Optimal local propensities for model proteins

pH and Charged Mutations Modulate Cold Shock Protein Folding and Stability: A Constant pH Monte Carlo Study

The folding and stability of proteins is a fundamental problem in several research fields. In the present paper, we have used different computational approaches to study the effects caused by changes in pH and for charged mutations in cold shock proteins from Bacillus subtilis (Bs-CspB). First, we have investigated the contribution of each ionizable residue for these proteins to their thermal stability using the TKSA-MC, a Web server for rational mutation via optimizing the protein charge interactions. Based on these results, we have proposed a new mutation in an already optimized Bs-CspB variant. We have evaluated the effects of this new mutation in the folding energy landscape using structure-based models in Monte Carlo simulation at constant pH, SBM-CpHMC. Our results using this approach have indicated that the charge rearrangements already in the unfolded state are critical to the thermal stability of Bs-CspB. Furthermore, the conjunction of these simplified methods was able not only to predict stabilizing mutations in different pHs but also to provide essential information about their effects in each stage of protein folding.

Structural propensities and entropy effects in peptide helix-coil transitions

The helix-coil transition in peptides is a critical structural transition leading to functioning proteins. Peptide chains have a large number of possible configurations that must be accounted for in statistical mechanical investigations. Using hydrogen bond and local helix propensity interaction terms, we develop a method for obtaining and incorporating the degeneracy factor that allows the exact calculation of the partition function for a peptide as a function of chain length. The partition function is used in calculations for engineered peptide chains of various lengths that allow comparison with a variety of different types of experimentally measured quantities, such as fraction of helicity as a function of both temperature and chain length, heat capacity, and denaturation studies. When experimental sensitivity in helicity measurements is properly accounted for in the calculations, the calculated curves fit well with the experimental curves. We determine values of interaction energies for comparison with known biochemical interactions, as well as quantify the difference in the number of configurations available to an amino acid in a random coil configuration compared to a helical configuration.

Tertiary DNA structure in the single-stranded hTERT promoter fragment unfolds and refolds by parallel pathways via cooperative or sequential events

The discovery of G-quadruplexes and other DNA secondary elements has increased the structural diversity of DNA well beyond the ubiquitous double helix. However, it remains to be determined whether tertiary interactions can take place in a DNA complex that contains more than one secondary structure. Using a new data analysis strategy that exploits the hysteresis region between the mechanical unfolding and refolding traces obtained by a laser-tweezers instrument, we now provide the first convincing kinetic and thermodynamic evidence that a higher order interaction takes place between a hairpin and a G-quadruplex in a single-stranded DNA fragment that is found in the promoter region of human telomerase. During the hierarchical unfolding or refolding of the DNA complex, a 15-nucleotide hairpin serves as a common species among three intermediates. Moreover, either a mutant that prevents this hairpin formation or the addition of a DNA fragment complementary to the hairpin destroys the cooperative kinetic events by removing the tertiary interaction mediated by the hairpin. The coexistence of the sequential and the cooperative refolding events provides direct evidence for a unifying kinetic partition mechanism previously observed only in large proteins and complex RNA structures. Not only does this result rationalize the current controversial observations for the long-range interaction in complex single-stranded DNA structures, but also this unexpected complexity in a promoter element provides additional justification for the biological function of these structures in cells.

The ruggedness of protein-protein energy landscape and the cutoff for 1/r(n) potentials

MOTIVATION

Computational studies of the energetics of protein association are important for revealing the underlying fundamental principles and for designing better tools to model protein complexes. The interaction cutoff contribution to the ruggedness of protein-protein energy landscape is studied in terms of relative energy fluctuations for 1/r(n) potentials based on a simplistic model of a protein complex. This artificial ruggedness exists for short cutoffs and gradually disappears with the cutoff increase.

RESULTS

The critical values of the cutoff were calculated for each of 11 popular power-type potentials with n=0/9, 12 and for two thresholds of 5% and 10%. The artificial ruggedness decreases to tolerable thresholds for cutoffs larger than the critical ones. The results showed that for both thresholds the critical cutoff is a non-monotonic function of the potential power n. The functions reach the maximum at n=3/4 and then decrease with the increase of the potential power. The difference between two cutoffs for 5% and 10% artificial ruggedness becomes negligible for potentials decreasing faster than 1/r(12). The analytical results obtained for the simple model of protein complexes agree with the analysis of artificial ruggedness in a dataset of 62 protein-protein complexes, with different parameterizations of soft Lennard-Jones potential and two types of protein representations: all-atom and coarse-grained. The results suggest that cutoffs larger than the critical ones can be recommended for protein-protein potentials.

Denatured state is critical in determining the properties of model proteins designed on different folds

The thermodynamics of proteins designed on three common folds (SH3, chymotrypsin inhibitor 2 [CI2], and protein G) is studied with a simplified C(alpha) model and compared with the thermodynamics of proteins designed on random-generated folds. The model allows to design sequences to fold within a dRMSD ranging from 1.2 to 4.2 A from the crystallographic native conformation and to study properties that are hard to be measured experimentally. It is found that the denatured state of all of them is not random but is, to different extents, partially structured. The degree of structure is more abundant for SH3 and protein G, giving rise to a weaker stability but a more efficient folding kinetics than CI2 and, even more, than the random-generated folds. Consequently, the features of the unfolded state seem to be as important in the determination of the thermodynamic properties of these proteins as the features of the native state.

