Surprisingly high correlation between early and late stages in non-two-state protein folding

We collected quantitative kinetic data on early and late stages of folding in non-two-state proteins from the literature, and studied the relationship between the kinetics of the two stages. There was a surprisingly high correlation between the rate constants of these stages. The correlation coefficient of the logarithmic rate constants was as high as 0.97, which could not be caused by chance. We also studied relationships of the logarithmic rate constants of the two stages with native three-dimensional structures represented by the residue-residue contact map. There were again surprisingly high correlations between the logarithmic rate constants and the number of non-local contact clusters obtained from the contact maps. Because the number of non-local contact clusters represents overall arrangement of substructures in a native protein, the results strongly suggested the importance of the arrangement of the substructures for the kinetics of both early and late stages of protein folding.     

Simulating protein evolution in sequence and structure space

Naturally occurring proteins comprise a special subset of all plausible sequences and structures selected through evolution. Simulating protein evolution with simplified and all-atom models has shed light on the evolutionary dynamics of protein populations, the nature of evolved sequences and structures, and the extent to which today's proteins are shaped by selection pressures on folding, structure and function. Extensive mapping of the native structure, stability and folding rate in sequence space using lattice proteins has revealed organizational principles of the sequence/structure map important for evolutionary dynamics. Evolutionary simulations with lattice proteins have highlighted the importance of fitness landscapes, evolutionary mechanisms, population dynamics and sequence space entropy in shaping the generic properties of proteins. Finally, evolutionary-like simulations with all-atom models, in particular computational protein design, have helped identify the dominant selection pressures on naturally occurring protein sequences and structures.     

Exploring the effects of sparse restraints on protein structure prediction

One of the main barriers to accurate computational protein structure prediction is searching the vast space of protein conformations. Distance restraints or inter‐residue contacts have been used to reduce this search space, easing the discovery of the correct folded state. It has been suggested that about 1 contact for every 12 residues may be sufficient to predict structure at fold level accuracy. Here, we use coarse‐grained structure‐based models in conjunction with molecular dynamics simulations to examine this empirical prediction. We generate sparse contact maps for 15 proteins of varying sequence lengths and topologies and find that given perfect secondary‐structural information, a small fraction of the native contact map (5%‐10%) suffices to fold proteins to their correct native states. We also find that different sparse maps are not equivalent and we make several observations about the type of maps that are successful at such structure prediction. Long range contacts are found to encode more information than shorter range ones, especially for α and αβ‐proteins. However, this distinction reduces for β‐proteins. Choosing contacts that are a consensus from successful maps gives predictive sparse maps as does choosing contacts that are well spread out over the protein structure. Additionally, the folding of proteins can also be used to choose predictive sparse maps. Overall, we conclude that structure‐based models can be used to understand the efficacy of structure‐prediction restraints and could, in future, be tuned to include specific force‐field interactions, secondary structure errors and noise in the sparse maps.     

Prediction of probable pathways of folding in globular proteins

A method is described for the prediction of probable folding pathways of globular proteins, based on the analysis of distance maps. It is applicable to proteins of unknown spatial structure but known amino acid sequence as well as to proteins of known structure. It is based on an objective procedure for the determination of the boundary of compact regions that contain high densities of interresidue contacts on the distance map of a globular protein. The procedure can be used both with contact maps derived from a known three-dimensional protein structure and with predicted contact maps computed by means of a statistical procedure from the amino acid sequence alone. The computed contact map can also be used to predict the location of compact short-range structures, viz. -helices and -turns, thereby complementing other statistical predictive procedures. The method provides an objective basis for the derivation of a theoretically predicted pathway of protein folding, proposed by us earlier [Tanaka and Scheraga (1977) Macromolecules10, 291–304; Némethy and Scheraga (1979) Proc. Natl. Acad. Sci., U.S.A.76, 6050–6054].     

