compatibility of osmolytes with gibbs energy of stabilization of proteins

Compatibility of osmolytes with Gibbs energy of stabilization of proteins

Farah Anjum, Vikas Rishi, Faizan Ahmad *Department of Biosciences, Jamia Millia Islamia, Jamia Nagar, New Delhi 110 025, India

Received 5 July 1999; received in revised form 15 September 1999; accepted 28 September 1999

Abstract

This study led to the conclusion that naturally occurring osmolytes which are known to protect proteins against denaturingstresses, do not perturb the Gibbs energy of stabilization of proteins at 25³C (vGD³) which has been shown to control the invivo rate of degradative protein turnover (Pace et al., Acta Biol. Med. Germ 40 (1981) 1385^1392). This conclusion has beenreached from our studies of heat-induced denaturation of lysozyme, ribonuclease A, cytochrome c and myoglobin in thepresence of different concentrations of osmolytes, namely, glycine, proline, sarcosine and glycine-betaine. At a fixedconcentration of osmolyte a heat-induced denaturation curve measured by following changes in the molar absorptioncoefficient of the protein, was analyzed for Tm, the midpoint of the denaturation and vHm, the enthalpy change ofdenaturation at Tm. Values of vGD³ were determined with Gibbs^Helmoltz equation using known values of Tm, vHm andvCp, the constant-pressure heat capacity change. It has been observed that Tm increases with the osmolyte concentration,whereas vGD³ remains unaffected in the presence of the osmolyte. This observation on vGD³ in the presence of osmolytes hasbeen considered in the physiological context. ß 2000 Elsevier Science B.V. All rights reserved.

Keywords: Osmolyte; Protein stability ; Lysozyme; Ribonuclease A ; Cytochrome c ; Myoglobin

1. Introduction

Many microorganisms, ¢shes, plants and animalshave adapted to harsh environmental conditions,such as water, salts, cold and heat stresses. It iswell known that these organisms have adapted onecommon strategy in protecting their cellular proteinsagainst these harsh environmental stresses [1,2]. Thisinvolves accumulation of low molecular weight or-ganic compounds, collectively called osmolytes whichfall into one of the three classes, namely, amino acidsand their derivatives, polyols and methylamines [2^4]. These osmolytes are further classi¢ed as `compat-

ible' or `counteracting' based on their e¡ect on thefunctional activity of proteins [2,3,5]. Compatible os-molytes are those which protect proteins against in-activation and denaturation without perturbing theprotein functional activity near room temperature [5^8]. Counteracting osmolytes are those which are builtup by organisms to cope with deleterious e¡ect ofurea on proteins' functional activity and stability[9^11]. It is noteworthy that accumulation of com-patible osmolytes (amino acids and their derivativesand polyols) occurs when organisms are under stress-es such as water, extremes of temperature and salin-ity, and accumulation of counteracting osmolytes(methylamines) occurs when urea concentration inthe cells of organisms is as high as 0.4^4 M [12].

A large body of data suggests that both compat-ible and counteracting osmolytes enhance thermal

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* Corresponding author. Fax: +91-11-579-1351;E-mail : [email protected]

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Biochimica et Biophysica Acta 1476 (2000) 75^84www.elsevier.com/locate/bba

stability of proteins [2,13^17]. The main factor re-sponsible for this stabilizing e¡ect was disclosed byTimashe¡ and co-workers [13,14] and is related tothe fact that these osmolytes are preferentially ex-cluded from the protein domain, that is, they causepreferential hydration of the protein; this e¡ectshould favor the protein state with the lower exposedsurface, thus displacing the denaturation equilibrium,native (N) conformationHdenatured (D) conforma-tion, towards the N state and bring about a higherstabilization of the N conformation in the presenceof osmolytes. It is interesting to note that almost allstudies used Tm (denaturation transition tempera-ture) as an index of conformational stability (vGD³,the Gibbs energy change of denaturation at 25³C) inthe presence of an osmolyte. One potentially interest-ing aspect of this mechanism that has received littleattention is the possible e¡ect of osmolytes on thedenaturation Gibbs energy (vGD³). The interest ofprobing this possible e¡ect is suggested by the twofollowing facts. (a) Tm is not a measure of vGD³. Forexample, lysozyme and cytochrome c have the sameTm of 80³C, but vGD³ values are 16 and 8 kcalmol31, respectively [18]. (b) There exists an inverserelation between vGD³ and susceptibility to proteindegradation [19,20]. If an osmolyte perturbs vGD³, itthen means that the degradative protein turnoverrate will also be perturbed. This scenario will poseenormous problems for the organisms.

