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Investigations on proteins and polymers. VII. The denaturation of egg albumin
Investigations on Proteins and Polymers. VH. The Denaturation of Egg Albumin Robert J. Gibbs, I M. Bier and F. F. Nord From the Department of Organic Chemistry and Enzymology, ~ Fordham University, New York 58, New York Received August 31, 1951 INTRODUCTION
As a result of denaturation, proteins suffer certain changes in their properties, such as solubility, crystallizability, and biological activity. These changes are generally ascribed to a loss of the specific structure of the protein. The denaturation of egg albumin has been a matter of much interest since the early kinetic investigations of Chick and Martin (1). In particular, the influence of pH and of temperature has come under special consideration (2,3,4) in an attempt io determine the mechanism of the denaturation of this protein. However, it has been noted (5) that previous measurements could not even establish with any large degree of certainty whether the reaction with unbuffered protein is first or second order. It was also reported (4) that results with different protein preparations did not show any agreement with one another. Besides, in neutral medium, the activation energy for denaturation was found to be about 130 kcal./ mole (2), while in strongly acid medium (3), a value of 35-37 kcal./mole has been reported. Whether the difference is representative of the effect of hydrogen ions, or indicates two distinct types of denaturation, due to heat and acid, respectively, could not be determined from those measurements. 1Predoctoral Fellow of the U. S. Atomic Energy Commission. Communication No. 240. For a preliminary communication see GIBBS, R. J., BIER, M., AND NORD, F. F., Arch. Biochem. Biophys. 33, 345 (1951). For previous communications of this series see TIMASHEFF, S. N., AND NORD, F. F., Arch. Biochem. Biophys. 31, 309, 320 (1951). This study was carried out under the aegis of the Atomic Energy Commission. Presented in part before the Division of Biological Chemistry of the American Chemical Society, Boston, Mass., April, 1951. 216
217
DENATURATION OF EGG ALBUMIN
Applying light-scattering measurements, it has been found (6) that egg albumin is a very labile system; its state of aggregation is greatly influenced by environmental conditions, such as the concentration of the protein and the temperature. In continuing the characterization (7) of this protein, it became of interest (8) to investigate the influence of acid strength upon the rate of denaturation of egg albumin. EXPERIMENTAL The egg albumin was prepared by the method of La Rosa (9), reerystallized three times, and dialyzed against running distilled water at 4~ until free of salts. The resulting solution was filtered through a sterilizing filter pad in a Seitz filter, and "722F ~ ) ~
+----- +~
+, - - - - - 7 " - ~ + -
"72~-V~ ~o--,-.,--~o ..._.....o ....__.. o
o~700-
\
,e~ A,
o~
\
.\ § 3.43 .660
332 ?, 3.13 o
2,88
x 2.70 o 2.53
T =34.9"C.
I
I
I
2
4
6
HOURS
FIG. 1. Fit of typical measurements with first-order kinetic interpretation, showing concentration of native protein (in arbitrary units) remaining after given time intervals.
218
ROBERT J. G1BBS, M. BIER AND F. F. NORD
stored in a refrigerator until needed, using merthiolatea (0.01%) as preservative (10). The solution was filtered again immediately before using. A measured amount of the protein (heated to the desired temperature) was added to a measured amount of dilute hydrochloric acid, in a thermostat (•176 and stirred gently to mix. At desired time intervals (6 rain. to 1 hr.), an aliquot (5-15 ml.) was removed and, to stop the reaction, was rapidly added to a cooled mixture of dilute NaOH and NaC1, to make a final volume of 25.0 ml. Sufficient NaOH was used to restore the protein solution to pH 4.8, and sufficient salt to give a final salt concentration of 0.6 N. Under these conditions a portion of the protein flocculated. The flocculent was considered to contain all the denatured protein, according to the definition of Wu (ll). The solution was centrifuged at 5000 r.p.m, in a Sorvall SS-1A angular centrifuge, to separate completely the flocculent. After discarding the supernatant, the floeculent was transferred, by suspending in 0.6 N NaC1 solution, to a weighed Selas No. 10 filtering crucible which had been overlaid with a fine layer of asbestos. The flocculent was then washed under suction four times with 5-ml. portions of 16% ethanol, to remove any native egg albumin and salt which might be present. The weight of denatured protein was determined by weighing the crucible after drying in a glass oven at 105~ The logarithm of the concentration of remaining native protein (obtained by difference) was plotted against the time (see Fig. 1). The rate of the denaturation was calculated by the method of least squares. For adequate temperature control in the above method it was not found necessary to stir the reaction mixture, except at the time of mixing. In this way it was possible to avoid interference with the measurements due to surface denaturation, which was found to be of significance even at low temperatures (12). The pH of each solution was determined at the temperature of the experiment with Cambridge meter, which was calibrated with an 0.0500 M solution of potassium hydrogen phthalate, using the previously reported values (13). The response of the meter in the most acid region was checked with 0.1 M HCI (14). RESULTS T h e results o b t a i n e d are s u m m a r i z e d in T a b l e I. T h e m e a s u r e m e n t s were m a d e in the p H r a n g e of 0.9-3.4, over t h e t e m p e r a t u r e r a n g e 25.0-44.4~ T h e e x p e r i m e n t s were carried out in reaction vessels cont a i n i n g i n i t i a l a m o u n t s of n a t i v e p r o t e i n r a n g i n g from as m u c h as 6 . 9 1 % to as little as 0.73%. Salt-free solutions were used, the p r o t e i n itself being the sole buffering agent. T h e r e a c t i o n was p e r m i t t e d to c o n t i n u e for v a r y i n g l e n g t h s of time, so t h a t the m a x i m u m a m o u n t of d e n a t u r e d p r o t e i n i n a r u n varied f r o m 0.89 to 8 6 . 5 ~ . F o u r s e p a r a t e p r e p a r a t i o n s of egg a l b u m i n were used in t h e e x p e r i m e n t s (Stock 1-4). F r o m the e x p e r i m e n t a l data, the over-all rates of d e n a t u r a t i o n were calculated. T h e values o b t a i n e d are also p r e s e n t e d i n T a b l e I. T h e procedure for d e t e r m i n i n g d i r e c t l y the a m o u n t of d e n a t u r e d proObtained through the courtesy of Dr. E. C. Kleiderer of Eli Lilly and Co.
