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Heat capacity of proteins
J. Mol. Biol. (1990) 213,385-391
H e a t Capacity o f Proteins II. Partial Molar Heat Capacity of the Unfolded Polypeptide Chain of Proteins: Protein Unfollding Effects P. L. Privalov
and
G . I. M a k h a t a d z e
Institute of protein Research Academy of Sciences of the U.S.S.R. 142292 Pushchino, Moscow Region, U.S.S.R. (Received 10 July 1989; accepted 5 December 1989) Using the heat capacity values for amino acid side-chains and the peptide unit determined in the accompanying paper, we calculated the partial heat capacities of the unfolded state for four proteins (apomyoglobin, apocytochrome c, ribonuelease A, lysozyme) in aqueous solution in the temperature range from 5 to 125°C, with an assumption that the constituent amino acid residues contribute additively to the integral heat capacity of a polypeptide chain. These ideal heat capacity functions of the extended polypeptide chains were compared with the calorimetrically determined heat capacity functions of the heat and aciddenatured proteins. The average deviation of the experimental functions from the calculated ideal ones in the whole studied temperature range does not exceed the experimental error (5%). Therefore, the heat-denatured state of a protein, in solutions with acidic pH preventing aggregation, approximates well the completely unfolded state of this macromolecule. The heat capacity change caused by hydration of amino acid residues upon protein unfolding was also determined and it was shown that this is the major contributor to the observed heat capacity effect of unfolding. Its value is different for different proteins and correlates well with the surface area of non-polar groups exposed upon unfolding. The heat capacity effect due to the configurational freedom gain by the polypeptide chain was found to contribute only a small part of the overall heat capacity change on unfolding.
account that direct calorimetric measurements of the heat capacity of a protein in strong denaturants, such as 8 M-urea or Gu. HCI in which the protein is supposed to be completely unfolded, lead to a much larger effect of the denaturant interaction with a protein (Pfeil & Privalov, 1976).
1. I n t r o d u c t i o n
Considering the unfolded state of a protein polypeptide chain as a random-coil conformation, in which amino acid residues do not interact with each other, one can easily calculate its partial molar heat capacity by direct summation of the partial molar heat capacity contributions of the amino acid residues constituting the chain. One should certainly bear in mind that this is an ideal model, since even in the random-coil conformation, the concentration of amino acid residues is far from infinitely dilute, as it is in the solutions in which the partial heat capacities are determined. However, as we have already shown in the accompanying paper (Makhadadze & Privalov, 1990), the apparent molar heat capacities of isolated amino acid residues are not very sensitive to their concentration, at least when the concentration is below 10 -2 M. Therefore, the likely error from approximating the heat capacity contribution of amino acid residues in the polypeptide chain by their constituent partial molar heat capacities cannot be large. In any case, the value determined in this way would be the closest approximation of the heat capacity of the unfolded polypeptide chain that can be presently obtained. This becomes especially clear ff one takes into 0022-2836/90/100385-07 $03.00/0
2. M a t e r i a l s a n d M e t h o d s
The partial heat capacity of the unfolded polypeptide chain of a protein can be presented in the following way: CpUpr% = Cp.,(-NH2) -I- (N- 1)" Cp.,(--CHOONH-) N
+ ~. Cp,~(-Rk)+Cp,~(-CHCOOH),
(1)
kffil
t Abbreviations used: ASA, water-accessible surface u partial heat capacity of an unfolded protein; area; Cp,pr, D Cpp. partial heat capacity of a denatured l~rotein; CpN pr, partial heat capacity of a native protein; C_~a.h, heat ' capacity of an anhydrous native protein; A NU C hyd p , heat capacity change due to hydration of internal groups of a native protein; ~-~N~p ^vpco.r, heat capacity effect of the configurational freedom gain upon protein unfolding; ACp,i, hydration capacity per an ASA unit; --aAh(?hydv,pheat capacity change due to hydration of external groups of U an anhydrous native protein; ANASAi = ASA Ui -ASA Ni , the water-accessible surface area difference of the native and unfolded states of protein. 385
© 1990 Academic Press Limited
P, L. Privalov and G. I. Makhatadze
386
The ASA~ data were kindly provided by Dr Chothia, who calculated them according to Shrake & Rupley (1973) from the known atomic co-ordinates of the corresponding native proteins. The values of
where C~.~(-NH2) and C~.,(-CHCOOH) are the heat capacity contributions of the terminal groups - N H 2 and - C H C O O H , C~.~(-CHCONH-) is the heat capacity contribution of the peptide unit, C~.~(-Rk) is the heat capacity contribution of the side-chain of the bth amino acid residue, and N is the number of amino acid residues in the polypeptide chain. The amino acid compositions of the considered proteins were taken from their known amino acid sequences (Dayhoff, 1972). The partial molar heat capacities of the polypeptide chain components in aqueous solution for various temperatures that figure in equation (1) are given in Table 5 of the accompanying paper (Makhatadze & Privalov,
A S A ~ -- Z A S A ~ I were calculated from the surface area of various amino acids given by Miller et al. (1987). A very similar method of ~^U•hyd calculation has been NVp used previously by Ooi et al. (1987), Ooi & Oobatake (1988) and Oobatake & Ooi (1988); their values of ACp.i differ considerably from ours as they were derived from experimental data on partial heat capacities of too far analogs of amino acid residues in aqueous solutions. Another reason for the difference in the ACp. i values is that the above authors did not take into account the temperature dependence of the partial heat capacity and, assuming that it did not change with temperature, applied the values, obtained at 25°C, for the whole temperature range.
1990).
