THE JOURNAL OF
PHYSICAL CHEMISTRY
i
(Registered in U. 9. Patent Office)
(Copyright, 1954, b y the American Chemical Society)
a
NUMBER R
FEBRUARY 27, 1954
VOLUME58
THE CHANGE I N HEAT CONTENT ACCOMPANYING DENATURATION* BY JULIAN M. STURTEVANT Sterling Chemistry Laboraloru, Yale University, New Haven, Connecticut Received J u l y $4. 1855
The available data on the enthalpy change accompanying protein denaturation are summarized. In the two cases where measurements have been made over a range of pH values, it has been found that the A H of denaturation is strongly dependent on pH. The maximum in the A H vs. pH curve for pepsin is so sharp that ordinary ionization equilibria cannot be invoked to explain it. The data for pepsin can, however, be reasonably well accounted for on the basis of a triggered ionization similar to that recently proposed by Steinhardt and Zaiser in the case of ferrihemoglobin
Introduction
!
The change in heat content accompanying a chemical reaction is devoid of fundamental significance unless the initial and final states of the systern are accurately defined. I n discussing the enthalpy changes accompanying the denaturation of proteins, we are faced With the difficulty that there is no adequate way of defining the state of a denatured protein. Indeed, there is no unanimity as to what is IIXant by the term denaturation. I n a situation beset by such ambiguities, it is hardly to be expected that thermochemical data will advance very our understanding of denaturation. On the other hand, it is particularly important, in the Case of a very complex problem, to bring to bear on it evidence obtained by as wide a variety of experimentation as possible. Thus, even though enthalpy data concerning denaturation cannot be assigned as much reliability as one Usually wishes for thermodynamic data, it is reasonable to assume that such data are of sufficient importance to justify the considerable efforts required to obtain them. In this paper review briefly the enthalpy data pertaining to denaturation. Data recently obtained for the denaturation of pepsin are discussed in some detail, and are shown to be of significance in connection with the mechanism of denaturation.
*
Based on a paper presented before the Division of Physical Qnd Inorganic Chemistry of the American Chemical Society, Loa Angeles, California, March, 1953. Contribution No. 1169 from the Sterling Chemistry Laboratory of Yale University.
97
Equilibrium Data.-The first quantitative estimate of the heat content change in a denaturation reaction was obtained by Anson and Mirsky' in 1934. They measured the equilibrium in the as estimated by proteo~ytic denaturation of activity, in 0.01 N hydrochloric acid Over the ternperature range 42-50', and calculated equilibrium constants on the assumption that the reaction is first order in protein in both directions. Application of the van,t ~ ~ equation f f gave the value 67,600 calmper mole for the AH of denaturation. A of importance is frequently overlooked in connectionwith free energy and enthalpy data based on equilibrium measurements. attaching any meaning to such data, one is necessarily making an assumption concerning molecular weight. particularly in the case of complicated substances such as proteins, one has no a priori justification for asserting that the molecular w,eight pertaining to some reversible reactionis the same as the molecular weight determined, for example, from sedimentation and diffusion experiments. (The same consideration applies to the calculation from rate data of heats and free energies of activation.) It should also be remembered that the AH value obtained from equilibrium measurementspertaills to the reaction T.Vithreactants and products in their standard states. I n the case of trypsin, although the equilibrium constant is presumably units, the standard independent of (1) M. L. Anson and A. E. Mirsky,
J. Gen. Phyaiol..
17, 393 (1934).
