ULTRACENTRIFUGAL ANALYSIS AND STABILITY I N PROTEIN SYSTEMS' HAROLD P . LUNDGREN AND 3. W . WILLIAMS Department of Chemistry, Universaty of Wasconsin, Madison, Wasconsiik Received August 1 , 1959
The molar friction constant of proteins determined in ultracentrifugal analysis may be modified in the presence of water by variations in the hydrogen-ion, electrolyte, and protein concentration of the solution, by the addition both of amides, amino acids, and other chemicals and of other proteins, by heat, by ultraviolet light, by ultrasonic waves, etc. It is important to understand the cause of such modifications in the sedimentation behavior of the dissolved unit. I n some cases the effect is due to a real dissociation, but it must be recognized that in other instances it may arise from a change in the shape of the molecule, or even from a change in the degree of solvation. I n extreme cases sedimentation velocity may be modified by orientations of the molecular kinetic unit. I n this study of protein stability in solution we shall (1) make the attempt to analyze the result of solvent change in influencing sedimentation and diffusion constants by setting up simple relationships between molecular weight, sedimentation constant (s), diffusion constant (D), and the Svedberg dissymmetry factor (flf0),(2) give representative experimental data to show how these constants are modified by the dissociation of dissolved units, and (3)consider other systems for which changes in molecular form rather than actual dissociation may be responsible in part for observed differences in molar friction constant. I . MATHEMATICAL RELATIONSHIPS
It will be convenient for the discussion following to have a t hand certain relationships between molecular weight, M , sedimentation constant, s, diffusion constant, D, and dissymmetry number, f/fo. The frictional resistance to sedimentation of a spherical molecule is
1 Presented at the Sixteenth Colloid Symposium, ,held at Stanford University, California, July 6-8, 1939. 989
990
HAROLD P. LUNDGREN AND J . W. WILLIAMS
In this expression 9 is the coefficient of viscosity of the solvent and V is the partial specific volume of the solute. The corresponding quantity for a moleoule of any non-spherical form is
The condition that f/jo remains constant gives
From kinetic theory
M kT = - Y O 2
If the temperature remains constant, the velocity of the particle increases with l/-. Also,
therefore s
/
a is constant
(2)
Since both conditions can not be fulfilled a t the same time, either the partial specific volume must change or the shape factor must change. The Svedberg formula for the molecular weight of a molecule in terms of s and D is
From its derivation this equation is valid strictly only for systems of two components. It will be correct in a three-component system in which no combination can occur between protein and any component. In the discussion to follow, we must assume no serious difficulty from this source in isoelectric dilute salt solutions when the major extra component is electrically neutral. I n the case of a sphere, we have
which gives
so
= kM2/'. Further,
Do= D -f
fo
991
STABILITY IN PROTEIN SYSTEMS
and M is a function of s / D alone. Therefore, s X f/fo tion,
=
SO.
By defini-
and
Now, inserting the values for DOand
SO, we
have
and
The ratio fo/f 5 1. Thus, if M decreases, one factor of D increases and the other decreases, while both factors in s decrease. Therefore, s will decrease while D may increase, remain constant, or even decrease as a molecule dissociates. On the other hand, if M remains constant and the protein unfolds, both s and D will decrease. 11. DISSOCIATION PHENOMENA
There are now a number of cases in which a dissociation of the protein in the system is well established. The following sedimentation and diffusion data for hemoglobin and phycocyan are sufficient to show that in these systems such a reaction takes place. In table 1 the ratios of s / D are used to calculate the molecular weight of the dissociated molecule, the dissymmetry factor (f/f~)is calculated from the observed diffusion constant, and its sedimentation constant is calculated from the ratio
- Ma’’ (flfo) 81
M:”
(f/fo)i
The values of s and D are always corrected to the basis of a process taking place in pure water a t 20°C. In making calculations for the ratio of major to minor axis from dissymmetry number data, use has been made of recent theoretical work of Perrin. Of course molecular dimensions can be calculated with a knowledge of molecular weight, density, and dissymmetry number, but we have
992
HAROLD P. LUNDGREN AND J. W. WILLIAMS
DISSOCIATED MOLECULE NORMAL MOLECULE
M . .. . . . . . . . . . . . . . . . . . . . . s 1 0 x 10". . . . . . . . . . . . . . . . D~~ x 107... . . . . . . . . . . . . . f / f Q. . . . . . . . . . . . . . . . . . . . . .
