Role of the chain termini for the folding transition state of the cold shock protein.

Residues Arg3 and Leu66 are crucially important for the enhanced stability of the cold shock protein Bc-Csp from the thermophile Bacillus caldolyticus relative to its homologue Bs-CspB from the mesophile Bacillus subtilis. Arg3, which replaces Glu3 of Bs-CspB, accounts for two-thirds of the stability difference and for the entire difference in Coulombic interactions between the two proteins. Leu66, which replaces Glu66 of Bs-CspB, contributes additional hydrophobic interactions. To elucidate the role of these two residues near the chain termini for the rapid folding of the cold shock proteins, we performed an extensive mutational analysis of the folding kinetics to characterize interactions between residues 3, 46, and 66 in the transition state of folding. We employed a pressure-jump apparatus which allows folding to be followed over a broad range of temperatures and urea concentrations in the time range of microseconds to minutes. The N-terminal region folds early, and the interactions that originate from residue 3 are present to a large extent in the transition state already. They include a hydrophobic contribution, a general electrostatic stabilization by the positive charge of Arg3 in Bc-Csp, and a pairwise Coulombic repulsion with Glu46 in the Arg3Glu variant. The C-terminus appears to be largely unfolded in the transition state. The interactions of Leu66, including those with the already structured N-terminal region, are established only after passage through the transition state. The N- and C-termini of the cold shock proteins thus contribute differently to the folding kinetics, although they are very close in space in the folded protein.     

Desolvation is a likely origin of robust enthalpic barriers to protein folding

Experimental data from global analyses of temperature (T) and denaturant dependence of the folding rates of small proteins led to an intrinsic enthalpic folding barrier hypothesis: to a good approximation, the T-dependence of folding rate under constant native stability conditions is Arrhenius. Furthermore, for a given protein, the slope of isostability folding rate versus 1/T is essentially independent of native stability. This hypothesis implies a simple relationship between chevron and Eyring plots of folding that is easily discernible when both sets of rates are expressed as functions of native stability. Using experimental data in the literature, we verify the predicted chevron-Eyring relationship for 14 proteins and determine their intrinsic enthalpic folding barriers, which vary approximately from 15 kcal/mol to 40 kcal/mol for different proteins. These enthalpic barriers do not appear to correlate with folding rates, but they exhibit correlation with equilibrium unfolding enthalpy at room temperature. Intrinsic enthalpic barriers with similarly high magnitudes apply as well to at least two cases of peptide-peptide and peptide-protein association, suggesting that these barriers are a hallmark of certain general and fundamental kinetic processes during folding and binding. Using a class of explicit-chain C(alpha) protein models with constant elementary enthalpic desolvation barriers between C(alpha) positions, we show that small microscopic pairwise desolvation barriers, which are a direct consequence of the particulate nature of water, can act cooperatively to give rise to a significant overall enthalpic barrier to folding. This theoretical finding provides a physical rationalization for the high intrinsic enthalpic barriers in protein folding energetics. Ramifications of entropy-enthalpy compensation in hydrophobic association for the height of enthalpic desolvation barrier are discussed.     

Electrostatic contributions to the stability of a thermophilic cold shock protein

The thermophilic Bacillus caldolyticus cold shock protein (Bc-Csp) differs from the mesophilic Bacillus subtilis cold shock protein B (Bs-CspB) in 11 of the 66 residues. Stability measurements of Schmid and co-workers have implicated contributions of electrostatic interactions to the thermostability. To further elucidate the physical basis of the difference in stability, previously developed theoretical methods that treat electrostatic effects in both the folded and the unfolded states were used in this paper to study the effects of mutations, ionic strength, and temperature. For 27 mutations that narrow the difference in sequence between Bc-Csp and Bs-CspB, calculated changes in unfolding free energy (Delta G) and experimental results have a correlation coefficient of 0.98. Bc-Csp appears to use destabilization of the unfolded state by unfavorable charge-charge interactions as a mechanism for increasing stability. Accounting for the effects of ionic strength and temperature on the electrostatic free energies in both the folded and the unfolded states, explanations for two important experimental observations are presented. The disparate ionic strength dependences of Delta G for Bc-Csp and Bs-CspB were attributed to the difference in the total charges (-2e and -6e, respectively). A main contribution to the much higher unfolding entropy of Bs-CspB was found to come from the less favorable electrostatic interactions in the folded state. These results should provide insight for understanding the thermostability of other thermophilic proteins.     