In order to investigate the e¡ect of osmolytes onvGD³, we have been carrying out systematic studiesof denaturation of several proteins in the presence ofdi¡erent concentrations of both compatible andcounteracting osmolytes. In this communication, wereport an interesting observation that osmolytes donot signi¢cantly perturb vGD³ values of proteinsnear room temperature suggesting that they do notalter the rate of degradative protein turnover. Thatis, osmolytes are compatible with protein stability(vGD³).

2. Materials and methods

Hen egg-white lysozyme (Lzm), ribonuclease A(RNase A), horse heart cytochrome c (cyt c) andhorse heart myoglobin (Mb) were purchased fromthe Sigma. Electrophoretic homogeneity of each pro-

tein was checked on SDS-polyacrylamide gel electro-phoresis according to the procedure described byLaemmli [21]. Since all proteins gave a single band,they were used without further puri¢cations. Osmo-lytes, namely, glycine (Gly), proline (Pro), sarcosine(Sar) and glycine-betaine (GB) were purchased fromthe Aldrich. Ultrapure guanidine hydrochloride(GdnHCl) was purchased from Schwarz/MannBiotech. These and other chemicals were of analyt-ical grade and were used without further puri¢ca-tion.

Stock solutions of Lzm, RNase A and those ofoxidized Mb and cyt c were prepared in 0.1 MKCl (pH 7.0) as described earlier [22,23]. Concentra-tions of proteins were determined using molar ab-sorption coe¤cient (M31 cm31) values of 39 000 at280 nm for Lzm [24], 9800 at 277.5 nm for RNase A[25], 171 000 at 409 nm for Mb [26] and 10 700 at 530nm for cyt c [27]. Concentration of GdnHCl stocksolution was determined by refractometric measure-ments [28]. All solutions for optical measurementswere prepared in degassed bu¡er containing 0.1 MKCl. Thermal denaturation studies were carried outin Jasco V-560 UV/Vis spectrophotometer with aheating rate of 1³C min31 using its peltier accessory(model ETC-505 temperature controller). The changein absorbance on heating was followed at 292 nm forLzm, 287 nm for RNase A, 409 nm for Mb, and 530nm for cyt c. About 350 data points were collected.Reversibility of each denaturation curve was checkedas described earlier [29]. Lzm, Mb and cyt c nearneutral pH have their Tm values near 80³C. In orderto bring the heat-induced transition to a measurabletemperature range, Lzm and Mb denaturation wasstudied in the presence of 1.60 M and 0.60 MGdnHCl, respectively, whereas the thermal denatura-tion of cyt c was studied at pH 3.0 at which it isalready 25% acid denatured at 25³C. Each thermaltransition curve was measured at least in triplicate,and analyzed for vGD(T), the Gibbs energy of dena-turation at temperature T for a two-state denatura-tion, using the relation,

vGD�T� � 3RT lny�T�3yN�T�yD�T�3y�T��

�1�

where y(T) is the observed optical property at tem-perature T, and yN and yD are, respectively, the op-tical properties of the native and denatured protein

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F. Anjum et al. / Biochimica et Biophysica Acta 1476 (2000) 75^8476

molecules at the same temperature at which y hasbeen measured. The plot of vGD(T) values in therange 31.39 vGD (T), kcal mol31 9 1.3 versus cor-responding T at constant concentration of an osmo-lyte was used to determine the values of Tm andvHm, the enthalpy change of denaturation at Tm

according to the procedure reported earlier [16].vGD³, the value of vGD at T = 298.15 K was deter-mined using the measured values of vHm, Tm, andvCp in the Gibbs^Helmoltz equation,

vGD � vHmTm3T

Tm

� �3vCp �Tm3T� � T ln

TTm

� ��2�

3. Results and discussion

In order to understand the question whether os-molytes are compatible with protein stability (vGD³),de¢ned as the decrease in Gibbs energy of the dena-tured polypeptide when it folds to give the nativefunctional protein under physiological conditions,usually taken as neutral dilute bu¡er and 25³C, wehave been measuring the thermal denaturation curvesof several proteins in the presence and absence ofdi¡erent osmolytes. Here we present and discussthe results of four proteins, namely, Lzm, RNaseA, Mb and cyt c in the presence of di¡erent concen-trations of two compatible osmolytes (Gly and Pro)and two counteracting osmolytes (Sar and GB).

