Free energy simulations of the HyHEL-10/HEL antibody-antigen complex

Free energy simulations are reported for the N31^L-D mutation,both in the HyHEL-10-HEL antibody-lysozyme complex and in theunliganded antibody, using the thermo-dynamic-cycle perturbationmethod. The present study suggests that the mutation would changethe free energy of binding of the complex by –5.6 kcal/mol(unrestrained free energy simulations), by –0.5 kcal/mol(free energy simulations with a restrained backbone) and by1.8 kcal/ mol (Poisson-Boltzmann calculations, which also usea restrained geometry model). A detailed structural analysishelps in estimating the contributions from various residuesand regions of the system. Enhanced recognition of HEL by themutant HyHEL-10 would arise from the combination of thermodynamicallymore favorable conformational changes of the CDR loops uponassociation and subsequent charge pairing with Lys96 in theantigen.     

Contribution of a proline residue and a salt bridge to the stability of a type I reverse turn in chymotrypsin inhibitor-2

The contributions of the components of a type I reverse turnto the stability of chymotrypsin inhibitor-2 (Lys43-Pro44-Gly45)have been determined by protein engineering methods. A double-mutantcycle was used to determine the interaction between Lys43 andGlu45 by replacing them with alanine. We also mutated Pro44,which gives the geometry of the turn, to alanine and analysedthe stability of the resulting mutants compared with wild-typechymotrypsin inhibitor-2, using equilibrium denaturation inducedby guanldinium chloride. There are decreases in stability (inkcal/mol) of 0.64 = 0.06 for Lys43 - Ala, 0.57 ± 0.15for Glu45 - Ala, 0.95 ± 0.06 for Lys43 - Ala/Glu45 -Ala and 1.93 ± 0.09 for Pro44 - Ala. The free energyof interaction between Lys43 and Glu45 is calculated to be only0.25 ± 0.09 kcal/mol. From the changes in denaturationmidpoint, T_m measured by circular dkhroism, we estimate theenergy of interaction between Lys43 and Glu45 to be 0.36 ±0.07 kcal/mol whereas the contribution of Pro44 is -2.0 kcal/mol.The contribution of the salt bridge to the stability of theprotein is very small and the residue Pro44 plays the key rolein stabilizing the turn     

Relative binding free energy calculations of inhibitors to two mutants (Glu46-- Ala/Gln) of ribonuclease T1 using molecular dynamics/free energy perturbation approaches

We present free energy perturbation calculations on the complexesof Glu46— Ala46 (E46A) and Glu46— Gln46 (E46Q) mutantsof ribonuclease T1 (RNaseT1) with inhibitors 2‘-guanosinemonophosphate (GMP) and 2’adenosine monophosphate (AMP)by a thermodynamic perturbation method implemented with moleculardynamics (MD). Using the available crystal structure of theRNaseT1–GMP complex, the structures of E46A-GMP and E46Q-GMPwere model built and equilibrated with MD simulations. The structuresof E46A-AMP and E46Q-AMP were obtained as a final structureof the GMP—AMP perturbation calculation respectively.The calculated difference in the free energy of binding (Gbind)was 0.31 kcal/mol for the E46A system and —1.04 kcal/molfor the E46Q system. The resultant free energies are much smallerthan the experimental and calculated value of 3 kcal/mol forthe native RNase T1, which suggests that both mutants have greaterrelative adenine affinities than native RNaseT1. EspeciallyE46Q is calculated to have a larger affinity for adenine thanguanine, as we suggested previously from the calculation onthe native RNaseT1. Thus, the molecular dynamics/free energyperturbation method may be helpful in protein engineering, directedtoward increasing or changing the substrate specificity of enzymes.     

