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Electrostatic effects on protein stability
An-SueiYangand BarryHonig
Columbia University,New York,USA
Recent experimental and theoretical studies have led to new insights intothe contribution of ionizable amino acids to protein stability. The role ofpolar groups is less clear, in part because their interactions are difficultto
control experimentally.
Current Opinion in Structural Biology 1992, 2:40-45
Introduction
The past few years have witnessed major advances inour understanding of electrostatic interactions in proteins(summarized in a number of recent reviews [1,2]). Elec-trostatic interactions, as defined here, arise both fromionizable amino acids and from polar groups that con-tain permanent dipoles. The major focus of this reviewwill be recent developments in elucidating the contri-butions of ionizable amino acids to protein stability.Progress has been facilitated by a combination of mod-ern experimental techniques, such as NMR and site-directed mutagenesis, and more traditional methods suchas the measurement of pH and salt effects on denatura-tion free energies. In parallel, new theoretical methodsnow make it possible to interpret experimental resultsin terms of specific molecular interactions. The interplaybetween increasinglyreliable theoretical methods and theimproved ability of experimental methods to probe welldefined interactions will be highlighted in this review.
Only a short section of this review is devoted to thediscussion of the contribution of dipolar groups to pro-tein stability. In our view, there has been only limitedprogress in this area; indeed, the fundamental questionas to whether or not hydrogen bonds stabilize proteinshas not yet been definitivelyresolved. In addition, little at-tention has been devoted to the destabilizing effects thatresult from the burial of permanent dipoles in the proteininterior. We will offer our opinion on these questions ina brief section near the end of the review.
Basic principles
In the first place, it is worth considering what is meantby the statement that a particular interaction stabilizes ordestabilizes a protein. If the focus is on the effect of asingle charge, the clearest experimental measure of itscontribution to protein stability can be obtained by neu-tralizing it through changes in pH. Unless one is deal-ing with small, designed peptides, however, changes in
pH affect more than one charged group, requiring thatan entire titration curve -be deconvoluted through somecombination of experimental and theoretical techniques.
Site-directed mutagenesis offers another way of neutraliz-ing a charge but the method substitutes a new interactionfor an old one, which introduces additional complexityto the process of separating variables. For example, theeffects on protein stability of pairwise Coulombic inter-actions have been identified through the use of doubleand triple mutant cycles in an important study by Fer-sht and coworkers [3]. Electrostatic interactions amongthree ionizable groups were found to have a net stabi-lizing effect but, nevertheless, the effect of replacing allthree with alanines was an increase in protein stability.That alanines provide a greater net stabilization of thenative state than ionizable groups of course says nothingas to whether the charges are themselves stabilizing ordestabilizing.
The change in the pKa of a group between the nativeand denatured states offers a direct measure of the effectof that group on protein stability. One way of measur-ing pKa's is to monitor proton release as a function ofpH for all the ionizable residues in a protein using two-dimensional NMR [4]. Measurement of the titrationcurves of proteins is another possibility [5] but, as men-tioned above, the pKa's of individual ionizable groups arenot easy to resolve. If the pKa's of all ionizable residuesare known for the native and denatured states of a pro-tein, the denaturation energy of the protein as a functionof pH can be obtained from an equation based on anexpression given by Tanford [6]:
pH
AG~n(pH) =2.3kT J AZ(pH)dpH (1)pH'h
whereAG3en (pH) is the denaturation energy at a givenpH with.respect to that at some reference pH, AZ(pH) isthe difference in net charge between the denatured andnative protein, and pHl/2 is the midpoint of the acid de-naturation"curve. It should be emphasized that Equation1 is an expression for a relative free energy, and does
40 @ Current Biology Ltd ISSN0959-440X
Electrostatic effects on protein stability Yang and Honig 41
not give the total electrostatic free energy of a system.Two proteins may have the same set of pKa's and, con-sequently, the same relative free energies as functions ofpH, but may have different total electrostatic free ener-gies. Thus, knowledge of pKa's is necessary but not suf-ficientfor a full understanding of electrostatic interactionsin proteins.