Panel A of Figs. 1^4 represents the typical dena-turation behavior of proteins in the presence andabsence of the osmolytes. The optical transitioncurves of each protein in the presence of di¡erentconcentrations of an osmolyte were converted intostability curve [30] using Eq. 1 (e.g. see panel B ofFigs. 1^4). Stability curves of a protein wereanalyzed for vHm and Tm values using the proceduredeveloped earlier [16]. Values of these parameters ofall proteins in di¡erent concentrations of osmolytesare given in Table 1.

In order to determine vGD³ values of proteins inthe presence and absence of di¡erent concentrationsof various osmolytes using Eq. 2, their vCp values atdi¡erent concentrations of each osmolytes shouldalso be known. The recommended procedure forthe experimental determination of vCp involves the

measurements of vHm and Tm from the heat-induceddenaturation of the protein at several pH values, us-ing di¡erential scanning calorimetry [18] or opticaltechniques [30]. We have measured thermal dena-turation curves of one protein, namely, Mb in thepresence of di¡erent ¢xed concentrations of eachosmolyte at four di¡erent pH values. For eachconcentration of an osmolyte, vHm versus corre-sponding Tm plot was constructed. Such plots ofMb in the presence of Gly are shown in Fig. 1D(plots for other osmolytes not shown). Assumingthat vCp is independent of temperature and pH be-tween 20 and 80³C [17,18,30], values of vCp

( = DvHm/DTm) were obtained from the least-squaresanalysis. These results are given in Table 2. It is seenin this table that vCp value remains, within experi-mental errors, unchanged in the presence of osmo-lytes in the concentration range 0^1 M. However, ithas been assumed that vCp values of other proteinsare independent of the presence of low osmolyte con-centrations. The assumption that the low concentra-tions of osmolytes do not a¡ect the vCp of RNase A,Lzm and cyt c is based on the following observa-tions. Di¡erential scanning calorimetric measure-ments of RNase A [17], Lzm [31] and cyt c (Ahmadand Pfeil, unpublished results) in the presence of upto 1 M of various osmolytes suggested that vCp ofthe protein is not signi¢cantly altered.

Using vHm and Tm values given in Table 1 andvCp (kcal mol31 K31) values of 1.23 þ 0.12 forRNase A [18], 1.56 þ 0.20 for Lzm [18], 2.74 þ 0.16for Mb ([18], this study) and 0.71 þ 0.03 for cyt c [16]measured in the absence of the osmolyte, we havecalculated vGD³ values of proteins using Eq. 2,which are given in Table 1. It is seen in Eq. 2 that,assuming no error in temperature, the error in theestimate of vGD³ depends on the experimental errorsin the vHm and vCp. For example, the value of vGD³of RNase A is 11.0 kcal mol31. On incorporatingerrors in the vHm and vCp the error in vGD³ areþ 0.4 and þ 0.5, respectively. It should be notedthat the errors in vGD³ of proteins given in Table1, are due to those in vCp only.

The e¡ect of osmolytes on the thermodynamic pa-rameters of proteins is summarized in Table 1. It isseen in this table that Tm of each protein increaseswith an increase in the concentration of each osmo-lyte. This ¢nding that proteins are stabilized in terms

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F. Anjum et al. / Biochimica et Biophysica Acta 1476 (2000) 75^84 77

of Tm agrees with those reported in the literature[2,13^17]. If it is assumed that Tm is an index ofstability of proteins [13,15,17], this observation onTm can be understood in the light of two recentmechanisms of stabilization by naturally occurringosmolytes proposed by Timashe¡ and coworkers[14] and by Bolen and coworkers [32^34]. Accordingto Timashe¡, the main factor for the stabilizing e¡ectof the osmolyte on protein is related to the fact that

these osmolytes are preferentially excluded from theprotein surface, i.e. they cause preferential hydrationof the protein; this e¡ect should favor protein statewith lower exposed surface, thus displacing the de-naturation equilibrium, N conformationHD confor-mation, towards the N state, bringing about a stabi-lization of the native protein in the presence ofosmolytes. Bolen and coworkers [32^34] have inter-preted the e¡ect of osmolytes on proteins in terms of

Fig. 1. Thermal stability of Mb at pH 6.1. (A) Transition curves of the protein in the presence of di¡erent concentrations of Gly. Forthe sake of clarity, all data points are not shown, and for the same reason, transition curves at 0.25 and 0.75 M have been omitted.(B) Plot of vGD(T) versus temperature. Symbols have the same meaning as in A. (C) Stability curves of Mb drawn using Eq. 2 withvHm, Tm and vCp values given in Tables 1 and 2. The error bars represent errors in vGD(T) values due to an error of þ 0.16 kcalmol31 K31 in vCp. (D) Plot of vHm versus Tm of the protein at di¡erent concentrations of Gly.