Influence of the chain stiffness on the thermodynamics of a Gō-type model for protein folding

The relative importance of local and long range interactions in the characteristics of the protein folding process has long been a matter of controversy. Computer simulations based on Gō-type models have been widely used to study this topic, but without much agreement on which type of interactions is more relevant for the foldability of a protein. In this work, the authors also employ a topology-based potential and simulation model to analyze the influence of local and long range interactions on the thermodynamics of the folding transition. The former are mainly used to control the degree of flexibility (or stiffness) of the chain, mostly appreciable in the unfolded (noncompact) state. Our results show the different effects that local and nonlocal interactions have on the entropy and the energy of the system. This implies that a balance between both types of interactions is required, so that a free energy barrier exists between the native and the denatured states. The variations in the contribution of both types of interactions have also a direct effect on the stability of the chain conformations, including the possible appearance of thermodynamic folding intermediates.

The Highly Cooperative Folding of Small Naturally Occurring Proteins Is Likely the Result of Natural Selection

To illuminate the evolutionary pressure acting on the folding free energy landscapes of naturally occurring proteins, we have systematically characterized the folding free energy landscape of Top7, a computationally designed protein lacking an evolutionary history. Stopped-flow kinetics, circular dichroism, and NMR experiments reveal that there are at least three distinct phases in the folding of Top7, that a nonnative conformation is stable at equilibrium, and that multiple fragments of Top7 are stable in isolation. These results indicate that the folding of Top7 is significantly less cooperative than the folding of similarly sized naturally occurring proteins, suggesting that the cooperative folding and smooth free energy landscapes observed for small naturally occurring proteins are not general properties of polypeptide chains that fold to unique stable structures but are instead a product of natural selection.

A protein evolution model with independent sites that reproduces site-specific amino acid distributions from the Protein Data Bank

BACKGROUND

Since thermodynamic stability is a global property of proteins that has to be conserved during evolution, the selective pressure at a given site of a protein sequence depends on the amino acids present at other sites. However, models of molecular evolution that aim at reconstructing the evolutionary history of macromolecules become computationally intractable if such correlations between sites are explicitly taken into account.

RESULTS

We introduce an evolutionary model with sites evolving independently under a global constraint on the conservation of structural stability. This model consists of a selection process, which depends on two hydrophobicity parameters that can be computed from protein sequences without any fit, and a mutation process for which we consider various models. It reproduces quantitatively the results of Structurally Constrained Neutral (SCN) simulations of protein evolution in which the stability of the native state is explicitly computed and conserved. We then compare the predicted site-specific amino acid distributions with those sampled from the Protein Data Bank (PDB). The parameters of the mutation model, whose number varies between zero and five, are fitted from the data. The mean correlation coefficient between predicted and observed site-specific amino acid distributions is larger than <r> = 0.70 for a mutation model with no free parameters and no genetic code. In contrast, considering only the mutation process with no selection yields a mean correlation coefficient of <r> = 0.56 with three fitted parameters. The mutation model that best fits the data takes into account increased mutation rate at CpG dinucleotides, yielding <r> = 0.90 with five parameters.

CONCLUSION

The effective selection process that we propose reproduces well amino acid distributions as observed in the protein sequences in the PDB. Its simplicity makes it very promising for likelihood calculations in phylogenetic studies. Interestingly, in this approach the mutation process influences the effective selection process, i.e. selection and mutation must be entangled in order to obtain effectively independent sites. This interdependence between mutation and selection reflects the deep influence that mutation has on the evolutionary process: The bias in the mutation influences the thermodynamic properties of the evolving proteins, in agreement with comparative studies of bacterial proteomes, and it also influences the rate of accepted mutations.

The Gō model revisited: Native structure and the geometric coupling between local and long-range contacts

Monte Carlo simulations show that long-range interactions play a major role in determining the folding rates of 48-mer three-dimensional lattice polymers modeled by the Gō potential. For three target structures with different native geometries we found a sharp increase in the folding time when the relative contribution of the long-range interactions to the native state's energy is decreased from approximately 50% towards zero. However, the dispersion of the simulated folding times is strongly dependent on native geometry and Gō polymers folding to one of the target structures exhibits folding times spanning three orders of magnitude. We have also found that, depending on the target geometry, a strong geometric coupling may exist between local and long-range contacts, which means that, when this coupling exists, the formation of long-range contacts is forced by the previous formation of local contacts. The absence of a strong geometric coupling results in a kinetics that is more sensitive to the interaction energy parameters; in this case, the formation of local contacts is not capable of promoting the establishment of long-range ones when the latter are strongly penalized energetically and this results in longer folding times.