98
JULIANM. STURTEVANT
states are by implication specified, though in an unknown way in the absence of activity data, in the assumption of unit activity coefficients under the conditions of the experiments. Enthalpy values usually do not change very rapidly with concentration, and it is probably frequently perfiissible to neglect the differences between standard and non-standard AH values, at least for reactions involving no change in mole number. Equilibrium measurements have been used to obtain AH values in other denaturation reactions. Anson and Mirsky2 found that the extent of the apparently reversible denaturation of methemoglobin by salicylate is independent of temperature, so that AH for this reaction appears to be small; and Herriott3 estimated 31 kcal. per mole for the enthalpy change in the reversible heat inactivation of pepsinogen. Kunitz4 studied the reversible heat denaturation of the soybean trypsin inhibitor a t pH 3, employing loss of solubility a t the isoelectric point as the criterion of denaturation. He found AH = 57.3 kcal. per mole for this reaction. Recently Eisenberg and Schwert5 have carried out a very thorough investigation of the reversible denaturation of chymotrypsinogen. They demonstrated quite convincingly that the reversed protein is identical with the native protein with respect to several properties. As Kunitz had done in the case of the soybean trypsin inhibitor, Eisenberg and Schwert measured the rates of the denaturation and renaturation reactions, and showed that the thermodynamic quantities for activation in the two directions are consistent with those for the overall process. Of particular interest is the fact that Eisenberg and Schwert carried out complete sets of measurements at two different pH values; they found for AH a t pH 2.0 the value 99.6 kcal. per mole, and a t pH 3.0, 143 kcal. per mole. Calorimetric Data.-Three calorimetric determinations of the heat of denaturation have been carried out by Kistiakowsky and his colleagues. Denaturations of methemoglobin6 and pepsin’ by alkali were investigated by observing the heats of reaction of the native protein and of the denatured protein with aIkali, the heat of denaturation being taken as the difference between these. Thus, in the case of pepsin, a typical experiment consisted of (1) mixing the native protein at a low pH where it is indefinitely stable with sufficient sodium hydroxide to raise the p H to a value where the denaturation is rapid; (2) returning the solution to the original pH with acid; and (3) treating the solution again with alkali to give the same final pH. The AH for step 1 less that for step 3 was taken as the heat of denaturation a t the initial pH. A procedure of this sort of course involves the assumption that the heat content of the denatured protein a t low pH is independent of whether the protein has or has not been exposed to a high pH. (2) M.L.Anson and A. E. Mirsky, J . Gen. PhysioE., 17,399 (1934). (3) R. M.Herriott, ibid., 21, 501 (1938). (4) M. Kunitz, zbid., 82, 241 (1948). (5) M. A. Eisenberg and G. W. Sohwert, ibid., 84, 583 (1951). (6) J. B. Conn, G. B. Kistiakowsky and R. M . Roberts, J . A n . Chem. SOC.,62, 1895 (1940). (7) J. B.Conn,D. C. Gregg, G. B. Kistiakowsky and R . M. Roberts, i b i d . , 68, 2080 (1941).
Vol. 58
By this sort of measurement, the value AH = 138 kcal. per mole was found for the denaturation of methemoglobin. The apparent AH value for the pepsin denaturation was found to decrease from 85 kcal. per mole at pH 4.3 to nearly zero a t pH 6.8 (at 31°), this decrease not following the same course as the decrease in the proteolytic activity of the enzyme observed over this pH range. The calorimetric data of Roberts8 on the denaturation of methemoglobin by salicylate appear to be in disagreement with equilibrium observations of Anson and Mirsky. Roberts found the heat of reaction to increase steadily as the salicylate concentration was increaged, and concluded that the reaction is not stoichiometric. The Denaturation of Pepsin.-Buzzell and the present authorgstudied the denaturation of pepsin. The calorimetric method10 used in their work permitted measuring t8heheat of the denaturation reaction carried out at constant pH, and also gave values for the rate of absorption of heat during the denaturation. Measurements were made in phosphate buffers over a pH range at 15 and 35”. A summary of the enthalpy changes observed is given in Fig. 1, in which the heat of reaction in joules per pepsin unit (hemoglobin substrate) is plotted against the pH. The various types of points refer to experiments using pepsin from different sources. l1 The crossed circles are data obtained with an earlier calorimeter, l 2 using p-nitrophenol buffers and a different pepsin assay method. The thermal data may be converted to kcal. per mole, taking the activity of pepsin to be 0.39 pepsin units per milligram of protein n i t r o ~ e nand , ~ assuming the protein to contain 14.6% nitrogen,13 and to have a molecular weight of 35,000. On this basis, 0.05 joule per pepsin unit becomes 24 kcal. - . per mole. Buzzell and Sturtevant found that the heat absorption during denaturation followed accurately a first-order law, the logarithm of the apparent rate constant increasing linearly with pH with a slope of 1.40. However, they found the loss of proteolytic activity under similar conditions to follow entirely different kinetics of non-integral order, with the half-times for inactivation increasing approximately as the inverse fourth power of hydrogen ion concentration. It appears that, just as different reagents and experimental conditions produce different reactions classed as denaturation, so the same experimental conditions can produce different kinetic results depending on the method of obseTvation. The situation concerning the kinetics of the loss of peptic activity is rather confused. Steinhardt14 (8) R . AI. Roberts, ibid., 64, 1472 (1942). (9) A. Buzzell and J. M . Sturtevant, ibid., 7 4 , 1983 (1952). (IO) A. Buzzell and J. M. Sturtevant, ibid.. 78, 2454 (1951). (11) All of the pepsin preparations for which data are given in Fig. 1 oontained approximately 20% of non-protein nitrogen (determined by trichloroacetic acid precipitation). (12) RI. Bender and J. M. Sturtevant, J . Am. Chem. SOC.,69, 607 (1947). (13) J. H.Northrop. M. Kunitz and R . M. Herriott, “Crystalline Enzymes,” Columbia University Press, New York, N. Y., 1948, p. 74. (14) J. Steinhardt, KgE. Danske Videnskab. Selskab. Math.-Fys. Medd., 14, No. 1 1 (1937).