DENATURATION OF EGG ALBUMIN
219
t e i n was d e v e l o p e d as t h e r e s u l t of a large n u m b e r of p r e l i m i n a r y e x p e r i m e n t s . W i t h t h e a b o v e m e t h o d , it w a s possible t o o b t a i n r e p r o d u c i b l e r es u l t s w i t h m a n y d i f f e r e n t k n o w n m i x t u r e s of n a t i v e a n d f u l l y d e n a t u r e d egg a l b u m i n . T h e a c c u r a c y of e a c h of t h e s e m o d e l m e a s u r e m e n t s was b e t t e r t h a n 1 ~ . DISCUSSION T h e r a t e of d e n a t u r a t i o n of egg a l b u m i n h as b e e n t h e s u b j e c t of i n v e s t i g a t i o n b o t h u n d e r t h e influence of h e a t (1,2) a n d of acid (3,4). TABLE I
Over-all Reaction Rates for Denaturation of Egg Albumin Temp. ~
25.0
29.9
pH 0.93 1.04 1.12 1.20 1.29 1.30 1.33 1.44 1.46 1.59 2.25 2.43 2.49 2.63 2.75 2.82 3.02
k X 106a 166.9 91.9 80.5 49.0 38.4 36.4 30.3 21.6 20.8 13.17 1.892 1.264 1.156 0.758 0.628 0.492 0.294
Stockb 3 4 4 4 3 4 3 4 3 4 1 1 3 1 1 1 1
(Prot)init.~ % 3.75 6.83 6.83 6.83 3.75 6.83 3.75 6.83 3.75 6.83 3.44 3.47 6.83 3.44 3.47 3.41 3.41
(Denat)maxfl % 66.8 37.2 31.0 29.6 31.2 24.8 26.4 23.1 15.86 15.16 4.51 3.47 1.25 2.01 1.87 1.60 1.03
1.05 1.20 1.26 1.39 1.47 1.61 2.34 2.52 2.69 2.78 2.85 3.16 3.32
235.6 149.5 139.9 84.6 52.3 33.0 4.17 2.94 1.750 1.525 1.256 0.658 0.375
4 4 4 4 4 4. 1 1 1 1 1 1 1
6.91 6.91 6.91 6.91 6.91 6.91 3.45 3.45 3.45 3.44 3.41 3.44 3.41
37.4 41.9 35.2 24.5 17.73 11.25 10.58 8.07 4.67 4.79 3.57 1.91 0.89
220
ROBERT J. GIBBS~ M. BIER AND F. F. NORD T A B L E I--Continued Temp, ~ 34.9
pH 1.86 2.10 2.53 2.70 2.88 3.13 3.32 3.43
k X 10~ 51.1 20.5 7.48 5.02 3.33 1.992 0.834 0.829
Stoekb 4 4 1 1 1 1 1 1
(Prot)init. r % 2.54 2.54 3.64 3.64 3.64 3.57 3.57 3.57
(Denat)max. ~ % 12.06 23.1 18.13 12.76 8.60 4.81 2.56 2.56
39.6
2.01 2.30 2.37 2.45 2.56 2.67 2.80 3.14 3.34
74.1 33.8 29.3 27.5 19.21 17.07 13.05 5.74 2.69
4 1 1 1 1 1 1 4 4
2.54 1.68 1.68 1.68 1.68 1.68 1.68 2.35 2.35
19.40 40.7 33.9 32.7 25.6 23.2 18.00 14.58 8.52
44.4
2.02 2.14 2.26 2.46 2.76 3.14 3.30 3.34
295.0 188.5 124.4 69.2 30.0 11.90 6.69 6.13
2 2 2 2 2 4 2 4
0.73 0.73 0.73 0.73 0.73 2.35 0.73 2.35
86.5 79.7 64.3 47.9 21.6 19.68 6.07 16.17
k in sec. -1
b Stock refers to protein preparation used. c (Prot)inlt. is initial protein concentration. ( D e n a t ) ~ . is per cent of denaturation when reaction was stopped.
From the data of Chick and Martin (1), the reaction observed could be interpreted either as first order or second order with respect to protein concentration. Lewis (2) obtained a first-order reaction in buffered solutions, but in unbuffered solutions he received uncertain results. In Cubin's study (3), with solutions containing some ammonium sulfate, the reaction was found to follow first-order kinetics fairly closely in the acid region of pH 1-2. In a more recent investigation (4), the kinetic data obtained were found to fit a first-order and second-order kinetic interpretation equally well. In order to establish the order of the reaction, some of the experi-
DENATURATION
OF EGG ALBUMIN
221
mental runs were allowed to proceed to the extent of 30--85% of completion. In each case it was found that the results obtained fit firstorder kinetics very well, but could not be at all fitted to a second-order treatment. This was found to be the case over almost a tenfold variation in the initial protein concentration. Moreover, calculation of secondorder "constants" indicates that, at 25.0~ for example, the rate of denaturation would be almost twice as much at pH 1.33 as would be found at pH 1.30. Over the entire range of the experiments, such irregularities in pattern would be evident. Therefore, it obvious that the rate of denaturation of egg albumin has, under the present conditions, a first-order dependence upon protein concentration. By measuring directly the amount of denatured protein, amounts as small as 2 mg. of denatured egg albumin could be accurately determined, in a total of as much as 500 mg. of native protein. Thus, the rate of the denaturation process could be measured during the early stages of the reaction. Since the changes observed are large relative to the total concentrations of denatured protein measured, the accuracy was greater than that possible when the amount of remaining native protein is measured directly (2,3). Accordingly, once the order of the reaction had been established, it was then possible to extend considerably the scope of the measurements to less acid solutions in which the appearance of denatured protein occurs only very slowly. Although it is true that egg albumin contains three different components, the results reported here do not show any difference in their behavior. However, due to the overwhelming preponderance of the A1 component, a difference in reactivity of the A~ component would be masked. Since it has been claimed that the A1 albumin is converted into the A2 on aging (15), it should be possible to detect such differences by an investigation of any change in rate of denaturation due to age. 4 Since it has been reported (4)that different protein preparations did not give the same denaturation rates, four separate egg albumin solutions were used in the present study. In no case was there found any deviation from the general reaction rate pattern. Thus it can be concluded that the results obtained are characteristic of the denaturation of egg albumin, in general, in the region of the present experiments. It is possible to detect the influence of pH upon the rate of denatura4 S u c h a n i n v e s t i g a t i o n is n o w u n d e r w a y .
222
ROBERT
J. GIBBS,
M. B I E R
AND
F.
F. N O R D
40
\ \ ,.
\.. ".