Re‐engineering a β‐lactamase using prototype peptides from a library of local structural motifs

B. licheniformis exo‐small β‐lactamase (ESBL) has a complex architecture with twelve α helices and a five‐stranded beta sheet. We replaced, separately or simultaneously, three of the ESBL α helices with prototype amphiphatic helices from a catalog of secondary structure elements. Although the substitutes bear no sequence similarity to the originals and pertain to unrelated protein families, all the engineered ESBL variants were found able to fold in native like structures with in vitro and in vivo enzymic activity. The triple substituted variant resembles a primitive protein, with folding defects such as a strong tendency to oligomerization and very low stability; however it mimics a non homologous recombinant abandoning the family sequence space while preserving fold. The results test protein folding and evolution theories.     

Relationship between energy distribution and fold stability: Insights from molecular dynamics simulations of native and mutant proteins

Most proteins must fold to a well-defined structure with a minimal stability to perform their function. Here we use a simple, molecular dynamics-based, energy decomposition approach to map the principal energetic interactions in a set of proteins representative of different folds. This work involves the all-atom simulation and analysis of the native structures and mutants of five different proteins representative of an all-alpha (yACPB, Protein A), all-beta (SH3), and a mixed alpha/beta fold (Proteins G and L). Given a certain structure, a native sequence and a set of mutants, we show that our model discriminates the ability of a mutation to yield a more or less stable protein, in agreement with experimental data, catching the principal energetic determinants of protein stabilization. Our approach identifies the interaction determinants responsible to define a fold and shows that mutations can either modulate the strength of pair-wise coupling between residues important for folding, or modify the profile of the principal interactions. Furthermore, we address the question of how to evaluate the fitness of a sequence to a given structure by comparing the information contained in the energy map, which recapitulates the chemistry of the sequence, to that contained in the contact map, which recapitulates the fold topology. The results show that the better fit between the energetic properties of the sequence and the fold topology corresponds to a higher stabilization of the protein. We discuss the relevance of these observations to the analysis of protein designability and to the rational evolution of new sequences.     

Sequence determinants of protein folding rates: positive correlation between contact energy and contact range indicates selection for fast folding

In comparison with intense investigation of the structural determinants of protein folding rates, the sequence features favoring fast folding have received little attention. Here, we investigate this subject using simple models of protein folding and a statistical analysis of the Protein Data Bank (PDB). The mean-field model by Plotkin and coworkers predicts that the folding rate is accelerated by stronger-than-average interactions at short distance along the sequence. We confirmed this prediction using the Finkelstein model of protein folding, which accounts for realistic features of polymer entropy. We then tested this prediction on the PDB. We found that native interactions are strongest at contact range l = 8. However, since short range contacts tend to be exposed and they are frequently formed in misfolded structures, selection for folding stability tends to make them less attractive, that is, stability and kinetics may have contrasting requirements. Using a recently proposed model, we predicted the relationship between contact range and contact energy based on buriedness and contact frequency. Deviations from this prediction induce a positive correlation between contact range and contact energy, that is, short range contacts are stronger than expected, for 2/3 of the proteins. This correlation increases with the absolute contact order (ACO), as expected if proteins that tend to fold slowly due to large ACO are subject to stronger selection for sequence features favoring fast folding. Our results suggest that the selective pressure for fast folding is detectable only for one third of the proteins in the PDB, in particular those with large contact order.     

Exploring the nonlinear geometry of protein homology

The explosion of biological data resulting from genomic and proteomic research has created a pressing need for data analysis techniques that work effectively on a large scale. An area of particular interest is the organization and visualization of large families of protein sequences. An increasingly popular approach is to embed the sequences into a low-dimensional Euclidean space in a way that preserves some predefined measure of sequence similarity. This method has been shown to produce maps that exhibit global order and continuity and reveal important evolutionary, structural, and functional relationships between the embedded proteins. However, protein sequences are related by evolutionary pathways that exhibit highly nonlinear geometry, which is invisible to classical embedding procedures such as multidimensional scaling (MDS) and nonlinear mapping (NLM). Here, we describe the use of stochastic proximity embedding (SPE) for producing Euclidean maps that preserve the intrinsic dimensionality and metric structure of the data. SPE extends previous approaches in two important ways: (1) It preserves only local relationships between closely related sequences, thus allowing the map to unfold and reveal its intrinsic dimension, and (2) it scales linearly with the number of sequences and therefore can be applied to very large protein families. The merits of the algorithm are illustrated using examples from the protein kinase and nuclear hormone receptor superfamilies.     

