Effective renaturation of denatured and reduced immunoglobulin G in vitro without assistance of chaperone

IgG is an oligomeric protein that consists of two heavy andtwo light chains. To form the oligomer, a highly concentratedprotein would be required on renaturation. On the other hand,refolding of proteins at high concentration often led to aggregation.Therefore, denatured and reduced oligomeric protein scarcelyrefolded to the native structure. As was expected, the foldingyield of the denatured and reduced IgG was below 5% under thecondition employed in rapid dilution. The low folding yieldwas elucidated to be due to assembly or aggregation. Using arenaturation method previously developed to depress aggregationeffectively by means of slow dialysis, the refolding yield ofthe denatured and reduced IgG at above 1 mg/ml was above 70%.Most of the refolded IgG was identical with the intact materialbased on analyses by affinity chromatography and SDS-PAGE.     

Effect of additives on the renaturation of reduced lysozyme in the presence of 4 M urea

Reduced lysozyme was renatured by sulfhydryl-disuffide interchangereactions at pH 8.0 in the presence of 4 M urea, with or withoutadditives at 40°C. In the absence of additives, the finalfolding yield of reduced lysozyme was 40%. In the presence ofsarcosine, glycerol, ammonium sulfate, N-acetyl glucosamineand glucose, its folding yields increased in all cases. In particular,yields increased up to 90% in the presence of 4 M sarcosine.On the other hand, the melting temperatures of lysozyme withor without additives in 0.02 M citrate buffer (pH 6.0) wereevaluated using differential scanning calorimetry. In the absenceof additive, the melting temperature of lysozyme was 73.8°C.In the presence of additives, all melting temperatures werehigher than that of lysozyme in the absence of additives. Moreover,there was a good correlation on addition of additives betweenan increase in the folding yield of reduced lysozyme with 4M urea and an increase in the melting temperature without 4M urea. Therefore, we conclude that additives, which stabilizenative lysozyme, are effective at increasing the folding yieldof reduced lysozyme in 4 M urea.     

The role of net charge on the renaturation of reduced lysozyme by the sulfhydryl-disulfide interchange reaction

Reduced and acetylated lysozymes are basic proteins. When theiramino groups were variously acetylated and then renatured bysulfhydryl-disulfide (SH-SS) interchange reaction at pH 8.0,the final folding yield decreased as the number of positivecharges decreased. The final folding yield of native and Ac1lysozyme, with one positive charge eliminated, was less sensitiveto increasing protein concentration than that of Ac2 lysozyme,where two positive charges had been eliminated. The final foldingyield of reduced Ac2 lysozyme increased in the presence of 1M urea, which reduced the aggregation of unfolded lysozyme.Thus, the aggregation of unfolded lysozymes, which leads toa decrease in the final folding yield, was found to be heavilydependent on their net charges. Moreover, the final foldingyield of reduced lysozyme was shown to be increased by use ofcystamine as an oxidizing reagent in comparison with 2-hydroxyethyldisulfide or dithiodiglycolic acid. This may support the ideathat the final folding yield is influenced by electrostaticinteraction between unfolded lysozymes in the early stage ofrenaturation. In contrast, the concentration dependency of thefinal folding yield of Ac1 lysozyme was different from thoseof carboxymethylated His15 and Asp106 lysozymes whose positivenet charges were similar to that of Ac1 lysozyme. On the basisof the observations, it is suggested that the formation of theaggregates in the renaturation process might also be affectedby the structure of the unfolded state of lysozyme in solution.     

Point mutation of alanine (31) to valine prohibits the folding of reduced lysozyme by sulfhydryl--disulfide interchange

In the preceding paper in this issue, we described the overproduction of one mutant chicken lysozyme in Escherichia coil.Since this lysozyme contained two amino acid substitutions (Ala³¹ValandAsn¹⁰⁶Ser)in addition to an extra methionine residue at theNH₂-terminus the substituted amino acid residues were convertedback to the original ones by means of oligonucleotide-directedsite-specific mutagenesis and in vitro recombination. Thus fourkinds of chicken lysozyme [Met^–1 Val³¹Ser¹⁰⁶-, Met^–1Ser¹⁰⁶-,Met^–1 Val³¹-and Met^–1 (wild type)] wereexpressed in E. coli. From the results of folding experimentsof the reduced lysozymes by sulfhydryl-disulfide interchangeat pH 8.0 and 38°C, follow ed by the specific activity measurementsof the folded en zymes, the following conclusions can be drawn:(i) an extra methionine residue at the NH₂-terminus reducesthe folding rate but does not affect the lysozyme activity ofthe folded enzyme; (ii) the substitution of Asn¹⁰⁶ by Ser decreasesthe activity to 58% of that of intact native lysozyme withoutchanging the folding rate; and (iii) the substitution of Ala³¹Val prohibits the correct folding of lysozyme. Since the wildtype enzyme (Met^–1-lysozyme) was activated in vitro withoutloss of specific activity, the systems described in this study(mutagenesis, overproduction, purification and folding of inactivemutant lysozymes) may be useful in the study of folding pathways,expression of biological activity and stability of lysozyme.     