\
\ +
I
,o
a'.o
~N
,,<.\
o 2S.S"
3 Io
FIG. 2. Rate of denaturation (k) as a function of pH (k in sec.-1). tion by a plot of the logarithm of the reaction rate constant against pH. From the data in Fig. 2 it is apparent that, at the lowest temperature, the rate of denaturation in the least acid region is linearly proportional to the hydrogen-ion activity, according to the equation: k = k'(H+),
(1)
where k is the observed over-all rate of denaturation, k' is, at present, an empirical constant, and (H +) is the hydrogen-ion activity. The above relationship is no longer observed in the most acid regions measured. Here the results fit the equation: k = k"(H+) 2 + k'(S+),
(2)
where k" is a constant of the same type as k'. This same general formulation is applicable to all the other temperatures investigated.
DENATURATION
OF E G G A L B U M I N
223
It has been proposed (2) that the hydrogen ions have merely a catalytic effect on denaturation. This seems to be in agreement with the observation (3) that in solutions in the pH region 1-2 there was no detectable change in pH while the denaturation was progressing. In the present measurements, it has also been observed that there is no shift in pH, even in the course of 24 hr. However, a simple indication that hydrogen ions are reactants, and not catalytic agents, is the observation that the pH of a solution drifts while the denaturation is proceeding in solutions of low hydrogen-ion activity (1,2,16). If, in denaturing, each protein molecule reacted with one hydrogen ion, a 4% egg albumin solution, completely denatured, would have reacted with only about 10-~ moles/1, of hydrogen ions. Due to the strong buffering action of this protein (17,18), the effective change in hydrogen-ion activity in the acidic solutions would be of the order of 5 X 10-5 moles/l. A change of this magnitude would not be measurable in moderately acid solutions, where the hydrogen-ion activity is of the order of 10-~ or 10-3 moles/l. Consequently, the pH of an acid solution would not change measurably. In the earlier literature, it has been found convenient to consider the denaturation of a protein by heat and by acid as two separate phenomena (3,5,11), although it is to be expected that the rate of denaturation is a simultaneous function of the temperature and the pH. In a study on the inactivation of pepsin, Steinhardt (19) observed a dependence of its inactivation upon the fifth power of the hydrogenion activity. Accordingly, he concluded that, in the case of pepsin, catalysis would not give a satisfactory explanation of the data. Therefore, he proposed that the denaturation of a pepsin molecule occurred after that molecule had undergone five special stages of dissociation, as follows: p0 ~_ 5H + + p-5 _., D, (3) where P represents the pepsin molecule which undergoes five dissociations before becoming denatured (D). In this way, Steinhardt was able to explain the denaturation of pepsin in terms of the simultaneous influence of temperature on the dissociation and denaturation of this protein. As he pointed out, the apparent energy of activation for the over-all denaturation could be separated into two components, the activation energy for the five
224
ROBERT
J.
GIBBS,
M. B I E R
A N D F. F . N O R D
dissociation steps, and the activation energy for the true denaturation process, which is the final step of Eq. (3) above. In order for denaturation to occur, it is not necessary that only one specific series of dissociation steps be involved. On the contrary, it is entirely reasonable to assume that each protein molecule has a specific rate of denaturation which is characteristic of its stage of dissociation. In a recent investigation of ricin (20), this was shown to be the case. Therefore, the following scheme can be assigned to the denaturation of egg albumin in the region of the present measurements: H + po
~
(K1)
) p+l (
H +
l(kl) (K') D
~ p+2,
l(ks) D
(4)
where P+~ and p+s are labile egg albumin molecules formed by successive steps of suppression of dissociation from p0. The dissociation of p+2 into p+l, and of P+I into p0 are represented by the dissociation constants Ks and K~, respectively. The true denaturation steps have the denaturation rate constants k~ and ks. In the region of moderate acidity, where the second suppression of dissociation is insignificant, the rate of denaturation is represented by the following equation:
k = k,(H+)/K1.
(5)
This equation is of the form of Eq. (1), where k' is now defined by
kl/K,. Similarly, the over-all equation for the more acid region, for the rate of denaturation, is as follows:
k = ks(H+)S/K,Ks + k,(H+)/K1. k" is now defined as ks/K~Ks.
(6)
Here, By successive approximations, it is possible to evaluate k t and k", which represent the over-all rate of denaturation by each of the two alternative paths presented in Eq. (4), at unit hydrogen-ion activity. The values obtained in this manner are presented in Table II. In order to determine the true rate of denaturation for each path, it is necessary to find the values of kl and ks. This can be done only in regions where the hydrogen-ion activity approaches the magnitude of the respective
DENATURATION
OF
225
EGG ALBUMIN
TABLE II Calvulated Rates of Denaturation kiD. sea. - I Temp. ~
k'
25.0 29.9 34.9 39.6 44.4
3.11 8.60 2.35 5.88 1.46
k"
• X X • X
10-4 10-4 10-3 10-s 10-~
7.91 2.87 1.20 4.27 1.46
X • X •
10-s 10-2 10-1 10-1
d i s s o c i a t i o n c o n s t a n t s . E x p e r i m e n t s i n such regions w o u l d t r a n s l a t e t h e m s e l v e s i n t o a d e c r e a s i n g slope i n t h e m o s t acid regions of t h e results as p l o t t e d i n Fig. 2. As this was n o t f o u n d t o he t h e case, it m u s t be a s s u m e d t h a t t h e p H v a l u e s for t h e d i s s o c i a t i o n r e a c t i o n s are
S.0
%
4.0
I
I
3.Z
3.3
I_
4.4.
.~ ~ I0 a
FIG. 3. Change with temperature (T) of rate of denaturation by the two paths in acid medium (k' and k").