273,000 11.4 4.05 1.2 1:4
b/a . . . . . . . . . . . . . . . . . . . . . .
Experimental
Caloulatd
146,000 6.2 4.6
131,000 6.1 1.35 1:8
B. Molecular weight data for hemoglobin and its dissociation product. Normal molecule in ordinary aqueous buffer solution. Dissociation product in 40 per cent aqueous urea solution. (Steinhardt: J. Biol. Chem. 123, 543 (1938)) Dl8BOCIATED MOLECULE NORMAL MOLECULE
Experimental
-M .. . . . . . . . . . . . . . . . . . . . . 8 2 0 x 10". . . . . . . . . . . . . . . . . D20
x 10'. . . . . . . . . . . . . . . .
f/fQ. . . . . . . . . . . . . . . . . . . . . . b/a . . . . . . . . . . . . . . . . . . . . . . .
76,000 4.6 6.3 1.20 1:4
38,000 3.2 7.7
Calculated
43,700 3.23 1.18 1:4
STABILITY IN PROTEIN SYSTEMS
993
ing cleavage along the major axis, but, although it is difficult to understand, there is no apparent modification of dissymmetry number for the dissociated hemoglobin. Other interesting dissociation phenomena are found in thc case of the hemocyanins, where the stability diagrams are markedly influenced by the hydrogen-ion concentration of the solution. Observations of sedimentation velocity and diffusion prove that the protein contains only one component a t the isoelectric point in the case of Helix pomatia and Helix nemoralis, while the hemocyanins of Helix arbustorum and Helix hortensis contain two components in the isoelectric region. As the pH of the solution is decreased or increased, points are reached where a small change in pH causes a pronounced change in the protein. Thus, the original molecule of Helix pomatia (molecular weight 6,750,000) dissociates stepwise into homogeneous half, eighth, and sixteenth components. The presence of certain ions, particularly Ca++ and Mg++, causes important changes in the stability of this system. It is important to note that the molecular weights of the hemocyanin molecules found in the blood of a certain species are always simple multiples of the lowest well-defined component. In most cases the components of the species are interconnected by reversible dissociation-association reactions which depend upon the pH value of the solution. 111. COMPLEX EQUILIBRIA
The changes in molar friction constant for the proteins considered in the preceding section are due to dissociation reactions. With other systems similar modifications of sedimentation diagrams and molar friction constant are observed, but the interpretation is more difficult to understand. I n some cases changes in the molecular weight of a protein are believed to be responsible for modified sedimentation diagrams, but in others it appears that a change in the shape of the sedimenting unit is responsible for the observed effects. As typical of cases where molecular weight changes are believed to be involved, we cite experiments of McFarlane (4) and of Pedersen ( 5 ) , in which the presence of another protein of lower molecular weight, a protamine, or an amino acid causes the amount of the substance of higher molecular weight to decrease and to be replaced by a slower sedimenting component, although the protein of higher molecular weight is perfectly stable under the same conditions when it is present alone except for the salt used to repress the Donnan effect. The action of the dissociating compound on a protein is highly specific, and the magnitude of the effect varies greatly from protein to protein. Pedersen writes, “From the experi-
e45
TIME AFTER START849 MIN SCALE DtSTANCE.50 CM
a0
”z1 u m5
.