All disulfide crosslinks in the studied proteins were reduced, and cysteines were carboxymethylated, to obtain completely unfolded polypeptide chains. Therefore, in the considered sequences all cysteine residues were modified. The hydration heat capacity change upon protein translation from the native state to the completely unfolded state, ~NVp ^u~hyd, was calculated assuming that the hydration heat capacity of a group is proportional to its water-accessible surface area (see e.g. Gill eta/., 1985): UC ph = AUASAI.A~pl; AN , (2)
3. Results The values of partial specific heat capacities in aqueous solution of the unfolded polypeptide chains of the four considered proteins, calculated for different temperatures, are summarized in Table 2 and presented as functions of temperature in Figure 1. The Figure also gives the calorimetrically determined values of the partial molar heat capacity functions for these proteins in the denatured state with disrupted disulfide crosslinks and c a r b o x y m e t h y l a t e d cysteines (ribonuclease and lysozyme) and w i t h o u t the heme group (apomyoglobin and apocytochrome) in acidic aqueous solutions in which t h e y do not aggregate and have a rather high intrinsic viscosity. The heat capacities of the denatured proteins are taken from our
here ANVASAiis the integral water-accessible surface area change of all groups of a definite i type in the protein upon its translation from the native state to the completely unfolded state, and AOp., is the hydration heat capacity of the corresponding group calculated per an ASA unit, derived in the accompanying paper (Makhatadze & Privaiov, 1990). The A~ASAi values, listed in Table 1, were obtained from the values of water-accessible surface area in the native and unfolded proteins, ASAN and ASAIU. The values of: ASAi N - E A S A ~ J were determined from the data of A S A ~ for all j groups that belong to the i type of groups in the native protein. Table
1
Water-accessible surface area of the native state.(ASA~, A 2) and its change upon transition from the native to the fully unfolded state (A~ASA I, A 2) for various groups of protein Cytochrome
Myoglobin
Surface
ASA N
A~ASA,
ASA N
Aliphatic Aromatic
2560
4328
579 662 579
1859 3433 526
18
36
0
86
0 184 207 177 245 570
70
-CHCONH-
-CH2CONHPolar parts o~ Trp Met Cys Asn Asp Gin Glu Lys Arg Ser Thr Tyr His
Ribonuclease
A~ASA,
ASA~
ANVASA,
ASA~
3441
7386
2807
4749
2175
715 1100 396
2689 5300 539
588 1169 197
1614 4276 58
515 1159 526
8
46
0
0
44
1
85
1
171
0
86
0
0
279 276
2
278
646 219 176
320
43
lll 122 347 283
230
34
35
25 187 140 198
223
183
1 414 147
196 673 156 45
259 536 239 272 171
251 185 363 189 236
54 62
86 ll0
85 76
224
315
60
19 106
195 38
8
188
16 6
199 92
Lysozyme
542
143 386 200 117 239 304 195
166 830 73 69
182
44
136
7
A~ASA i 5385 1894 4106
494 124
187 97
129
85 42
Heat Capacity of Proteins. II previous paper devoted to the study of the denatured state of globular proteins (Privalov et al., 1989). As seen from Figure 1, the calculated values for the unfolded polypeptide chains and the heat capacities measured calorimetrically for denatured proteins are in reasonable agreement, which is much better than that found by us earlier from the published data (Privalov et al., 1989). This average deviation between the calculated and measured
387
partial heat capacity functions in the whole studied temperature range does not exceed 5 ~/o, i.e. it is of an order of experimental error. It should be noted that the shape and slope of the curves in Figure l, which represents the relative change of heat capacity with temperature, can be determined with a much higher accuracy by differential calorimetry than from the absolute values of the protein partial heat capacity (see Privalov & Potekhin, 1986).
Table 2 Partial molar heat capacities of proteins in denatured (Cp,pr),D unfolded (Cp,o,),v native (experimental, C~.p,(exp), and calculated, C~.p,(calc) ) states, and contributions of hydration i[^V~hyd~ ' - - ~ N V p N / , and configurational ,,^Vozoz~ freedom gain ~,.,m~pl^v~¢°'f/~,to the total heat capacity change on protein unfolding ~,-,H-p /, the heat capacity increment of hydration of the native anhydrous protein tAhC,hy~) and the heat capacity of native anhydrous proteins (Co.anh) N at various temperatures Temperature (°C) Protein
5
25
50
75
100
125
a
25"2 26"7 6'6 18"2 2"5
29"5 31'1 8'4 22"2 3"1 19.1 22"2 8"9
31' 1 31'8 8"1 24"4t 3"3 21.0t 24.3 7'4
31"4 32"4 7"7 26"7t 3"3 22"83" 26"1 5"7
31"5 32'5 6"8 28"9t 3"3 24"8t 28"1 3"6
0"8 1"4 1"6 0"6 0"6 0.8 1"0 1"5
Lysozyme v
N Cp,an h
15.7
CpN.p,.(calc) U Iol ANC p
18"2 8"5
27'5 29'1 7'8 20'0 2"8 17.2 20.0 9'1
23' 1 24' 1 3"7 19"5 3"1 16.4 19'5 4'6
26"0 26"0 4"9 20"8 3"2 17.6 20"8 5"2
27"7 27"8 5"7 22"5 3"4 19.1 22"5 5"3
29"2 28"5 5"5 24"2t 3"5 20"6t 24'1 4"3
29"8 29"3 5-5 25"8t 3"5 22.1t 25"6 3"5
30"1 29"5 4"9 27"5t 3"5 23"6t 27"1 2"0
0"8 1"3 1'0 0"6 0"6 0.8 1"0 1"4
31"9 35"6 10'2 21"8 5"3 16.5 21 '8 14.4
34"9 37"6 11"5 24"2 5"1 19"1 24"2 14.0
36"9 39"5 12' 1 27"3 5"0 22.3 27"3 12.8
39'2 40"0 11'5 30"3t 5'0 25.5~ 30"5 10.3
39"3 40"5 10"8 33"4t 4"9 28-8t 33"7 7.9
39"5 40"3 9"5 36"5t 4"7 32.0t 36"7 4.3
1"0 1"8 2"2 0"7 1"0 1.2 1"6 1-9
21"4 22"7 5-4 15"8 3"8 12"0 ]5"8 7"5
23'8 24"3 6-5 17"5 3"7 13"8 17"5 7"4
25"2 25"8 7-1 19'7 3"7 16"0 19"7 6"7
26"0 26"3 6-8 21"91" 3"8 18"2~ 22"0 5"0
26"1 26"8 6-5 24'0t 3"7 20"5t 24"2 3"3
26"3 26"8 5.8 26"2t 3"5 22"7~ 26"2 1"1
0"7 1"2 1-3 0"5 0"7 0"9 1"1 1"3
Cp.pr
Cp.pr U U ehyd ANC p CpN.pr(exp) h hyd A,Cp
Ribonuclease O Cp,pr U Cp.pr U hyd ANC p CpN,pr(eXp) h hyd AaC p Cp.anh N CpN.pr(calc) U lot ANC p
Myoglobin (apo) Cp,p¢ D (apo) Cp,pr u U hyd ANC p CpN.pr(exp) A~h Cphyd N Cp,an h
CpNpr(CalC) A~C~p°t Cytochrome (apo) Cp.pr D (apo) Cp,pr v AsUCp hyd CpNpr(exp) Ah~hyd avp
CpN..,h CpN,pr(calc) Au~tot N~p
U hyd ANC p and AUf~conf include the hydration effect of hemine for myoglobin and cytochrome. Avf~ot •~m,p include the partial molar heat ~N~p capacity of heroine for myoglobin and cytoehrome. t Extrapolated values; a is standard deviation. All heat capacity values axe given in k J K -1 rno1-1.