226
ROBERT J. GIBBS, M. B I E R AND F. F. NORD
in a region more acidic than that herein investigated. Therefore, neither the dissociation constants nor the true rates of denaturation could be determined exactly. The customary interpretation of the data in terms of the Arrhenius equation is shown in Fig. 3, where the logarithm of k' and k" is plotted against the reciprocal of the temperature. From the slope of these lines, it is possible to obtain the apparent activation energy for each reaction system. However, the inadequacy of the collision theory for the complete interpretation of a denaturation process has been brought out in several reviews (5,21,22) where the applicability of the absolute reaction rate theory (23) is shown for reactions which have such anomalous activation energies as are found in various protein denaturation studies. From the data presented above, it is readily possible to calculate the values of the thermodynamic properties, AH*, AF*, and AS*, for the activation reactions involved in the two over-all processes of denaturation which have been observed in the present investigation. The values obtained are summarized in Table III. As has been pointed out (21), the magnitude of AF* is in the usual range for reactions of this type, even though AH* is higher than that encountered in most normal reactions. TABLE IH Thermodynamic Valuesfor the Denaturation Processes AH* and AF* in kcal./mole; AS* in cal./deg. AH* AF*29s. ~o AS*
k' 36.7 22.2 48.5
kt~ 50.0 20.3 99.6
In terms of Steinhardt's theory, the value of AH* obtained would be a composite of the values for the dissociation stages and the actual denaturation itself. Since the pK values for K1 and K2 are in a region more acidic than that covered by the experiment, they are indicative either of the amide groups in asparagine and glutamine residues (24), or of unusual dissociations. If they do correspond to the usual acidic groups of the protein, e.g. phosphoric acid or carboxyl, it must be concluded that there is some unusual effect of the protein molecule upon this type of group A comparison of AS* for the two paths of denaturation indicates that the loss of rigidity is about double, where two stages of dissocia-
DENATURATION OF EGG ALBUMIN
227
tion must be overcome. This incremental relationship may be merely fortuitous, although it would indicate the possibility that the two dissociation stages are of the same type. If this is the case, the true denaturation step may be similar in both paths. Then, the difference in the two AH* ~r could be designated as numerically equivalent to either of the dissociation stages. From this, one would have a value of AH* for the true denaturation step equal to about 23.4 kcal./mole. That the normal salt bridges of egg albumin are not of great significance in the denaturation of the protein (25) is indicated by the pH dependence of the process. However, it must be concluded that two stages of dissociation are of great importance to the stability of the protein molecule. The nature of these groups is not immediately obvious from the present data, although they do not appear to be of a type which is generally associated with the peptide backbone of the protein. However, the familiar acidic groups of egg albumin cannot be excluded from consideration, due to the limitations of our knowledge of the structure of globular proteins. The present lack of an appropriate and sufficient protein model of known structure makes necessary this caution. It can only be said that there is some evidence (26) of the unfolding of the egg albumin molecule as a result of denaturation, in accordance with the proposal of Talmud (27) and others. The only other thorough investigation of egg albumin in this region was made by Cubin (3). However, in his method the solutions were stirred during the entire reaction period, a condition which would lead to undesired denaturation (12). Also, the solutions were not entirely free of salts, and it has been demonstrated (1) that the reaction rate is lowered by the introduction of salts. Therefore, the results he obtained are not exactly comparable to those of the present investigation. However, it is noteworthy that his values are of the same order of magnitude, giving a heat of activation of 35-7 kcal./mole, a value which is in remarkable agreement with that for the first path of denaturation, when one considers that Cubin states that his method has an over-all accuracy somewhat poorer than 3%. SUMMARY
The denaturation of egg albumin; in the pH range of 0.9--3.4, over the temperature range 25.0-44.4~ has been found to follow first-order kinetics, over a wide range of initial protein concentrations and for a wide range of the total denaturation process. Two distinct ways of
228
ROBERT J. GIBBS, M. BIER AND F. F. NORD
denaturation have been detected. The first involves the suppression of the dissociation of one hydrogen ion in the protein molecule, while the second involves two such suppressions. In a moderately acid solution, only the first such dissociation is of significance, while the second dissociation enters into prominence in more acid regions. From the respective rate constants, the apparent heats of activation, ~H*, were found to be 36.7 and 50.0 kcal./mole. REFERENCES 1. CHICK, H., AND MARTIN, C. J., J. Physiol. (London) 40, 404 (1910); ibid. 43. 1 (1911); ibid. 45, 61, 261 (1912). 2. LEwis, P. S., Biochem. J. 20, 978 (1926). 3. CUBIN, H. K., Biochem. J. 23, 25 (1929). 4. MAcPHERSON, C. F. C., AND HEIDELBERGER, M., J. Am. Chem. Soc. 67, 547 (1945). 5. NEURATH, H., GREENSTEIN, J. P., PUTNAM, F. W., AND ERICKSON, J. O., Chem. Revs. 34, 157 (1944). 6. BIER, M., AND NORD, F. F., Proc. Natl. Acad. Sci. U. S. 35, 17 (1949). 7. TIMASHEFF,S. N., ANDNORD, F. F., Arch. Biochem. Biophys. 31, 309, 320 (1951). 8. GIBBS, R. J., BIER, M., AND NORD, F. F., Arch. Biochem. Biophys. 33, 345 (1951). 9. LA Rosa, W., Chemist-Analyst 16, 3 (1927). 10. HECHT, R., RAPPAPORT, B. Z., AND BRIGGS, F., J. Allergy 7, 261 (1936). 11. Wu, H., Chinese J. Physiol. 5, 321 (1931). 12. Wu, H., AND LIMa, S. M., Chinese J. Physiol. 1, 407 (1927). 13. HAMER, W. J., PINCHING, G. D., AND ACREE, S. F., J. Research Natl. Bur. Standards 36, 47 (1946). 14. HITCHCOCK,D. I., AND TAYLOR, A. C., J. Am. Chem. Soc. 59, 1812 (1937). 15. MACPItERSON,C. F. C., MOORE, D. H., AND LONGSWORTH,L. G., ]. Biol. Chem. 156, 381 (1944). 16. CANNAN,R. K., Chem. Revs. 30, 395 (1942). 17. CANNAN, R. K., KII~RICK,A., AND PALMER, A. H., Ann. N. Y. Acad. Sci. 41, 243 (1941). 18. STEINHARDT, J., Ann. N. Y. Acad. Sci. 41, 287 (1941). 19. STEIrCHARDT,J., Kgl. Danske Videnskab. Selskab, Mat.-fys. Medd. 14, No. 11 (1037). 20. LEVY, M., AND BENAGLIA,A. E., J. Biol. Chem. 186, 829 (1950). 21. EYRING, H., AND STEARN, A. E., Chem. Revs. 24, 253 (1939). 22. STEAI~'r A. E., Advances in Enzymol. 9, 25 (1949). 23. GLASSTONE,S., LAIDLER,K. J., AND EYRINO, H., The Theory of Rate Processes. McGraw-Hill Book Co., Ine, New York, 1941. 24. STEIr~HARDT,J., ANDFUGITr, C., J. Research Natl. Bur. Standards 29, 315 (1942). 25. JACOBSEN, C. F., AN~ LINDERSTHCM-LAN~,K., Nature 164, 411 (1949). 26. FOSTER,J. F., AND SAMSA,E. G., J. Am. Chem. Soc. 73, 3187 (1951). 27. TALMCV, D. L., Acta Physicochim. U. R. S. S. 14, 562 (1941).