/
1 ow
STABILITY IN PROTEIN SYSTEMS
995
x 10-13; M = 650,000). Furthermore, it appears appreciably stable in electrolytes, becoming somewhat less homogeneous on long standing, as judged from the sharpness of the boundary on sedimentation. When the protein is denatured in salt solutions by heating, by ultraviolet light, or by acid, it becomes polydisperse, the boundary being spread over a considerable distance in the centrifuge cell, presumably indicating dissociation and aggregation (figure 2). When the protein is brought outside the pH stability region in salt solutions, welldefined slower sedimenting boundaries are present, indicating a dissociation of the protein. Thus thyroglobulin behaves as a typical protem in the electrolyte solutions. Studies with electrolyte-free solutions of this protein have revealed profound changes in the sedimentation behavior within the usual pH sta-
FIO.3. Sedimentation diagram for N thyroglobulin in salt-free solution
bility region. These changes are well defined, as distinguished from the ordinary increases in polydispersity which occur on long standing in salt solutions. When sedimented, a freshly dialyzed salt-free solution of thyroglobulin less alkaline than pH 8 to 9 gives a single boundary, which moves in the cell at a slower rate due to the failure to repress the Donnan effect. In addition, the boundary possesses a considerably greater sharpness than it does in the presence of salt. In the discussions to follow we shall term this “N protein” (figure 3). I n salt-free solutions with protein concentration higher than 1.0 per cent a single welldefined slower sedimenting component, which we shall call for convenience “a-protein”, is formed on standing (figure 4). An equilibrium is established, and the rate a t which the change takes place is a function of the pH value of the solution. In alkaline solutions attainment of
996
HAROLD P. LUNDGHEN AND f . W. WILLIAMS
equilibrium is rapid. At 4%. several weeks are required for the change in solutions more acid than pH 7, but the reaction is immediate in solut,ions more alkaline than pH 9 to 10. The process is immediately reversed by
79
65
6.0
FIQ.4. Sedimentation diagram for N thyroglobulin (right) and a-thyroglobulin (left) in equilibrium in salt-free solution (protein concentration = 4.5 per cent; pH = 9.5).
N=
a
PROT. CONC. 0.8%
. .20 -
A0
30.IO.
6
8
IO
12
PH FIG.5 . Equilibrium N F? a as a function of pH
the addition of electrolyte to 0.02 M , giving native protein with normal sedimentation and electrochemical behavior. At this salt concentration Donnan effects are largely repressed in routine sedimentation experiments.
STABILITY IN PROTEIN SYSTEMS
997
Beyond pH 11.3 the equilibrium is shifted, perhaps to a reaction product from a-protein, since the process is now no longer reversible with electrolyte (figure 5 ) . On dilution to less than 0.1 per cent protein concentration of a solution containing the equilibrium system N F? a, a new equilibrium is rapidly established between a third slower sedimentation component (figure 6). That the newly formed, slower sedimenting protein formed in dilute solutions arises from the a-component is apparent, since freshly dialyzed dilute solutions of thyroglobulin sedimenting with a single sharp boundary do nH€i4 l n h ISrcc. ajkr/uttpp.rd
OODW
SCALIOISTANCC: 12.0 Cn.
I
FIG.6. Sedimentation for N thyroglobulin (right) and a-thyroglobulin (center) and slower sedimenting protein in salt-free solution (protein concentration = 0.08 per cent; pH = 9.5).
SCALE DISTANCE' 5 0 CM.
55
60 CY
x IN
e5
FIG.7. Sedimentation diagram for isolated a-thyroglobulin
not appear to undergo immediate dissociation. This is further confirmed by isolation of the a-component with use of the two-compartment separation cell of Svedberg (6) (figure 7). The separated a-form of the protein is unstable. An equilibrium is again established with time with the N protein. If the solution containing a-protein is diluted to less than 0.1 per cent protein concentration, the new slower sedimenting protein is again formed. If heated, the a-form changes to homogeneous denatured protein with sedimentation behavior like that of N protein but with different solubility and electrophoretic properties. If allowed to stand in high concentrations, especially near pH 5, components sedimenting faster than N protein have been observed.