P. L. Privalov and G. I. Makhatadze
388
2"5
2.5 Non-pal
N
I"5
2.0
-" " " Lys
I
I
I
I
"1" 5 -
I T
2"5
I'0-
~
1.5 -
T
0"5-
RNase
v
I
I
l
•~2.5
I
Pal
I
........
.............
-0"5 0 1-5 -
Cyt I
I
I
I
t
I
I
2.5
1,5
~
~ I
0
25
"'~ ~ 50 75 Temperature (=C)
"'" "" "~ Mb I
I
I00
125
Figure 1. Temperature dependence of the heat capacity of proteins. Lines labelled U represent the calculated values for the unfolded state, continuous lines (D) show experimentally obtained values for the denatured state (Privalov et a/., 1989), lines with a broken extension (N) show the experimentally obtained values for the native state (Privalov et al., 1989), Mb, myoglobin; Cyt, cytochrome c; Lys, hen egg white lysozyme; RNase, ribonuclease A.
4. D i s c u s s i o n
(a) Deviation of the denatured state from the ideal random coil In one of our previous papers we showed that the partial heat capacity values of heat and aciddenatured proteins are indistinguishable in the temperature range from 5 to 125°C and the disruption of the disulfide crosslinks does not lead to noticeable changes in heat capacity (Privalov et al., 1989). It was shown also that the intrinsic viscosities of heat and acid-denatured proteins are very similar to those of the Gu" HCl-denatured proteins, if compared at the same temperatures. Earlier it was shown by one of us that the heat capacity of heat and acid-denatured lysozyme is indistinguishable from that of Gu" HCl-denatured lysozyme if the heat effects of the denaturant interaction with protein are correctly taken into account (Pfeil & Privalov, 1976). Since a protein in a concentrated Gu. HCI solution is regarded usually as completely unfolded, this might mean that the heat-denatured state of lysozyme is similar thermodynamically to the unfolded state. Now we see that this conclusion is not far from reality. According to the results reported in this paper, the partial heat capacity of the heatdenatured protein at acidic pH values, which
I 25
I I 50 75 Temperature (°C)
I I00
I 125
Figure 2. Contribution of the non-polar groups (Nonpol) and all other groups (Pol) constituting the protein to the beat capacity of the unfolded lysozyme (U) as a function of temperature.
prevent aggregation, is close indeed to the partial heat capacity of the ideal unfolded polypeptide chain. (b) Contribution of polar, charged and non-polar groups The other important fact that has been established is that the heat capacity function for the ideal random coil is non-linear, a curved function of temperature, asymptotically approaching some constant level at high temperatures, as was found earlier for the denatured protein (Privalov et al., 1989). The correspondence of these two functions for the unfolded and denatured proteins makes clear that the bend in the heat capacity function, found previously for the denatured protein, is not caused by gradual melting of the residual structure in denatured protein at increasing temperature, but is an intrinsic property of the unfolded polypeptide chain. The results obtained by us for the heat capacities of the groups constituting proteins, reported in the accompanying paper (Makhatadze & Privalov, 1990), permit us to analyze the contribution of various components of the polypeptide chain to its heat capacity. This analysis shows that the observed functional dependence of the heat capacity of the unfolded polypeptide chain is due to a superposition of two tendencies: the non-linearly increasing heat capacity of polar and charged groups and the linearly decreasing heat capacity of non-polar groups at increasing temperature (Fig. 2). In contrast, in the native protein, in which many groups do not contact water, the heat capacity appears to be an almost linearly increasing function of temperature, as is usually observed for solid bodies in this temperature range. The most essential difference between the heat capacity of the native
Heat Capacity of Proteins. I I
0"7f
389
80
Mb
70
A 7
Cyt
M
~
=o 6o
Tv ..)
0-5
~2
L y s ~ 50
<1
40 0"3
50 0'2 0
I 25
I 50
I I 75 I00 Temperature (°C)
I 125
Figure 3. Temperature dependence of the hydration heat capacity increment for the 4 studied proteins ~NVp ^unhyd calculated according to eqn (2).
and denatured or unfolded protein is a much higher value of the latter. This difference is evidently caused by the hydration of protein internal groups, which are exposed to water upon protein unfolding, and by the rise of the configurational freedom of protein groups resulting from the disruption of its solid native structure. (c) Contribution of hydration to the heat capacity The heat capacity effect of hydration of protein groups upon unfolding can be found if we know the change of water-accessible surface area of protein groups, ASA, and the heat capacity effect upon transfer of a given group i from the gaseous phase to water (see Materials and Methods, eqn (2)). The ASA values for the studied proteins are listed in Table 1. The values of L-aNV ^Uphrd p calculated for various temperatures are summarized in Table 2, and in Figure 3; they are presented as functions of temperature. We see that the hydration heat capacity increment is maximal at about 50°C. At a lower temperature, it decreases due to the decrease of the heat capacity contribution of polar and charged group hydration, while at high temperatures it decreases due to the decrease of the contribution of the non-polar group hydration. Another remarkable feature of the hydration heat capacity increment is that it varies for different proteins; it is most pronounced for myoglobin (even without taking into account the contribution of the heme hydration effect upon unfolding) and least pronounced for ribonuclease. Since, as we have already shown in the accompanying paper (Makhatadze & Privalov, 1990), only non-polar group hydration results in a rise of heat capacity at temperatures below 70 °C and the hydration of polar groups results in a decrease of heat capacity, one
I
60
=
I
70
I
I
80
Z~%SA "p(~2)
Figure 4. The A~ASA plot versus the denaturational heat capacity change, A~Cp (both values calculated per amino acid residue) at 25°C for the studied proteins. The values of ADCpare taken from Privalov et al. (1989).
can conclude that there is a much larger amount of non-polar groups screened from water in myoglobin than in ribonuclease. The AASA plot versus denaturational heat capacity change (both quantities calculated per amino acid residue) at 25°C for the studied proteins presented in Figure 4 confirm this conclusion. This is in agreement with our previous findings that the myoglobin structure is most saturated with the contacts between non-polar groups, i.e. it has the most developed hydrophobic core in the native state, while the hydrophobic core of ribonuclease is the least developed (Privalov & Khechinashvili, 1974).