Stabilization of lysozyme by the introduction of Gly-Pro sequence

Three mutant lysozymes where the Asp¹⁰¹ – Gly¹⁰² sequenceof lysozyme was converted to Asp¹⁰¹–Pro¹⁰², Gly¹⁰¹–Pro102and Pro¹⁰¹–Gly¹⁰² were prepared to investigate the effectof proline residues on the stabilization of proteins. The freeenergy changes of lysozymes for the unfolding in aqueous solutionat pH 5.5 and 35°C were 10.0, 10.1, 11.0 and 7.7 kcal/molfor wild type, Asp¹⁰¹Pro¹⁰², Gly¹⁰¹Pro¹⁰² and Pro¹⁰¹Gly¹⁰² lysozymerespectively. When the energy level in the unfolded state ofwild type lysozyme was fixed at a standard level, the energylevels in the folded state of Asp¹⁰¹Pro¹⁰² and Pro¹⁰¹Gly¹⁰²lysozymes were found to be higher than that of wild type lysozymeon the basis of G_D(H₂O) and entropy losses of their polypeptidechains in the unfolded state. The presence of some strain inthe folded state of these lysozymes was supported by both thecalculation of conformational energy for a trans-L-prolyl residue[Schimmel, P.R. and Flory,P.J. (1968) J. Mol. Biol, 34, 105–120] and the analysis of structures of energy-minimizedmutant lysozymes. Therefore, it is concluded that the formationof the Gly-Pro sequence is effective in avoiding possible strainin the folded state of a protein caused by the introductionof proline residue(s).     

Stabilization of lysozyme against irreversible inactivation by alterations of the Asp-Gly sequences

Site-directed mutagenesis was performed at Asp-Gly (48–49,66–67, 101–102) and Asn-Gly (103–104) sequencesof hen egg-white lysozyme to protect the enzyme against irreversiblethermoinactivation. Because the lysozyme inactivation was causedby the accumulation of multiple chemical reactions, includingthe isomerization of the Asp-Gly sequence and the deamidationof Asn [Tomizawa et al.(1994) Biochemistry, 33, 13032–13037],the suppression of these reactions by the substitution of Glyto Ala, or the introduction of a sequence of human-type lysozyme,was attempted and the mutants (where each or all labile sequenceswere replaced) were prepared. The substitution resulted in thereversible destabilization from 1 to 2 kcal/mol per substitution.The destabilization was caused by the introduction of ß-carbonto the constrained position that had conformational angles withinthe allowed range for the Gly residue. Despite the decreasein the reversible conformational stability, the mutants hadmore resistance to irreversible inactivation at pH 4 and 100°C.In particular, the rate of irreversible inactivation of themutant, which was replaced at four chemically labile sequences,was the latest and corresponded to 18 kcal/mol of the reversibleconformational stability. Therefore, replacement of the chemicallylabile sequence was found to be more effective at protectingenzymes against irreversible thermoinactivation than at strengtheningreversible conformational stability.     

Engineering of human lysozyme as a polyelectrolyte by the alteration of molecular surface charge

The surface positive charges of human lysozyme were either increasedor decreased to alter the electrostatic interaction betweenenzyme and substrate in the lytic action of human lysozyme usingsite-directed mutagenesis. The amino acid substitutions accompanyingeither the addition or the removal of two units of positivecharge have shifted the optimal ionic strength (NaCl concentrationin 10 mM Mes buffer, pH 6.2) for the lysis of Micrococcus lysodeikticuscell from 0.04 M to 0.1 M and from 0.04 M to 0.02 M respectively.In addition to the change in ionic strength–activity profile,the pH–activity profile and the effect of a polycationicelectrolyte, poly-L-Lys-HCl, on the lytic activity were significantlychanged. Owing to the shifts in both ionic strength profilesand pH profiles the Arg⁷⁴/Arg¹²⁶ mutant has become a bettercatalyst than wild-type enzyme under the conditions of highionic strength and high pH, and the Gln⁴¹/Ser¹⁰¹ mutant hasbecome a better catalyst under the conditions of low ionic strengthand low pH.     