Contribution of a disulfide bridge to the stability of 1,3-1,4-P-D-glucan 4-glucanohydrolase from Bacillus licheniformis

Bacillus 1,3-1,4-ß-glucanases possess a highly conserveddisulfide bridge connecting a ß-strand with a solventexposedloop lying on top of the extended binding site cleft The contributionof the disulfide bond and of both individual cysteines (Cys61and Cys90) in the Bacillus licheniformis enzyme to stabilityand activity has been evaluated by protein engineering methods.Reduction of the disulfide bond has no effect on kinetic parameters,has only a minor effect on the activity-temperature profileat high temperatures, and destabilizes the protein by less than0.7 kcal/mol as measured by equilibrium urea denatu ration at37°C. Replacing either of the Cys residues with Ala destabilizesthe protein and lowers the specific activity. C90A retains 70%of wild-type (wt) activity (in terms of Vmax), whereas C61Aand the double mutant C61A–C90A have 10% of wt V_max. Alarger change in free energy of unfolding is seen by equilibriumurea denaturation for the C61A mutation (loop residue, 3.2 kcal/molrelative to reduced wt) as compared with the C90A mutation (ß-strandresidue, 1.8 kcal/mol relative to reduced wt), while the doublemutant C61A–C90A is 0.8 kcal/mol less stable than thesingle C61A mutant. The effects on stability are interpretedas a result of the change in hydrophobic packing that occursupon removal of the sulfur atoms in the Cys to Ala mutations     

The nature of the ion binding interactions in EF-hand peptide analogs: free energy simulation of Asp to Asn mutations

The binding of the La³⁺ ion to a tridecapeptide, which is amodel for the EF-hand in calcium-binding proteins, is studiedhi solution by free energy simulations. The calculations analyzethe effect on the La³⁺ ion binding of the mutation of Asp toAsn for side chains that interact directly with the ion. Theresults are compared with the measurements of Marsden.B.J.,Hodges, R.S. and Sykes, B.D. (1989) Biochemistry, 28,8839, onthe same system. They found that the Asp to Asn mutation hasonly a small effect on the binding; the observed differencesin the free energies on changing one Asp to an Asn are between-0.3 and 1.8 kcal/ mol. This result is analyzed by alchemicalsimulations for the tridecapeptide in the bound Qoop) structureand free (extended) form. The free energy changes due to themutation of an Asp to an Asn are large and positive for boththe bound and free forms. However, since the values of the freeenergy changes are calculated to be similar hi the two forms,the difference in the binding free energy of Asp and Asn peptidesis found to be small, in agreement with experiment. By use ofthermodynamic integration, the various contributions to thefree energy changes are estimated. In the com-plexed form, theAsp to Asn mutation is favored by the reduction in the repulsiveinteraction with other charged residues of the peptide; it isdisfavored by the reduction of the stabilization of the ionand the surrounding water has a small effect. When the peptideadopts an extended conformation in the absence of the ion, themutation Asp to Asn is strongly disfavored by the interactionswith the water and is favored by the interactions within thepeptide. The results demonstrate the essential role of contributionsto the binding of EF-hands from interactions other than thosebetween the ion and the charged amino acid side chains. Theresults obtained from the simulations suggest, in accord withcrystal structures of La³⁺ bound to various ligands, that thecalcium-binding loop complexed with La³⁺ in solution has a significantlydifferent structure from that observed hi proteins.     

Free energy perturbation studies on binding of A-74704 and its diester analog to HIV-1 protease

Free energy simulations have been employed to rationalize thebinding differences between A-74704, a pseudo C₂- symmetricinhibitor of HIV-1 protease and its diester analog. The diesteranalog inhibitor, which misses two hydrogen bonds with the enzymeactive site, is surprisingly only 10-fold weaker. The calculatedfree energy difference of 1.7 ± 0.6 kcal/mol is in agreementwith the experimental result. Further, the simulations showthat such a small difference in binding free energies is dueto (1) weaker hydrogen bond interactions between the two (P₁and P₁) NH groups of A-74704 with Gly27/Gly27' carbonyls ofthe enzyme and (2) the higher desolvation free energy of A-74704compared with its ester analog. The results of these calculationsand their implications for design of HIV-1 protease inhibitorsare discussed.     