(d) Heat capacity effect of the configu~'ational freedom
gain upon polypeptide chain unfolding As the heat capacity effect of hydration of protein groups upon exposure to water on unfolding of the native structure is known, we can compare it with the total heat capacity increment of unfolding of the native protein. Such comparison will give us an idea of the heat capacity increment caused by the gain of the configurational freedom ^ur~=o.e by the polypeptide chain upon disruption of the native structure of the protein maeromoleeule. The heat capacity of the native protein can be measured calorimetrically in a rather limited temperature range in which the native state could exist. Even for proteins from extreme thermophiles, this temperature range does not exceed 80°C, but for the majority of globular proteins it is much lower, about 60°C. In this temperature range, the heat capacity of the native protein appears to be an almost linear function of temperature (Privalov & Kheehinashvili, 1974; Privalov et al., 1989) and it was easiest to suppose t h a t it should be linear at
390
P. L. Privalov and O. I. Makhatadze
I.O
.-]
~zO4<~ 0"2 I 0
25
I
I
50 75 Temperoture (°C)
I
I
I00
125
Figure 5. Temperature dependence of the total heat capacity change upon protein unfolding.
higher temperatures as well, in contrast to the heat capacity of denatured proteins. The only possibility of checking the correctness of this assumption is the determination of the partial heat capacity of the native protein in aqueous solution from the heat capacity of the anhydrous protein. The absolute heat capacities of various anhydrous proteins in a broad temperature range were measured with great accuracy by ttutchens et al. (1969). It was found that the specific heat capacities of all studied anhydrous proteins are very similar and, what is the most important, they all are linear functions of temperature in the temperature range of our interest (Privalov, 1980). Unfortunately, Hutchens has not studied proteins that we consider here. However, it seems rather probable that the temperature dependence of the heat capacity of these proteins should be linear as well. Assuming that dehydration does not lead to a significant rearrangement of the globular protein interior, from the known three-dimensional structure of proteins one can calculate the hydration heat capacity effect, Ah~'hYd the ACp i values for the ~a vp , USing groups that we determined in the accompanying paper (see Table 2). Excluding it from the experimentally obtained values of the partial molar heat capacity for native proteins in the temperature range 5 to 50°C, one gets the heat capacity functions of anhydrous proteins, Cp,.,h, N in the same temperature range. As this function is linear, one can easily extrapolate it to higher temperatures and, adding to it the hydration heat capacity effect, get the heat capacity function for the hydrated protein in a broad temperature range from 5 to 125°C. As seen from Table 2, this derived function coincides with that calculated as a linear extrapolation of the experimentally obtained values of the heat capacity of the native state. This means that the linear extrapolation of the heat capacity function of the native state is quite correct.
The values of AO/~tot u N are given in ~N'~p = Cp.pr--Cp.p, Table 2. In the case of myoglobin and cytochrome, they include also the heat capacity of the heme group that, according to our estimate based on the data for the model compounds, is about 600 J K-1 mol- i~, which is less than 5 ~ of the heat capacity of the polypeptide chain. As seen from Table 2, the value of the hydration heat capacity increment of unfolding of native proteins is rather close to the total heat capacity change of unfolding, a-~NV AU~to~ p . The hydration heat capacity increment contributes 70 °/o to the total heat capacity change of unfolding. So, hydration effects play the major role in determination of the heat capacity increment of unfolding. The deviation between hydration heat capacity increment and the total heat capacity increment of unfolding should be assigned to the heat capacity effect of the confi~.urational freedom gain upon protein unfolding, A~C~°"r. Unfortunately, this small difference of two large quantities is on the limit of the experimental error. Therefore its temperature dependence is rather uncertain. (e) Heat capacity change upon protein unfolding
The evaluated heat capacity change of protein upon its complete unfolding, AUc~°t, is the most important parameter, considered here because it determines the temperature dependence of all thermodynamic functions responsible for the stability of the native protein structure in that ideal case, when the final state of protein presents an ideal random coil. These difference functions for the considered proteins are listed in Table 2 and presented in Figure 5. As seen, the heat capacity increment upon protein unfolding is not temperature-independent, as it was assumed when heat capacity of the native and denatured protein appeared to be linear functions of temperature with identical slopes (Privalov & Khechinashvili, 1974). It appeared to be very close, but in all cases somewhat larger, to the denaturational heat capacity increment and also drop to zero although at a somewhat higher temperature than 130°C, as was supposed earlier (Privalov et al., 1989). The main practical consequence of the presented results is that knowing the three-dimensional structure of the native protein one can calculate now the heat capacity increment of its unfolding, i.e. the parameter that determines the temperature dependences of all thermodynamic functions specifying the unfolding process and therefore determines the behavior of protein on temperature variation. We thank Dr C. Chothia for the sets of the wateraccessible surface area for native proteins; Drs S. J. Gill and J. Finney for helpful discussions of the manuscript in its preparation. References
Dayhoff, M. O. (1972). Atlas of Protein Sequence and Structure, vol. 5, National Biomedical Research Foundation, Washington, DC.
Heat Capacity of Proteins. I I
Gill, S. J., Dec, S. F., Olafsson, G. & WadsS, I. J. (1985). J. Phys. Chem. 89, 3758-3761. Hutchens, J. O., Cole, A. G. & Stout, J. W. (1969). J. Biol. Chem. 244, 25-32. Makhatadze, G. I. & Privalov, P. L. (1990). J. Mol. Biol. 213,375-384. Miller, S., Janin, J., Lesk, A. M. & Chothia, C. (1987). J. Mol. Biol. 196, 641-656. Oobatake, M. & Ooi, T. (1988). J. Biochem. 104, 433-439. Ooi, T. & Oobatake, M. (1988). J. Biochem. 103, 114-120. Ooi, T., Oobatake, G., N6methy, R. & Scheraga, H. A. (1987). Proe. Nat. Aead. Sei., U.S.A. 84, 3086-3090. Pfeil, W. & Privalov, P. L. (1976). Biophys. Chem. 4, 33-40.
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Privalov, P. L. (1980). In Biological Mierocalorimetry (Beezer, E. A., ed.), pp. 413--451, Academic Press, London, New York, Toronto, Sydney, San Francisco. Privalov. P. L. & Khechinashvili, N. N. (1974). J. Mol. Biol. 86, 665-684. Privalov, P. L. & Potekhin, S. A. (1986). Methods Enzymol. 131, 4-51. Privalov, P. L., Venyaminov, S. Yu., Tiktopulo, E. I., Griko, Yu, V., Makhatadze, G. I. & Kheehinashvili, N. N. (1989). J. Mol. Biol. 205, 737-750. Shrake, A. & Rupley, J. A. (1973). J. Mot. Biol. 79, 351-371.
