Electrolyte Systems Light-scattering results for isoionic conalbumin in the presence of 0.001, 0.01, and 0.1 M NaC1 are shown in Fig. 3. The salt-free curve calculated from the least-squares equation given previously is included for comparison. A least-squares treatment of the data obtained in the presence of 0.1 and 0.01 M NaC1 yielded the following equations: 0.1 M NaCh Hc~/~- = (1.32 ~: .01) X 10-5 + (5 ~ 2) X 10_5 c2 0.01 M NaCI: Hc2/r = (1.30 :i: .01) X 10-s - (19 4- 2) X 10-5 c2 The 0.001 M NaC1 data were not treated by the method of least squares because at this salt concentration neither Eq. (4) nor (5) should apply since the contributions of the salt and the protein to the ionic strength are of similar magnitude. Equations (1) and (5) can be used to calculate the slope of Hc~/T vs. c2 in the presence of salt. The slopes thus calculated by use of (z2) obtained from the salt4ree light scattering and the net charge of the protein due to the chloride binding (6) are: (2.8 ± 3.5) X 10-5 for 0.1 M NaC1 and ( - 2 . 1 ~ 0.3) X 10-5 for 0.01 M NaC1. For 0.001 M NaC1, one can 1/2 calculate that Hc~/T should be linear neither in c2 nor in c2 . However, quantitative agreement with the experimental data is poor. The fact that only qualitative agreement is obtained between calculated and experimental light-scattering slopes indicates that other fac-
433
LIGHT SCATTERING OF ISOIONIC CONALBUMIN 1.4
~°
o
L3 -
o
~
-
I.I
~
O- I.OOXl(~tMNaCI qD- i.OOXlO"ZMNaCI O- [OOXI()aM NaCI 1.0 - - - - - - Salt-free
0.~
•
'
°
"
\ ""\'~ ~. ~
I
1.0
•
2.0
I0
I,
3
Concentration
40
I
5.0
6,0
(g/I)
FIG. 3. Light scattering of isoionic conalbumin, in the presence of various concentrations of sodium chloride, plotted against the concentration of conalbumin.
tors (non-electrostatic forces, etc.) in the B" term of Eq. (5) are important. A summary of the light-scattering results is given in Table I. Considering the approximations made in the theory and the derivation of Eqs. (4) and (5), the light-scattering results are quite consistent with the TABLE I Light-Scattering Data on Conalbumin Salt concentration
Molecular welght
Salt-free 0.1M 0.01M 0.001M Mean
73,600 75,800 77,100 78,100 76,200 =E 1,700
Slope
1000 /
Slope parameter defined by Edsall et al. (19).
295
--1,135
434
TIMASHEFF AND TINOCO, JR.
concept that the attractive forces found in isoionic conalbumin solutions are due to a great extent to fluctuating charges.
