Coevolution of function and the folding landscape: correlation with density of native contacts

The relationship between the folding landscape and function of evolved proteins is explored by comparison of the folding mechanisms for members of the flavodoxin fold. CheY, Spo0F, and NtrC have unrelated functions and low sequence homology but share an identical topology. Recent coarse-grained simulations show that their folding landscapes are uniquely tuned to properly suit their respective biological functions. Enhanced packing in Spo0F and its limited conformational dynamics compared to CheY or NtrC lead to frustration in its folding landscape. Simulation as well as experimental results correlate with the local density of native contacts for these and a sample of other proteins. In particular, protein regions of low contact density are observed to become structured late in folding; concomitantly, these dynamic regions are often involved in binding or conformational rearrangements of functional importance. These observations help to explain the widespread success of Gomacr;-like coarse-grained models in reproducing protein dynamics.     

On the precision of experimentally determined protein folding rates and phi-values

Phi-values, a relatively direct probe of transition-state structure, are an important benchmark in both experimental and theoretical studies of protein folding. Recently, however, significant controversy has emerged regarding the reliability with which phi-values can be determined experimentally: Because phi is a ratio of differences between experimental observables it is extremely sensitive to errors in those observations when the differences are small. Here we address this issue directly by performing blind, replicate measurements in three laboratories. By monitoring within- and between-laboratory variability, we have determined the precision with which folding rates and phi-values are measured using generally accepted laboratory practices and under conditions typical of our laboratories. We find that, unless the change in free energy associated with the probing mutation is quite large, the precision of phi-values is relatively poor when determined using rates extrapolated to the absence of denaturant. In contrast, when we employ rates estimated at nonzero denaturant concentrations or assume that the slopes of the chevron arms (mf and mu) are invariant upon mutation, the precision of our estimates of phi is significantly improved. Nevertheless, the reproducibility we thus obtain still compares poorly with the confidence intervals typically reported in the literature. This discrepancy appears to arise due to differences in how precision is calculated, the dependence of precision on the number of data points employed in defining a chevron, and interlaboratory sources of variability that may have been largely ignored in the prior literature.     

Crystallographic and NMR spectroscopic protein structures: the inter-residue contacts

Inter-residue pair contacts have been analyzed in detail for the four pairs of protein structures determined both by X-ray analysis (X-ray) and nuclear magnetic resonance (NMR). At contact distances < or = 4.0 angstroms in the four NMR structures the overall number of pair contacts are less by 4-9% and pair contacts are in average shorter by 0.02-0.16 angstroms than those in corresponding X-ray structures. In each of four structure pairs 83-94% of common pair contacts are formed by the same residues in both structures and rest 6-17% ones are longer own pair contacts formed by the different residues in the NMR and X-ray structures. The amount of the longer own contacts is higher in the X-ray structure of the pair. In the each NMR structure there are three types of common pair contacts, which are shorter, longer or equal length in comparison with identical pair contacts in the X-ray structure of the same protein. The methodological different shortened common pair contacts predominate in the known distant dependence of the inter-residue contact densities of the 60-61 pair of the NMR/X-ray structure. Among four pairs analyzed the contact shortening proceeds upon the energy minimization of the crambin NMR structure and upon the resolving by the program X-PLOR with decreased atom van der Waals radius of the NMR structures of ubiquitin, hen lysozyme and monomeric hemoglobin. An extent of the NMR contact shortening decreased as the amount of NMR information upon the calculation of the NMR structures increased. Among 60-61 pairs of NMR/X-ray structures the main difference between alpha-helical and beta-structural proteins on the inter-residue distant dependence of the average contact densities arises from the strong alpha/beta difference in the local backbone geometry.     

Important inter-residue contacts for enhancing the thermal stability of thermophilic proteins

Proteins from thermophilic organisms exhibit high thermal stability, but have structures that are very similar to their mesophilic homologues. In order to gain insight into the basis of thermostability, we have analyzed the medium- and long-range contacts in mesophilic and thermophilic proteins of 16 different families. We found that the thermophiles prefer to have contacts between residues with hydrogen-bond-forming capability. Apart from hydrophobic contacts, more contacts are observed between polar and non-polar residues in thermophiles than mesophiles. Residue-wise analysis showed that Tyr has good contacts with several other residues, and Cys has considerably higher long-range contacts in thermophiles compared with mesophiles. Furthermore, the residues occurring in the range of 31-34 residues apart in the sequence contribute significant long-range contacts to the stability of thermophilic proteins.     