Edited by R. Huber
H e a t Capacity o f Proteins II. Partial Molar Heat Capacity of the Unfolded Polypeptide Chain of Proteins: Protein Unfollding Effects P. L. Privalov
and
G . I. M a k h a t a d z e
Institute of protein Research Academy of Sciences of the U.S.S.R. 142292 Pushchino, Moscow Region, U.S.S.R. (Received 10 July 1989; accepted 5 December 1989) Using the heat capacity values for amino acid side-chains and the peptide unit determined in the accompanying paper, we calculated the partial heat capacities of the unfolded state for four proteins (apomyoglobin, apocytochrome c, ribonuelease A, lysozyme) in aqueous solution in the temperature range from 5 to 125°C, with an assumption that the constituent amino acid residues contribute additively to the integral heat capacity of a polypeptide chain. These ideal heat capacity functions of the extended polypeptide chains were compared with the calorimetrically determined heat capacity functions of the heat and aciddenatured proteins. The average deviation of the experimental functions from the calculated ideal ones in the whole studied temperature range does not exceed the experimental error (5%). Therefore, the heat-denatured state of a protein, in solutions with acidic pH preventing aggregation, approximates well the completely unfolded state of this macromolecule. The heat capacity change caused by hydration of amino acid residues upon protein unfolding was also determined and it was shown that this is the major contributor to the observed heat capacity effect of unfolding. Its value is different for different proteins and correlates well with the surface area of non-polar groups exposed upon unfolding. The heat capacity effect due to the configurational freedom gain by the polypeptide chain was found to contribute only a small part of the overall heat capacity change on unfolding.
account that direct calorimetric measurements of the heat capacity of a protein in strong denaturants, such as 8 M-urea or Gu. HCI in which the protein is supposed to be completely unfolded, lead to a much larger effect of the denaturant interaction with a protein (Pfeil & Privalov, 1976).
1. I n t r o d u c t i o n
Considering the unfolded state of a protein polypeptide chain as a random-coil conformation, in which amino acid residues do not interact with each other, one can easily calculate its partial molar heat capacity by direct summation of the partial molar heat capacity contributions of the amino acid residues constituting the chain. One should certainly bear in mind that this is an ideal model, since even in the random-coil conformation, the concentration of amino acid residues is far from infinitely dilute, as it is in the solutions in which the partial heat capacities are determined. However, as we have already shown in the accompanying paper (Makhadadze & Privalov, 1990), the apparent molar heat capacities of isolated amino acid residues are not very sensitive to their concentration, at least when the concentration is below 10 -2 M. Therefore, the likely error from approximating the heat capacity contribution of amino acid residues in the polypeptide chain by their constituent partial molar heat capacities cannot be large. In any case, the value determined in this way would be the closest approximation of the heat capacity of the unfolded polypeptide chain that can be presently obtained. This becomes especially clear ff one takes into 0022-2836/90/100385-07 $03.00/0
2. M a t e r i a l s a n d M e t h o d s
The partial heat capacity of the unfolded polypeptide chain of a protein can be presented in the following way: CpUpr% = Cp.,(-NH2) -I- (N- 1)" Cp.,(--CHOONH-) N
+ ~. Cp,~(-Rk)+Cp,~(-CHCOOH),
(1)
kffil
t Abbreviations used: ASA, water-accessible surface u partial heat capacity of an unfolded protein; area; Cp,pr, D Cpp. partial heat capacity of a denatured l~rotein; CpN pr, partial heat capacity of a native protein; C_~a.h, heat ' capacity of an anhydrous native protein; A NU C hyd p , heat capacity change due to hydration of internal groups of a native protein; ~-~N~p ^vpco.r, heat capacity effect of the configurational freedom gain upon protein unfolding; ACp,i, hydration capacity per an ASA unit; --aAh(?hydv,pheat capacity change due to hydration of external groups of U an anhydrous native protein; ANASAi = ASA Ui -ASA Ni , the water-accessible surface area difference of the native and unfolded states of protein. 385
© 1990 Academic Press Limited
P, L. Privalov and G. I. Makhatadze
386
The ASA~ data were kindly provided by Dr Chothia, who calculated them according to Shrake & Rupley (1973) from the known atomic co-ordinates of the corresponding native proteins. The values of
where C~.~(-NH2) and C~.,(-CHCOOH) are the heat capacity contributions of the terminal groups - N H 2 and - C H C O O H , C~.~(-CHCONH-) is the heat capacity contribution of the peptide unit, C~.~(-Rk) is the heat capacity contribution of the side-chain of the bth amino acid residue, and N is the number of amino acid residues in the polypeptide chain. The amino acid compositions of the considered proteins were taken from their known amino acid sequences (Dayhoff, 1972). The partial molar heat capacities of the polypeptide chain components in aqueous solution for various temperatures that figure in equation (1) are given in Table 5 of the accompanying paper (Makhatadze & Privalov,
A S A ~ -- Z A S A ~ I were calculated from the surface area of various amino acids given by Miller et al. (1987). A very similar method of ~^U•hyd calculation has been NVp used previously by Ooi et al. (1987), Ooi & Oobatake (1988) and Oobatake & Ooi (1988); their values of ACp.i differ considerably from ours as they were derived from experimental data on partial heat capacities of too far analogs of amino acid residues in aqueous solutions. Another reason for the difference in the ACp. i values is that the above authors did not take into account the temperature dependence of the partial heat capacity and, assuming that it did not change with temperature, applied the values, obtained at 25°C, for the whole temperature range.
1990).