Comparison with Other Experiments Values of the mean-square fluctuation charge can be calculated from the amino acid composition of a protein or, better, from a titration curve. Using the equation for the charge fluctuations (1) of ni groups with acid dissociation constants K~,
(z2) = ~ n,[2 + [H+]/K~ + K~/[H~]] -1 i
(6)
and an amino acid composition of conalbumin (13): 23 tyrosine (pK = 10), 15 histidine (pK = 6.5), 64 lysine (pK = 10), 97 carboxyl (pK = 4), 40 arginine (pK = 12), one calculates a value of (z~)1/2 of 1.9 at pH 6.8. Linderstr~m-Lang has given an equation for the mean-square charge (14) which can be written as:
O(z)/OpH = 2.303[(z 2) -
(z) 2]
(7)
As (z) is zero at the isoionic point, the slope of a plot of the average number of protons bound by the protein (which is equal to a constant plus (z)) against pH will give the mean-square charge. Titration experiments in this laboratory on isoionic salt-free conalbumin (6) give a value of (z2)1/2 = 1.6 ± 0.2. Both of these values are lower than the value of 3.5 calculated from the light-scattering data. The value calculated from the amino acid analysis is the least reliable because of the approximations (1) made in the derivation of Eq. (6). Furthermore, the pK values used are averages for the various types of groups and their values may be different for conalbumin; also, the presence of a amino groups, not considered in the calculation, will raise the apparent (z2)I/2 value. Equation (7) is correct if only protons are bound by the protein. If more than one type of ion is bound and there is competition for sites by the various types of ions, Eq. (7) is replaced by the more general equation:
0 (z ) OSi - ~_~ - 2.303 ~ ((z~zj) apH ~=1 0pit ~.j=l
(z,) (zj))
(7a)
LIGHT SCATTERING OF ISOIONIC CONALBUMIN
435
where St is the number of ions of type i bound per molecule of protein, and zi is the charge on the molecule due to bound ions of type i. In the absence of competition for sites i = j. Kirkwood and Shumaker (15) have also shown that the fluctuation of protons should give rise to a fluctuating dipole moment in the protein. Although no dielectric increment measurements have been reported on conalbumin, nevertheless it would be of interest to estimate the magnitude that the ~fluctuating dipole moment would have for this protein. Thus, assuming the conalbumin molecule to be a sphere with a radius of 30 A., and neglecting all electrostatic interaction effects, it is possible to calculate a value of 500 Debye units for this quantity, using (z2)1/2 = 3.5. The molecular weight of conalbumin determined by light scattering was found to be 76,200 4- 1700. This is in good agreement with the recent value of 76,600 obtained by Warner and Weber (16) by titrating the protein with various metal ions which are bound stoichiometrically, and with the value of 77,300 obtained by J. R. Cann from osmoticpressure measurements (17). In the calculation of the molecular weight from light scattering, no depolarization correction was applied because recent experiments seem to show that this correction is negligible for proteins (18). Ultracentrifuge experiments on the isoionic conalbumin in 0.1 and 0.001 M NaC1 showed no evidence of any soluble aggregation or dissociation products after any of the stages of preparation for these light-scattering measurements. Therefore, from this excellent agreement between light scattering (weight average), osmotic pressure (number average), and metal binding (minimum stoichiometric), it is possible to conclude that conalbumin is a truly monodisperse protein with a molecular weight of c a . 76,500. ACKNOWLEDGMENTS We would like to thank Professor J. G. Kirkwood for his interest in this work, his helpful suggestions, and his derivation of Eq. (7a). Th~nks are also due Mrs. Marta Shapiro for her excellent technical assistance. SUMMARY
A new simplified preparation of conalbumin utilizing electrophoresisconvection has been described. Light-scattering measurements of isoionic conalbumin in 0.1, 0.01, and 0.001 M NaC1 and in salt-free solutions are reported. A molecular weight of 76,200 and a root-mean-square charge of 3.5 protonic units
436
TIMASHEFF AND TINOCO, JR.