Statistical and visual morph movie analysis of crystallographic mutant selection bias in protein mutation resource data

Structural studies of the effects of non-silent mutations on protein conformational change are an important key in deciphering the language that relates protein amino acid primary structure to tertiary structure. Elsewhere, we presented the Protein Mutant Resource (PMR) database, a set of online tools that systematically identified groups of related mutant structures in the Protein DataBank (PDB), accurately inferred mutant classifications in the Gene Ontology using an innovative, statistically rigorous data-mining algorithm with more general applicability, and illustrated the relationship of these mutant structures via an intuitive user interface. Here, we perform a comprehensive statistical analysis of the effect of PMR mutations on protein tertiary structure. We find that, although the PMR does contain spectacular examples of conformational change, in general there is a counter-intuitive inverse relationship between conformational change (measured as C-alpha displacement or RMS of the core structure) and the number of mutations in a structure. That is, point mutations by structural biologists present in the PDB contrast naturally evolved mutations. We compare the frequency of mutations in the PMR/PDB datasets against the accepted PAM250 natural amino acid mutation frequency to confirm these observations. We generated morph movies from PMR structure pairs using technology previously developed for the Macromolecular Motions Database (http://molmovdb.org), allowing bioinformaticians, geneticists, protein engineers, and rational drug designers to analyze visually the mechanisms of protein conformational change and distinguish between conformational change due to motions (e.g., ligand binding) and mutations. The PMR morph movies and statistics can be freely viewed from the PMR website, http://pmr.sdsc.edu.

Structural determinants of the rate of protein folding

To understand the mechanism of protein folding and to assist rational design of fast-folding, non-aggregating and stable artificial enzymes, it is essential to determine the structural parameters which govern the rate constants of folding, kf. It has been found that -logkf is a linear function of the so-called chain topology parameter (CTP) within the range of 10(-1)s(-1)< or = kf < or =10(8)s(-1). The correlation between -logkf and CTP is much improved than using previously published contact order (CO) method. It has been further suggested that short sequence separations may be preferred for the establishment of stable interactions for the design of novel artificial enzymes and the modification of slow-folding proteins with aggregating intermediates.

Use of conserved key amino acid positions to morph protein folds

By using three-dimensional (3D) structure alignments and a previously published method to determine Conserved Key Amino Acid Positions (CKAAPs) we propose a theoretical method to design mutations that can be used to morph the protein folds. The original Paracelsus challenge, met by several groups, called for the engineering of a stable but different structure by modifying less than 50% of the amino acid residues. We have used the sequences from the Protein Data Bank (PDB) identifiers 1ROP, and 2CRO, which were previously used in the Paracelsus challenge by those groups, and suggest mutation to CKAAPs to morph the protein fold. The total number of mutations suggested is less than 40% of the starting sequence theoretically improving the challenge results. From secondary structure prediction experiments of the proposed mutant sequence structures, we observe that each of the suggested mutant protein sequences likely folds to a different, non-native potentially stable target structure. These results are an early indicator that analyses using structure alignments leading to CKAAPs of a given structure are of value in protein engineering experiments.

Identification and ab initio simulations of early folding units in proteins

The location of protein subunits that form early during folding, constituted of consecutive secondary structure elements with some intrinsic stability and favorable tertiary interactions, is predicted using a combination of threading algorithms and local structure prediction methods. Two folding units are selected among the candidates identified in a database of known protein structures: the fragment 15-55 of 434 cro, an all-alpha protein, and the fragment 1-35 of ubiquitin, an alpha/beta protein. These units are further analyzed by means of Monte Carlo simulated annealing using several database-derived potentials describing different types of interactions. Our results suggest that the local interactions along the chain dominate in the first folding steps of both fragments, and that the formation of some of the secondary structures necessarily occurs before structure compaction. These findings led us to define a prediction protocol, which is efficient to improve the accuracy of the predicted structures. It involves a first simulation with a local interaction potential only, whose final conformation is used as a starting structure of a second simulation that uses a combination of local interaction and distance potentials. The root mean square deviations between the coordinates of predicted and native structures are as low as 2-4 A in most trials. The possibility of extending this protocol to the prediction of full proteins is discussed. Proteins 2001;42:164-176.

Exploring local and non-local interactions for protein stability by structural motif engineering

In order to probe the relative contribution of local and non-local interactions to the thermodynamic stability of proteins, we have devised an experimental approach based on a combination of motif engineering and sequence shuffling. Candidate chain segments in an immunoglobulin V(L) domain were identified whose conformation is proposed to be dominated by non-local interactions. Locally interacting structural motifs of a different conformation were then constructed as replacements, by introducing motif consensus sequences. We find that all nine replacements we constructed systematically reduce the folding cooperativity. By comparing this destabilising effect with the folding transitions of shuffled sequences for three of these motifs, we estimate the contribution of local, native interactions to the free energy of folding. Our results suggest that local and non-local interactions contribute to stability by an approximately equal amount, but that local interactions stabilise by increasing the resistance to denaturation while non-local interactions increase folding cooperativity. The systematic loss of stability by sequence shuffling in these host-guest experiments suggests that the designed interactions indeed are present in the native state, thus consensus sequence engineering may be a useful tool in structure design, but non-local interactions must be taken into account for global stability engineering. Statistical approaches are powerful tools for engineering protein structure and stability, but an analysis based on local sequence propensities alone does not adequately represent the balance of sequence and context in protein structures.

Effects of varying the local propensity to form secondary structure on the stability and folding kinetics of a rapid folding mixed alpha/beta protein: characterization of a truncation mutant of the N-terminal domain of the ribosomal protein L9

The N-terminal domain of the ribosomal protein L9 forms a split betaalphabeta structure with a long C-terminal helix. The folding transitions of a 56 residue version of this protein have previously been characterized, here we report the results of a study of a truncation mutant corresponding to residues 1-51. The 51 residue protein adopts the same fold as the 56 residue protein as judged by CD and two-dimensional NMR, but it is less stable as judged by chemical and thermal denaturation experiments. Studies with synthetic peptides demonstrate that the C-terminal helix of the 51 residue version has very little propensity to fold in isolation in contrast to the C-terminal helix of the 56 residue variant. The folding rates of the two proteins, as measured by stopped-flow fluorescence, are essentially identical, indicating that formation of local structure in the C-terminal helix is not involved in the rate-limiting step of folding.