Experimental observations
Saltbridges(hydrogen-bondedion pairs)A number of laboratories have used site-directed mu-tagenesis or chemical synthesis to study the stabilizingeffects of acidic and basic residues which have beenplaced in locations (such as the i and i + 4 positionson ex-helices)where they are able to form salt bridges[7",8;9..,10;11]. In general, it appears that the engi-neered salt bridges have only marginal effects, contribut-ing '" 0 to - 0.5kcalmol- I to stabilization of the foldedstate. These findings appear to contradict the earlier workof Marqusee and Baldwin [12], who found that lysinesand glutamic acids placed in positions i and i + 4 in analanine-based ex-helixstabilized the helical conformation.The actual stabilization energy was not determined in thatstudy, however, and, based on the small pKa shifts of theresidues involved, the effects were not large.
The factors that account for the small stabilizing effectsof salt bridges have been clearly elucidated in the abovestudies. Firstly,coulombic interactions between chargedresidues on the surface of proteins are largely screenedby the high dielectric solvent. Secondly, there is a freeenergy penalty associated with desolvating both chargeswhen a salt bridge forms. Finally,there is an entropic costassociated with fixing the mobile side chains in a welldefined salt bridge. Indeed, in many cases, the residuesinvolved in the salt bridge are not seen in the crystalstructure, apparently preferring to remain mobile andwell solvated. Nonetheless, if some other factor (suchas hydrophobic interactions between the hydrocarbonside chains of lysine and glutamate and the interveningalanines in a helix) also favors fixingthe side chains in thefavored salt-bridge conformation, the apparent stabilizingeffect of the ion pair can be high. Some combination ofsuch salt-bridge-favoringinteractions is probably respon-sible for the large stabilizing effect of the Asp70-His31ion pair in T4lysozyme [13.] and may have contributedto the effects observed by Marqusee and Baldwin [12]mentioned above.
Total charge effects
Pace et al [14.] have studied the urea denaturation ofRNase A and RNase n at pH 2 to 10. Over this range,the total charge of RNase A varies from 18 to - 2 whilethe denaturation energy varies from 2 to 10kcalmol-I.For RNasen, the total charge varies from 6 to -12, andthe denaturation energy is 3-9 kcalmol-I. These obser-vations, in keeping with earlier studies of Hollecker andCreighton [15], indicate that the magnitude of electro-
static interactions involving charged residues are of thesame order as the denaturation energies of proteins. Itshould be emphasized that these effects can arise onlyfrom the few groups that have anomalous pKa's, as nicelydemonstratedby the recent studyof McNuttet al [16].
BuriedchargesWhereas charges on surfaces may do very little to stabi-lize proteins, buried charges are likely to be extremelydestabilizing unless the protein succeeds in compensat-ing for the loss of aqueous solvation. For example, theactive-site Asp26 in Escherichia coli thioredoxin is buriedin a hydrophobic region and has an anomalous pKa of7.5, suggesting that it destabilizes the native protein by5kcalmol-I [17.]. Similarly,a lysine that replaces Val66of staphylococcal nuclease was found to be buried in thehydrophobic core, to have a pKa < 6.4 and to destabilizethe protein [18.]. In contrast, McGrath et al (M McGrathet al, unpublished data) have replaced Ser214 in trypsinwith a lysine residue which, though buried, retains itscharge asa result of favorable interactions with hydrogen-bonding groups in the vicinity.
Acid denaturation
Hughson et al [19"] havedetected a partiallyunfoldedintermediate in apomyoglobin which exists at pH 4-5. Onthe basis of two-dimensional NMRexperiments, whichwere used to identify slowly and rapidly exchangingamide protons, a model for the intermediatewas pro-posed in which a compact subdomain consisting of he-lices A, G and H retains native-likestructure. The remain-ing helices appear to unfold at the same pH. The par-tial unfolding is likely to be caused by the presence ofhistidines with anomalous pKa's, such as His113, His119and His24, which titrate in this pH range. We have foundthat the protonation of a small number of these residuessignificantlydecreases the stability of the native protein,partly as a result of their burial in the interior and partlybecause of their repulsive interactions with other charges(A-S Yang and B Honig, unpublished data). As thesegroups are located near the interface between the stablesubdomain and the remaining helices, this destabilizingelectrostatic force can be relieved by partial unfolding.