Methods for the accurate estimation of confidence intervals on protein folding phi-values

Phi-values provide an important benchmark for the comparison of experimental protein folding studies to computer simulations and theories of the folding process. Despite the growing importance of phi measurements, however, formulas to quantify the precision with which phi is measured have seen little significant discussion. Moreover, a commonly employed method for the determination of standard errors on phi estimates assumes that estimates of the changes in free energy of the transition and folded states are independent. Here we demonstrate that this assumption is usually incorrect and that this typically leads to the underestimation of phi precision. We derive an analytical expression for the precision of phi estimates (assuming linear chevron behavior) that explicitly takes this dependence into account. We also describe an alternative method that implicitly corrects for the effect. By simulating experimental chevron data, we show that both methods accurately estimate phi confidence intervals. We also explore the effects of the commonly employed techniques of calculating phi from kinetics estimated at non-zero denaturant concentrations and via the assumption of parallel chevron arms. We find that these approaches can produce significantly different estimates for phi (again, even for truly linear chevron behavior), indicating that they are not equivalent, interchangeable measures of transition state structure. Lastly, we describe a Web-based implementation of the above algorithms for general use by the protein folding community.     

Conservation of inter-residue interactions and prediction of folding rates of domain repeats

Domains are the main structural and functional units of larger proteins. They tend to be contiguous in primary structure and can fold and function independently. It has been observed that 10–20% of all encoded proteins contain duplicated domains and the average pairwise sequence identity between them is usually low. In the present study, we have analyzed the structural similarity between domain repeats of proteins with known structures available in the Protein Data Bank using structure-based inter-residue interaction measures such as the number of long-range contacts, surrounding hydrophobicity, and pairwise interaction energy. We used RADAR program for detecting the repeats in a protein sequence which were further validated using Pfam domain assignments. The sequence identity between the repeats in domains ranges from 20 to 40% and their secondary structural elements are well conserved. The number of long-range contacts, surrounding hydrophobicity calculations and pairwise interaction energy of the domain repeats clearly reveal the conservation of 3-D structure environment in the repeats of domains. The proportions of mainchain–mainchain hydrogen bonds and hydrophobic interactions are also highly conserved between the repeats. The present study has suggested that the computation of these structure-based parameters will give better clues about the tertiary environment of the repeats in domains. The folding rates of individual domains in the repeats predicted using the long-range order parameter indicate that the predicted folding rates correlate well with most of the experimentally observed folding rates for the analyzed independently folded domains.     

Transition states in protein folding kinetics: modeling phi-values of small beta-sheet proteins

Small single-domain proteins often exhibit only a single free-energy barrier, or transition state, between the denatured and the native state. The folding kinetics of these proteins is usually explored via mutational analysis. A central question is which structural information on the transition state can be derived from the mutational data. In this article, we model and structurally interpret mutational Φ-values for two small β-sheet proteins, the PIN and the FBP WW domains. The native structure of these WW domains comprises two β-hairpins that form a three-stranded β-sheet. In our model, we assume that the transition state consists of two conformations in which either one of the hairpins is formed. Such a transition state has been recently observed in molecular dynamics folding-unfolding simulations of a small designed three-stranded β-sheet protein. We obtain good agreement with the experimental data 1), by splitting up the mutation-induced free-energy changes into terms for the two hairpins and for the small hydrophobic core of the proteins; and 2), by fitting a single parameter, the relative degree to which hairpins 1 and 2 are formed in the transition state. The model helps us to understand how mutations affect the folding kinetics of WW domains, and captures also negative Φ-values that have been difficult to interpret.     

Origin of unusual phi-values in protein folding: evidence against specific nucleation sites

phi(f)-value analysis is one of the most common methods to characterize the structure of protein folding transition states. It compares the effects of mutations on the folding kinetics with the respective effects on equilibrium stability. The interpretation of the results usually focuses on a few unusual phi(f)-values, which are either particularly high or which are larger than 1 or smaller than 0. These mutations are believed to affect the most important regions for the folding process. A major uncertainty in experimental phi(f)-values is introduced by the commonly used analysis of only a single mutant at various positions in a protein (two-point analysis). To test the reliability of two-point phi(f)-values we used reference data from three positions in two different proteins at which multiple mutations have been introduced. The results show that two-point phi(f)-values are highly inaccurate if the difference in stability between two variants is less than 7 kJ/mol, corresponding to a 20-fold difference in equilibrium constant. Comparison with reported phi(f)-values for 11 proteins shows that most unusual phi(f)-values are observed in mutants which show changes in protein stability that are too small to allow a reliable analysis. The results argue against specific nucleation sites in protein folding and give a picture of transition states as distorted native states for the major part of a protein or for large substructures.     