have been obtained. The light-scattering results are consistent with the concepts that the attractive forces are principally due to fluctuating charges, and that eonalbumin is a monodisperse protein. NOTE ADDED IN PROOF
Since the preparation of this manuscript, another paper has appeared on the determination of the molecular weight of eonalbumin [Fuller, R. A., and Briggs, D. R., J. Am. Chem. Soc. 78, 5253 (1956)]. The value of 82,400 for the molecular weight of this protein, obtained from lightscattering measurements reported in that paper, is much higher than that reported in the present work. Furthermore, if the values for the depolarization correction, which are extremely high in view of Geiduschek's measurements (18), are omitted, the discrepancy becomes even larger. Although no obvious explanation could be found for the disagreement between our value and that of Fuller and Briggs, we would like to point out that the close agreement obtained between our value (76,200) and those of Warner and Weber (76,600) and of Phelps and Cann (77,300) becomes even more striking when it is realized that the three measurements were carried out on three different samples of conalbumin prepared by three different techniques. ~:~EFERENCES 1. KIRKWOOD, J. G., AND SHUMAKER,J. B., Proc. Natl. Acad. Sci. U. S. 38, 863 (1952). 2. TIMASttEFF, S. N., DINTZIS, H. M., •IRKWOOD, J. G., AND COLEMAN,B. D., Proe. Natl. Acad. Sci. U. S. 41,710 (1955). 3. TIMASHEFF, S. •., DINTZlS, H. M., :KIRKWOOD,J. G., AND COLEMAN, B. D., J. Am. Chem. Soc., in press. 4. DANDLICKER,W. B., J. Am. Chem. Soe. 76, 6036 (1954). 5. SCATCHARD,A., SCHEINB:ERG,I. H., AND ARMSTRONG,S. H., JR., J. Am. Chem. Soc. 72,535 (1950). 6. LowEr, S., Arch. Biochem. and Biophys. 64, 111 (1956). 7. CANN, J. R., KIRKWOOD,J. G., BROWN, R. A., AND PLESCIA, O., ,)r. Am. Chem. Soc. 71, 1603 (1949). 8. ~TNoRD,F. F., BIER, M., AND TIMASHEFF, S. N., J. Am. Chem. Soc. 73, 289 (1951). 9. WARNER, R. C., AND WEBER, I., J. Biol. Chem. 191, 173 (1951). 10. DINTZIS, H. M., Doctoral Dissertation, Harvard University, 1952. 11. KIRKWOOD,J. G., AND GOLDBERG, I~. J., J. Chem. Phys. 18, 54 (1950). 12. I~IRKWOOD,J. G., AND TIMASHEFF,S. N., Arch. Biochem. and Biophys. 65, 50 (1956). 13. TRISTRAM,G. R., in "The Proteins" (Neurath, H., and Bailey, K., eds.), Vol. I, Pt. A, p. 219. Academic Press, New York~ 1953.
LIGHT SCATTERING OF ISOIONIC CONALBUMII~
437
14. COliN, E. J., AN]) EDSALL, J. T., "Proteins, Amino Acids and Peptides," p. 402. Reinhold Publ. Corp., New York, 1943. 15. KIRKWOOD,J. G., AND SHUI~J[AKER,J. B., Proc. Natl. Acad. Sci. U. S. 38, 855 (1952). 16. WARNER, R. C., AND WEBER, I., J. Am. Chem. Soe. 74, 5094 (1953). 17. PHELPS, R. A., AND CANN, J. R., Arch. Biochem. and Biophys. 61, 51 (1956). 18. GEIDUSCHEK,E. P., J, Polymer Sci. 13,408 (1954). 19. EDSALL,J. T., EDELHOCH, J., LONTIE, R., AND MORRISON, P. R., ] . Am. Chem. Soc. 72, 4641 (1950).
66, 427-437 (1957)
Light Scattering of Isoionic Conalbumin I Serge N. Timasheff 2 and Ignaci0 Tinoco, Jr. 3 From the Department of Chemistry, Yale University, New Haven, Connecticut Received June 20, 1956 INTRODUCTION
The Kirkwood-Shumaker theory (1) of forces between protein molecules arising from charge fluctuations can be tested by light-scattering measurements. Such measurements have been made on isoionic ~ serum albumin in the absence and presence of salt (2-4). The interpretation of the serum albumin experiments is complicated by the net negative charge on the isoionic salt-free protein which is a function of the protein concentration; 5 also, the chloride binding of the protein (5) makes the experiments in salt more difficult to interpret. Conalbumin has an isoionic point in water which is very close to p H 7; therefore, the net charge of the isoionic protein will be nearly zero at all concentrations. Furthermore, the chloride binding is less extensive than with serum albumin (6). Light-scattering measurements on isoionic conalbumin can thus be used to provide a further and more unequivocal test of the Kirkwood-Shumaker theory. METHODS The electrophoresis-convection apparatus has been described previously (7). The electrophoresis experiments were done at 0°C. in a Perkin-Elmer model 38 i Contribution No. 1382 from the Sterling Chemistry Laboratory, Yale University. This work was supported in part by the Office of Naval Research, Contract No. Nonr 659 (00). Present address: Eastern Regional Research Laboratory, U. S. Dept. of Agriculture, Philadelphia, Pa. 3 Public Health Service Research Fellow of the National Cancer Institute. 4 An isoionie protein is defined as a protein which has been passed through an ion-exchange column so as to remove all ions except hydrogen or hydroxyl. 5 The net negative charge of salt-free bovine serum albumin varies from approximately 0.1 to 1 protonic unit as the concentration changes from 1 to 0.05% (3). 427
428
TIMASHEFF AND TINOCO~ JR.