In-vitro selection of highly stabilized protein variants with optimized surface

Thermostable proteins are of prime importance in protein science, but it has remained difficult to develop general strategies for stabilizing a protein. Site-directed mutagenesis based on comparisons with thermophilic homologs is rarely successful because the sequence differences are too numerous and dominated by neutral mutations. Here we used a method of directed evolution to increase the stability of a mesophilic protein, the cold shock protein Bs-CspB from Bacillus subtilis. It differs from its thermophilic counterpart Bc-Csp from Bacillus caldolyticus at 12 surface-exposed positions. To elucidate the stabilizing potential of exposed amino acid residues, six of these variant positions were randomized by saturation mutagenesis, the corresponding library of sequences was inserted into the gene-3-protein of the filamentous phage fd, and stabilized variants were selected by the Proside technique. Proside links the increased protease resistance of stabilized protein variants with the infectivity of the phage. Many strongly stabilized variants of Bs-CspB were identified in two selections, one in the presence of a denaturant and the other at elevated temperature. Several of them are significantly more stable than the naturally thermostable homolog Bc-Csp, and the best variant reaches Tm-Csp (the homolog from the hyperthermophile Thermotoga maritima) in stability. Remarkably, this variant differs from Tm-Csp at five and from Bc-Csp at all six randomized positions. This indicates that proteins can be strongly stabilized by many different sets of surface mutations, and Proside selects them efficiently from large libraries. The course of the selection could be directed by the conditions. In an ionic denaturant non-polar surface interactions were optimized, whereas at elevated temperature variants with improved electrostatics were selected, pointing to two different strategies for stabilization at protein surfaces.     

Correspondence between anomalous m- and DeltaCp-values in protein folding

Proteins folding according to a classical two-state system characteristically show V-shaped chevron plots. We have previously interpreted the symmetrically curved chevron plot of the protein U1A as denaturant-dependent movements in the position of the transition state ensemble (TSE). S6, a structural analog of U1A, shows a classical V-shaped chevron plot indicative of straightforward two-state kinetics, but the mutant LA30 has a curved unfolding limb, which is most consistent with TSE mobility. The kinetic m-values (derivatives of the rate constants with respect to denaturant concentration) in themselves depend on denaturant concentration. To obtain complementary information about putative mobile TSEs, we have carried out a thermodynamic analysis of the three proteins, based on data for refolding and unfolding over the range 10 degrees C to 70 degrees C. The data at all temperatures can be fitted to two-state model systems. Importantly, for all three proteins the activation heat capacities are, within error, identical to the heat capacities measured in independent experiments under equilibrium conditions. Although the equilibrium heat capacities are essentially invariant with regard to denaturant concentration, the activation heat capacities, similar to the structurally equivalent kinetic m-values, show marked denaturant dependence. Furthermore, the values of beta++ at different denaturant concentrations measured by m-values and by heat capacity values are very similar. These observations are consistent with significant transition state movements within the framework of two-state folding. The basis for TSE movement appears to be enthalpic rather than entropic, suggesting that the binding energy of denaturant-protein interactions is a major determinant of the response of energy landscape contours to changing environments.     

残基突变对冷休克蛋白热稳定性影响的计算分析研究(英文)

残基突变是提高蛋白质热稳定性最直接有效的方式。在本文中,我们选取一对冷休克蛋白质作为研究对象,其中一个来自嗜温的Bacillus subtilis(Bs-CspB),另一个来自嗜热的Bacillus caldolyticus(Bc-Csp),这两个蛋白质在序列和结构上具有高度的相似性,但两者的耐热能力却相差很大。我们利用全原子模型计算残基突变前后蛋白质的自由能和氨基酸之间相互作用能的变化,分析残基突变对冷休克蛋白热稳定性的影响。通过对比两个蛋白质对应位置上残基的能量,我们成功鉴别出对Bc-Csp的高热稳定性有突出贡献的残基。我们计算了这些残基突变前后,该残基的静电相互作用和范德华相互作用的变化,以分析该残基对Bc-Csp高热稳定性的主要贡献。同时,我们分析了离子键对蛋白质热稳定性的贡献。我们的计算结果和实验结果吻合得很好,关键在于利用该方法可以详细地说明残基突变影响蛋白质热稳定性的根本原因。本文为研究残基突变对蛋白质热稳定性的影响提供了一种计算思路和方法,并有助于设计具有高耐热能力的蛋白质。     

Protein folding as a diffusional process.