Folding of chymotrypsin inhibitor 2. 2. Influence of proline isomerization on the folding kinetics and thermodynamic characterization of the transition state of folding

The refolding of chymotrypsin inhibitor 2 (CI2) is, at least, a triphasic process. The rate constants are 53 s-1 for the major phase (77% of the total amplitude) and 0.43 and 0.024 s-1 for the slower phases (23% of the total amplitude) at 25 degrees C and pH 6.3. The multiphase nature of the refolding reaction results from heterogeneity in the denatured state because of proline isomerization. The fast phase corresponds to the refolding of the fraction of protein that has all its prolines in a native trans conformation in the denatured state. It is not catalyzed by peptidyl-prolyl isomerase. The rate-limiting step of folding for the slower phases, however, is proline isomerization, and they are both catalyzed by peptidyl-prolyl isomerase. The slowest phase has properties consistent with a process involving proline isomerization in a denatured state. In particular, the activation enthalpy is large, 16 kcal mol-1 K-1, and the rate is independent of guanidinium chloride concentration ([GdnHCl]). In comparison, the intermediate phase shows properties consistent with a process involving proline isomerization in a partially structured state. The activation enthalpy is small, 8 kcal mol-1 K-1, and the rate has a strong dependence on [GdnHCl]. Temperature dependences of the rate constants for unfolding and for the fast refolding phase, both in the absence and in the presence of GdnHCl, were used to characterize the thermodynamic nature of the transition state and its relative exposure to solvent. The Eyring plot for unfolding is linear, indicating that there is relatively little change in heat capacity between native state and transition state.(ABSTRACT TRUNCATED AT 250 WORDS)     

The two-disulphide intermediates and the folding pathway of reduced pancreatic trypsin inhibitor.

We have studied bacteriophage λ head assembly under conditions in which the normal pathways for late phage DNA (concatemer) synthesis are blocked, and early (monomeric circular) DNA replication products accumulate. Our results show that under such conditions, the amount of late protein per amount of DNA is normal, but the amount of phage produced is not. Electron microscopic examination of thin sections of these bacteria shows that large numbers of “empty” head-shaped particles are produced. We conclude that the packaging of λ DNA depends on some structure (or property) possessed by DNA concatemers and absent in monomeric circular molecules and that the empty head-shaped particles which accumulate when concatemer production is blocked are head precursors which would normally accept concatemer DNA.These empty particles are the same size (approximately 550 Å vertex-to-vertex diameter) as the electron-dense, DNA-filled particles observed in similar sections of wild-type infected bacteria. In lysates the empty particles are approximately the same size as they are within the bacteria. However, filled heads observed in thin sections (or in negatively stained preparations) of lysates are larger than they are within the bacteria. This observation is contrary to what was previously suspected, since there seems to be little or no change in the size of intracellular λ capsids as a direct consequence of DNA packaging. Instead, an increase in the size of completed phage heads seems to take place as a consequence of cell lysis.     

Conformational dynamics of chymotrypsin inhibitor 2 by coarse-grained simulations

A coarse-grained dynamic Monte Carlo (MC) simulation method is used to investigate the conformational dynamics of chymotrypsin inhibitor 2 (CI2). Each residue is represented therein by two interaction sites, one at the alpha-carbon and the other on the amino acid side-chain. The energy and geometry parameters extracted from databank structures are used. The calculated rms fluctuations of alpha-carbon atoms are in good agreement with crystallographic temperature factors. The two regions of the protein that pack against each other to form the main hydrophobic core exhibit negatively correlated fluctuations. The conformational dynamics could efficiently be probed by the time-delayed orientational and conformational correlation functions of the virtual bonds: the active site loop, excluding the active site bond, the turn region, and the N-terminal of the alpha-helix are relatively more mobile regions of the structure. A correlation is observed between the hydrogen/deuterium (H/D) exchange behavior and the long-time orientational and conformational autocorrelation function values for CI2. A cooperativity in the rotations of the bonds near in sequence is observed at all time windows, whereas the cooperative rotations of the bonds far along the sequence appear at long time windows; these correlations contribute to the stability of the secondary structures and the tertiary structure, respectively.     