All disulfide crosslinks in the studied proteins were reduced, and cysteines were carboxymethylated, to obtain completely unfolded polypeptide chains. Therefore, in the considered sequences all cysteine residues were modified. The hydration heat capacity change upon protein translation from the native state to the completely unfolded state, ~NVp ^u~hyd, was calculated assuming that the hydration heat capacity of a group is proportional to its water-accessible surface area (see e.g. Gill eta/., 1985): UC ph = AUASAI.A~pl; AN , (2)
3. Results The values of partial specific heat capacities in aqueous solution of the unfolded polypeptide chains of the four considered proteins, calculated for different temperatures, are summarized in Table 2 and presented as functions of temperature in Figure 1. The Figure also gives the calorimetrically determined values of the partial molar heat capacity functions for these proteins in the denatured state with disrupted disulfide crosslinks and c a r b o x y m e t h y l a t e d cysteines (ribonuclease and lysozyme) and w i t h o u t the heme group (apomyoglobin and apocytochrome) in acidic aqueous solutions in which t h e y do not aggregate and have a rather high intrinsic viscosity. The heat capacities of the denatured proteins are taken from our
here ANVASAiis the integral water-accessible surface area change of all groups of a definite i type in the protein upon its translation from the native state to the completely unfolded state, and AOp., is the hydration heat capacity of the corresponding group calculated per an ASA unit, derived in the accompanying paper (Makhatadze & Privaiov, 1990). The A~ASAi values, listed in Table 1, were obtained from the values of water-accessible surface area in the native and unfolded proteins, ASAN and ASAIU. The values of: ASAi N - E A S A ~ J were determined from the data of A S A ~ for all j groups that belong to the i type of groups in the native protein. Table
1
Water-accessible surface area of the native state.(ASA~, A 2) and its change upon transition from the native to the fully unfolded state (A~ASA I, A 2) for various groups of protein Cytochrome
Myoglobin
Surface
ASA N
A~ASA,
ASA N
Aliphatic Aromatic
2560
4328
579 662 579
1859 3433 526
18
36
0
86
0 184 207 177 245 570
70
-CHCONH-
-CH2CONHPolar parts o~ Trp Met Cys Asn Asp Gin Glu Lys Arg Ser Thr Tyr His
Ribonuclease
A~ASA,
ASA~
ANVASA,
ASA~
3441
7386
2807
4749
2175
715 1100 396
2689 5300 539
588 1169 197
1614 4276 58
515 1159 526
8
46
0
0
44
1
85
1
171
0
86
0
0
279 276
2
278
646 219 176
320
43
lll 122 347 283
230
34
35
25 187 140 198
223
183
1 414 147
196 673 156 45
259 536 239 272 171
251 185 363 189 236
54 62
86 ll0
85 76
224
315
60
19 106
195 38
8
188
16 6
199 92
Lysozyme
542
143 386 200 117 239 304 195
166 830 73 69
182
44
136
7
A~ASA i 5385 1894 4106
494 124
187 97
129
85 42
Heat Capacity of Proteins. II previous paper devoted to the study of the denatured state of globular proteins (Privalov et al., 1989). As seen from Figure 1, the calculated values for the unfolded polypeptide chains and the heat capacities measured calorimetrically for denatured proteins are in reasonable agreement, which is much better than that found by us earlier from the published data (Privalov et al., 1989). This average deviation between the calculated and measured
387
partial heat capacity functions in the whole studied temperature range does not exceed 5 ~/o, i.e. it is of an order of experimental error. It should be noted that the shape and slope of the curves in Figure l, which represents the relative change of heat capacity with temperature, can be determined with a much higher accuracy by differential calorimetry than from the absolute values of the protein partial heat capacity (see Privalov & Potekhin, 1986).
Table 2 Partial molar heat capacities of proteins in denatured (Cp,pr),D unfolded (Cp,o,),v native (experimental, C~.p,(exp), and calculated, C~.p,(calc) ) states, and contributions of hydration i[^V~hyd~ ' - - ~ N V p N / , and configurational ,,^Vozoz~ freedom gain ~,.,m~pl^v~¢°'f/~,to the total heat capacity change on protein unfolding ~,-,H-p /, the heat capacity increment of hydration of the native anhydrous protein tAhC,hy~) and the heat capacity of native anhydrous proteins (Co.anh) N at various temperatures Temperature (°C) Protein
5
25
50
75
100
125
a
25"2 26"7 6'6 18"2 2"5
29"5 31'1 8'4 22"2 3"1 19.1 22"2 8"9
31' 1 31'8 8"1 24"4t 3"3 21.0t 24.3 7'4
31"4 32"4 7"7 26"7t 3"3 22"83" 26"1 5"7
31"5 32'5 6"8 28"9t 3"3 24"8t 28"1 3"6
0"8 1"4 1"6 0"6 0"6 0.8 1"0 1"5
Lysozyme v
N Cp,an h
15.7
CpN.p,.(calc) U Iol ANC p
18"2 8"5
27'5 29'1 7'8 20'0 2"8 17.2 20.0 9'1
23' 1 24' 1 3"7 19"5 3"1 16.4 19'5 4'6
26"0 26"0 4"9 20"8 3"2 17.6 20"8 5"2
27"7 27"8 5"7 22"5 3"4 19.1 22"5 5"3
29"2 28"5 5"5 24"2t 3"5 20"6t 24'1 4"3
29"8 29"3 5-5 25"8t 3"5 22.1t 25"6 3"5
30"1 29"5 4"9 27"5t 3"5 23"6t 27"1 2"0
0"8 1"3 1'0 0"6 0"6 0.8 1"0 1"4
31"9 35"6 10'2 21"8 5"3 16.5 21 '8 14.4
34"9 37"6 11"5 24"2 5"1 19"1 24"2 14.0
36"9 39"5 12' 1 27"3 5"0 22.3 27"3 12.8
39'2 40"0 11'5 30"3t 5'0 25.5~ 30"5 10.3
39"3 40"5 10"8 33"4t 4"9 28-8t 33"7 7.9
39"5 40"3 9"5 36"5t 4"7 32.0t 36"7 4.3
1"0 1"8 2"2 0"7 1"0 1.2 1"6 1-9
21"4 22"7 5-4 15"8 3"8 12"0 ]5"8 7"5
23'8 24"3 6-5 17"5 3"7 13"8 17"5 7"4
25"2 25"8 7-1 19'7 3"7 16"0 19"7 6"7
26"0 26"3 6-8 21"91" 3"8 18"2~ 22"0 5"0
26"1 26"8 6-5 24'0t 3"7 20"5t 24"2 3"3
26"3 26"8 5.8 26"2t 3"5 22"7~ 26"2 1"1
0"7 1"2 1-3 0"5 0"7 0"9 1"1 1"3
Cp.pr
Cp.pr U U ehyd ANC p CpN.pr(exp) h hyd A,Cp
Ribonuclease O Cp,pr U Cp.pr U hyd ANC p CpN,pr(eXp) h hyd AaC p Cp.anh N CpN.pr(calc) U lot ANC p
Myoglobin (apo) Cp,p¢ D (apo) Cp,pr u U hyd ANC p CpN.pr(exp) A~h Cphyd N Cp,an h
CpNpr(CalC) A~C~p°t Cytochrome (apo) Cp.pr D (apo) Cp,pr v AsUCp hyd CpNpr(exp) Ah~hyd avp
CpN..,h CpN,pr(calc) Au~tot N~p
U hyd ANC p and AUf~conf include the hydration effect of hemine for myoglobin and cytochrome. Avf~ot •~m,p include the partial molar heat ~N~p capacity of heroine for myoglobin and cytoehrome. t Extrapolated values; a is standard deviation. All heat capacity values axe given in k J K -1 rno1-1.