A protein chain must move relative to the solvent molecules and explore many conformations when it folds from the extended unfolded state to the compact native state. Experimental and theoretical approaches suggest that diffusional processes in fact contribute to the kinetics of protein folding. We describe here how variations of the solvent viscosity can be employed to uncover the diffusional contributions to a folding reaction and assess the use of transition state theory and Kramers' rate theory for the analysis of protein folding reactions.     

Aggregation as the basis for complex behaviour of cutinase in different denaturants

We have previously described the complexity of the folding of the lipolytic enzyme cutinase from F. solani pisi in guanidinium chloride. Here we extend the refolding analysis by refolding from the pH-denatured state and analyze the folding behaviour in the presence of the weaker denaturant urea and the stronger denaturant guanidinium thiocyanate. In urea there is excellent consistency between equilibrium and kinetic data, and the intermediate accumulating at low denaturant concentrations is off-pathway. However, in GdmCl, refolding rates, and consequently the stability of the native state, vary significantly depending on whether refolding takes place from the pH- or GdmCl-denatured state, possibly due to transient formation of aggregates during folding from the GdmCl-denatured state. In GdmSCN, stability is reduced by several kcal/mol with significant aggregation in the unfolding transition region. The basis for the large variation in folding behaviour may be the denaturants' differential ability to support formation of exposed hydrophobic regions and consequent changes in aggregative properties during refolding.     

Thermal stability and atomic-resolution crystal structure of the Bacillus caldolyticus cold shock protein

The bacterial cold shock proteins are small compact beta-barrel proteins without disulfide bonds, cis-proline residues or tightly bound cofactors. Bc-Csp, the cold shock protein from the thermophile Bacillus caldolyticus shows a twofold increase in the free energy of stabilization relative to its homolog Bs-CspB from the mesophile Bacillus subtilis, although the two proteins differ by only 12 out of 67 amino acid residues. This pair of cold shock proteins thus represents a good system to study the atomic determinants of protein thermostability. Bs-CspB and Bc-Csp both unfold reversibly in cooperative transitions with T(M) values of 49.0 degrees C and 77.3 degrees C, respectively, at pH 7.0. Addition of 0.5 M salt stabilizes Bs-CspB but destabilizes Bc-Csp. To understand these differences at the structural level, the crystal structure of Bc-Csp was determined at 1.17 A resolution and refined to R=12.5% (R(free)=17.9%). The molecular structures of Bc-Csp and Bs-CspB are virtually identical in the central beta-sheet and in the binding region for nucleic acids. Significant differences are found in the distribution of surface charges including a sodium ion binding site present in Bc-Csp, which was not observed in the crystal structure of the Bs-CspB. Electrostatic interactions are overall favorable for Bc-Csp, but unfavorable for Bs-CspB. They provide the major source for the increased thermostability of Bc-Csp. This can be explained based on the atomic-resolution crystal structure of Bc-Csp. It identifies a number of potentially stabilizing ionic interactions including a cation-binding site and reveals significant changes in the electrostatic surface potential.     

Folding pathway of FKBP12 and characterisation of the transition state.

The folding pathway of human FKBP12, a 12 kDa FK506-binding protein (immunophilin), has been characterised. Unfolding and refolding rate constants have been determined over a wide range of denaturant concentrations and data are shown to fit to a two-state model of folding in which only the denatured and native states are significantly populated, even in the absence of denaturant. This simple model for folding, in which no intermediate states are significantly populated, is further supported from stopped-flow circular dichroism experiments in which no fast "burst" phases are observed. FKBP12, with 107 residues, is the largest protein to date which folds with simple two-state kinetics in water (kF=4 s(-1)at 25 degrees C). The topological crossing of two loops in FKBP12, a structural element suggested to cause kinetic traps during folding, seems to have little effect on the folding pathway.The transition state for folding has been characterised by a series of experiments on wild-type FKBP12. Information on the thermodynamic nature of, the solvent accessibility of, and secondary structure in, the transition state was obtained from experiments measuring the unfolding and refolding rate constants as a function of temperature, denaturant concentration and trifluoroethanol concentration. In addition, unfolding and refolding studies in the presence of ligand provided information on the structure of the ligand-binding pocket in the transition state. The data suggest a compact transition state relative to the unfolded state with some 70 % of the surface area buried. The ligand-binding site, which is formed mainly by two loops, is largely unstructured in the transition state. The trifluoroethanol experiments suggest that the alpha-helix may be formed in the transition state. These results are compared with results from protein engineering studies and molecular dynamics simulations (see the accompanying paper).     