apparatus. The electrophoretic patterns were enlarged and traced to determine the mobilities and measure the areas of the schlieren peaks. The sedimentation experiments were carried Out in a Spinco model E analytical ultracentrifuge at room temperature and a speed of 59,780 r.p.m.
Light Scattering The clarification of the solutions for light scattering was accomplished by filtration through a specially designed ultrafine sintered-glass filter (8). Concentrated, deionized protein stock solution in water was successively added to the weighed Solvent in a 3-ml. light-scattering cell using a microburet. If the solvent contained NaC1, concentrated (1 M) salt solution was added at the same time from a separate microburet to keep the salt concentration constant. Water redistilled from an M1-Pyrex glass still was used for the preparation of all solutions. The concentration of the stock solution was determined from a dry weight obtained by drying the proteins at 107 ° and atmospheric pressure. The scattering intensities at 90 ° at a wavelength of 436 m~ were measured with a modified Brice-Phoenix photometer. The opal diffuser supplied by the manufacturer was used as a primary standard in the determination of the turbidities. The refractive increment of isoionic conalbumin [dn/dc~ = 0.192(g./ml.) -1] was determined using a Brice-Phoenix differential refractometer. Further details of the light-scattering technique used can be found in other publications from this laboratory (2, 3). ~ViATERIALS The eonalbumin was prepared from fresh eggs using a modified Warner (9) method. The procedure of Warner was followed through the ethanol precipitation step; then, instead of crystallizing the conalbumin as the iron complex, and removing the iron on an ion-exchange column in the presence of citrate, a singlestage electrophoresis-eonvection fractionation was used for the final purification. The electrophoretic pattern at pH 5.76 of the ethanol precipitate (Fig. 1, top) shows that there are approximately equal amounts of components with mobilities greater and less than the isoelectric conalbumin. To remove the positively charged component (lysozyme, u = 5.9 X 10-5 sq. cm./see, v.) a 2% solution of deoxyribonucleic acid (DNA) (Schwarz Laboratories, Lot No. 4904) in pH 5.76, r / 2 = 0.1, phosphate buffer was added to the eonalbumin solution in the same buffer. A precipitate formed immediately. The amount of D N A needed to precipitate completely the lysozyme was determined by trim on a small portion; a slight excess of D N A was used as its presence would not interfere in the eleetrophoresis-conveetion purification. The electrophoretie pattern of the supernatant from the I ) N A precipitation is shown (Fig. 1, middle); the lysozyme is now absent, but the negatively charged ovalbumin (u = 6.2 X 10-~ sq. em./see, v.) remains. The eleetrophoresis-convection fractionation of this D N A - t r e a t e d solution was carried out in a pH 5.76, r / 2 = 0.1 phosphate buffer at a field strength of 2 v./cm, applied for 48 hr. at 3-4°C. The electrophoretie pattern of the solution removed from the top reservoir at the end of the fraetionation is shown in Fig. 1, bottom. The conalbumin is electrophoretieally pure. The pure eonalbumin solution was dialyzed against water; it then was pervapo-
LIGHT SCATTERING OF ISOIONIC CONALBUMIN
429
FIG. 1. Electrophoretic patterns of protein fractions obtained in the preparation of conalbumin : after ethanol precipitation (top) ; supernatant from DNA precipitation (middle); contents of upper reservoir of electrophoresis-convection cell (bottom). All photographs were taken after 30 min. at 13 v./cm. rated to approximately half its volume to give a 4% solution. This solution was deionized by passing through a column containing a mixed cation- and anionexchange resin (Amberlite MB-1) above a cation-exchange resin (Amberlite IRC-120) ; the resins were in the hydrogen or hydroxyl form (10). Electrophoretie and ultracentrifugal analyses of the conalbumin before and after deionization showed that no gross changes in the protein had occurred during passage through the resin. The pH of the deionized eonalbumin was 6.8. The optical density at 470 mg of a 1% conalbumin solution in a 1-cm. cell was approximately 0.01, showing that no appreciable iron complex was present (9). RESULTS
AND
DISCUSSION
Theory T h e excess t u r b i d i t y r (11) of a t h r e e - c o m p o n e n t s y s t e m (macromolecule, c o m p o n e n t 2; small molecule, c o m p o n e n t 1; solvent, com-
430
TIMASHEFF AND TINOCO, JR.