998
HAROLD P. LUNDGREN AND J. W. WILLIAMS
It appears from these experiments that the a-component is an intermediate unstable form of the protein. Equilibria of the type N F? a are not specific to thyroglobulin, because similar reactions have been found in other protein systems. Analogous equilibria are shown for thymus nucleohistone and antitoxic diphtheria
4
FIQ. 8. Sedimentation diagram showing equilibrium N Ft a in various proteins. From left to right in each diagram, labile and native components. Concentration and pH for each protein as follows: thyroglobulin, 4.3 per cent, pH = 6.1; antitoxic diphtheria pseudoglobulin, 5.5 per cent, pH = 7.6; thymus nucleohistone, 1.2 per cent, pH = 6.0.
4 0
I B CONCENTRATION
3
4
GMllOOCC SOL.
FIG.9. Effect of protein concentration in shifting equilibrium N e a
pseudoglobulin and are compared with the equilibrium in thyroglobulin (figure 8). Although the system N F? a gives a sedimentation diagram which resembles that of a dissociation, there are reasons to believe that the changes now being considered do not involve a change in mass of the kinetic unit. For instance, the equilibrium N a a is not shifted to the right on dilution, as would be expected on the basis of the law of mass aotion if the process involved an increase in the number of molecules.
STABILITY I N PROTEIN SYSTEMS
999
Instead the equilibrium is shifted toward the N-form, as shown in the accompanying diagram (figure 9). Such a process might be considered as a change involving an unfolding of the protein molecule in solutions. Another view would be the orientation of the rodshaped particles in solution. However, the change is much more labile to electrolyte than the layering effects noted in concentrated solutions of tobacco mosaic virus protein ascribed by Bernal (1) as due to an orientation of the rodshaped particles. Furthermore, it is di5cult to account on this basis for the existence of equilibrium in dilute solution.
SEMMENTATION CONSTANT A S FUNCTION OF SHAPE FACTOR FOR OIVEN MOLECULAR WEIGHT NPb!
m5.r
1
0
lo
sxtd'
30
FIQ.10 FIQ.11 FIG.10. Upper curve: relation of dissymmetry coefficient to sedimentation constant. Lower curve: ratio of major to minor axis, ala, through Perrin's equation and the relation between the diffusion constant for the protein and for a spherical molecule of the same molecular weight. FIQ.11. Sedimentation rate of N and of a-thyroglobulin as a function of concentration
An unfolding of the molecule to account for the change in sedimentation behavior is indicated by the following calculation: On the basis of the dissymmetry number 1.5, given by Heidelberger and Pedersen (2) for normal thyroglobulin, it is possible to calculate the ratio of the major to the minor axis by assuming the molecule to have the shape of an ellipsoid of revolution. The ratio b/a for normal native thyroglobulin corresponds approximately to 8.7 to 1 (figure 10). If we assume the molecule to undergo simple unfolding such that it becomes twice as long and one-half as wide, we arrive at a value, 2.63, for the dissymmetry number. This number
1000
HAROLD P. LUNDGREN AND J. W. WILLIAMS
corresponds to a sedimentation constant of 10.9 X for the unfolded form, as compared with 19.2 X for normal native thyroglobulin. The actual sedimentation behavior of the N and the a-thyroglobulin as a function of concentration is shown by the accompanying diagram (figure 11). On extrapolation to zero concentration specific sedimentation constant values of approximately 10 x 10-13 and 17.5 X 10-13 are obtained. Although no attempt has been made to correct these values to the basis of a sedimentation in salt solution, it is evident that the theoretical and observed values are in reasonable agreement.
M
f
FIG.12. Sedimentation diagram showing effect of urea on equilibrium in a single salt-free thyroglobulin solution. Upper left: equilibrium in salt-free thyroglobulin (pH = 5.5). Upper right: effect of presence of 50 per cent urea at this pH. Lower left: effect of making this solution 1 per cent in sodium chloride. Lower right: effect of addition of urea to thyroglobulin which is already in 1 per cent sodium chloride.