Effects of guanidine hydrochloride on the refolding kinetics of denatured thioredoxin

The effect of guanidine hydrochloride concentration on the kinetics of the conformational change of Escherichia coli thioredoxin was examined by using fluorescence, absorbance, circular dichroic, and viscosity measurements. Native thioredoxin unfolds in a single kinetic phase whose time constant decreases markedly with increasing denaturant concentration in the denaturation base-line zone. This dependency merges with the time constant of the slowest refolding kinetic phase at the midpoint of the equilibrium transition in 2.5 M denaturant. The time constant of the slowest refolding phase becomes denaturant independent below 1 M denaturant in the native base-line region. The denaturant-independent slowest refolding phase has an activation energy of 16 kcal/mol and is generated in the denatured base-line zone in a denaturant-independent reaction having a time constant of 19 s at 25 degrees C. The fractional amplitude of the slowest refolding phase diminishes in the native base-line zone to a minimum value of 0.25. This decrease is accompanied by an increase in the fractional amplitudes of two faster refolding kinetic phases, an increase describing a sigmoidal transition centered at about 1.6 M denaturant. Manual multimixing measurements indicate that only the slowest refolding kinetic phase generates a product having the stability of the native protein. We suggest that the two faster refolding phases reflect the transient accumulation of folding intermediates which can contain a nonnative isomer of proline peptide 76.     

Posttransition state desolvation of the hydrophobic core of the src-SH3 protein domain

The folding thermodynamics of the src-SH3 protein domain were characterized under refolding conditions through biased fully atomic molecular dynamics simulations with explicit solvent. The calculated free energy surfaces along several reaction coordinates revealed two barriers. The first, larger barrier was identified as the transition state barrier for folding, associated with the formation of the first hydrophobic sheet of the protein. phi values calculated from structures residing at the transition state barrier agree well with experimental phi values. The microscopic information obtained from our simulations allowed us to unambiguously assign intermediate phi values as the result of multiple folding pathways. The second, smaller barrier occurs later in the folding process and is associated with the cooperative expulsion of water molecules between the hydrophobic sheets of the protein. This posttransition state desolvation barrier cannot be observed through traditional folding experiments, but is found to be critical to the correct packing of the hydrophobic core in the final stages of folding. Hydrogen exchange and NMR experiments are suggested to probe this barrier.     

Specificity of the initial collapse in the folding of the cold shock protein

The two-state folding reaction of the cold shock protein from Bacillus caldolyticus (Bc-Csp) is preceded by a rapid chain collapse. A fast shortening of intra-protein distances was revealed by F?rster resonance energy transfer (FRET) measurements with protein variants that carried individual pairs of donor and acceptor chromophores at various positions along the polypeptide chain. Here we investigated the specificity of this rapid compaction. Energy transfer experiments that probed the stretching of strand beta2 and the close approach between the strands beta1 and beta2 revealed that the beta1-beta2 hairpin is barely formed in the collapsed form, although it is native-like in the folding transition state of Bc-Csp. The time course of the collapse could not be resolved by pressure or temperature jump experiments, indicating that the collapsed and extended forms are not separated by an energy barrier. The co-solute (NH4)2SO4 stabilizes both native Bc-Csp and the collapsed form, which suggests that the large hydrated SO4(2-) ions are excluded from the surface of the collapsed form in a similar fashion as they are excluded from folded Bc-Csp. Ethylene glycol increases the stability of proteins because it is excluded preferentially from the backbone, which is accessible in the unfolded state. The collapsed form of Bc-Csp resembles the unfolded form in its interaction with ethylene glycol, suggesting that in the collapsed form the backbone is still accessible to water and small molecules. Our results thus rule out that the collapsed form is a folding intermediate with native-like chain topology. It is better described as a mixture of compact conformations that belong to the unfolded state ensemble. However, some of its structural elements are reminiscent of the native protein.     