ponent 0) may be written in terms of the molecular weights M~, and the 0 chemical potentials, gi = R T in ca ÷ g~e ÷ g~(T, P), of the solutes in the following manner. At constant temperature and pressure:
M~ \~$-~/o~\OC~/o~ + L M~ \~/o~ \-~-(/o~j ILl
32~%'~(an/OcD~
(~n/OcDo.
3X4N
(On~Oct)el
(1)
where c~ is the concentration in g./ml, of component i, n is the refractive index of the solution, X is the wavelength of the light, N is Avogadro's number, R is the gas constant, and T is the thermodynamic temperature. In the absence of strong interaction between components 1 and 2, Eq. (1) reduces to the usual two-component equation.
T
M~
k ~ \0-~-:/d
(2)
Kirkwood and Shumaker (1) give the following expression for the derivative of the excess chemical potential of a protein with an average charge of zero, but a non-zero mean square charge,
M2 ( 0 ~ = -~rNe4{z 2) 7vNa 3 R--T \O-c~/r,e (DkT)2~(1 -4- ~a) 2 + ~ -4- 2B' --
]
(3) = 4
-~g2
where (z2 is the mean square charge of the protein in protonic units e, D is the dielectric constant of the solvent, k is Boltzmann's constant, a is the radius of a protein molecule, and 1~/2 is the ionic strength of the added electrolyte. The first term on the right in Eq. (3) gives the fluctuating charge interaction; the second term is the excluded volume contribution; the last term, 2B', includes the effects of permanent and fluctuating multipoles and non-electrostatic forces. Binomial expansion of (1 ÷ Ka)-2 gives for the salt-free system:
C2 (Og~ R-T \0-~2]
=
-
-
7r,/2N,/2ea/ kz 2,a/2 ? c2,/2 2(DkT)a~2M~I 2
0
÷ B c~ ÷ . . . .
(4)
431
LIGHT SCATTERING OF ISOIONIC COXALBUMIi~
In the presence of excess salt, the equivalent expression is:
RT\O-~/c,
- L ( D k T ) ~
+
K0a)2 - B "
c2 + . . .
(5)
In the absence of added electrolyte, the limiting slope of Hc2/r is linear in c~/2 and the only unknown parameter in the slope is the mean square charge (z2}. When the ionic strength of the solution is governed solely by the added electrolyte, the limiting slope of Hc2/r is linear in c2, but the slope now also depends on the intermolecular forces other than those due to the fluctuating charges. The terms B ° and B", contain the contribution of multipolar attractive forces and both attractive and repulsive non-electrostatic forces. B" also coniains the contribution of the net charge resulting fl'om the bound chloride. At low concentrations of added electrolyte, neither term contributing to K2 will be negligible and Hc2/r will not be linear in any simple function of c2.