Protein stability for single substitution mutants and the extent of local compactness in the denatured state

The stability changes caused by single amino acid substitutionsare studied by a simple, empirical method which takes accountof the free energy change in the compact denatured state aswell as in the native state. The conformational free energyis estimated from effective inter-residue contact energies,as evaluated in our previous study. When this method is applied,with a simple assumption about the compactness of the denaturedstate, for single amino acid replacements at Glu49 of the tryptophansynthase subunit and at Ile3 of bacteriophage T4 lysozyme,the estimates of the unfolding Gibbs free energy changes correlatewell with observed values, especially for hydrophobic aminoacids, and it also yields the same magnitudes of energy as theobserved values for both proteins. When it is also applied foramino acid replacements at various positions to estimate theaverage number of contacts at each position in the denaturedstate from the observed value of unfolding free energy change,those values for replacements with Gly and Ala at the same residueposition in staphylococcal nuclease correlate well with eachother. The estimated numbers of contacts indicate that the proteinis not fully expanded in the denatured state and also that thecompact denatured state may have a substantially native-liketopology, like the molten globule state, in that there is aweak correlation between the estimated average number of contactsat each residue position in the denatured state and the numberof contacts in the native structure. These results provide somefurther evidence that the inter-residue contact energies asapplied here (i) properly reflect actual inter-residue interactionsand (ii) can be considered to be a pairwise hydrophobicity scale.Also, the results indicate that characterization of the denaturedstate is critical to understanding the folding process.     

The Trp-cage: optimizing the stability of a globular miniprotein

The Trp-cage, as the smallest miniprotein, remains the subject of numerous computational and experimental studies of protein folding dynamics and pathways. The original Trp-cage (NLYIQWLKDGGPSSGRPPPS, Tm = 42 degrees C) can be significantly stabilized by mutations; melting points as high as 64 degrees C are reported. In helical portions of the structure, each allowed replacement of Leu, Ile, Lys or Ser residues by Ala results in a 1.5 (+/-0.35) kJ/mol fold stabilization. No changes in structure or fluxionality of the core results upon stabilization. Contrary to the initial hypothesis, specific Pro/Trp interactions are not essential for core formation. The entropic advantage of Pro versus Ala (DeltaDeltaS(U) = 11 +/- 2 J/mol K) was measured at the solvent-exposed P17 site. Pro-Ala mutations at two of the three prolines (P12 and P18) that encage the indole ring result in less fold destabilization (2.3-3.4 kJ/mol). However, a P19A mutation reduces fold stability by 16 kJ/mol reflecting a favorable Y3/P19 interaction as well as Trp burial. The Y3/P19 hydrophobic staple interaction defines the folding motif as an 18-residue unit. Other stabilizing features that have been identified include a solvent-exposed Arg/Asp salt bridge (3.4-6 kJ/mol) and a buried H-bonded Ser side chain ( approximately 10 kJ/mol).     

Effects of substitutions in the binding surface of an antibody on antigen affinity