Apparent two-state tendamistat folding is a sequential process along a defined route

The small all-beta-sheet protein tendamistat folds and unfolds rapidly in apparent two-state reactions. Kinetic measurements of two tendamistat variants under various solvent conditions reveal, however, that folding occurs in at least two sequential steps through a metastable obligatory intermediate. Depending on the solvent conditions either step can become rate limiting. The activation parameters indicate that the first step represents an enthalpic barrier whereas the second step is an entropic barrier at 25 degrees C. Our results suggest that initial non-specific collapse precedes formation of native secondary and tertiary structure in tendamistat folding. This points at a distinct route in tendamistat folding and indicates that partially folded metastable intermediates might play an important role in the mechanism of apparent two-state folding.     

Ultrafast events in the folding of ferrocytochrome c

Laser flash photolysis and stopped-flow methods have been used to study the dynamic events in the micro- to millisecond time bin in the refolding of horse ferrocytochrome c in the full range of guanidine hydrochloride concentration at pH 12.8 (+/-0.1), 22 degrees C. Under the absolute refolding condition, the earliest relaxation time of the unfolded protein chain is less than 1 micros. The chain then undergoes diffusive dynamics-mediated contraction and expansion, in which intrapolypeptide ligands make transient contacts with the heme iron, giving rise to two distinct kinetic phases of approximately 0.4 and approximately 3 micros. Under moderate to absolute refolding conditions, the rates of these processes show little dependence on the denaturant concentration, indicating the absence of structural element in the incipient or the relaxed state. Chain expansion and contraction events continue until the polypeptide finds a stable and supportive transition state. The crossing of this transition barrier, which rate-limits the folding of alkaline ferrocytochrome c, is characterized by a stopped-flow measured time constant of approximately 3 ms in aqueous solvent. Observed kinetics thus implicate no submillisecond folding structure. The folding kinetics is effectively two state in which the unfolded polypeptide first relaxes to an unstructured chain and then crosses over a late rate-limiting barrier to achieve the native conformation. The experimentally observed rates as a function of guanidine hydrochloride concentration have been simulated by numerically calculated microscopic rates of a simple kinetic model that captures the essential features of folding.     

Shape of the free energy barriers for protein folding probed by multiple perturbation analysis

The characterization of the free energy barriers has been a major goal in studies on the mechanism of protein folding. Testing the effect of mutations or denaturants on protein folding reactions revealed that transition state movement is rare, suggesting that folding barriers are robust and narrow maxima on the free energy landscape. Here we demonstrate that the application of multiple perturbations allows the observation of small transition state movements that escape detection in single perturbation experiments. We used tendamistat as a model protein to test the broadness of the free energy barriers. Tendamistat folds over two consecutive transition states and through a high-energy intermediate. Measuring the combined effect of temperature and denaturant on the position of the transition state in the wild-type protein and in several mutants revealed that the early transition state shows significant transition state movement. Its accessible surface area state becomes more native-like with destabilization of the native state by temperature. To the same extent, the entropy of the early transition state becomes more native-like with increasing denaturant concentration, in accordance with Hammond behavior. The position of the late transition state, in contrast, is much less sensitive to the applied perturbations. These results suggest that the barriers in protein folding become increasingly narrow as the folding polypeptide chain approaches the native state.     

Sequential barriers and an obligatory metastable intermediate define the apparent two-state folding pathway of the ubiquitin-like PB1 domain of NBR1