Salt-Free System Light-scattering results for the isoionic salt-free conalbumin in water are shown in Fig. 2. It is seen that Hc2/r approaches linearity in c~/2 at high dilution as predicted by the Kirkwood-Shumaker theory. The data can be represented by the least-squares equation:
Hc2/r = (1.36-4-.01) X 10-5 _
o
(2.8±0.2)
o
X
1 ~u- 5
Light
c21/2
Scattering
--
Data
(42.2±0.4)
X
10-5c~
of
-o_ × Q]lz
0'90.0
01.5
I'.O
I,Sr
2r.O
2.5
(Protein C0ncantralion, graml/litar) I/z
FIG. 2. Light scattering of iseionic salt-free conalbumin plotted against the s q u a r e r o o t of c o n c e n t r a t i o n .
432
TIMASHEFF
AND
TINOCO,
JR.
This leads to a molecular weight of M: = 73,600 and a root-mean-square charge (z2)1/2 - 3.53 q- 0.25 protonic unit. The data show also that over the concentration range studied, the constant B ° in Eq. (4) has a negative value, indicating a net attractive force. As shown recently (12), the interpretation of light-scattering data obtained with isoionic salt-free protein solutions is complicated by the fact that with dilution the protein becomes progressively ionized. This gives rise to an additional positive term in the first power of c2, the magnitude of which increases with dilution of the protein solution. Thus, data obtained on such a solution has to be corrected for this term prior to its interpretation by the theory of Kirkwood and Shumaker (1). In conalbumin, however, as its isoionic point is very close to pH 7.0, the contribution of progressive ionization with dilution remains negligibly small down to the lowest concentrations used in the present measurements.
Added Electrolyte Systems Light-scattering results for isoionic conalbumin in the presence of 0.001, 0.01, and 0.1 M NaC1 are shown in Fig. 3. The salt-free curve calculated from the least-squares equation given previously is included for comparison. A least-squares treatment of the data obtained in the presence of 0.1 and 0.01 M NaC1 yielded the following equations: 0.1 M NaCh Hc~/~- = (1.32 ~: .01) X 10-5 + (5 ~ 2) X 10_5 c2 0.01 M NaCI: Hc2/r = (1.30 :i: .01) X 10-s - (19 4- 2) X 10-5 c2 The 0.001 M NaC1 data were not treated by the method of least squares because at this salt concentration neither Eq. (4) nor (5) should apply since the contributions of the salt and the protein to the ionic strength are of similar magnitude. Equations (1) and (5) can be used to calculate the slope of Hc~/T vs. c2 in the presence of salt. The slopes thus calculated by use of (z2) obtained from the salt4ree light scattering and the net charge of the protein due to the chloride binding (6) are: (2.8 ± 3.5) X 10-5 for 0.1 M NaC1 and ( - 2 . 1 ~ 0.3) X 10-5 for 0.01 M NaC1. For 0.001 M NaC1, one can 1/2 calculate that Hc~/T should be linear neither in c2 nor in c2 . However, quantitative agreement with the experimental data is poor. The fact that only qualitative agreement is obtained between calculated and experimental light-scattering slopes indicates that other fac-
433
LIGHT SCATTERING OF ISOIONIC CONALBUMIN 1.4
~°
o
L3 -
o
~
-
I.I
~
O- I.OOXl(~tMNaCI qD- i.OOXlO"ZMNaCI O- [OOXI()aM NaCI 1.0 - - - - - - Salt-free
0.~
•
'
°
"
\ ""\'~ ~. ~
I
1.0
•
2.0
I0
I,
3
Concentration
40
I
5.0
6,0
(g/I)
FIG. 3. Light scattering of isoionic conalbumin, in the presence of various concentrations of sodium chloride, plotted against the concentration of conalbumin.
tors (non-electrostatic forces, etc.) in the B" term of Eq. (5) are important. A summary of the light-scattering results is given in Table I. Considering the approximations made in the theory and the derivation of Eqs. (4) and (5), the light-scattering results are quite consistent with the TABLE I Light-Scattering Data on Conalbumin Salt concentration
Molecular welght
Salt-free 0.1M 0.01M 0.001M Mean
73,600 75,800 77,100 78,100 76,200 =E 1,700
Slope
1000 /
Slope parameter defined by Edsall et al. (19).