Enhancement of protein stability by the combination of point mutations in T4 lysozyme is additive

A number of mutations have been shown previously to stabilizeT4 lysozyme. By combining up to seven such mutations in thesame protein, the melting temperature was incrementally increasedby up to 83°C at pH 5.4 (G = 3.6 kcal/mol). This shows thatit is possible to engineer a protein of enhanced thermostabilityby combining a series of rationally designed point mutations.It is also shown that this stabilization is achieved with onlyminor, localized changes in the structure of the protein. Thisis consistent with the observation that the change in stabilityof each of the multiple mutants is, in each case, additive,i.e. equal to the sum of the stability changes associated withthe constituent single mutants. One of the seven substitutions,Asn116 Asp, changes a residue that participates in substratebinding; not surprisingly, it causes a significant loss in activity.Ignoring this mutation, there is a gradual reduction in activityas successively more mutations are combined.     

Association and dissociation kinetics of bobwhite quail lysozyme with monoclonal antibody HyHEL-5

The anti-hen egg lysozyme monoclonal antibody HyHEL-5 and itscomplexes with various species-variant and mutant lysozymeshave been the subject of considerable experimental and theoreticalinvestigation. The affinity of HyHEL-5 for bobwhite quail lysozyme(BWQL) is over 1000-fold lower than its affinity for the originalantigen, hen egg lysozyme (HEL). This difference is believedto arise almost entirely from the replacement in BWQL of thestructural and energetic epitope residue Arg68 by lysine. Inthis study, the association and dissociation kinetics of BWQLwith HyHEL-5 were investigated under a variety of conditionsand compared with previous results for HEL. HyHEL-5–BWQLassociation follows a bimolecular mechanism and the dissociationof the antibody–antigen complex is a first-order process.Changes in ionic strength (from 27 to 500 mM) and pH (from 6.0to 10.0) produced about a 2-fold change in the association anddissociation rates. The effect of viscosity modifiers on theassociation reaction was also studied. The large differencein the HEL and BWQL affinities for HyHEL-5 is essentially dueto differences in the dissociation rate constant.     

Use of site-directed mutagenesis to obtain isomorphous heavy-atom derivatives for protein crystallography: cysteine-containing mutants of phage T4 lysozyme

Five different cysteine-containing mutants of the lysozyme frombacteriopbage T4 were used to explore the feasibility of usingsite-directed mutagenesis to generate isomorphous heavy-atomderivatives for protein crystallography. Cysteines 54 and 97,present in wild-type lysozyme, can be readily reacted with mercuricion to produce an excellent isomorphous heavy-atom derivative.Mutants with an additional cysteine at position 86,146,153 or157, or with Cys 97 replaced by Val, were engineered by site-directedmutagenesis. The mutant lysozyme Thr 157 - Cys reacts with mercuricchloride to give an excellent new derivatve although Cys 157is only -60% substituted with the heavy atom. The cysteine atposition 146 is largely buried but reacts readily with mercuricchloride. In this case the isomorphism is poor and the resultantderivative is of marginal quality. Cys 153 reacts rapidly withmercuric ion but the derivative crystals do not diffract. Themutant Pro 86 - Cys does not yield a particularly good heavy-atomderivative. This is due in part to a loss of isomorphism associatedwith the mutation. In addition, Cys 86 shows very little reactivitytowards mercurials even though it is fully exposed to solvent.The mutation Cys 97 Val was used to explore the possibilityof creating an independent derivative by deleting a heavy-atomsite already present in wild-type lysozyme. In all cases thatwere tested, the quality of the heavy-atom derivative was improvedby using as an isomorphous pair mercury-substituted mutant versusnon-substituted mutant rather than mercury-substituted mutantversus (non-substituted) wild-type lysozyme. Unexpectedly, thecysteines that are most exposed to solvent and most mobile areleast reactive toward mercuric chloride. The cysteines thatprovide the best heavy-atom sites are those that are locatedin surface crevices and are only partly exposed to solvent.     