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transfer-free energy of protein groups from waterto osmolyte solutions, and in terms of dimensionsof the native and denatured proteins in osmolytesolutions. They concluded that in addition to raisingthe overall vGtr, the Gibbs energy of transfer(vGtr =vGtr; D3vGtr; N), the unfavorable interactionof the backbone with osmolyte causes a collaterale¡ect that results in the contraction of the denaturedmolecules; this e¡ect should decrease the entropy of

the denatured molecule, i.e. osmolyte should pro-mote N state, thus displacing the denatured equili-brium towards N state and bringing about a stabili-zation of the N conformation in the presence ofosmolytes.

In fact, both the mechanisms of stabilization ofproteins, mentioned in the preceding paragraph, pre-dict that the Gibbs energy change on denaturation(vGD) should increase in the presence of osmolytes.

Fig. 2. Thermal stability of RNase A at pH 6.0. (A) Heat denaturation curves of the protein in the presence of di¡erent concentra-tions of Sar. All data points and transition curves have not been shown for the same reason given in Fig. 1A. (B) Plot of vGD(T) ver-sus temperature. Symbols have the same meaning as in A. (C) Stability curves of the protein drawn using Eq. 2 with vHm and Tm

values given in Table 1 and vCp = 1.23 þ 0.12 kcal mol31 K31. The error bars have the same meaning as in Fig. 1C.

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It is seen in Table 1 that, on the contrary, vGD³values of proteins remain, within experimental er-rors, unchanged in the presence of osmolytes. In or-der to see how osmolytes a¡ect vGD at other temper-atures, we constructed stability curves of proteinsusing Eq. 2, the Gibbs^Helmoltz equation derivedon the assumption that vCp is independent of tem-perature in the range 20^80³C [17,18,30]. Panel C ofFigs. 1^4 shows the typical stability curves of pro-

teins. It is seen in these ¢gures that all proteins arestabilized in the presence of osmolytes around theirTm values, i.e. in the temperature range 40^80³C. Wehave constructed stability curves of each protein inother three osmolytes, and observed that all osmo-lytes stabilize proteins in terms of vGD in the temper-ature range 40^80³C (curves not shown). Thus, ourobservation in this temperature range is consistentwith the prediction that the Gibbs energy change

Fig. 3. Thermal stability of Lzm at pH 4.8. (A) Thermal denaturation curves of the protein in the presence of various concentrationsof Pro. All data points and transition curves have not been shown for the same reason given in Fig. 1A. (B) Plot of vGD(T) versustemperature. Symbols have the same meaning as in A. (C) Stability curves of Lzm drawn using Eq. 2 with vHm and Tm values givenin Table 1 and vCp = 1.56 þ 0.20 kcal mol31 K31. The error bars have the same meaning as in Fig. 1C.

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on denaturation should increase in the presence ofosmolytes [14,23,24].

RNase A, Lzm and Mb exist predominantly intheir N conformations at 25³C (see Figs. 1^3). TheirvGD³ values are not perturbed in the presence ofosmolytes (see Table 1, and also Figs. 1C, 2C and3C). It should be noted that vGD³ values of theseproteins are obtained from long extrapolation of(vGD, T) data obtained at higher temperatures, i.e.

in the transition region. Thus vGD³ values of pro-teins have larger error components than the experi-mentally determined vGD values in the transitionregion. In order to see whether our conclusion thatosmolytes do not a¡ect the Gibbs energy changenear room temperature is valid, we studied the e¡ectof osmolytes on cyt c at pH 3.0 where the protein isnot only in equilibrium between N and D states [16],but the vGD value can also be experimentally deter-

Fig. 4. Thermal stability of cyt c at pH 3.0. (A) Transition curves of the protein in the presence of di¡erent concentrations of GB.All data points and transition curves have not been shown for the same reason given in Fig. 1A. (B) Plot of vGD(T) versus tempera-ture. Symbols have the same meaning as in A. (C) Stability curves of cyt c drawn using Eq. 2 with vHm and Tm values given in Table1 and vCp = 0.71 þ 0.03 kcal mol31 K31. The error bars have the same meaning as in Fig. 1C.