Conformational analysis of a set of peptides corresponding to the entire primary sequence of the N-terminal domain of the ribosomal protein L9: evidence for stable native-like secondary structure in the unfolded state

There is considerable interest in the structure of the denatured state and in the role local interactions play in protein stability and protein folding. Studies of peptide fragments provide one method to assess local conformational preferences which may be present in the denatured state under native-like conditions. A set of peptides corresponding to the individual elements of secondary structure derived from the N-terminal domain of the ribosomal protein L9 have been synthesized. This small 56 residue protein adopts a mixed alpha-beta topology and has been shown to fold rapidly in an apparent two-state fashion. The conformational preferences of each peptide have been analyzed by proton nuclear magnetic resonance spectroscopy and circular dichroism spectroscopy. Peptides corresponding to each of the three beta-stands and to the first alpha-helix are unstructured as judged by CD and NMR. In contrast, a peptide corresponding to the C-terminal helix is remarkably structured. This 17 residue peptide is 53 % helical at pH 5.4, 4 degrees C. Two-dimensional NMR studies demonstrate that the helical structure is distributed approximately uniformly throughout the peptide, although there is some evidence for fraying at the C terminus. Detailed analysis of the NMR spectra indicate that the helix is stabilized, in part, by a native N-capping interaction involving Thr40. A mutant peptide which lacks Thr40 is only 32 % helical. pH and ionic strength-dependent studies suggested that charge charge interactions make only a modest net contribution to the stability of the peptide. The protein contains a trans proline peptide bond located at the first position of the C-terminal helix. NMR analysis of the helical peptide and of a smaller peptide containing the proline residue indicates that only a small amount of cis proline isomer (8 %) is likely to be populated in the unfolded state.

Conformational analysis of peptide fragments derived from the peripheral subunit-binding domain from the pyruvate dehydrogenase multienzyme complex of Bacillus stearothermophilus: evidence for nonrandom structure in the unfolded state

There is currently a great deal of interest in the early events in protein folding. Two issues that have generated particular interest are the nature of the unfolded state under native conditions and the role of local interactions in folding. Here, we report the results of a study of a set of peptides derived from a small two-helix protein, the peripheral subunit-binding domain of the pyruvate dehydrogenase multienzyme complex. Five peptides of overlapping sequence were prepared, including sequences corresponding to each of the helices and to the region connecting them. The peptides were characterized by CD and, where possible, nmr. A peptide corresponding to the second helix is between 12 and 17% helical at neutral pH. CD also indicates a lower percentage of helical structure in the peptide corresponding to the first alpha-helix, although the values of the alpha-proton chemical shifts suggest some preference for nonrandom structure. Peptides corresponding to the interhelical loop, which in the full domain contains two overlapping beta-turns and a 5-residue 3(10)-helix, are less structured. There is no significant change in the helicity of any of these peptides with pH. To test for fragment complementation, CD spectra of the two peptides derived from each helix and the long connecting peptide were compared to the spectra of each possible pair, as well as to a mixture containing all three. No increase in structure was observed. We complement our peptide studies by characterizing a point mutant, D34V, which disrupts a critical hydrogen bonding network. This mutant is unable to fold and provides a useful model of the denatured state. The mutant is between 9 and 16% helical as judged by CD. The modest amount of helical structure formed in some of the peptide fragments and in the point mutant suggests that the denatured state of the peripheral subunit binding domain is not completely unstructured. This may contribute to the very rapid folding observed for the intact protein.

Use of quantitative structure-property relationships to predict the folding ability of model proteins

We investigate the folding of a 125-bead heteropolymer model for proteins subject to Monte Carlo dynamics on a simple cubic lattice. Detailed study of a few sequences revealed a folding mechanism consisting of a rapid collapse followed by a slow search for a stable core that served as the transition state for folding to a near-native intermediate. Rearrangement from the intermediate to the native state slowed folding further because it required breaking native-like local structure between surface monomers so that those residues could condense onto the core. We demonstrate here the generality of this mechanism by a statistical analysis of a 200 sequence database using a method that employs a genetic algorithm to pick the sequence attributes that are most important for folding and an artificial neural network to derive the corresponding functional dependence of folding ability on the chosen sequence attributes [quantitative structure-property relationships (QSPRs)]. QSPRs that use three sequence attributes yielded substantially more accurate predictions than those that use only one. The results suggest that efficient search for the core is dependent on both the native state's overall stability and its amount of kinetically accessible, cooperative structure, whereas rearrangement from the intermediate is facilitated by destabilization of contacts between surface monomers. Implications for folding and design are discussed.