Biosynthetic incorporation of 7-azatryptophan into the phage lambda lysozyme: estimation of tryptophan accessibility, effect on enzymatic activity and protein stability

The phage lambda lysozyme (L) contains four tryptophans. Thesehave been efficiently replaced by 7-azatryptophan (7aW) throughbiosynthetic incorporation into the overexpressed protein. Comparativeanalysis of the effect of temperature or pH on the fluorescenceof the wild-type L and 7aWs-containing protein (aL) shows thatthe stability of the protein is only mildly reduced by 7aW incorporationabove pH 5 but that it is strongly decreased below pH 4 on protonationof inaccessible 7aWs. The aL fluorescence depends on pH as aconsequence of its effect on the denaturation equilibrium, onthe state of protonation of accessible 7aWs in the native stateand of all 7aWs in the denatured state. The pH dependence ofthe fluorescenceis used to estimate the number of accessibletryptophans in the protein. The result agrees with that derivedfrom tryptophan NH exchange measurements by ¹H-NMR. The acidlimb of the activity-pH profile is characterized by a sharpdrop that might arise from a cooperative acidinduced denaturation.The difference in acid stability of aL versus L is used to ruleout this acid denaturation hypothesis as tryptophan replacementdoes not affect the lytic activity on chloroform-sensitizedEscherichia coli cells or its pH profile.     

Expression of a synthetic gene encoding canine milk lysozyme in Escherichia coli and characterization of the expressed protein

A high-expression plasmid of the canine milk lysozyme, whichbelongs to the family of calcium-binding lysozymes, was constructedin order to study its physico-chemical properties. Because thecDNA sequence of the protein has not yet been determined, a400 base-pair gene encoding canine milk lysozyme was first designedon the basis of the known amino acid sequence. The gene wasconstructed by an enzymatic assembly of 21 chemically synthesizedoligonucleotides and inserted into an Escherichia coli expressionvector by stepwise ligation. The expression plasmid thus constructedwas transformed into BL21(DE3)/pLysS cells. The gene productaccumulated as inclusion bodies in an insoluble fraction. Recombinantcanine milk lysozyme was obtained by purification and refoldingof the product and showed the same characteristics in termsof bacteriolytic activity and far- and near-UV circular dichroismspectra as the authentic protein. The NMR spectra of refoldedlysozyme were also characteristic of a native globular protein.It was concluded that recombinant canine milk lysozyme was foldedinto the correct native structure. Moreover, the thermal unfoldingprofiles of the refolded recombinant lysozyme showed a stableequilibrium intermediate, indicating that the molten globulestate of this protein was extraordinarily stable. This expressionsystem of canine milk lysozyme will enable biophysical and structuralstudies of this protein to be extended.     

Highly controlled carbodiimide reaction for the modification of lysozyme. Modification of Leu129 or Asp119

In the cross-linking reaction of lysozyme between Leu¹²⁹ (-COO^–)and Lys¹³ (-NH₃⁺ using imidazole and 1-ethyl-3-[3-(dimethylamino)propyl]carbodiimidehydrochloride (EDC), a side reaction of the peptide bond inversionfrom to ß between A and Gly¹⁰² was greatly reducedby addition of ß-(1,4)-linked trimer of N-acetyl-D-glucosamine[(NAG)₃] When methylamine or 2-hydroxyethylamine was furtheradded, the extent of the cross-link formation was decreasedand the derivative where the -carboxyl group of Leu¹²⁹ was modifiedwith the amine was newly obtained. On the other hand, when ammoniawas added, the ß-carboxyl group of Asp¹¹⁹ insteadof the -carboxyl group was mainly amidated. From these results,the presence of a salt bridge between Asp¹¹⁹ and Arg¹²⁵ besidesthat between Lys¹³ and Leu¹²⁹ is proposed. Enzymatic activitiesof the derivatives prepared here indicated that the modificationof the -carboxyl group reduced the activity to {small tilde}90% of that of native lysozyme. Des-Leu¹²⁹ lysozyme, which lacksLeu¹²⁹ also showed {small tilde} 90% of the activity of nativelysozyme. Therefore, the salt bridge between Lys¹³ and Leu¹²⁹may play some role in maintaining the active conformation oflysozyine.     