P. L. Privalov and G. I. Makhatadze
388
2"5
2.5 Non-pal
N
I"5
2.0
-" " " Lys
I
I
I
I
"1" 5 -
I T
2"5
I'0-
~
1.5 -
T
0"5-
RNase
v
I
I
l
•~2.5
I
Pal
I
........
.............
-0"5 0 1-5 -
Cyt I
I
I
I
t
I
I
2.5
1,5
~
~ I
0
25
"'~ ~ 50 75 Temperature (=C)
"'" "" "~ Mb I
I
I00
125
Figure 1. Temperature dependence of the heat capacity of proteins. Lines labelled U represent the calculated values for the unfolded state, continuous lines (D) show experimentally obtained values for the denatured state (Privalov et a/., 1989), lines with a broken extension (N) show the experimentally obtained values for the native state (Privalov et al., 1989), Mb, myoglobin; Cyt, cytochrome c; Lys, hen egg white lysozyme; RNase, ribonuclease A.
4. D i s c u s s i o n
(a) Deviation of the denatured state from the ideal random coil In one of our previous papers we showed that the partial heat capacity values of heat and aciddenatured proteins are indistinguishable in the temperature range from 5 to 125°C and the disruption of the disulfide crosslinks does not lead to noticeable changes in heat capacity (Privalov et al., 1989). It was shown also that the intrinsic viscosities of heat and acid-denatured proteins are very similar to those of the Gu" HCl-denatured proteins, if compared at the same temperatures. Earlier it was shown by one of us that the heat capacity of heat and acid-denatured lysozyme is indistinguishable from that of Gu" HCl-denatured lysozyme if the heat effects of the denaturant interaction with protein are correctly taken into account (Pfeil & Privalov, 1976). Since a protein in a concentrated Gu. HCI solution is regarded usually as completely unfolded, this might mean that the heat-denatured state of lysozyme is similar thermodynamically to the unfolded state. Now we see that this conclusion is not far from reality. According to the results reported in this paper, the partial heat capacity of the heatdenatured protein at acidic pH values, which
I 25
I I 50 75 Temperature (°C)
I I00
I 125
Figure 2. Contribution of the non-polar groups (Nonpol) and all other groups (Pol) constituting the protein to the beat capacity of the unfolded lysozyme (U) as a function of temperature.
prevent aggregation, is close indeed to the partial heat capacity of the ideal unfolded polypeptide chain. (b) Contribution of polar, charged and non-polar groups The other important fact that has been established is that the heat capacity function for the ideal random coil is non-linear, a curved function of temperature, asymptotically approaching some constant level at high temperatures, as was found earlier for the denatured protein (Privalov et al., 1989). The correspondence of these two functions for the unfolded and denatured proteins makes clear that the bend in the heat capacity function, found previously for the denatured protein, is not caused by gradual melting of the residual structure in denatured protein at increasing temperature, but is an intrinsic property of the unfolded polypeptide chain. The results obtained by us for the heat capacities of the groups constituting proteins, reported in the accompanying paper (Makhatadze & Privalov, 1990), permit us to analyze the contribution of various components of the polypeptide chain to its heat capacity. This analysis shows that the observed functional dependence of the heat capacity of the unfolded polypeptide chain is due to a superposition of two tendencies: the non-linearly increasing heat capacity of polar and charged groups and the linearly decreasing heat capacity of non-polar groups at increasing temperature (Fig. 2). In contrast, in the native protein, in which many groups do not contact water, the heat capacity appears to be an almost linearly increasing function of temperature, as is usually observed for solid bodies in this temperature range. The most essential difference between the heat capacity of the native
Heat Capacity of Proteins. I I
0"7f
389
80
Mb
70
A 7
Cyt
M
~
=o 6o
Tv ..)
0-5
~2
L y s ~ 50
<1
40 0"3
50 0'2 0
I 25
I 50
I I 75 I00 Temperature (°C)
I 125
Figure 3. Temperature dependence of the hydration heat capacity increment for the 4 studied proteins ~NVp ^unhyd calculated according to eqn (2).
and denatured or unfolded protein is a much higher value of the latter. This difference is evidently caused by the hydration of protein internal groups, which are exposed to water upon protein unfolding, and by the rise of the configurational freedom of protein groups resulting from the disruption of its solid native structure. (c) Contribution of hydration to the heat capacity The heat capacity effect of hydration of protein groups upon unfolding can be found if we know the change of water-accessible surface area of protein groups, ASA, and the heat capacity effect upon transfer of a given group i from the gaseous phase to water (see Materials and Methods, eqn (2)). The ASA values for the studied proteins are listed in Table 1. The values of L-aNV ^Uphrd p calculated for various temperatures are summarized in Table 2, and in Figure 3; they are presented as functions of temperature. We see that the hydration heat capacity increment is maximal at about 50°C. At a lower temperature, it decreases due to the decrease of the heat capacity contribution of polar and charged group hydration, while at high temperatures it decreases due to the decrease of the contribution of the non-polar group hydration. Another remarkable feature of the hydration heat capacity increment is that it varies for different proteins; it is most pronounced for myoglobin (even without taking into account the contribution of the heme hydration effect upon unfolding) and least pronounced for ribonuclease. Since, as we have already shown in the accompanying paper (Makhatadze & Privalov, 1990), only non-polar group hydration results in a rise of heat capacity at temperatures below 70 °C and the hydration of polar groups results in a decrease of heat capacity, one
I
60
=
I
70
I
I
80
Z~%SA "p(~2)
Figure 4. The A~ASA plot versus the denaturational heat capacity change, A~Cp (both values calculated per amino acid residue) at 25°C for the studied proteins. The values of ADCpare taken from Privalov et al. (1989).
can conclude that there is a much larger amount of non-polar groups screened from water in myoglobin than in ribonuclease. The AASA plot versus denaturational heat capacity change (both quantities calculated per amino acid residue) at 25°C for the studied proteins presented in Figure 4 confirm this conclusion. This is in agreement with our previous findings that the myoglobin structure is most saturated with the contacts between non-polar groups, i.e. it has the most developed hydrophobic core in the native state, while the hydrophobic core of ribonuclease is the least developed (Privalov & Khechinashvili, 1974).