8
. ’
s
CHANGE IN HEATCONTENT ACCOMPANYING PROTEIN DENATURATION
Feb., 1954
6.0
6.2
6.4
6.6
6.8
7.0
7.2
55
7.4
PH Fig. 1.-Heat
content change in the denaturation of pepsin as a function of pH.8
has reported good first-order kinetics for the inactivation in p-nitrophenol buffers, the rate increasing as the inverse fifth power of the hydrogen ion concentration. He was able to obtain pepsin free from non-protein nitrogen in the dilute solutions used in his kinetic experiments. Casey and Laidler15found the order of the reaction to vary between one and five, depending on the initial concentration of the protein, in pH 4.8 acetate buffer at 50 to 60". The variation of AH with pH recorded in Fig. 1 is most unusual. It is perhaps significant that the maxima in the AH curves for 15 and 35" both occur a t a pH corresponding to a specific rate of heat absorption of 0.0021 set.-'. It is interesting that the only other AH values for denaturation which have been reported over a pH range, those of Eisenberg and Schwert and of Conn, Gregg, Kistiakowsky and Roberts, have also indicated unusual pH dependence. Buzzell and Sturtevant were unable to determine whether the AH of denaturation becomes negative at low and high pH because the rates of reaction become respectively too low and too high to permit measurements to be made. It seems reasonable to assume that the heat of reaction is close to zero except in the pH range where measurements were made, which means that the heat contents of native and denatured pepsin are nearly equal at low and high pH. The observed heats of reaction would then be consistent with the schematic enthalpy diagram given in Fig. 2. The type of result observed by Kistiakowsky, et al.,? can be qualitatively accounted for by the assumption that the heat content of pepsin denatured at a high p H is not reversible with respect to pH changes. According to this view, Kistiakowsky, et aE., measured the quantity denoted by AH,,, which bears no direct relation t o the heat of denaturation. It is planned to explore calorimetrically the variation with pH(15) E. J. Casey and K. J. Laidler, J . Am. Chem. Soc., 7 8 , 1455 (1951).
PH. Fig. 2-Schematic representation of proposed variation with pH of the heat contents of native and denatured pepsin.
of the heat content of denatured pepsin, to throw further light on its peculiar thermal behavior. Following the treatments proposed by Steinhardt14 and Levy and Benaglial6 to explain the variation of the rate of denaturation with pH, we may investigate the possibility of accounting for the variation of AH in terms of ionization equilibria. We assume that in the pH range of interest native 1 ionized forms and denatured pepsin exists in m 1 ionized forms, related by the pepsin in n equilibria Ni-, = Ni + H+; K N . ~ ;i = 1, . ,, m (1)
+
+
,
Di-1 = Di f Hf; K D , ~ i; = 1, . . .,71.
(2)
Since the denaturation of pepsin appears to be irreversible, it is unnecessary to include equilibria (16) M. Levy and A. E. Benaglia, J . B i d . Chem., 186, 829 (1950).