Lattice models for proteins reveal multiple folding nuclei for nucleation-collapse mechanism

The nature of the nucleation-collapse mechanism in protein folding is probed using 27-mer and 36-mer lattice models. Three different forms for the interaction potentials are used. Three of the four 27-mer sequences have maximally compact and identical native state while the other has a non-compact native conformation. All the sequences fold thermodynamically and kinetically by a two-state process. Analysis of individual trajectories for each sequence using a self-organizing neural net algorithm shows that upon formation of a critical set of contacts the polypeptide chain rapidly reaches the native conformation which is consistent with a nucleation-collapse mechanism. The algorithm, which reduces the identification of the folding nucleus for each trajectory to one of pattern recognition, is used to show that there are multiple folding nuclei. There is a distribution of nucleation contacts in the transition states with some of them occurring with more probability (when averaged over the denatured ensemble) than others. We also show that there is a distribution in the size of the nuclei with the average number of residues in the folding nuclei being less than about one-third of the chain size. The fluctuations in the sizes of the nuclei are large, suggestive of a broad transition region. The folding nuclei, the structures of each are the corresponding transition states, have varying degree of overlap with the native conformation. The distribution of the radius of gyration of the transition states shows that these structures are an expanded form (by about 25% in the radius of gyration) of the native conformation. Local contacts are most dominant in the folding nuclei while a certain fraction of non-local contacts is necessary to stabilize the transition states. The search for the critical nuclei initially involves the formation of local contacts, while non-local contacts are formed later. The fractional values of PhiF for the two 27-mer mutants found by using the protein engineering protocol are consistent with the microscopic picture of partial formation of structures involving these residues in the transition state. These observations lead to a multiple folding nuclei (MFN) model for nucleation-collapse mechanism in protein folding. The major implication of the MFN model is that, even if the residues whose tertiary interactions are formed nearly completely in the transition state are mutated, it does not disrupt the nature of the nucleation-collapse mechanism. We analyze the experiments on chymotrypsin inhibitor 2 and alpha-spectrin SH3 domain and two circular permutants in light of the MFN model. It is shown that the PhiF-value analysis for these proteins gives considerable support to the MFN model. The theoretical and experimental studies give a coherent picture of the nucleation-collapse mechanism in which there is a distribution of folding nuclei with some more probable than others. The formation of any specific nucleus is not necessary for efficient two-state folding.

Intrahelical side chain interactions in alpha-helices: poor correlation between energetics and frequency

Polypeptide sequences in proteins may increase their tendency to adopt helical conformations in several ways. One is the recruiting of amino acid residues with high helical propensity. Another is the appropriate distribution of residues along the helix to establish stabilising side chain interactions. The first strategy is known to be followed by natural proteins because amino acids with high helical propensity are more frequent in alpha-helices. If proteins also followed the second strategy, stabilising amino acid pairs should be more frequent than others. To test this possibility we compared empirical energies of side chain interactions in alpha-helices with statistical energies calculated from a data base of proteins with low homology. We find some correlation between the stability afforded by the pairs and their relative abundance in alpha-helices but the realisation of energetic preferences into statistical preferences is very low. This indicates that natural alpha-helices do not regularly use intrahelical side chain interactions to increase their stability.

Contact order, transition state placement and the refolding rates of single domain proteins

Theoretical studies have suggested relationships between the size, stability and topology of a protein fold and the rate and mechanisms by which it is achieved. The recent characterization of the refolding of a number of simple, single domain proteins has provided a means of testing these assertions. Our investigations have revealed statistically significant correlations between the average sequence separation between contacting residues in the native state and the rate and transition state placement of folding for a non-homologous set of simple, single domain proteins. These indicate that proteins featuring primarily sequence-local contacts tend to fold more rapidly and exhibit less compact folding transition states than those characterized by more non-local interactions. No significant relationship is apparent between protein length and folding rates, but a weak correlation is observed between length and the fraction of solvent-exposed surface area buried in the transition state. Anticipated strong relationships between equilibrium folding free energy and folding kinetics, or between chemical denaturant and temperature dependence-derived measures of transition state placement, are not apparent. The observed correlations are consistent with a model of protein folding in which the size and stability of the polypeptide segments organized in the transition state are largely independent of protein length, but are related to the topological complexity of the native state. The correlation between topological complexity and folding rates may reflect chain entropy contributions to the folding barrier.

A metastable state in folding simulations of a protein model

The native state of a protein is generally believed to be the global free energy minimum. However, there is increasing evidence that kinetically selected states play a role in the biological function of some proteins. In a recent folding study of a 125-residue heteropolymer model, one of 200 sequences was found to fold repeatedly to a particular local minimum that did not interconvert to the global minimum. The kinetic preference for this 'metastable' state is shown to derive from an entropic barrier associated with inserting a tail segment into the protein interior of the serpin-like global minimum structure. The relation of the present results to the role of metastable states in functioning and pathogenic proteins is discussed.

The nucleation-collapse mechanism in protein folding: evidence for the non-uniqueness of the folding nucleus

BACKGROUND

Recent experimental and theoretical studies have shown that several small proteins reach the native state by a nucleation-collapse mechanism. Studies based on lattice models have been used to suggest that the critical nucleus is specific, leading to the notion that the transition state may be unique. On the other hand, results of studies using off-lattice models show that the critical nuclei should be viewed as fluctuating mobile structures, thus implying non-unique transition states.

RESULTS

The microscopic underpinnings of the nucleation-collapse mechanism in protein folding are probed using minimal off-lattice models and Langevin dynamics. We consider a 46-mer continuum model which has a native beta-barrel-like structure. The fast-folding trajectories reach the native state by a nucleation-collapse process. An algorithm based on the self-organized neural nets is used to identify the critical nuclei for a large number of rapidly folding trajectories. This method, which reduces the determination of the critical nucleus to one of 'pattern recognition', unambiguously shows that the folding nucleus is not unique. The only common characteristics of the mobile critical nuclei are that they are small (containing on average 15-22 residues) and are largely composed of residues near the loop regions of the molecule. The structures of the transition states, corresponding to the critical nuclei, show the existence of spatially localized ordered regions that are largely made up of residues that are close to each other. These structures are stabilized by a few long-range contacts. The structures in the ensemble of transition states exhibit a rather diverse degree of similarity to the native conformation.