The classical model of Ilnderstrom-Lang assumes thatthe electrostatic free energy of a protein results fromthe net repulsions between charged groups in the na-tive state [6]. Stigter et al [20] have introduced amodel that can account for net charge effects in theunfolded state as well. The recent experimental evi-dence summarized above, however, suggests that, insome cases, the contribution of ionizable amino acidsto protein stability arises from a small number ofresidues with anomalous pKa's rather than from theeffects of net charge. Indeed, the fact that increasingsalt concentration destabilizes apomyoglobin near neu-tral pH, and stabilizes a partially denatured interme-diate at low pH [21], suggests that coulombic inter-actions are attractive in the former case and only repul-sive at low pH.
42 Foldingand binding
Calculating electrostatic properties
pKa'sThe intrinsic pKa of a single ionizable group in a proteinis usually defined as:
. ")'(i)MG~nvpK3jmt =pKa? - I (2)2.3kT
where pKa? is the pKa of the ith group in an isolatedmodel compound and y(i) is + 1 when the group isbasic and - 1 when acidic. AAGfnvis the change in elec-trostatic free energy associated with charging the groupin the protein environment relative to the same process inthe model compound [1,22-]. AAGenvdepends on boththe extent to which the group is desolvated in the proteinand on any compensating interactions with permanentdipoles.
When a protein has more than one titratable group, theproton affinitiesat titrating sites become mutually depen-dent. In this case, p~ can only be determined froma calculated titration curve, which will yield the pH atwhich the group is 50%protonated. When more than oneionizable group is being considered, it is convenient todefine the intrinsic p~ as the pKa that group i wouldhave if all other groups were in their neutral form. ThepKa of group i can now be written in the form:
int ttr 0 ")'(i)MGfnv ttrpKai =pKaj +L\pKaj =pKaj - + L\pKaj2.3kT
(3)
where ApKaF is simply the difference between the intrin-sic pKa and the one obtained from the titration curve.
The titration curve of each ionizable group in a proteincan be obtained from a statistical mechanical averageover the 2N states that arise from N ionizable residues.The average charge, < Pi> of each group is defined bythe expression:
where on(i) = 0 when group i is neutral in state n, andon(i) = 1 when group i is charged. Q is the partitionfunction of the system of 2N states. A reference state ofzero free energy is defined to correspond to all ionizablegroups in their neutral forms. AGfi is the free energy ofthe nth state and is given by:
N
L\Gn =tr6n(i) { ")'(i)2.3kT(pH- pK3jint)+
L 6nG)L\aij}
(5)
lSj<i
where AGiiis the electrostatic interaction energy betweenthe charged forms of groups i and j. Thus, if both groupsi and j are charged in the nth state, this term will accountfor the additional free energy resulting from their interac-tion relativeto the reference state where both are neutral.
(4)
Equation 4 and 5 provide a prescription for calculatingthe titration curves of N ionizable residues. It is onlynecessaty to determine the average protonation states, orthe fractional charges, at each pH of interest. The largenumber of possible states, however, makes this approachimpractical as N reaches several tens of titratable groups.The first attempt to circumvent the problem was intro-duced by Tanford and Roxby [23], who assumed thateach residue could be defined in terms of an averageprotonation state, which was then used to calculate inter-residue interactions. This approximation is generallyvalidbut breaks down when the two groups have similar pKa'sand the interaction between them is large [22-].
Bashford and Karplus [22-] have calculated electrostaticfree energies with the finite difference Poisson-Boltz-mann method (see review by Sharp and Honig [1]) andobtained pKa's "from the statistical mechanical expres-sion. They limited the number of states that had to beconsidered by introducing a reduced site approximationin which residues whose pKa's were far from the pH ofinterest were assumed to be in their appropriate protona-tion states. More recently, Beroza et al [24] used a MonteCarlo approach to deal with the problem of sampling alarge number of possible states. We have developed ahybrid method which exploits the Tanford-Roxby treat-ment for weakly interacting groups and uses the statisticalmechanical expression for strong interactions (AS Yanget al, unpublished data).
Perhaps the greatest uncertainty in such calculationsarises from the uncertainty in the three-dimensionalstructure. Problems can arise ftom: possible errors inthe X-ray coordinates; conformational changes that mayaccompany protonation and deprotonation; uncertaintyin the position of polar hydrogens; and, possible differ-ences between the ctystal and solution conformations.Nevertheless, good agreement with experiment has beenobtained for those proteins that have been studied todate. Calculations are generally within about 1pKa unitfrom experimental values, although larger errors are ob-tained in a number of cases. At this stage, the calculationsprovide an important tool with which to interpret exper-imental results but they have not yet reached the stagewhere they have true predictive value.