As a result of denaturation, proteins suffer certain changes in their properties, such as solubility, crystallizability, and biological activity. These changes are generally ascribed to a loss of the specific structure of the protein. The denaturation of egg albumin has been a matter of much interest since the early kinetic investigations of Chick and Martin (1). In particular, the influence of pH and of temperature has come under special consideration (2,3,4) in an attempt io determine the mechanism of the denaturation of this protein. However, it has been noted (5) that previous measurements could not even establish with any large degree of certainty whether the reaction with unbuffered protein is first or second order. It was also reported (4) that results with different protein preparations did not show any agreement with one another. Besides, in neutral medium, the activation energy for denaturation was found to be about 130 kcal./ mole (2), while in strongly acid medium (3), a value of 35-37 kcal./mole has been reported. Whether the difference is representative of the effect of hydrogen ions, or indicates two distinct types of denaturation, due to heat and acid, respectively, could not be determined from those measurements. 1Predoctoral Fellow of the U. S. Atomic Energy Commission. Communication No. 240. For a preliminary communication see GIBBS, R. J., BIER, M., AND NORD, F. F., Arch. Biochem. Biophys. 33, 345 (1951). For previous communications of this series see TIMASHEFF, S. N., AND NORD, F. F., Arch. Biochem. Biophys. 31, 309, 320 (1951). This study was carried out under the aegis of the Atomic Energy Commission. Presented in part before the Division of Biological Chemistry of the American Chemical Society, Boston, Mass., April, 1951. 216
217
DENATURATION OF EGG ALBUMIN
Applying light-scattering measurements, it has been found (6) that egg albumin is a very labile system; its state of aggregation is greatly influenced by environmental conditions, such as the concentration of the protein and the temperature. In continuing the characterization (7) of this protein, it became of interest (8) to investigate the influence of acid strength upon the rate of denaturation of egg albumin. EXPERIMENTAL The egg albumin was prepared by the method of La Rosa (9), reerystallized three times, and dialyzed against running distilled water at 4~ until free of salts. The resulting solution was filtered through a sterilizing filter pad in a Seitz filter, and "722F ~ ) ~
+----- +~
+, - - - - - 7 " - ~ + -
"72~-V~ ~o--,-.,--~o ..._.....o ....__.. o
o~700-
\
,e~ A,
o~
\
.\ § 3.43 .660
332 ?, 3.13 o
2,88
x 2.70 o 2.53
T =34.9"C.
I
I
I
2
4
6
HOURS
FIG. 1. Fit of typical measurements with first-order kinetic interpretation, showing concentration of native protein (in arbitrary units) remaining after given time intervals.
218
ROBERT J. G1BBS, M. BIER AND F. F. NORD
stored in a refrigerator until needed, using merthiolatea (0.01%) as preservative (10). The solution was filtered again immediately before using. A measured amount of the protein (heated to the desired temperature) was added to a measured amount of dilute hydrochloric acid, in a thermostat (•176 and stirred gently to mix. At desired time intervals (6 rain. to 1 hr.), an aliquot (5-15 ml.) was removed and, to stop the reaction, was rapidly added to a cooled mixture of dilute NaOH and NaC1, to make a final volume of 25.0 ml. Sufficient NaOH was used to restore the protein solution to pH 4.8, and sufficient salt to give a final salt concentration of 0.6 N. Under these conditions a portion of the protein flocculated. The flocculent was considered to contain all the denatured protein, according to the definition of Wu (ll). The solution was centrifuged at 5000 r.p.m, in a Sorvall SS-1A angular centrifuge, to separate completely the flocculent. After discarding the supernatant, the floeculent was transferred, by suspending in 0.6 N NaC1 solution, to a weighed Selas No. 10 filtering crucible which had been overlaid with a fine layer of asbestos. The flocculent was then washed under suction four times with 5-ml. portions of 16% ethanol, to remove any native egg albumin and salt which might be present. The weight of denatured protein was determined by weighing the crucible after drying in a glass oven at 105~ The logarithm of the concentration of remaining native protein (obtained by difference) was plotted against the time (see Fig. 1). The rate of the denaturation was calculated by the method of least squares. For adequate temperature control in the above method it was not found necessary to stir the reaction mixture, except at the time of mixing. In this way it was possible to avoid interference with the measurements due to surface denaturation, which was found to be of significance even at low temperatures (12). The pH of each solution was determined at the temperature of the experiment with Cambridge meter, which was calibrated with an 0.0500 M solution of potassium hydrogen phthalate, using the previously reported values (13). The response of the meter in the most acid region was checked with 0.1 M HCI (14). RESULTS T h e results o b t a i n e d are s u m m a r i z e d in T a b l e I. T h e m e a s u r e m e n t s were m a d e in the p H r a n g e of 0.9-3.4, over t h e t e m p e r a t u r e r a n g e 25.0-44.4~ T h e e x p e r i m e n t s were carried out in reaction vessels cont a i n i n g i n i t i a l a m o u n t s of n a t i v e p r o t e i n r a n g i n g from as m u c h as 6 . 9 1 % to as little as 0.73%. Salt-free solutions were used, the p r o t e i n itself being the sole buffering agent. T h e r e a c t i o n was p e r m i t t e d to c o n t i n u e for v a r y i n g l e n g t h s of time, so t h a t the m a x i m u m a m o u n t of d e n a t u r e d p r o t e i n i n a r u n varied f r o m 0.89 to 8 6 . 5 ~ . F o u r s e p a r a t e p r e p a r a t i o n s of egg a l b u m i n were used in t h e e x p e r i m e n t s (Stock 1-4). F r o m the e x p e r i m e n t a l data, the over-all rates of d e n a t u r a t i o n were calculated. T h e values o b t a i n e d are also p r e s e n t e d i n T a b l e I. T h e procedure for d e t e r m i n i n g d i r e c t l y the a m o u n t of d e n a t u r e d proObtained through the courtesy of Dr. E. C. Kleiderer of Eli Lilly and Co.