CONCLUSIONS

The multiplicity of delocalized nucleation regions can explain the two-state folding by a nucleation-collapse mechanism for small single-domain proteins (such as chymotrypsin inhibitor 2) and their mutants. Because there are many distinct critical nuclei, we predict that the folding kinetics of fast-folding proteins will not be drastically changed even if some of the residues in a 'typical' nucleus are altered.

Contrasting roles for symmetrically disposed beta-turns in the folding of a small protein

To investigate the role of turns in protein folding, we have characterized the effects of combinatorial and site-directed mutations in the two beta-turns of peptostreptococcal protein L on folding thermodynamics and kinetics. Sequences of folded variants recovered from combinatorial libraries using a phase display selection method were considerably more variable in the second turn than in the first turn. These combinatorial mutants as well as strategically placed point mutants in the two turns had a similar range of thermodynamic stabilities, but strikingly different folding kinetics. A glycine to alanine substitution in the second beta-turn increased the rate of unfolding more than tenfold but had little effect on the rate of folding, while mutation of a symmetrically disposed glycine residue in the first turn had little effect on unfolding but slowed the rate of folding nearly tenfold. These results demonstrate that the role of beta-turns in protein folding is strongly context-dependent, and suggests that the first turn is formed and the second turn disrupted in the folding transition state.

Evolution of model proteins on a foldability landscape

We model the evolution of simple lattice proteins as a random walk in a fitness landscape, where the fitness represents the ability of the protein to fold. At higher selective pressure, the evolutionary trajectories are confined to neutral networks where the native structure is conserved and the dynamics are non self-averaging and nonexponential. The optimizability of the corresponding native structure has a strong effect on the size of these neutral networks and thus on the nature of the evolutionary process.

Local interactions and the optimization of protein folding

The role of local interactions in protein folding has recently been the subject of some controversy. Here we investigate an extension of Zwanzig's simple and general model of folding in which local and nonlocal interactions are represented by functions of single and multiple conformational degrees of freedom, respectively. The kinetics and thermodynamics of folding are studied for a series of energy functions in which the energy of the native structure is fixed, but the relative contributions of local and nonlocal interactions to this energy are varied over a broad range. For funnel shaped energy landscapes, we find that 1) the rate of folding increases, but the stability of the folded state decreases, as the contribution of local interactions to the energy of the native structure increases, and 2) the amount of native structure in the unfolded state and the transition state vary considerably with the local interaction strength. Simple exponential kinetics and a well-defined free energy barrier separating folded and unfolded states are observed when nonlocal interactions make an appreciable contribution to the energy of the native structure; in such cases a transition state theory type approximation yields reasonably accurate estimates of the folding rate. Bumps in the folding funnel near the native state, which could result from desolvation effects, side chain freezing, or the breaking of nonnative contacts, significantly alter the dependence of the folding rate on the local interaction strength: the rate of folding decreases when the local interaction strength is increased beyond a certain point. A survey of the distribution of strong contacts in the protein structure database suggests that evolutionary optimization has involved both kinetics and thermodynamics: strong contacts are enriched at both very short and very long sequence separations.

The foldability landscape of model proteins

Molecular evolution may be considered as a walk in a multidimensional fitness landscape, where the fitness at each point is associated with features such as the function, stability, and survivability of these molecules. We present a simple model for the evolution of protein sequences on a landscape with a precisely defined fitness function. We use simple lattice models to represent protein structures, with the ability of a protein sequence to fold into the structure with lowest energy, quantified as the foldability, representing the fitness of the sequence. The foldability of the sequence is characterized based on the spin glass model of protein folding. We consider evolution as a walk in this foldability landscape and study the nature of the landscape and the resulting dynamics. Selective pressure is explicitly included in this model in the form of a minimum foldability requirement. We find that different native structures are not evenly distributed in interaction space, with similar structures and structures with similar optimal foldabilities clustered together. Evolving proteins marginally fulfill the selective criteria of foldability. As the selective pressure is increased, evolutionary trajectories become increasingly confined to "neutral networks," where the sequence and the interactions can be significantly changed while a constant structure is maintained.

Predicting protein stability changes upon mutation using database-derived potentials: solvent accessibility determines the importance of local versus non-local interactions along the sequence

For 238 mutations of residues totally or partially buried in the protein core, we estimate the folding free energy changes upon mutation using database-derived potentials and correlate them with the experimentally measured ones. Several potentials are tested, representing different kinds of interactions. Local interactions along the chain are described by torsion potentials, based on propensities of amino acids to be associated with backbone torsion angle domains. Non-local interactions along the sequence are represented by distance potentials, derived from propensities of amino acid pairs or triplets to be at a given spatial distance. We find that for the set of totally buried residues, the best performing potential is a combination of a distance potential and a torsion potential weighted by a factor of 0.4; it yields a correlation coefficient between computed and measured changes in folding free energy of 0.80. For mutations of partially buried residues, the best potential is a combination of a torsion potential and a distance potential weighted by a factor of 0.7, and for the previously analysed mutations of solvent accessible residues, it is a torsion potential taken individually; the respective correlation coefficients reach 0.82 and 0.87. These results show that distance potentials, dominated by hydrophobic interactions, represent best the main interactions stabilizing the protein core, whereas torsion potentials, describing local interactions along the chain, represent best the interactions at the protein surface. The prediction accuracy reached by the distance potentials is, however, lower than that of the torsion potentials. A possible reason for this is that distance potentials would not describe correctly the effect on protein stability due to cavity formation upon mutating a large into a small amino acid. Last but not least, our results indicate that although local interactions, responsible for secondary structure formation, do not dominate in the protein core, they are not negligible for all that. They have a significant weight in the delicate balance between all the interactions that ensure protein stability.