(d) Heat capacity effect of the configu~'ational freedom
gain upon polypeptide chain unfolding As the heat capacity effect of hydration of protein groups upon exposure to water on unfolding of the native structure is known, we can compare it with the total heat capacity increment of unfolding of the native protein. Such comparison will give us an idea of the heat capacity increment caused by the gain of the configurational freedom ^ur~=o.e by the polypeptide chain upon disruption of the native structure of the protein maeromoleeule. The heat capacity of the native protein can be measured calorimetrically in a rather limited temperature range in which the native state could exist. Even for proteins from extreme thermophiles, this temperature range does not exceed 80°C, but for the majority of globular proteins it is much lower, about 60°C. In this temperature range, the heat capacity of the native protein appears to be an almost linear function of temperature (Privalov & Kheehinashvili, 1974; Privalov et al., 1989) and it was easiest to suppose t h a t it should be linear at
390
P. L. Privalov and O. I. Makhatadze
I.O
.-]
~zO4<~ 0"2 I 0
25
I
I
50 75 Temperoture (°C)
I
I
I00
125
Figure 5. Temperature dependence of the total heat capacity change upon protein unfolding.
higher temperatures as well, in contrast to the heat capacity of denatured proteins. The only possibility of checking the correctness of this assumption is the determination of the partial heat capacity of the native protein in aqueous solution from the heat capacity of the anhydrous protein. The absolute heat capacities of various anhydrous proteins in a broad temperature range were measured with great accuracy by ttutchens et al. (1969). It was found that the specific heat capacities of all studied anhydrous proteins are very similar and, what is the most important, they all are linear functions of temperature in the temperature range of our interest (Privalov, 1980). Unfortunately, Hutchens has not studied proteins that we consider here. However, it seems rather probable that the temperature dependence of the heat capacity of these proteins should be linear as well. Assuming that dehydration does not lead to a significant rearrangement of the globular protein interior, from the known three-dimensional structure of proteins one can calculate the hydration heat capacity effect, Ah~'hYd the ACp i values for the ~a vp , USing groups that we determined in the accompanying paper (see Table 2). Excluding it from the experimentally obtained values of the partial molar heat capacity for native proteins in the temperature range 5 to 50°C, one gets the heat capacity functions of anhydrous proteins, Cp,.,h, N in the same temperature range. As this function is linear, one can easily extrapolate it to higher temperatures and, adding to it the hydration heat capacity effect, get the heat capacity function for the hydrated protein in a broad temperature range from 5 to 125°C. As seen from Table 2, this derived function coincides with that calculated as a linear extrapolation of the experimentally obtained values of the heat capacity of the native state. This means that the linear extrapolation of the heat capacity function of the native state is quite correct.
The values of AO/~tot u N are given in ~N'~p = Cp.pr--Cp.p, Table 2. In the case of myoglobin and cytochrome, they include also the heat capacity of the heme group that, according to our estimate based on the data for the model compounds, is about 600 J K-1 mol- i~, which is less than 5 ~ of the heat capacity of the polypeptide chain. As seen from Table 2, the value of the hydration heat capacity increment of unfolding of native proteins is rather close to the total heat capacity change of unfolding, a-~NV AU~to~ p . The hydration heat capacity increment contributes 70 °/o to the total heat capacity change of unfolding. So, hydration effects play the major role in determination of the heat capacity increment of unfolding. The deviation between hydration heat capacity increment and the total heat capacity increment of unfolding should be assigned to the heat capacity effect of the confi~.urational freedom gain upon protein unfolding, A~C~°"r. Unfortunately, this small difference of two large quantities is on the limit of the experimental error. Therefore its temperature dependence is rather uncertain. (e) Heat capacity change upon protein unfolding
The evaluated heat capacity change of protein upon its complete unfolding, AUc~°t, is the most important parameter, considered here because it determines the temperature dependence of all thermodynamic functions responsible for the stability of the native protein structure in that ideal case, when the final state of protein presents an ideal random coil. These difference functions for the considered proteins are listed in Table 2 and presented in Figure 5. As seen, the heat capacity increment upon protein unfolding is not temperature-independent, as it was assumed when heat capacity of the native and denatured protein appeared to be linear functions of temperature with identical slopes (Privalov & Khechinashvili, 1974). It appeared to be very close, but in all cases somewhat larger, to the denaturational heat capacity increment and also drop to zero although at a somewhat higher temperature than 130°C, as was supposed earlier (Privalov et al., 1989). The main practical consequence of the presented results is that knowing the three-dimensional structure of the native protein one can calculate now the heat capacity increment of its unfolding, i.e. the parameter that determines the temperature dependences of all thermodynamic functions specifying the unfolding process and therefore determines the behavior of protein on temperature variation. We thank Dr C. Chothia for the sets of the wateraccessible surface area for native proteins; Drs S. J. Gill and J. Finney for helpful discussions of the manuscript in its preparation. References
Dayhoff, M. O. (1972). Atlas of Protein Sequence and Structure, vol. 5, National Biomedical Research Foundation, Washington, DC.
Heat Capacity of Proteins. I I
Gill, S. J., Dec, S. F., Olafsson, G. & WadsS, I. J. (1985). J. Phys. Chem. 89, 3758-3761. Hutchens, J. O., Cole, A. G. & Stout, J. W. (1969). J. Biol. Chem. 244, 25-32. Makhatadze, G. I. & Privalov, P. L. (1990). J. Mol. Biol. 213,375-384. Miller, S., Janin, J., Lesk, A. M. & Chothia, C. (1987). J. Mol. Biol. 196, 641-656. Oobatake, M. & Ooi, T. (1988). J. Biochem. 104, 433-439. Ooi, T. & Oobatake, M. (1988). J. Biochem. 103, 114-120. Ooi, T., Oobatake, G., N6methy, R. & Scheraga, H. A. (1987). Proe. Nat. Aead. Sei., U.S.A. 84, 3086-3090. Pfeil, W. & Privalov, P. L. (1976). Biophys. Chem. 4, 33-40.
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Privalov, P. L. (1980). In Biological Mierocalorimetry (Beezer, E. A., ed.), pp. 413--451, Academic Press, London, New York, Toronto, Sydney, San Francisco. Privalov. P. L. & Khechinashvili, N. N. (1974). J. Mol. Biol. 86, 665-684. Privalov, P. L. & Potekhin, S. A. (1986). Methods Enzymol. 131, 4-51. Privalov, P. L., Venyaminov, S. Yu., Tiktopulo, E. I., Griko, Yu, V., Makhatadze, G. I. & Kheehinashvili, N. N. (1989). J. Mol. Biol. 205, 737-750. Shrake, A. & Rupley, J. A. (1973). J. Mot. Biol. 79, 351-371.
Edited by R. Huber