Overexpression of the phage lambda lysozyme cloned in Escherichia coli: use of a degenerative mixture of synthetic ribosome binding sites and increase of the protein stability in vivo

The R gene of the phage lambda coding for a lysozyme expressedat the end of an infection cycle in Escherichia coli has beencloned in a series of vector plasmids. Two methods for improvingthe efficiency of translation have been tested. First, the useof a bicistronic construction in which the ribosome bindingsite (RBS) of the first cistron is that of a highly expressedgene or the use of a degenerate mixture of synthetic oligonucleotidesfor the optimization of a RBS. The second strategy is more efficient:the analysis of a number of clones reveals that the LaL expressionlevels are increased by a factor between 3 and 6 times comparedwith the clone using the natural RBS. The expression levelsare described by an approximately Gaussian histogram. The translationpromoter that was found to afford the best expression (P_L) isunder the control of a thermolabile repressor. Under the expressionconditions, the protein is partially proteolysed. The proteolysisis significantly decreased by adding salt to the growth medium.After optimization, an increase in expression by a factor of40 is obtained compared with the initial conditions. An efficientpurification protocol is described.     

Contribution of amino acid substitutions at two different interior positions to the conformational stability of human lysozyme

To elucidate correlative relationships between structural changeand thermodynamic stability in proteins, a series of mutanthuman lysozymes modified at two buried positions (Ile56 andIle59) were examined. Their thermodynamic parameters of denaturationand crystal structures were studied by calorimetry and X-raycrystallography. The mutants at positions 56 and 59 exhibiteddifferent responses to a series of amino acid substitutions.The changes in stability due to substitutions showed a linearcorrelation with changes in hydrophobicity of substituted residues,having different slopes at each mutation site. However, thestability of each mutant was found to be represented by a uniqueequation involving physical properties calculated from mutantstructures. By fitting present and previous stability data formutant human lysozymes substituted at various positions to theequation, the magnitudes of the hydrophobicity of a carbon atomand the hydrophobicity of nitrogen and neutral oxygen atomswere found to be 0.178 and –0.013 kJ/mol.Ų, respectively.It was also found that the contribution of a hydrogen bond witha length of 3.0 Å to protein stability was 5.1 kJ/moland the entropy loss of newly introduction of a water moleculeswas 7.8 kJ/mol.     

An improved linker for single-chain Fv with reduced aggregation and enhanced proteolytic stability

The effects of linker length on binding affinity and degreeof aggregation have been examined in the antifluorescein 4-4-20and anticarcinoma CC49 single-chain Fvs. Longer linkers in theantifluorescein sFvs have higher affinities for fluoresceinand aggregate less. A proteolytically susceptible site betweenLys8 and Ser9, in the previously reported 212 linker has beenidentified. A new linker sequence, 218 (GSTSGSGKPGSGEGSTKG)was designed in which a praline was placed at the C-terminalside of the proteolytic clip site in the 212 linker. The CC49sFv containing the 218 linker showed reduced aggregation andwas found to be more stable to proteolysis in vitro, when comparedto the CC49/212 sFv. The CC49 sFv with the longer 218 linkerhad higher affinity than CC49/212 sFv. An aggregated CC49/212sFv sample had higher affinity than CC49/218 sFv. The CC49/218and CC49/212 sFvs had similar blood clearances in mice, whilethe aggregated CC49/212 sFv remained in circulation significantlylonger. In mice bearing LS-174T human colon carcinoma xenografts,the CC49/218 sFv showed higher tumor uptake than the CC49/212sFv and lower tumor uptake than the aggregated CC49/212 sFv.The higher tumor uptake of the CC49/218 is most likely a resultof its higher resistance to proteolysis. The higher affinityand higher tumor uptake of the aggregated CC49/212 sFv are mostlikely due to the repetitive nature of the TAG-72 antigen andthe higher avidity of multivalent aggregates. When the sFvswere radiolabeled with a lutetium-chelate the CC49/218 sFv showeda lower accumulation in the liver and spleen compared to theaggregated CC49/212 sFv.     

Analysis of disuiphide bridge function in recombinant bovine prolactin using site-specific mutagenesis and renaturation under mild alkaline conditions: a crucial role for the central disuiphide bridge in the mitogenic activity of the hormone