Free energies of unfoldingThe contribution of ionizable groups to the electrostaticfree energy of a folded protein can be obtained by a sta-tistical mechanical sum over the 2Npossible protonationstates, thus:
where AGelec(protein) is the average electrostatic freeenergy of the native protein with respect to the neutralreference state.
It should be clear from Equations 4-6 that the ability tocalculate a titration curve of both the native and dena-
Electrostatic effects on protein stability Yang and Honig 43
tured states implies the ability to predict the electrostaticcontributions to denaturation. We have found that thesummation over 2Nstates contained in Equation 6 can beapproximated accurately by a sum over the N ionizablegroups, with the expression:
N
AGe1ec(folded)=2:{(Pi)2.3kT(PH- pK~nt)+i=l
2: I(Pi)lI(pj)IAGij} (7)l~<i
where < Pi> is the average charge on ionizable group i(A-SYang and B Honig, unpublished data). In the dena-tured state, it is generally assumed that the intrinsic pKa'sare those of the individual amino acids, and that screen-ing by high dielectric solvent and mobile ions reducesthe interaction between ionizable groups to zero. Thus:
N
AGe1ec(unfolded) =2: (pD2.3kT(pH - pKa?) (8)i=l
where < Pi'> is the average charge on ionizable groupi of the unfolded protein. Note that the terms < Pi> ,< p{> , AGelec(folded), and AGelec(unfolded) in Equa-tions 7 and 8 are all functions of pH. The evaluationof Equation 7 for the folded state involves the sameterms that must be evaluated in the calculation of titrationcurves and can be carried out quite rapidly. The differ-ence, AGelec (unfolded) - AGelec (folded), is the pH-dependent electrostatic contribution to protein unfold-ing.
Equations 1, 7 and 8 imply that if the titration curves ofboth the native and denatured protein are known, therelative denaturation energy of the protein can be deter-mined as a function of pH. The titration curves of nativeproteins can be determined experimentally, or from cal-culations. Thus, the tools are now in hand to combinetheory and experiment so as to gain a full understandingof pH and salt effects on protein stability.
DipolargroupsThere has been considerable uncertainty for many yearsas to whether hydrogen bonds contribute to protein sta-bility. The most widely held point of view has been thatthey do not, as every group that forms an intramolecularhydrogen bond in the native state will form a hydrogenbond with water in the denatured state. The accumulat-ing evidence (see above) that (X-helicesare marginallystable in water, however, suggests that peptide NH...COhydrogen bonds do in fact contribute to protein stabil-ity. Scholtz et al [25-] have found that each hydrogenbond makes an enthalpic contribution of -1 kcalmol-I,which may compensate in pan for the loss of conforma-tional entropy associated with fixing the peptide back-bone into an (X-helix.
The location of hydrogen bonds in a putative preformed(X-helixis very different from their location in a finalthree-dimensional structure. The process of tertiary-struc-
ture formation requires that peptide dipoles, as well asmany dipolar groups in amino acid side chains, be re-moved from proximity to water and buried in the pro-tein interior. We have recently found that the free en-ergy penalty associated with this process is quite large;indeed, it appears to be roughly equivalent in magni-tude (although opposite in sign) to the hydrophobic freeenergy resulting from tertiary interactions between non-polar side chains (A-SYang, K Sharp and B Honig, un-published data). The existence of these two 'compen-sating' interactions may account in pan for the fact that,despite large individual contributions to the free energybalance of proteins (conformational entropy, hydropho-bic effect, etc.), proteins of very different size and averagehydrophobicities are all only marginally stable [26].
Conclusions
A considerable body of experimental evidence now in-dicates that electrostatic interactions involving ionizableamino acids make only a small contribution to the totalfree energy balance of protein stability. Nevertheless, themagnitude of the interactions is of the same order asthe denaturation energies of proteins and, consequently,charged groups can make important contributions toprotein stability.Moreover, electrostatic interactions, andhence protein stabilities, are relatively easy to controlthrough changes in pH and salt concentration.
Perhaps the most surprising insight to emerge recentlyis that most ionizable amino acids in proteins have un-shifted pKa's (relative to the isolated amino acid) andhence make essentially no contribution to protein sta-bility. The pH and salt effects that have been observedarise from a relatively small number of amino acidswith abnormal pKa's rather than from net charge effectswhich are predicted from the classical Understfom-Langmodel. Abnormal pKa's can arise from salt bridges be-tween groups whose locations have been fixed in part bynon-electrostatic interactions, or from individual residuesburied in a non-polar environment.