The interactions between the Fab and single-chain Fv (scFv) fragments of an antibody (NC10) and its antigen, influenza virus neuraminidase, were analysed in the crystal structures of the Fab-neuraminidase and scFv-neuraminidase complexes. To investigate the contribution to binding made by cavities, salt links and hydrogen bonds in the antibody- antigen interface, 14 single amino acid replacements were made at six contact residues in the scFv fragment by site-directed mutagenesis. The binding affinity of each mutant scFv antibody for neuraminidase was determined with a BIAcore optical biosensor. Four of the mutations resulted in large changes in the free energy of binding to neuraminidase (deltadeltaG > 1 kcal/mol) and together may account for approximately 70% of the free energy of binding. Hence these data support the theory that a small number of residues form the 'functional epitope' and are most important for binding of NC10 to neuraminidase. The salt link between antibody residue (Asp)H56 and (Lys)N432 from neuraminidase was demonstrated to be important for affinity, since substitution of (Asp)H56 with Asn caused a large reduction in the free energy of binding (deltadeltaG = +2.8 kcal/mol). Hydrogen bonds provided by (Tyr)L32 and (Asp)H56 were also important for binding: mutation of (Tyr)L32 to Phe resulted in a significant reduction in binding affinity (deltadeltaG = +1.7 kcal/mol). Disruption of hydrophobic interactions (van der Waals contacts) led to significant reductions in affinity also ((Tyr)H99 to Ala, deltadeltaG = +1.5 kcal/mol; (Leu)L94 to Ala, deltadeltaG > +3.0 kcal/mol). An attempt to increase binding affinity by filling a cavity in the interface with a larger antibody side chain was unsuccessful, as the free energy gained by new antibody-antigen interactions did not compensate for the removal of cavity-bound water molecules.      

Binding free energy calculations for P450cam-substrate complexes

A recently proposed semi-empirical method for calculating bindingfree energies was used to examine the binding of a variety ofsubstrates to cytochrome P450cam. For a set of 11 differentpotential substrates of cytochrome P450cam, both the absoluteand relative binding free energies were generally well reproduced.The mean error in the calculated absolute binding free energyfor all 11 compounds is 0.55 kcal/mol. Forty-eight out of 55calculated relative binding free energies have the correct signand the mean unsigned error between calculated and experimentalrelative binding free energies is 0.77 kcal/mol. For one substrate,thiocamphor, the effect of substrate orientation on the calculatedbinding free energy was examined. The ability of this methodto predict the effect of active site mutations was also examinedin two cases.     

A model for adhesion-producing interactions of zinc oxide surfaces with alcohols,amines, and alkenes

The interactions between paint/adhesive polymers and metal surfaces that are critical for adhesion have been studied theoretically. This study used zinc oxide as a model of a galvanized steel surface, and ammonia, water, and ethylene as models for amino, hydroxy, and unsaturated functionalities in paint/adhesive polymers. Ab initio molecular orbital calculations were carried out on zinc oxide and zinc oxide dimer. Geometries were optimized at the HF/3-21G level and relative energies were calculated by CASSCF/3-21G and by MP2 with the DZP basis set of Wachters and Hay. Ethylene forms a stable complex with zinc oxide dimer that has a stabilization energy of 24.9 kcal/mol. Insertion of ethylene into zinc oxide dimer to form a stable six-membered ring adduct occurs with a surprisingly low activation energy of 8.8 kcal/mol. The binding energy of ammonia with zinc oxide dimer is 38.5 kcal/mol and the activation energy for insertion of ammonia forming covalent Zn-NH₂ and O-H bonds is calculated to be 9.6 kcal/mol. Aminolysis of zinc oxide dimer with two ammonia molecules has a predicted barrier height of 6.7 kcal/mol. The transition structure for Zn-O bond rupture with one NH₃ and one H₂O molecule is only 1.5 kcal/mol higher in energy than the reactant cluster. The calculations suggest that alkenes, amines, and alcohols could readily form covalent bonds with the ZnO surface, thereby facilitating adhesion of the polymer containing these functional groups to a galvanized surface.     