DENATURATION OF EGG ALBUMIN
219
t e i n was d e v e l o p e d as t h e r e s u l t of a large n u m b e r of p r e l i m i n a r y e x p e r i m e n t s . W i t h t h e a b o v e m e t h o d , it w a s possible t o o b t a i n r e p r o d u c i b l e r es u l t s w i t h m a n y d i f f e r e n t k n o w n m i x t u r e s of n a t i v e a n d f u l l y d e n a t u r e d egg a l b u m i n . T h e a c c u r a c y of e a c h of t h e s e m o d e l m e a s u r e m e n t s was b e t t e r t h a n 1 ~ . DISCUSSION T h e r a t e of d e n a t u r a t i o n of egg a l b u m i n h as b e e n t h e s u b j e c t of i n v e s t i g a t i o n b o t h u n d e r t h e influence of h e a t (1,2) a n d of acid (3,4). TABLE I
Over-all Reaction Rates for Denaturation of Egg Albumin Temp. ~
25.0
29.9
pH 0.93 1.04 1.12 1.20 1.29 1.30 1.33 1.44 1.46 1.59 2.25 2.43 2.49 2.63 2.75 2.82 3.02
k X 106a 166.9 91.9 80.5 49.0 38.4 36.4 30.3 21.6 20.8 13.17 1.892 1.264 1.156 0.758 0.628 0.492 0.294
Stockb 3 4 4 4 3 4 3 4 3 4 1 1 3 1 1 1 1
(Prot)init.~ % 3.75 6.83 6.83 6.83 3.75 6.83 3.75 6.83 3.75 6.83 3.44 3.47 6.83 3.44 3.47 3.41 3.41
(Denat)maxfl % 66.8 37.2 31.0 29.6 31.2 24.8 26.4 23.1 15.86 15.16 4.51 3.47 1.25 2.01 1.87 1.60 1.03
1.05 1.20 1.26 1.39 1.47 1.61 2.34 2.52 2.69 2.78 2.85 3.16 3.32
235.6 149.5 139.9 84.6 52.3 33.0 4.17 2.94 1.750 1.525 1.256 0.658 0.375
4 4 4 4 4 4. 1 1 1 1 1 1 1
6.91 6.91 6.91 6.91 6.91 6.91 3.45 3.45 3.45 3.44 3.41 3.44 3.41
37.4 41.9 35.2 24.5 17.73 11.25 10.58 8.07 4.67 4.79 3.57 1.91 0.89
220
ROBERT J. GIBBS~ M. BIER AND F. F. NORD T A B L E I--Continued Temp, ~ 34.9
pH 1.86 2.10 2.53 2.70 2.88 3.13 3.32 3.43
k X 10~ 51.1 20.5 7.48 5.02 3.33 1.992 0.834 0.829
Stoekb 4 4 1 1 1 1 1 1
(Prot)init. r % 2.54 2.54 3.64 3.64 3.64 3.57 3.57 3.57
(Denat)max. ~ % 12.06 23.1 18.13 12.76 8.60 4.81 2.56 2.56
39.6
2.01 2.30 2.37 2.45 2.56 2.67 2.80 3.14 3.34
74.1 33.8 29.3 27.5 19.21 17.07 13.05 5.74 2.69
4 1 1 1 1 1 1 4 4
2.54 1.68 1.68 1.68 1.68 1.68 1.68 2.35 2.35
19.40 40.7 33.9 32.7 25.6 23.2 18.00 14.58 8.52
44.4
2.02 2.14 2.26 2.46 2.76 3.14 3.30 3.34
295.0 188.5 124.4 69.2 30.0 11.90 6.69 6.13
2 2 2 2 2 4 2 4
0.73 0.73 0.73 0.73 0.73 2.35 0.73 2.35
86.5 79.7 64.3 47.9 21.6 19.68 6.07 16.17
k in sec. -1
b Stock refers to protein preparation used. c (Prot)inlt. is initial protein concentration. ( D e n a t ) ~ . is per cent of denaturation when reaction was stopped.
From the data of Chick and Martin (1), the reaction observed could be interpreted either as first order or second order with respect to protein concentration. Lewis (2) obtained a first-order reaction in buffered solutions, but in unbuffered solutions he received uncertain results. In Cubin's study (3), with solutions containing some ammonium sulfate, the reaction was found to follow first-order kinetics fairly closely in the acid region of pH 1-2. In a more recent investigation (4), the kinetic data obtained were found to fit a first-order and second-order kinetic interpretation equally well. In order to establish the order of the reaction, some of the experi-
DENATURATION
OF EGG ALBUMIN
221
mental runs were allowed to proceed to the extent of 30--85% of completion. In each case it was found that the results obtained fit firstorder kinetics very well, but could not be at all fitted to a second-order treatment. This was found to be the case over almost a tenfold variation in the initial protein concentration. Moreover, calculation of secondorder "constants" indicates that, at 25.0~ for example, the rate of denaturation would be almost twice as much at pH 1.33 as would be found at pH 1.30. Over the entire range of the experiments, such irregularities in pattern would be evident. Therefore, it obvious that the rate of denaturation of egg albumin has, under the present conditions, a first-order dependence upon protein concentration. By measuring directly the amount of denatured protein, amounts as small as 2 mg. of denatured egg albumin could be accurately determined, in a total of as much as 500 mg. of native protein. Thus, the rate of the denaturation process could be measured during the early stages of the reaction. Since the changes observed are large relative to the total concentrations of denatured protein measured, the accuracy was greater than that possible when the amount of remaining native protein is measured directly (2,3). Accordingly, once the order of the reaction had been established, it was then possible to extend considerably the scope of the measurements to less acid solutions in which the appearance of denatured protein occurs only very slowly. Although it is true that egg albumin contains three different components, the results reported here do not show any difference in their behavior. However, due to the overwhelming preponderance of the A1 component, a difference in reactivity of the A~ component would be masked. Since it has been claimed that the A1 albumin is converted into the A2 on aging (15), it should be possible to detect such differences by an investigation of any change in rate of denaturation due to age. 4 Since it has been reported (4)that different protein preparations did not give the same denaturation rates, four separate egg albumin solutions were used in the present study. In no case was there found any deviation from the general reaction rate pattern. Thus it can be concluded that the results obtained are characteristic of the denaturation of egg albumin, in general, in the region of the present experiments. It is possible to detect the influence of pH upon the rate of denatura4 S u c h a n i n v e s t i g a t i o n is n o w u n d e r w a y .
222
ROBERT
J. GIBBS,
M. B I E R
AND
F.
F. N O R D
40
\ \ ,.
\.. ".