Recent theoretical advances now make it possible to cal-culate pKa's in proteins and hence to account for pH andsalt effects on protein stability. Although the reliabilityof the calculations is reduced by uncertainties in three-dimensional structure and in the potential functions thatare used, they are accurate enough to provide an im-portant tool in the interpretation of experimental results.The existence of marginallystable elements of secondarystructure suggests that peptide hydrogen bonds make asignificant contribution to protein stability. Theoreticalcalculations, however, indicate that the burial in the pro-tein interior of these groups and polar groups on aminoacid side chains has a large destabilizing effect.
Acknowledgements
We thank M Gunner and K Sharp for stimulating discussions. Thiswork was supported by Nlli grant GM30518.
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44 Foldingand binding
References and recommended reading
Papers of particular interest, published within the annual period of reoview, have been highlighted as:. ofspecialinterest.. ofoutstandinginterest
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4. KOIIDA0, SAWADAT, lNAGAKIF: Characterization of pH Titra-tion Shifts for All the Nonlabile Proton Resonances in a
Protein by Two-dimensional NMR: the Case of Mouse Epi-dermal Growth Factor. Biochemistry 1991, 30:4896-4900.
5. BARKERPO, MAUK MR, MAUK AG: Proton Titration Curveof Yeast Iso-1-ferricytochrome (: Electrostatic and Con-formational Effects of Point Mutations. Biochemistry 1991,30:2377-2383.
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7. DAO-PIN S, SAUERU, NICHOLSONH, MATTHEWSBW: Contri-.. bution of Engineered Surface Salt Bridges to the Stability
of T4 Lysozyme Determined by Directed Mutagenesis. Bio-chemistry 1991, 30:7142-7153.
Several mutants of T4 lysozyme are designed to test the free energycontributions of the engineered salt bridges at different locations inthe protein. The salt bridges have little effect on stability, which is con-sistent with the idea that they are not located in a fixed conformation.The crystal structures of the mutant proteins are consistent with thisinterpretation.
8. BRADLEYEK, THOMASON]F, COHENFE, KOSENPA, KUNJ'ZID:Studies of Synthetic Helical Peptides Using Circular Dichro-ism and Nuclear Magnetic Resonance. ] Mol BioI 1990,215:607-622.
9. Sm 0, BYCROfTM, FERSHTAR: Surface Electrostatic Inter-.. actions Contribute Uttle to Stability of Barnase. ] Mol BioI
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Site.directed mutagenesis is used to engineer an ion pair (Glu28...Lys32) on the surface of barnase. The side chains are separated by oneturn of an (X.helix such that they are able to form a salt bridge. A doublemutant cycle is used to measure the electrostatic interaction betweenthese groups, which is found to be only 0.2 kcal mol- I.
10. SERRANOL, HOROVITZA, AVRON B, BYCROfT M, FERSHTAR:Estimating the Contribution of Engineered Surface Elec-trostatic Interactions to Protein Stability by Using Double-mutant Cycles. Biochemistry 1990, 29:9343-9352.
11. MERUTKAG, SHALONGOW, STELLWAGENE: A Model Peptidewith Enhanced Helicity. Biochemistry 1991, 30:424s-4248.
12. MARQUSEES, BAlDWINRL: Helix Stabilization by Glu - ...Lys+Salt Bridges in Short Peptides of de novo Design. Proc NatlAcad Sci USA 1987, 84:8898-8902.
13. ANDERSONDE, BECKTELW], DAHLQUISTFW: pH-induced De-naturation of Proteins: a Single Salt Bridge Contributes.
3-5 kcal/mol to the Free energy of Folding of T4-lysozyme.Biochemistry 1990, 29:2403-2408.
The free energy contribution of a salt bridge (Asp70...His31) in T4lysozyme is studied using both NMR and heat.denaturation methods.The results indicate that the salt bridge has an unusually large electro-static effect, contributing 3-5 kcal mol-1 to the stability of the protein.
14. PACE CN, LAURENTSDV, THOMSON]A: pH Dependence of. the Urea and Guanidine Hydrochloride Denaturation ofRibonuclease A and Ribonuclease Tl. Biochemistry 1990,29:2564-2572.