295
--1,135
434
TIMASHEFF AND TINOCO, JR.
concept that the attractive forces found in isoionic conalbumin solutions are due to a great extent to fluctuating charges.
Comparison with Other Experiments Values of the mean-square fluctuation charge can be calculated from the amino acid composition of a protein or, better, from a titration curve. Using the equation for the charge fluctuations (1) of ni groups with acid dissociation constants K~,
(z2) = ~ n,[2 + [H+]/K~ + K~/[H~]] -1 i
(6)
and an amino acid composition of conalbumin (13): 23 tyrosine (pK = 10), 15 histidine (pK = 6.5), 64 lysine (pK = 10), 97 carboxyl (pK = 4), 40 arginine (pK = 12), one calculates a value of (z~)1/2 of 1.9 at pH 6.8. Linderstr~m-Lang has given an equation for the mean-square charge (14) which can be written as:
O(z)/OpH = 2.303[(z 2) -
(z) 2]
(7)
As (z) is zero at the isoionic point, the slope of a plot of the average number of protons bound by the protein (which is equal to a constant plus (z)) against pH will give the mean-square charge. Titration experiments in this laboratory on isoionic salt-free conalbumin (6) give a value of (z2)1/2 = 1.6 ± 0.2. Both of these values are lower than the value of 3.5 calculated from the light-scattering data. The value calculated from the amino acid analysis is the least reliable because of the approximations (1) made in the derivation of Eq. (6). Furthermore, the pK values used are averages for the various types of groups and their values may be different for conalbumin; also, the presence of a amino groups, not considered in the calculation, will raise the apparent (z2)I/2 value. Equation (7) is correct if only protons are bound by the protein. If more than one type of ion is bound and there is competition for sites by the various types of ions, Eq. (7) is replaced by the more general equation:
0 (z ) OSi - ~_~ - 2.303 ~ ((z~zj) apH ~=1 0pit ~.j=l
(z,) (zj))
(7a)
LIGHT SCATTERING OF ISOIONIC CONALBUMIN
435
where St is the number of ions of type i bound per molecule of protein, and zi is the charge on the molecule due to bound ions of type i. In the absence of competition for sites i = j. Kirkwood and Shumaker (15) have also shown that the fluctuation of protons should give rise to a fluctuating dipole moment in the protein. Although no dielectric increment measurements have been reported on conalbumin, nevertheless it would be of interest to estimate the magnitude that the ~fluctuating dipole moment would have for this protein. Thus, assuming the conalbumin molecule to be a sphere with a radius of 30 A., and neglecting all electrostatic interaction effects, it is possible to calculate a value of 500 Debye units for this quantity, using (z2)1/2 = 3.5. The molecular weight of conalbumin determined by light scattering was found to be 76,200 4- 1700. This is in good agreement with the recent value of 76,600 obtained by Warner and Weber (16) by titrating the protein with various metal ions which are bound stoichiometrically, and with the value of 77,300 obtained by J. R. Cann from osmoticpressure measurements (17). In the calculation of the molecular weight from light scattering, no depolarization correction was applied because recent experiments seem to show that this correction is negligible for proteins (18). Ultracentrifuge experiments on the isoionic conalbumin in 0.1 and 0.001 M NaC1 showed no evidence of any soluble aggregation or dissociation products after any of the stages of preparation for these light-scattering measurements. Therefore, from this excellent agreement between light scattering (weight average), osmotic pressure (number average), and metal binding (minimum stoichiometric), it is possible to conclude that conalbumin is a truly monodisperse protein with a molecular weight of c a . 76,500. ACKNOWLEDGMENTS We would like to thank Professor J. G. Kirkwood for his interest in this work, his helpful suggestions, and his derivation of Eq. (7a). Th~nks are also due Mrs. Marta Shapiro for her excellent technical assistance. SUMMARY
A new simplified preparation of conalbumin utilizing electrophoresisconvection has been described. Light-scattering measurements of isoionic conalbumin in 0.1, 0.01, and 0.001 M NaC1 and in salt-free solutions are reported. A molecular weight of 76,200 and a root-mean-square charge of 3.5 protonic units
436
TIMASHEFF AND TINOCO, JR.