Non-native local interactions in protein folding and stability: introducing a helical tendency in the all beta-sheet alpha-spectrin SH3 domain

The relative importance of secondary structure interactions versus tertiary interactions for stabilising and guiding the folding process is a matter for discussion. Phenomenological models of protein folding assign an important role to local contacts in protein folding and stability. On the other hand, simplistic lattice simulations find that secondary structure is mainly the product of protein compaction and that optimisation of folding speed seems to require small contributions of local contacts to the stability of the folded state. To examine the extent to which secondary structure propensities influence protein folding and stability, we have designed mutations that introduce a strong non-native helical propensity in the first 19 residues of the alpha-spectrin SH3 domain. The mutant proteins have the same three-dimensional structure as the wild-type, but they are less stable and have less co-operative folding transitions. There seems to be a relationship between the non-native helical propensity and the compaction of the denatured state. This suggests that in the denatured ensemble under native conditions there is a significant proportion of compact structures with non-native secondary structures. Our results demonstrate that non-local interactions can overcome strong non-native secondary structure propensities and, more important, that optimisation of folding speed and co-operativity requires the latter to be relatively small.

Mutation matrices and physical-chemical properties: correlations and implications

To investigate how the properties of individual amino acids result in proteins with particular structures and functions, we have examined the correlations between previously derived structure-dependent mutation rates and changes in various physical-chemical properties of the amino acids such as volume, charge, alpha-helical and beta-sheet propensity, and hydrophobicity. In most cases we found the delta G of transfer from octanol to water to be the best model for evolutionary constraints, in contrast to the much weaker correlation with the delta G of transfer from cyclohexane to water, a property found to be highly correlated to changes in stability in site-directed mutagenesis studies. This suggests that natural evolution may follow different rules than those suggested by results obtained in the laboratory. A high degree of conservation of a surface residue's relative hydrophobicity was also observed, a fact that cannot be explained by constraints on protein stability but that may reflect the consequences of the reverse-hydrophobic effect. Local propensity, especially alpha-helical propensity, is rather poorly conserved during evolution, indicating that non-local interactions dominate protein structure formation. We found that changes in volume were important in specific cases, most significantly in transitions among the hydrophobic residues in buried locations. To demonstrate how these techniques could be used to understand particular protein families, we derived and analyzed mutation matrices for the hypervariable and framework regions of antibody light chain V regions. We found surprisingly high conservation of hydrophobicity in the hypervariable region, possibly indicating an important role for hydrophobicity in antigen recognition.

Folding kinetics of Che Y mutants with enhanced native alpha-helix propensities

In this work we study the folding kinetics of Che Y mutants in which the helical propensity of each of its five alpha-helices has been greatly enhanced by local interactions (between residues close in sequence). This constitutes an experimental test on the role of local interactions in protein folding, as well as providing new information on the details of the folding pathway of the protein Che Y. With respect to the first issue, our results show that the enhancement of helical propensities by native-like local interactions in Che Y has the following general effects: (1) the energetics of the whole Che Y folding energy landscape (folded state, intermediate, denatured state and main transition state) are affected by the enhancement of helical propensities, thus, native-like local interactions appear to have a low specificity for the native conformation; (2) our results support the idea, proposed from thermodynamic analysis of the mutants, that the denatured state under native conditions becomes more compact upon enhancement of helical propensities; (3) the rate of folding in aqueous solution decreases in all the mutants, suggesting that the optimization of the folding rate in this protein requires low secondary structure propensities. Regarding the description of the folding pathway of Che Y, we find evidence that the folding transition state of Che Y is constituted by two sub-domains with different degree of helical structure. The first includes helices 1 and 2 which are rather structured, while the second encompasses the last three helices, which are very unstructured. On the other hand, the same analysis for the folding intermediate indicates that all the five alpha-helices are, on average, rather structured. Thus, suggesting that a large structural reorganization of the last three alpha-helices must take place before folding can be completed. This conclusion indicates that the folding intermediate of Che Y is a misfolded species.

Nucleation mechanisms in protein folding

Experiment and theory are converging on the importance of nucleation mechanisms in protein folding. These mechanisms do not use classic nuclei, which are well formed elements of structure present in ground states, but they use diffuse, extended regions, which are observed in transition states.