The denaturation energies of ribonuclease A and T1 as functions ofpH are reported. The proteins are most stable at pHs which are close,but not identical, to the isoelectric points. The pH dependence suggeststhat the electrostatic contributions to the stability of these ribonucleasesamount to only a few kilocalories per mole.
15. HOLLECKERM, CREIGHTONTE: Effect on Protein Stability ofReversing the Charge on Amino Groups. Biochim BiophysActa 1982, 701:395-404.
16. McNUTTM, MULLINSLS,RAUSHELFM, PACECN: Contributionof Histidine Residues to the Conformational Stability of Ri-bonuclease Tl and Mutant Glu-58-+AIa. Biochemistry 1990,29:7572-7576.
17. LANGSETMOK, FUCHS]A, WOODWARDC, SHARPKA: Linkage of. lbioredoxin Stabilityto Titration of IonizableGroups with
Perturbed pKa. Biochemistry 1991, 30:7609-7614.The pKa of a buried aspartic acid in thioredoxin is determined. A thor-ough theoretical analysis generates possible interpretations of the un.usual properties of this group.
18. STITESWE, GIT11SAG, LATTMANE, SHORTLE0: In a Staphylo-. coccal Nuclease Mutant the Side-chain of a Lysine Replac-
ing Valine 66 is Fully Buried in the Hydrophobic Core. ]Mol BioI 1991, 221:7-14.
A buried lysine in a hydrophobic environment is found to have a pKa< 6.4 and to significantlydestabilize the protein. The paper containsa thoughtful analysis of the free energy changes that accompany themutation.
19. HUGHSON FM, WRIGHT PE, BAlDWIN RL: StructUral Charac-.. terization of a Partly Folded ApomyoglobinIntermediate.
Science 1990, 249:1544-1548.Proton-exchange NMR is used to characterize the add-denatured inter-mediate of apomyoglobin at pH 4.2. The partly unfolded intermediateappears to consist of a subdomain involving folded helices A, G and H,whereas helices B and E appear to remain unfolded.
20. Sl1GTER0, AlONSO DOV, DILLKA: Protein Stability: Electro-static and Compact Denatured States. Proc Natl Acad SciUSA 1991, 88:4176-4180.
21. Goro Y, FINKAI.:Phase Diagram for Acidic ConformationalStates of Apomyoglobin. ] Mol BioI 1990, 214:803-805.
22. BASHFORD0, KARPLUSM: pKa's of Ionizable Groups in Pro- .. teins: Atomic Detail from a Continuum Electrostatic Model.Biochemistry 1990, 29:10219-10225.
The finite difference Poisson-Boltzmann method is used to calculate
the pKas of the ionizable groups in lysozyme. An important innovation,in addition to the introduction of the theoretical methodology, is theuse of a reduced site approximation to limit the sum over 2N statesrequired if all interactions are considered. Most of the calculated pKasare consistent with experimental data, although a number of noticeabledeviations are encountered.
23. TANFORD C, ROXBY R: Interpretation of Protein Titra-tion Curves. Application to Lysozyme. Biochemistry 1972,11:2192-2198.
Electrostaticeffectson proteinstabilityYang and Honig 4S
24. BEROZA P, F'REDKIN DR, OKAMURA MY, FEHER G: Protonation of
Interacting Residues in a Protein by a Monte Carlo Method:Application to Lysozyme and the Photosynthetic ReactionCenter of Rbodobaaer spbaerotdes. Pro<; Nat/ Acad Set USA1991, 88:5804-5808.
25. SCHOLTZJM, MARQUSEES, BAlDWIN R, YORK EJ, STEWARTJM,. SANToROM, BoIJ!NOW: Calorimetric Detennination of theEnthalpy Change for the Alpha-helix to Coil Transition ofan Alanine Peptide in Water. Proc Nat/ Acad Set USA 1991,88:2854-2858.
A calorimetric method is used to estimate the enthalpy of (X.helix torandom.coil transition. A range of Mi [0.9-1.3 kcal (mol residue)-i] is
determined for the unfolding of the (X.helix. The enthalpy of unfoldingresults largely from the disruption of peptide hydrogen bonds.
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A.S Yang and B Honig, Deparanent of Biochemistry and Molecular Bio-physics, Columbia University, 630 West 168 SI, New- York, New- York10032, USA
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