\
\ +
I
,o
a'.o
~N
,,<.\
o 2S.S"
3 Io
FIG. 2. Rate of denaturation (k) as a function of pH (k in sec.-1). tion by a plot of the logarithm of the reaction rate constant against pH. From the data in Fig. 2 it is apparent that, at the lowest temperature, the rate of denaturation in the least acid region is linearly proportional to the hydrogen-ion activity, according to the equation: k = k'(H+),
(1)
where k is the observed over-all rate of denaturation, k' is, at present, an empirical constant, and (H +) is the hydrogen-ion activity. The above relationship is no longer observed in the most acid regions measured. Here the results fit the equation: k = k"(H+) 2 + k'(S+),
(2)
where k" is a constant of the same type as k'. This same general formulation is applicable to all the other temperatures investigated.
DENATURATION
OF E G G A L B U M I N
223
It has been proposed (2) that the hydrogen ions have merely a catalytic effect on denaturation. This seems to be in agreement with the observation (3) that in solutions in the pH region 1-2 there was no detectable change in pH while the denaturation was progressing. In the present measurements, it has also been observed that there is no shift in pH, even in the course of 24 hr. However, a simple indication that hydrogen ions are reactants, and not catalytic agents, is the observation that the pH of a solution drifts while the denaturation is proceeding in solutions of low hydrogen-ion activity (1,2,16). If, in denaturing, each protein molecule reacted with one hydrogen ion, a 4% egg albumin solution, completely denatured, would have reacted with only about 10-~ moles/1, of hydrogen ions. Due to the strong buffering action of this protein (17,18), the effective change in hydrogen-ion activity in the acidic solutions would be of the order of 5 X 10-5 moles/l. A change of this magnitude would not be measurable in moderately acid solutions, where the hydrogen-ion activity is of the order of 10-~ or 10-3 moles/l. Consequently, the pH of an acid solution would not change measurably. In the earlier literature, it has been found convenient to consider the denaturation of a protein by heat and by acid as two separate phenomena (3,5,11), although it is to be expected that the rate of denaturation is a simultaneous function of the temperature and the pH. In a study on the inactivation of pepsin, Steinhardt (19) observed a dependence of its inactivation upon the fifth power of the hydrogenion activity. Accordingly, he concluded that, in the case of pepsin, catalysis would not give a satisfactory explanation of the data. Therefore, he proposed that the denaturation of a pepsin molecule occurred after that molecule had undergone five special stages of dissociation, as follows: p0 ~_ 5H + + p-5 _., D, (3) where P represents the pepsin molecule which undergoes five dissociations before becoming denatured (D). In this way, Steinhardt was able to explain the denaturation of pepsin in terms of the simultaneous influence of temperature on the dissociation and denaturation of this protein. As he pointed out, the apparent energy of activation for the over-all denaturation could be separated into two components, the activation energy for the five
224
ROBERT
J.
GIBBS,
M. B I E R
A N D F. F . N O R D
dissociation steps, and the activation energy for the true denaturation process, which is the final step of Eq. (3) above. In order for denaturation to occur, it is not necessary that only one specific series of dissociation steps be involved. On the contrary, it is entirely reasonable to assume that each protein molecule has a specific rate of denaturation which is characteristic of its stage of dissociation. In a recent investigation of ricin (20), this was shown to be the case. Therefore, the following scheme can be assigned to the denaturation of egg albumin in the region of the present measurements: H + po
~
(K1)
) p+l (
H +
l(kl) (K') D
~ p+2,
l(ks) D
(4)
where P+~ and p+s are labile egg albumin molecules formed by successive steps of suppression of dissociation from p0. The dissociation of p+2 into p+l, and of P+I into p0 are represented by the dissociation constants Ks and K~, respectively. The true denaturation steps have the denaturation rate constants k~ and ks. In the region of moderate acidity, where the second suppression of dissociation is insignificant, the rate of denaturation is represented by the following equation:
k = k,(H+)/K1.
(5)
This equation is of the form of Eq. (1), where k' is now defined by
kl/K,. Similarly, the over-all equation for the more acid region, for the rate of denaturation, is as follows:
k = ks(H+)S/K,Ks + k,(H+)/K1. k" is now defined as ks/K~Ks.
(6)
Here, By successive approximations, it is possible to evaluate k t and k", which represent the over-all rate of denaturation by each of the two alternative paths presented in Eq. (4), at unit hydrogen-ion activity. The values obtained in this manner are presented in Table II. In order to determine the true rate of denaturation for each path, it is necessary to find the values of kl and ks. This can be done only in regions where the hydrogen-ion activity approaches the magnitude of the respective
DENATURATION
OF
225
EGG ALBUMIN
TABLE II Calvulated Rates of Denaturation kiD. sea. - I Temp. ~
k'
25.0 29.9 34.9 39.6 44.4
3.11 8.60 2.35 5.88 1.46
k"
• X X • X
10-4 10-4 10-3 10-s 10-~
7.91 2.87 1.20 4.27 1.46
X • X •
10-s 10-2 10-1 10-1
d i s s o c i a t i o n c o n s t a n t s . E x p e r i m e n t s i n such regions w o u l d t r a n s l a t e t h e m s e l v e s i n t o a d e c r e a s i n g slope i n t h e m o s t acid regions of t h e results as p l o t t e d i n Fig. 2. As this was n o t f o u n d t o he t h e case, it m u s t be a s s u m e d t h a t t h e p H v a l u e s for t h e d i s s o c i a t i o n r e a c t i o n s are
S.0
%
4.0
I
I
3.Z
3.3
I_
4.4.
.~ ~ I0 a
FIG. 3. Change with temperature (T) of rate of denaturation by the two paths in acid medium (k' and k").