The 90-residue N-terminal Phox and Bem1p (PB1) domain of NBR1 forms an α/β ubiquitin-like fold. Kinetic analysis using stopped-flow fluorescence reveals two-state kinetics; however, nonlinear effects in the denaturant dependence of the unfolding data demonstrate changes in the position of the rate-limiting barrier along the folding coordinate as the folding conditions change. The kinetics of wt-PB1 and several mutants show that this curvature is consistent with a single-pathway mechanism involving sequential transition states (TS1 and TS2) separated by a transiently populated high-energy intermediate, rather than movement of the transition state on a broad energy plateau. We show that the two transition states within the sequential model represent structurally and thermodynamically distinct species. TS1 is a collapsed state (α_TS1 = 0.71) with a large enthalpic barrier to formation that is rate-limiting under conditions that strongly favour folding. TS2 is highly native-like (α_TS2 = 0.93) and represents a late entropic barrier to formation of the native state. In support of the sequential transition state mechanism, we show that the G62A helix 2 substitution stabilises TS1 and the intermediate to such an extent that the latter becomes significantly populated, leading to the observation of a fast kinetic phase representing the initial U → I transition, with TS2 (α_TS2 = 0.87) becoming rate-limiting. The folding rate is not retarded by populating an intermediate, which would be expected for a misfold state, but is accelerated, suggesting that the I state is productive and on-pathway. The results show that the apparent two-state folding of the wt-PB1 domain occurs along a well-defined pathway involving structurally and thermodynamically distinct sequential transition states and an obligatory metastable intermediate that represents a productive local minimum in the energy landscape that increases the efficiency of barrier crossing through favourable effects on the entropy of activation.     

Heterogeneous folding of the trpzip hairpin: full atom simulation and experiment

The beta-hairpin trpzip2 can be tuned continuously from a two-state folder to folding on a rough energy landscape without a dominant refolding barrier. At high denaturant concentration, this extremely stable peptide exhibits a single apparent "two-state" transition temperature when monitored by different spectroscopic techniques. However, under optimal folding conditions the hairpin undergoes an unusual folding process with three clusters of melting transitions ranging from 15 degrees C to 160 degrees C, as monitored by 12 different experimental and computational observables. We explain this behavior in terms of a rough free energy landscape of the unfolded peptide caused by multiple tryptophan interactions and alternative backbone conformations. The landscape is mapped out by potentials of mean force derived from replica-exchange molecular dynamics simulations. Implications for deducing cooperativity from denaturant titrations, for the origin of folding cooperativity, and for the folding of thermophilic proteins are pointed out. trpzip is an excellent small tunable model system for the glass-like folding transitions predicted by landscape theory.     

Water contributes actively to the rapid crossing of a protein unfolding barrier

The cold-shock protein CspB folds rapidly in a N <= => U two-state reaction via a transition state that is about 90% native in its interactions with denaturants and water. This suggested that the energy barrier to unfolding is overcome by processes occurring in the protein itself, rather than in the solvent. Nevertheless, CspB unfolding depends on the solvent viscosity. We determined the activation volumes of unfolding and refolding by pressure-jump and high-pressure stopped-flow techniques in the presence of various denaturants. The results obtained by these methods agree well. The activation volume of unfolding is positive (Delta V(++)(NU)=16(+/-4) ml/mol) and virtually independent of the nature and the concentration of the denaturant. We suggest that in the transition state the protein is expanded and water molecules start to invade the hydrophobic core. They have, however, not yet established favorable interactions to compensate for the loss of intra-protein interactions. The activation volume of refolding is positive as well (Delta V(++)(NU)=53(+/-6) ml/mol) and, above 3 M urea, independent of the concentration of the denaturant. At low concentrations of urea or guanidinium thiocyanate, Delta V(++)(UN) decreases significantly, suggesting that compact unfolded forms become populated under these conditions.     

Characterization of a slow folding reaction for the alpha subunit of tryptophan synthase

The equilibria and kinetics of urea-induced unfolding and refolding of the alpha subunit of tryptophan synthase of E. coli have been examined for their dependences on viscosity, pH, and temperature in order to investigate the properties of one of the rate-limiting steps, domain association. A viscosity enhancer, 0.58 M sucrose, was found to slow unfolding and accelerate refolding. This apparently anomalous result was shown to be due to the stabilizing effect of sucrose on the folding reaction. After accounting for this stabilization effect by using linear free-energy plots, the unfolding and refolding kinetics were found to have a viscosity dependence. A decrease in pH was found to stabilize the domain association reaction by increasing the refolding rate and decreasing the unfolding rate. This effect was accounted for by protonation of a single residue with a pK value of 8.8 in the native state and 7.1 in the intermediate, in which the two domains are not yet associated. The activation energy of unfolding is 4.8 kcal/mol, close to the diffusion limit. The negative activation entropy of unfolding, -47 cal/deg-mol, which controls this reaction, may result from ordering of solvent about the newly exposed domain interface of the transition state. These results may provide information on the types of noncovalent interactions involved in domain association and improve the ability to interpret the folding of mutants with single amino-acid substitutions at the interface.