Hydrophobic effects on protein/nucleic acid interaction: enhancement of substrate binding by mutating tyrosine 45 to tryptophan in ribonuclease Tl

Hydrophobic effects on binding of ribonuclease Tl to guaninebases of several ribonucleotides have been proved by mutatinga hydrophobic residue at the recognition site and by measuringthe effect on binding. Mutation of a hydrophobic surface residueto a more hydrophobic residue (Tyr45 – Trp) enhances thebinding to ribonucleotides, including mononucleotide inhibitorand product, and a synthetic substrate-analog trinudeotide aswell as the binding to dinucleotide substrates and RNA. Enhancementson binding to non-substrate ribonucleotides by the mutationhave been observed with free energy changes ranging from –2.2 to – 3 .9 kJ/mol. These changes are in good agreementwith that of substrate binding, –2.3 kJ/mol, which iscalculated from Michaelis constants obtained from kinetic studies.It is shown, by comparing the observed and calculated changesin binding free energy with differences in the observed transferfree energy changes of the amino acid side chains from organicsolvents to water, that the enhancement observed on guaninebinding comes from the difference in the hydrophobic effectsof the side chains of tyrosine and tryptophan. Furthermore,a linear relationship between nucleolytic activities and hydrophobicityof the residues (Ala, Phe, Tyr, Trp) at position 45 is observed.The mutation could not change substantially the base specificityof RNase Tl, which exhibits a prime requirement for guaninebases of substrates.     

Free energy perturbation study on a Trp-binding mutant (Ser88 ->Cys) of the trp-repressor

The Ser⁸⁸Cys mutant of the trp-repressor showed a lower affinityfor the corepressor than the wild-type repressor [G = 1.7 ±0.3 kcal/mol, Chou and Matthews (1989) J. Biol. Chem., 264,18314–18319].A molecular dynamics/free energy cycle perturbation study wasperformed to understand the origin of the decreased affinity.A value (G = 1.58 ± 0.28 kcal/mol) comparable with theexperimental value was obtained by the simulation. Free energycomponent analysis revealed that destabilization of the vander Waals interaction between Ser⁸⁸ and Trp¹⁰⁹ (corepressor)mainly contributed to the decreased affinity of the mutant.The rotational transition of the hydroxyl (sulfhydryl) groupof Ser⁸⁸ (Cys⁸⁸) during the simulations affected the contributionsof Arg⁸⁴ and water to the free energy change in the aporepressorand those of Arg⁸⁴ and Trp ¹⁰⁹ to that in the holorepressor.However, the contributions from different residues compensatedeach other, and the total free energy changes were almost invariablein the various simulations.     

Analysis of a catalytic pathway via a covalent adduct of D52E hen egg white mutant lysozyme by further mutation

We previously demonstrated by X-ray crystallography and electrospraymass spectrometry that D52E mutant hen lysozyme formed a covalentenzyme–substrate adduct on reaction with N-acetylglucosamineoligomer. This observation indicates that D52E lysozyme mayacquire a catalytic pathway via a covalent adduct. To explainthis pathway, the formation and hydrolysis reactions of thecovalent adduct were investigated. Kinetic analysis indicatedthat the hydrolysis step was the rate-limiting step, 60-foldslower than the formation reaction. In the formation reaction,the pH dependence was bell-shaped, which was plausibly explainedby the functions of the two catalytic pK_as of Glu35 and Glu52.On the other hand, the pH dependence in the hydrolysis was sigmoidalwith a transition at pH 4.5, which was identical with the experimentallydetermined pK_a of Glu35 in the covalent adduct, indicating thatGlu35 functions as a general base to hydrolyze the adduct. Toimprove the turnover rate of D52E lysozyme, the mutation ofN46D was designed and introduced to D52E lysozyme. This mutationreduced the activation energy in the hydrolysis reaction ofthe covalent adduct by 1.8 kcal/mol at pH 5.0 and 40°C butdid not affect the formation reaction. Our data may providea useful approach to understanding the precise mechanism ofthe function of natural glycosidases, which catalyze via a covalentadduct.     

Threonine 81 of the trp repressor of Escherichia coli plays an auxiliary role in the formation of the corepressor binding pocket

A mutational study was performed on the corepressor (Ltryptophan)binding site of the trp repressor of Escherichia coli. Threonine81, one of the residues forming the hydrophobic pocket of thebinding site, was replaced with Ser, Cys and Met by cassettemutagenesis. Biochemical characterization showed that all thesemutations caused a moderate decrease in tryptophan binding activity(free energy change 1 kcal/mol). The results suggested thatthe binding pocket is rather flexible in the vicinity of Thr81.On the other hand, the mutations produced a discernible decreasein the repressor activity in vivo, apparently by weakening oreliminating the hydrogen bond between Thr81 and the operatorDNA, as well as by introducing possible side-chain rearrangement.     