226
ROBERT J. GIBBS, M. B I E R AND F. F. NORD
in a region more acidic than that herein investigated. Therefore, neither the dissociation constants nor the true rates of denaturation could be determined exactly. The customary interpretation of the data in terms of the Arrhenius equation is shown in Fig. 3, where the logarithm of k' and k" is plotted against the reciprocal of the temperature. From the slope of these lines, it is possible to obtain the apparent activation energy for each reaction system. However, the inadequacy of the collision theory for the complete interpretation of a denaturation process has been brought out in several reviews (5,21,22) where the applicability of the absolute reaction rate theory (23) is shown for reactions which have such anomalous activation energies as are found in various protein denaturation studies. From the data presented above, it is readily possible to calculate the values of the thermodynamic properties, AH*, AF*, and AS*, for the activation reactions involved in the two over-all processes of denaturation which have been observed in the present investigation. The values obtained are summarized in Table III. As has been pointed out (21), the magnitude of AF* is in the usual range for reactions of this type, even though AH* is higher than that encountered in most normal reactions. TABLE IH Thermodynamic Valuesfor the Denaturation Processes AH* and AF* in kcal./mole; AS* in cal./deg. AH* AF*29s. ~o AS*
k' 36.7 22.2 48.5
kt~ 50.0 20.3 99.6
In terms of Steinhardt's theory, the value of AH* obtained would be a composite of the values for the dissociation stages and the actual denaturation itself. Since the pK values for K1 and K2 are in a region more acidic than that covered by the experiment, they are indicative either of the amide groups in asparagine and glutamine residues (24), or of unusual dissociations. If they do correspond to the usual acidic groups of the protein, e.g. phosphoric acid or carboxyl, it must be concluded that there is some unusual effect of the protein molecule upon this type of group A comparison of AS* for the two paths of denaturation indicates that the loss of rigidity is about double, where two stages of dissocia-
DENATURATION OF EGG ALBUMIN
227
tion must be overcome. This incremental relationship may be merely fortuitous, although it would indicate the possibility that the two dissociation stages are of the same type. If this is the case, the true denaturation step may be similar in both paths. Then, the difference in the two AH* ~r could be designated as numerically equivalent to either of the dissociation stages. From this, one would have a value of AH* for the true denaturation step equal to about 23.4 kcal./mole. That the normal salt bridges of egg albumin are not of great significance in the denaturation of the protein (25) is indicated by the pH dependence of the process. However, it must be concluded that two stages of dissociation are of great importance to the stability of the protein molecule. The nature of these groups is not immediately obvious from the present data, although they do not appear to be of a type which is generally associated with the peptide backbone of the protein. However, the familiar acidic groups of egg albumin cannot be excluded from consideration, due to the limitations of our knowledge of the structure of globular proteins. The present lack of an appropriate and sufficient protein model of known structure makes necessary this caution. It can only be said that there is some evidence (26) of the unfolding of the egg albumin molecule as a result of denaturation, in accordance with the proposal of Talmud (27) and others. The only other thorough investigation of egg albumin in this region was made by Cubin (3). However, in his method the solutions were stirred during the entire reaction period, a condition which would lead to undesired denaturation (12). Also, the solutions were not entirely free of salts, and it has been demonstrated (1) that the reaction rate is lowered by the introduction of salts. Therefore, the results he obtained are not exactly comparable to those of the present investigation. However, it is noteworthy that his values are of the same order of magnitude, giving a heat of activation of 35-7 kcal./mole, a value which is in remarkable agreement with that for the first path of denaturation, when one considers that Cubin states that his method has an over-all accuracy somewhat poorer than 3%. SUMMARY
The denaturation of egg albumin; in the pH range of 0.9--3.4, over the temperature range 25.0-44.4~ has been found to follow first-order kinetics, over a wide range of initial protein concentrations and for a wide range of the total denaturation process. Two distinct ways of
228
ROBERT J. GIBBS, M. BIER AND F. F. NORD
denaturation have been detected. The first involves the suppression of the dissociation of one hydrogen ion in the protein molecule, while the second involves two such suppressions. In a moderately acid solution, only the first such dissociation is of significance, while the second dissociation enters into prominence in more acid regions. From the respective rate constants, the apparent heats of activation, ~H*, were found to be 36.7 and 50.0 kcal./mole. REFERENCES 1. CHICK, H., AND MARTIN, C. J., J. Physiol. (London) 40, 404 (1910); ibid. 43. 1 (1911); ibid. 45, 61, 261 (1912). 2. LEwis, P. S., Biochem. J. 20, 978 (1926). 3. CUBIN, H. K., Biochem. J. 23, 25 (1929). 4. MAcPHERSON, C. F. C., AND HEIDELBERGER, M., J. Am. Chem. Soc. 67, 547 (1945). 5. NEURATH, H., GREENSTEIN, J. P., PUTNAM, F. W., AND ERICKSON, J. O., Chem. Revs. 34, 157 (1944). 6. BIER, M., AND NORD, F. F., Proc. Natl. Acad. Sci. U. S. 35, 17 (1949). 7. TIMASHEFF,S. N., ANDNORD, F. F., Arch. Biochem. Biophys. 31, 309, 320 (1951). 8. GIBBS, R. J., BIER, M., AND NORD, F. F., Arch. Biochem. Biophys. 33, 345 (1951). 9. LA Rosa, W., Chemist-Analyst 16, 3 (1927). 10. HECHT, R., RAPPAPORT, B. Z., AND BRIGGS, F., J. Allergy 7, 261 (1936). 11. Wu, H., Chinese J. Physiol. 5, 321 (1931). 12. Wu, H., AND LIMa, S. M., Chinese J. Physiol. 1, 407 (1927). 13. HAMER, W. J., PINCHING, G. D., AND ACREE, S. F., J. Research Natl. Bur. Standards 36, 47 (1946). 14. HITCHCOCK,D. I., AND TAYLOR, A. C., J. Am. Chem. Soc. 59, 1812 (1937). 15. MACPItERSON,C. F. C., MOORE, D. H., AND LONGSWORTH,L. G., ]. Biol. Chem. 156, 381 (1944). 16. CANNAN,R. K., Chem. Revs. 30, 395 (1942). 17. CANNAN, R. K., KII~RICK,A., AND PALMER, A. H., Ann. N. Y. Acad. Sci. 41, 243 (1941). 18. STEINHARDT, J., Ann. N. Y. Acad. Sci. 41, 287 (1941). 19. STEIrCHARDT,J., Kgl. Danske Videnskab. Selskab, Mat.-fys. Medd. 14, No. 11 (1037). 20. LEVY, M., AND BENAGLIA,A. E., J. Biol. Chem. 186, 829 (1950). 21. EYRING, H., AND STEARN, A. E., Chem. Revs. 24, 253 (1939). 22. STEAI~'r A. E., Advances in Enzymol. 9, 25 (1949). 23. GLASSTONE,S., LAIDLER,K. J., AND EYRINO, H., The Theory of Rate Processes. McGraw-Hill Book Co., Ine, New York, 1941. 24. STEIr~HARDT,J., ANDFUGITr, C., J. Research Natl. Bur. Standards 29, 315 (1942). 25. JACOBSEN, C. F., AN~ LINDERSTHCM-LAN~,K., Nature 164, 411 (1949). 26. FOSTER,J. F., AND SAMSA,E. G., J. Am. Chem. Soc. 73, 3187 (1951). 27. TALMCV, D. L., Acta Physicochim. U. R. S. S. 14, 562 (1941).