have been obtained. The light-scattering results are consistent with the concepts that the attractive forces are principally due to fluctuating charges, and that eonalbumin is a monodisperse protein. NOTE ADDED IN PROOF
Since the preparation of this manuscript, another paper has appeared on the determination of the molecular weight of eonalbumin [Fuller, R. A., and Briggs, D. R., J. Am. Chem. Soc. 78, 5253 (1956)]. The value of 82,400 for the molecular weight of this protein, obtained from lightscattering measurements reported in that paper, is much higher than that reported in the present work. Furthermore, if the values for the depolarization correction, which are extremely high in view of Geiduschek's measurements (18), are omitted, the discrepancy becomes even larger. Although no obvious explanation could be found for the disagreement between our value and that of Fuller and Briggs, we would like to point out that the close agreement obtained between our value (76,200) and those of Warner and Weber (76,600) and of Phelps and Cann (77,300) becomes even more striking when it is realized that the three measurements were carried out on three different samples of conalbumin prepared by three different techniques. ~:~EFERENCES 1. KIRKWOOD, J. G., AND SHUMAKER,J. B., Proc. Natl. Acad. Sci. U. S. 38, 863 (1952). 2. TIMASttEFF, S. N., DINTZIS, H. M., •IRKWOOD, J. G., AND COLEMAN,B. D., Proe. Natl. Acad. Sci. U. S. 41,710 (1955). 3. TIMASHEFF, S. •., DINTZlS, H. M., :KIRKWOOD,J. G., AND COLEMAN, B. D., J. Am. Chem. Soc., in press. 4. DANDLICKER,W. B., J. Am. Chem. Soe. 76, 6036 (1954). 5. SCATCHARD,A., SCHEINB:ERG,I. H., AND ARMSTRONG,S. H., JR., J. Am. Chem. Soc. 72,535 (1950). 6. LowEr, S., Arch. Biochem. and Biophys. 64, 111 (1956). 7. CANN, J. R., KIRKWOOD,J. G., BROWN, R. A., AND PLESCIA, O., ,)r. Am. Chem. Soc. 71, 1603 (1949). 8. ~TNoRD,F. F., BIER, M., AND TIMASHEFF, S. N., J. Am. Chem. Soc. 73, 289 (1951). 9. WARNER, R. C., AND WEBER, I., J. Biol. Chem. 191, 173 (1951). 10. DINTZIS, H. M., Doctoral Dissertation, Harvard University, 1952. 11. KIRKWOOD,J. G., AND GOLDBERG, I~. J., J. Chem. Phys. 18, 54 (1950). 12. I~IRKWOOD,J. G., AND TIMASHEFF,S. N., Arch. Biochem. and Biophys. 65, 50 (1956). 13. TRISTRAM,G. R., in "The Proteins" (Neurath, H., and Bailey, K., eds.), Vol. I, Pt. A, p. 219. Academic Press, New York~ 1953.
LIGHT SCATTERING OF ISOIONIC CONALBUMII~
437
14. COliN, E. J., AN]) EDSALL, J. T., "Proteins, Amino Acids and Peptides," p. 402. Reinhold Publ. Corp., New York, 1943. 15. KIRKWOOD,J. G., AND SHUI~J[AKER,J. B., Proc. Natl. Acad. Sci. U. S. 38, 855 (1952). 16. WARNER, R. C., AND WEBER, I., J. Am. Chem. Soe. 74, 5094 (1953). 17. PHELPS, R. A., AND CANN, J. R., Arch. Biochem. and Biophys. 61, 51 (1956). 18. GEIDUSCHEK,E. P., J, Polymer Sci. 13,408 (1954). 19. EDSALL,J. T., EDELHOCH, J., LONTIE, R., AND MORRISON, P. R., ] . Am. Chem. Soc. 72, 4641 (1950).