Favourable native-like helical local interactions can accelerate protein folding

BACKGROUND

Extensive studies of peptide conformation have provided reasonable knowledge of the rules determining helix stability. This knowledge can be used to stabilize proteins against chemical and thermal denaturation. This has been done in two proteins: the chemotactic protein from Escherichia coli, Che Y (a 129 aa alpha/beta parallel protein with five alpha-helices, which shows an accumulating intermediate during refolding) and the activation domain of human procarboxypeptidase A2, ADA2h (a 81 aa alpha + beta protein domain, with two alpha-helices, which follows a two-state mechanism). As the introduced stabilizing interactions are local in nature, the energy balance between the contribution of local and nonlocal interactions changes considerably. Recent theoretical analyses of protein folding using simplified models have indicated that optimization of folding speed requires this balance to be biased towards nonlocal interactions. To determine whether this is the case, we study here the folding kinetics of two ADA2h mutants in which alpha-helix 1 (mutant M1) or 2 (mutant M2) has been stabilized through local interactions, as well as the equilibrium and kinetic behaviour of a double mutant (DM) in which both helices have been stabilized.

RESULTS

The stability of DM is considerably enhanced with respect to wild type (WI) and this mutant can be considered as a thermoresistant protein (Tm > 363 K). The thermodynamic parameters obtained by chemical denaturation (urea and GdnHCl) show that DM is approximately 2.6 kcal mol-1 more stable than WT. The effects on folding kinetics are different in each of the single mutants. M1 shows very little effect in refolding, while its unfolding is greatly decelerated with respect to WT. M2 shows, together with a deceleration in unfolding, a significant acceleration in refolding. As with equilibrium parameters, the kinetics of the double mutant can be explained by the simple addition of the effects found in each single mutant. Interestingly enough, the refolding slope mkf in mutants M2 and DM is smaller than in the wild-type and M1 mutant.

CONCLUSIONS

Thermoresistance can be achieved, in some cases, by increasing favourable native local interactions. The balance between local and nonlocal interactions can be significantly changed in some proteins and still keep a cooperative unfolding transition similar to that of the wild type. The introduction of favourable local interactions by mutational redesign can also be used to increase the folding speed of certain proteins, showing that not all proteins in nature have been optimized for rapid folding, contrary to what has been theoretically indicated. This behaviour is probably also shared by other polypeptides with highly unstructured denatured states. All these phenomena have been shown experimentally in ADA2h by mutations that increase helix stability. However, the effects promoted for such an approach in proteins with residual structure and/or intermediates in the denatured ensemble could be different. This has been shown by experiments performed on CheY in which the cooperativity of the folding process was greatly affected.

Role of a nonnative interaction in the folding of the protein G B1 domain as inferred from the conformational analysis of the alpha-helix fragment

BACKGROUND

The role of local interactions in protein folding and stability can be investigated by the conformational analysis of protein fragments. The hydrophobic staple and Schellman motifs have been described at the N and C terminus, respectively, of protein alpha-helices. These motifs are characterized by an interaction between two hydrophobic residues, one outside the helix and one within the helix, and their importance for helix stability has been analyzed in model peptides. In the alpha-helix of the protein G B1 domain, only the Schellman motif is formed--the hydrophobic staple motif is absent despite the favourable sequence pattern. We have experimentally analyzed the solution conformation of the 19-41 fragment of protein G. This peptide comprises the helical residues and contains both the hydrophobic staple and Schellman motif sequences.

RESULTS

In the isolated peptide in water, the hydrophobic staple motif is formed and stabilizes the helical structure as compared with a shorter peptide lacking it, but the Schellman motif is not formed. In 30% aqueous TFE, the helix is more stable than in pure water and both motifs are formed.

CONCLUSIONS

The results suggest that the importance of each motif for the folding and stability of protein G is different. The nonnative hydrophobic staple interaction can help to nucleate the helix at the beginning of folding but has later to be disrupted. The Schellman motif, while not providing enough energy for substantial helix stabilization in the unfolded state, could be important for determining the local fold of the sequence in the context of the rest of the protein.

Conformational analysis of peptides corresponding to all the secondary structure elements of protein L B1 domain: secondary structure propensities are not conserved in proteins with the same fold

The solution conformation of three peptides corresponding to the two beta-hairpins and the alpha-helix of the protein L B1 domain have been analyzed by circular dichroism (CD) and nuclear magnetic resonance spectroscopy (NMR). In aqueous solution, the three peptides show low populations of native and non-native locally folded structures, but no well-defined hairpin or helix structures are formed. In 30% aqueous trifluoroethanol (TFE), the peptide corresponding to the alpha-helix adopts a high populated helical conformation three residues longer than in the protein. The hairpin peptides aggregate in TFE, and no significant conformational change occurs in the NMR observable fraction of molecules. These results indicate that the helical peptide has a significant intrinsic tendency to adopt its native structure and that the hairpin sequences seem to be selected as non-helical. This suggests that these sequences favor the structure finally attained in the protein, but the contribution of the local interactions alone is not enough to drive the formation of a detectable population of native secondary structures. This pattern of secondary structure tendencies is different to those observed in two structurally related proteins: ubiquitin and the protein G B1 domain. The only common feature is a certain propensity of the helical segments to form the native structure. These results indicate that for a protein to fold, there is no need for large native-like secondary structure propensities, although a minimum tendency to avoid non-native structures and to favor native ones could be required.

Why are some proteins structures so common?

Many biological proteins are observed to fold into one of a limited number of structural motifs. By considering the requirements imposed on proteins by their need to fold rapidly, and the ease with which such requirements can be fulfilled as a function of the native structure, we can explain why certain structures are repeatedly observed among proteins with negligible sequence similarity. This work has implications for the understanding of protein sequence structure relationships as well as protein evolution.