JULIAN M. STURTEVANT
100
involving both native and denatured forms. The concentration of N i is given by
where [PI = Z[Ni] = Z[Di] is the total protein concentration. K N . is~ defined as being equal to unity. A similar expression holds for [Di]. If we ~ H D . i the apparent molar represent by H N , and heat contents, referred to any convenient origin, of Ni and Di, respectively, and if concentrations are expressed in moles per liter, then the change in heat content, A H , per mole of protein is given by n
m
[PI AH = z H ~ , i [ D i] zH~,i[Nil 0
(4)
0
The simplest assumptions one can make to obtain equation (4) in manageable form are as follows: (a) H D . ~and HN.i are independent of concentration; (b) the number of ionized forms is the same in both native and denatured forms; (c) all ionizing sites have the same intrinsic dissociation constants, K D Z K N and there is no interaction between sites, so that K N , I=
n
- ( i - 1) i
KN
(5)
This leads to the closest spacing of dissociation constants, and the largest dependence on p H , which can be obtained with ordinary ionizations. It then follows that
j-0
A similar expression holds for [Di]. We may assume further that, (d) the heat contents of the various forms are given by
+
HNoi = HN.O ihN H D ,= ~ HD.O4-i h D
(7) (8)
However, since AH +.0 a t both low and high pH HN,O= HD,O= Ho and hN
= hD =
h
(9)
Equation (4) then becomes
where x = [ H + ] / d K xhas the value unity a t the maximum of the AH curve. Of course, a symmetrical set of assumptions such as we have chosen here will give a symmetrical AH us. p H curve, while the observed curve appears to be unsymmetrical a t both 15 and 35". However, this model fails for a more serious reason. If q1 is the value of x a t which AH = '/z AH,,,
Since the right side of this equation is greater than 6 for K N # K D ,it follows that
IpHmax - p H ! / %I > 0.765
(12)
whereas, a t 35") the observed pH differences are 0.23 and 0.12 on the low and high p H sides, respectively.
Vol. 58
A sufficiently sharp, though still symmetrical, AH maximum can be obtained by replacing the equilibria of equations 1 and 2 by '
[Nil
+ +
NO= N . nH+; K N DO = D, nH+; K D [Di] = 0 ; i = I, . . ., n - 1
=i
(13) (14) (15)
These equilibria are of an unorthodox type, and require some sort of a structural change accompanying the ionizations which causes the liberation of the n protons to be an all-or-none process. Equilibria similar to these have recently been postulated by Steinhardt and Zaiser" to account for their observation of the liberation of acid-binding groups in the denaturation of ferrihemoglobin. If H N . ~ H N .= ~ HD,N - H D , = ~ A, these equilibria lead to an equation of the form of equation (lo), with nh = A and x' = [ H + ] " / d K x . Taking the mean value of IpH,,, - pH,/, I to be 0.18 (at 35"), the smallest integral value of n which can be used turns out to be 5. Equation 11 then gives v'KDIKN = 3.81. The expression
-
with AH,,, = 69 kcal. per mole, gives the value A = 118 kcal. per mole. This value is not unreasonably large since it may well be that a number of hydrogen bonds18are broken in the process in addition to the dissociation of five protons. As a necessary result of the calculations, K D = (6.3)6 and K N =: (6.5).' Asymmetry of the type observed in the AH us. p H curve could be introduced by assuming fewer than 5 ionizable protons in the denatured protein. However, in view of the unsubstantiated nature of the assumed mechanism and the scatter of the experimental data, detailed calculations are not warran ted. The mechanism considered here is certainly not unique, though it is the most reasonable one based on ionization equilibria we have been able to devise. Two obvious weaknesses should be emphasized. (1) the AH maximum a t 15" is considerably broader than a t 35", so that a smaller n can be used. I n any case, a much smaller A is necessary at 15". (2) Although a consideration of the heat data at 35" leads to an ionization involving approximately five protons (the same number as indicated by Steinhardt's kinetic data), the variation with pH of the rate of heat absorption points toward an ionization of an average of 1.4 protons. We are thus faced with the problem of accounting for an essentially instantaneous establishment (after initiating the reaction by raising the p H of the native pepsin solution) of an equilibrium mixture of NO and N,, followed by conversion of this to an equilibrium mixture of Do and D, a t a rate controlled by the concentration of native protein which has lost only an average of 1.4 protons relative to No. (17) J. Steinhardt and E. Zaiser, J . Am. Chem. Soc., 75, 1599 (1953). (18) A. E. Mirsky and L. Pauling, Proc. N a l . Acad. Sci., 22, 439 (1936).
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