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.     

Modeling protein stability: a theoretical analysis of the stability of T4 lysozyme mutants

Free energy calculations were conducted to determine the relative stability of the unnatural amino acid mutants of T4 lysozyme norvaline (Nvl) and O-methyl-serine (Mse) and of alanine at residue 133, which is leucine in the native sequence. These calculations were performed both to assess the validity of the methodology and to gain a better understanding of the forces which contribute to protein stability. Peptides of different length were used to model the denatured state. Restraints were employed to force sampling of the side chain chi1 dihedral of the perturbed side chain, and the effect of protein repacking in response to mutation was studied through the use of different constraint sets. In addition, the convergence behavior and hysteresis of the simulations in the folded and unfolded states were determined. The calculated results agree well with experiment, + 1.84 versus + 1.56 kcal/mol for Mse-->Nvl and -3.48 versus -2.2 to -3.6 kcal/mol for Nvl-->Ala. We find that free energy calculations can provide useful insights to protein stability when conducted carefully on a well chosen system. Our results suggest that loss of packing interactions in the native state is a major source of destabilization for mutants which decrease the amount of buried nonpolar surface area and that subtle responses of the backbone affect the magnitude of the loss of stability. We show that the conformational freedom of the chi1 dihedral has a noticeable effect on protein stability and that the solvation of amino acid side chains is strongly influenced by interactions with the peptide backbone.      

Application of free energy simulations to the binding of a transition-state-analogue inhibitor to HTV protease

Free energy simulations (slow-change method) have been usedto estimate quantitatively the ratio of the binding constantsof (S) and (R) isomers of a novel HIV protease inhibitor, JG365.As a starting geometry, we used the X-ray crystallographic structureof a complex of HTV protease and JG365 provided by A.Wlodawer.According to our results the (S) configuration, i.e. the formpreviously identified experimentally, binds considerably moretightly to the protease (G° = 2.9 kcal/mol). When the (S)inhibitor is bound, there is a very strong preference for protonationof the Aspl25 (rather than the Asp25) residue of the protease.This study is the first to apply a new method for quantitativelyassessing the precision of free energies calculated by the slow-changemethod     

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.     

Antagonism, non-native interactions and non-two-state folding in S6 revealed by double-mutant cycle analysis

When folding to the native state N in the presence of salt, the apparent two-state folder S6 transiently forms a transient off-pathway state C with substantial secondary and tertiary structure. Fifteen double mutant cycles were analysed to compare side-chain interaction energies DeltaDeltaG(int) in C, N and TS (the transition state between N and the denatured state). The kinetic signatures of these destabilizing mutants suggest folding scenarios involving unfolding intermediates and even alternative unfolding pathways. However, restricting the kinetic data to linear parts of the chevron plot allows reliable extrapolation to zero molar denaturant of rate constants of folding, unfolding and misfolding. Side-chain interactions appear to contribute to the stability of C, but in a substantially non-native environment, as shown by changes in the sign of DeltaDeltaG(int) between C and N. Remarkably, there appear to be significant (0.7-2 kcal/mol) antagonistic interactions between the two residues Leu30 and Leu75 in N and TS, which may be linked to subtle structural changes seen in the crystal structures of the mutants. A small number of overlapping residues are involved in these kinds of antagonistic interactions in N, TS and C, suggesting that repulsive interactions are coded into the protein topology whether the protein folds or misfolds. Destabilizing double mutants indicate that apparent two-state folders can be induced to behave in more complex ways provided that the native state is suitably destabilized.