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mined at 25³C (e.g. see Fig. 4). These results also ledto the conclusion that: (1) vGD³ of cyt c is not af-fected by the presence of osmolytes (see Table 1);and (2) osmolytes stabilize the protein at higher tem-peratures (e.g. see Fig. 4)

There seems to exist a paradox that the osmolytestabilizes proteins in terms of Gibbs energy at highertemperatures, but it has no signi¢cant e¡ect nearroom temperature. One possible explanation forthese di¡erent e¡ects of the osmolytes on the Gibbsenergy of stabilization at di¡erent temperatures maystem from the di¡erent natures of the denatured pro-tein in the presence and absence of the osmolyte.This view is supported by the recent ¢ndings thatosmolyte^protein interaction results in the contrac-tion of the denatured ensembles (i.e. it promotesthe formation of native molecules), and has no e¡ect

on the dimensions of the native molecules [32^34].That is, the action of osmolytes is on the denaturedensembles and not on the native state [33].

If we considered our vGD³ results (Table 1) in thephysiological context, the important role played byosmolytes in governing protein stability^function re-lationship may be appreciated. It is well known thatthe adaptation of organisms to denaturing stresses isenabled by the accumulation of osmolytes that pro-tect proteins and other cellular components from del-eterious e¡ects of denaturing stresses [2]. However,this adaptive pattern should not signi¢cantly a¡ectprotein stability in terms of vGD³, for there exists aninverse relation between vGD³ and in vivo rate ofdegradative protein turnover [19,20]. For instance,if vGD³ values of proteins are increased in the pres-ence of osmolytes, it then means that osmolytes will

Table 1Stability parameters of proteins in presence of osmolytesa

[Osmolyte](M)

Mb (pH 6.1) RNase A (pH 6.0) Lzm (pH 4.8) Cyt c (pH 3.0)

Tm

(³C)vHm

(kcalmol31)

vGD³(kcalmol31)

Tm

(³C)vHm

(kcalmol31)

vGD³(kcalmol31)

Tm

(³C)vHm

(kcalmol31)

vGD³ (kcalmol31)

Tm

(³C)vHm

(kcalmol31)

vGD³(kcalmol31)

Gly0.00 67.4 82 þ 4 2.7 þ 0.4 65.5 118 þ 2 11.0 þ 0.3 62.7 89 þ 5 6.6 þ 0.6 45.0 16 þ 1 0.6 þ 0.07

0.25 69.1 83 þ 3 2.6 þ 0.4 66.1 119 þ 2 11.2 þ 0.3 64.1 91 þ 3 6.9 þ 0.3 45.3 13 þ 1 0.4 þ 0.06

0.50 70.5 84 þ 2 2.7 þ 0.5 68.0 119 þ 4 11.5 þ 0.3 65.4 90 þ 3 6.8 þ 0.4 46.0 12 þ 1 0.3 þ 0.03

0.75 71.2 85 þ 3 2.7 þ 0.6 68.3 120 þ 3 11.7 þ 0.4 66.8 92 þ 3 7.1 þ 0.4 46.3 11 þ 1 0.2 þ 0.02

1.00 72.6 88 þ 3 2.8 þ 0.6 69.4 121 þ 4 12.0 þ 0.4 68.4 93 þ 3 7.3 þ 0.4 48.3 11 þ 1 0.2 þ 0.04

Pro0.25 68.1 85 þ 3 2.6 þ 0.4 65.9 115 þ 2 10.8 þ 0.4 63.9 90 þ 4 6.7 þ 0.5 45.8 16 þ 1 0.6 þ 0.02

0.50 68.2 85 þ 2 2.6 þ 0.3 66.4 119 þ 2 11.3 þ 0.3 64.5 92 þ 3 7.0 þ 0.5 46.5 16 þ 1 0.6 þ 0.02

0.75 67.8 82 þ 3 2.8 þ 0.2 66.5 120 þ 4 11.4 þ 0.3 64.8 92 þ 3 7.0 þ 0.5 47.0 14 þ 1 0.4 þ 0.02

1.00 68.0 83 þ 3 2.4 þ 0.3 66.7 120 þ 2 11.4 þ 0.3 65.1 87 þ 3 6.5 þ 0.5 49.3 14 þ 1 0.4 þ 0.03

Sar0.25 68.5 85 þ 2 2.8 þ 0.5 65.9 118 þ 4 11.1 þ 0.3 64.0 88 þ 4 6.5 þ 0.5 46.8 16 þ 1 0.6 þ 0.02