Conformational restrictions on the pathway of folding and unfolding of the pancreatic trypsin inhibitor

The kinetic roles of the partially folded, intermediate protein species with two disulphide bonds in folding and unfolding of the pancreatic trypsin inhibitor have been investigated further. Formation of a second disulphide bond between Cys5 and Cys55 during refolding of the reduced inhibitor, which would yield the species with the 30–51 and 5–55 disulphide bonds and, possibly, the native-like conformation of the protein, is not significant. Instead, three other second disulphide bonds (5–14, 5–38 and 14–38) are formed approximately 10⁵ times more readily, but each of these two-disulphide species then rearranges intramolecularly to the native-like, two-disulphide intermediate. Therefore, the reduced protein does not simply form sequentially the three disulphide bonds of the native state. Unfolding of the native state takes place by the reverse of this process.The kinetic importance for folding and unfolding of this transition between two-disulphide intermediates under the conditions used here was illustrated experimentally by a modified form of the inhibitor in which the thiols of Cys14 and Cys38 were blocked irreversibly. In the folded conformation, this modified protein is more stable to unfolding than normal, but after unfolding cannot readily regain the native-like conformation, because Cys14 or Cys38 are required to be involved in disulphide bonds during the interconversion of the two-disulphide intermediates.Some conception of the conformational transitions that take place at each stage of the folding transition may be inferred from the relative propensities of the six cysteine residues to make or rearrange disulphide bonds. It is concluded that the inhibitor probably does not refold by sequential adoption of the native conformation by the unfolded polypeptide chain. Instead, it appears that essentially all elements of the native conformation are attained simultaneously in the final stage of folding, within an unstable and flexible, yet relatively compact, form of the entire polypeptide chain produced by weak interactions between groups distant in the primary structure.     

Stabilization of proteins by enhancement of inter-residue hydrophobic contacts: lessons of T4 lysozyme and barnase

Although the hydrophobic interactions are considered as the main contributors to the protein stability, not much examples of protein stabilization by rational increasing of this type of interactions still can be found in literature. This is partly due to the lack of proper theoretical "measure" of hydrophobic interactions and their changes upon mutations. In the present paper the molecular hydrophobicity potential approach is used to assess how the changes in type and the strength of inter-residue contacts upon single amino acid mutations are correlated with the changes in thermodynamic stability of T4 lysozyme and barnase mutants, and which factors affect these correlations. Mutations changing unfavorable hydrophilic-to-hydrophobic contacts into favorable hydrophobic were found to enhance the thermodynamic stability in more than 81 % of cases, if these mutations do not create steric bumps and do not involve proline residues and hydrogen-bonded side-chains. Mutations increasing hydrophobic contributions (according to molecular hydrophobicity potential formalism) lead to increase of thermodynamic stability in more than 94% of cases for certain type of mutations (i.e., mutations not involving charged residues, Pro and residues with side-chain hydrogen bonds, when these mutations do not introduce steric bumps and do not involve strongly exposed residues and residues situated at helix N- and C-cap positions). For this type of mutations the correlation was found between the change in hydrophobic contributions of mutated residues deltaCphob and thermodynamic parameters deltaTm (change in melting temperature) and deltadeltaG (change in free energy of unfolding). Although the correlation coefficients were larger if the experimental structures of mutants were used for the calculations (correlation coefficients r(exp) deltaC,deltaT = .85 and r(exp) deltaC,deltadeltaG = 0.87) than if the modeled structures were used instead (r(mod) deltaC,deltaT = 0.74 and r(mod)deltaC,deltadeltaG = 0.76), the modelled structures of mutants in the vast majority of cases can be used for qualitative predictition of the protein stabilization. Basing on the analysis of mutations increasing hydrophobic contributions in T4 lysozyme the substitution matrix was derived, which can be used to decide which new residue should be put instead the old one to increase the stability of protein. The estimation shows that the number of potential mutation sites for enhancement of hydrophobic interactions in T4 lysozyme is quite large, and only approximately 10 per cent of them were studied thus far. Basing on the current analysis of T4 lysozyme and barnase mutations the algorithm for increasing of protein stability via increasing of hydrophobic interactions for the proteins with known spatial structure is proposed.     

Sensitivity of the folding/unfolding transition state ensemble of chymotrypsin inhibitor 2 to changes in temperature and solvent

To better characterize the transition state for folding/unfolding and its sensitivity to environmental changes, we have run multiple molecular dynamics simulations of chymotrypsin inhibitor 2 (CI2) under varying solvent conditions and temperature. The transition state structures agree well with experiment, and are similar under all of the conditions investigated here. Increasing the temperature leads to some movement in the position of the transition state along several reaction coordinates, as measured by changes in properties of the transition state structures. These structural changes are in the direction of a more native-like transition state as denaturation conditions become more severe, as expected for a Hammond effect. These structural changes are not, however, reflected in the global structure as measured by the total number of contacts or the average S-values. These results suggest that the small changes in average Phi-values with temperature seen by experiment may be due to an increase in the sensitivity of the transition state to mutation rather than a change in the average structure of the transition state. A simple analysis of the rates of unfolding indicates that the free energy barrier to unfolding decreases with increasing temperature, but even in our very high temperature simulations there is a small free energy barrier.