We have previously described a method for isolating Escherichiacoli-produced methionyl bovine prolactin (Met-bPRL) and itsrenaturation using thioredoxin. This report describes an alternativerenaturation procedure in which extracted Met-bPRL is incubatedin air at pH 10 and 20°C. Within 1 h of such treatment essentiallyall of the reduced Met-bPRL was converted to the oxidized form;this was accompanied by an increase to full mitogenic activityin the Nb2 cell bioassay. It was also found that, to minimizecontamination by high mol. wt Met-bPRL derivatives, it is essentialto have a reducing agent (dithiothreitol) present during disruptionof the bacteria and to extract the protein at neutral pH. Thecontribution of each of the three disuiphide bridges in bPRLto its bioactivity was studied with Met-bPRL variants, preparedvia site-specific mutagenesis, in which cysteines were replacedby serines to prevent disulphide bond formation. Variants lackingthe C4–C11 bridge, the C191–C199 bridge or boththese terminal bridges were as mitogenic as authentic bPRL.(Variants lacking the C191–C199 bridge had markedly increasedsolubility in the presence of deoxycholate.) In contrast, variantslacking the C58–C174 bridge had greatly reduced bioactivity,indicating that integrity of the large disulphide loop is crucialto the hormone's mitogenic activity.     

Construction of a plasmid vector for the regulatable high level expression of eukaryotic genes in Escherichia coli: an application to overproduction of chicken lysozyme

A novel expression vector pKPl500 for synthesizing unfused proteinin Escherichia coli was constructed. pKP1500 perserves the tacpromoter, the lacZ SD sequence, unique restriction sites (EcoRI,SmaI, BamHI, SalI, PstI and HindIII) and the rrnB terminatorsof pKK223-3, but the replication origin is replaced with thatof pUC9. Construction of this plasmid is based upon the observationthat the copy number control of pUC9 is temperature dependent.At 28°C, the copy number of pKP1500 is less than 25 perchromosome, approximately the same copy number as that of pKK223-3,which contains the replication origin of pBR322, whereas at42°C, the copy number increases about 10 times and reachesup to 230 copies per chromosome. The main advantage of thissystem is that the temperature-dependent copy control and regulatableexpression of the tac promoter make cells car rying pKPl500derivatives stable against selective pressure by detrimentaloverproduction of foreign proteins at a low temperature andpermits high expression of cloned DNAs at a high temperature.When chicken lysozyme cDNA carrying the initiation codon (ATG)immediately upstream from the Lys¹ codon was inserted downstreamfrom the tac promoter and the SD sequence, the pKP1500 derivativeproduced lysozyme at about 25% of the total cellular proteins.This value is more than 10 times higher than that obtained withthe pKK223-3 derivative carrying the same lysozyine cDNA. Bycomparison, the expression of eukaryotic genes from the tacpromoter reported by others has usually been less than a few% of the total cellular protein. pKPl500 would therefore beuseful for the high level production of unfused proteins fromeukaryotic cDNAs in E. coli.     

Engineering aggregation-resistant proteins by directed evolution

A method was recently described for selecting aggregation-resistant antibody domains. A repertoire of domains displayed on filamentous bacteriophage were heated/cooled and selected for binding to the affinity ligand protein A specific for the folded domains. Here we describe a generalization of the method based on the selection for retained phage infectivity and for the binding of an appended sequence tag, and applicable to any protein displayable in multivalent form on phage.     

Extrapolation to water of kinetic and equilibrium data for the unfolding of barnase in urea solutions

Assumptions about the dependence of protein unfolding on theconcentration of urea have been examined by an extensive surveyof the equilibrium unfolding of barnase and many of its mutantsmeasured by urea denaturation and differential scanning calorimetry.The free energy of equilibrium unfolding and the activationenergy for the kinetics of unfolding of proteins are generallyassumed to change linearly with [urea]. A slight downward curvatureis detected, however, in plots of highly precise measurementsof logjtu versus [urea] (where k_u is the observed rate constantfor the unfolding of barnase). The data fit the equation logkk_u= logk_u^H₂O* + mk_u^*.[urea] – 0.014[urea]², where mk_u^*is a variable which depends on the mutation. The constant 0.014 was measured directly on four destabilized mutants and wildtype, and was also determined from a global analysis of data from>60 mutants of barnase. Any equivalent deviations from linearityin the equilibrium unfolding are small and in the same region,as determined from measurements on 166 mutants. The free energyof unfolding of barnase, G_U–F, appears significantly largerby 1.6 kcal mol^–1 when measured by calorimetry than whendetermined by urea denaturation. However, the changes in G_U–Fon mutation, G_U–F, determined by calorimetry and by ureadenaturation are identical. We show analytically how, hi general,the curvature in plots of activation or equilibrium energiesagainst [denaturant] should not affect the changes of thesevalues on mutation provided measurements are made over the sameconcentration ranges of denaturant and the curvature is independentof mutation.