Although the formation of a-protein appears to involve no change in the mass, the effect of dilution in causing the formation of slower sedimenting protein from the a-form apparently dpes involve a change in the number of molecules and hence a dissociation. The dissociated form from a-protein is still labile to salt and is perhaps an unfolded and dissociated form of the protein. It has been observed (3) that the presence of urea, glycine, tyrosine, and related compounds in high concentration in freshly dialyzed electrolyte-free thyroglobulin solutions favors a change in the sedimentation behavior of the protein which appears similar to that described above. These reactions can occur even in the presence of electrolytes, although in such cases higher concentrations of the addition compound are required to
STABILI'Ff IN PROTEIN SYSTEMS
1001
produce the same magnitude of change. It would appear that in salt solutions these compounds act to overcome the effect of electrolyte in preventing the formation of a-protein. It makes no difference whether salt is added prior to the addition of urea or afterwards (figure 12). These effects appear similar to those noted by McFarlane (4) and b y Pedersen ( 5 ) in other protein mixtures ( b c . cit.). It was shown in the section describing dissociation phenomena that, a t least in certain proteins, the effect of urea or pH beyond the alkaline limits of the pH stability region in the presence of electrolyte is to cause a dissociation. With the data available it is not possible to decide whether the more complex equilibria in protein mixtures represent merely a change corresponding to a-protein or a dissociation. It is true that dissociation START IH YIY
IIAIT,DIYIY SCALE Do7A*CDlio CY
X A L I D(TANC1.W C U
I
I
1
--
FIG.13. Sedimentation diagram showing the effect of heat on the equilibrium in salt-free thyroglobulin solution. Upper left: equilibrium a t pH 6.5. Upper right: effect of heating 10 min. a t 50°C. Lower left: effect of heating 10 min. a t 60°C. Lower right: effect of heating 10 min. a t 95°C. to give homogeneous denatured protein.
may follow the formation of a-protein. The effect of the presence or absence of salt is very incompletely understood a t the present time. A high concentration of urea is known to favor denaturation. It would appear from this that the forces involved in dissociation and denaturation are similar. A reaction N - + a - + D appears involved because ( 1 ) the reaction N --+ a,in the case of thyroglobulin, is favored by heat (figure 13) and (2) further heating above 55OC. causes the a-protein to disappear with the formation, first, of an intermediate component which disappears and, finally, of a single homogeneous component which cannot be resolved from normal native thyroglobulin and which is unstable to,salt to give the characteristic properties of denatured protein. It would appear that the
1002
HAROLD P. LUNDOREN AND J. W. WILLIAMS
denatured as well as the dissociated form arose from the a-protein. changes may be represented in the following diagram:
These
Associated protein
N protein
t e Labile protein lt
-+ Denatured protein
(CY)
Dissociated protein Grateful acknowledgement is made to the Wisconsin Alumni Research Foundation and to the University Research Committee for financial assistance which has made this work possible. We wish also to thank Dr. Margarete Bruch-Willstatter for material assistance in the preparation of this report. The early thyroglobulin work was done by one of us (Harold P. Lundgren) in the Institute of Physical Chemistry at the University of Upsala, and we wish to acknowledge the assistance and interest of the Director of this Institute, Professor The Svedberg. REFERENCES (1) BERNAL,3. D.:Paper presented at the Cell Centenary Symposium, held at Stanford University, California, 1939. M.,AND PEDERBEN, K. 0.:J . Gen. Physiol. 19, 95 (1935). (2) HEIDELBERGER, (3) LUNDQREN, H'. P . : Nature 158, 122 (1936); J. Chem. Phys. 6, 177 (1938); Nature 148, 899 (1939); and unpublished work. (4) MCFARLANE, A. S.: Biochem. J. 29, 407 (1935). (5) PEDERSEN, K.0.:Compt. rend. trav. lab. Carlsberg, S6r. chim. 22,427 (1938). (6) SVEDBERG, T.:Ind. Eng. Chem., Anal. Ed. 10, 119 (1938).