0.50 69.1 87 þ 3 2.9 þ 0.5 67.5 119 þ 4 11.4 þ 0.3 65.1 89 þ 5 6.7 þ 0.5 48.4 16 þ 1 0.6 þ 0.03

0.75 70.5 86 þ 3 2.8 þ 0.6 67.8 119 þ 3 11.5 þ 0.3 66.4 90 þ 3 6.9 þ 0.5 50.1 15 þ 1 0.5 þ 0.03

1.00 72.1 88 þ 3 3.1 þ 0.5 70.1 119 þ 4 11.8 þ 0.3 67.9 91 þ 3 7.1 þ 0.6 51.1 16 þ 1 0.5 þ 0.03

GB0.25 68.0 85 þ 2 2.9 þ 0.6 66.1 122 þ 4 11.6 þ 0.3 63.1 89 þ 5 6.6 þ 0.5 45.8 16 þ 2 0.6 þ 0.02

0.50 68.8 85 þ 3 2.8 þ 0.5 66.3 120 þ 3 11.4 þ 0.3 64.9 90 þ 3 6.8 þ 0.5 46.5 16 þ 1 0.6 þ 0.02

0.75 69.5 86 þ 2 2.9 þ 0.6 67.0 122 þ 2 11.7 þ 0.3 65.0 91 þ 3 6.9 þ 0.5 47.5 15 þ 1 0.5 þ 0.03

1.00 70.2 87 þ 3 3.1 þ 0.4 68.1 120 þ 3 11.7 þ 0.4 65.8 89 þ 4 6.7 þ 0.5 49.7 16 þ 1 0.5 þ 0.03

A ` þ ' with a value of vHm represents the standard deviation of the ¢t. The average error from several independent measurements arewithin errors of the least-squares ¢t. Values of vGD³ were calculated with Eq. 2 using values of vCp given in the text.

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decrease the protein turnover rates of all proteinsincluding the metabolic regulatory enzymes whichhave a very high turnover rate [35]. This scenariowill pose enormous problems for the organisms, be-cause now it would be energetically di¤cult to de-grade proteins [19,20] and to maintain a steady-statecondition [35]. It is noteworthy that Burg [36] hasshown that in vivo rate of degradation of aldosereductase remained unchanged during the accumula-tion of sorbitol which is a compatible osmolyte. Hisstudy provides support to our ¢nding that vGD³ ofproteins is not a¡ected by osmolytes. In summary,we conclude that: (1) osmolytes protect proteinsagainst denaturing stresses by working on thermody-namics variables in such a way that the denaturationtemperature (Tm) is raised without perturbing vGD

values near physiological temperatures; and (2) thatosmolytes are compatible with protein stability(vGD³) as well.

Acknowledgements

This work has been supported by grants from theUniversity Grants Commission, Council of Scienti¢cand Industrial Research, and Department of Scienceand Technology. We thank Dr. Peter McPhie(NIDDK, NIH, Bethesda, MD) for his valuablecomments. F.A. is very grateful to Professor D.Wayne Bolen (Department of Human BiologicalChemistry and Genetics, University of Texas Medi-cal Branch, Texas, USA) for enlightening discussionswhile the author was a visiting Professor in his labo-ratory, and for the ¢nancial support from the JohnSealy Memorial Endowment Fund for BiomedicalResearch (Grant 2512-98R).

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Table 2Values of temperature-dependence of the enthalpy change of Mb in presence of di¡erent concentrations of osmolytesa

[Osmolyte] (M) vCp (kcal mol31 K31)

Gly Sar GB Pro

0.00 2.74 þ 0.16 2.74 þ 0.16 2.74 þ 0.16 2.74 þ 0.160.25 2.71 þ 0.12 2.78 þ 0.17 2.77 þ 0.20 2.76 þ 0.150.50 2.74 þ 0.15 2.81 þ 0.18 2.77 þ 0.18 2.75 þ 0.120.75 2.68 þ 0.17 2.71 þ 0.21 2.73 þ 0.19 2.69 þ 0.071.00 2.72 þ 0.16 2.63 þ 0.20 2.68 þ 0.14 2.71 þ 0.09aA ` þ ' with a value of vCp represents the standard deviation of the ¢t.

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[12] R.E. MacMillen, A.K. Lee, Australian desert mice: inde-pendence of exogenous water, Science 158 (1967) 383^385.

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compatibility of osmolytes with gibbs energy of stabilization of proteins

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