Analysis of the differences in the folding kinetics of structurally homologous proteins based on predictions of the gross features of residue contacts

It is a general notion that proteins with very similar three-dimensional structures would show very similar folding kinetics. However, recent studies reveal that the folding kinetic properties of some proteins contradict this thought (i.e., the members in a same protein family fold through different pathways). For example, it has been reported that some beta-proteins in the intracellular lipid-binding protein family fold through quite different pathways (Burns et al., Proteins 1998;33:107-118). Similar differences in folding kinetics are also observed in the members of the globin family (Nishimura et al., Nat Struct Biol 2000;7:679-686). In our study, we examine the possibility of predicting qualitative differences in folding kinetics of the intracellular lipid-binding proteins and two globin proteins (i.e., myoglobin and leghemoglobin). The problem is tackled by means of a contact map based on the average distance statistics between residues, the Average Distance Map (ADM), as constructed from sequence. The ADMs for the three proteins show overall similarity, but some local differences among maps are also observed. Our results demonstrate that some properties of the protein folding kinetics are consistent with local differences in the ADMs. We also discuss the general possibility of predicting folding kinetics from sequence information.     

Juxtamembrane tryptophans have distinct roles in defining the OmpX barrel–micelle boundary and facilitating protein–micelle association

Defining the span of the transmembrane region, a key requirement to ensure correct folding, stability and function of bacterial outer membrane β-barrels, is assisted by the amphipathic property of tryptophan. We demonstrate the unique and distinctive properties of the interface Trp76 and Trp140 of outer membrane protein X, and map their positional relevance to the refolding process, barrel formation and the resulting stability in dodecylphosphocholine micelles. The solvent-exposed Trp76 displays a rigid interfacial localization, whereas Trp140 is relatively micelle-solvated and contributes to barrel folding and global OmpX stability. Kinetic contribution to OmpX stability is influenced by the two tryptophans. Differential associations of the indoles with the detergent milieu therefore contribute to micelle-assisted β-barrel folding and concomitant OmpX stability.     

Folding rates and low-entropy-loss routes of two-state proteins

We develop a simple model for computing the rates and routes of folding of two-state proteins from the contact maps of their native structures. The model is based on the graph-theoretical concept of effective contact order (ECO). The model predicts that proteins fold by "zipping up" in a sequence of small-loop-closure events, depending on the native chain fold. Using a simple equation, with a few physical rate parameters, we obtain a good correlation with the folding rates of 24 two-state folding proteins. The model rationalizes data from Phi-value analysis that have been interpreted in terms of delocalized or polarized transition states. This model indicates how much of protein folding may take place in parallel, not along a single reaction coordinate or with a single transition state.     

Principles of protein folding--a perspective from simple exact models.

General principles of protein structure, stability, and folding kinetics have recently been explored in computer simulations of simple exact lattice models. These models represent protein chains at a rudimentary level, but they involve few parameters, approximations, or implicit biases, and they allow complete explorations of conformational and sequence spaces. Such simulations have resulted in testable predictions that are sometimes unanticipated: The folding code is mainly binary and delocalized throughout the amino acid sequence. The secondary and tertiary structures of a protein are specified mainly by the sequence of polar and nonpolar monomers. More specific interactions may refine the structure, rather than dominate the folding code. Simple exact models can account for the properties that characterize protein folding: two-state cooperativity, secondary and tertiary structures, and multistage folding kinetics--fast hydrophobic collapse followed by slower annealing. These studies suggest the possibility of creating "foldable" chain molecules other than proteins. The encoding of a unique compact chain conformation may not require amino acids; it may require only the ability to synthesize specific monomer sequences in which at least one monomer type is solvent-averse.     

Sub-microsecond protein folding

We have investigated the structure, equilibria, and folding kinetics of an engineered 35-residue subdomain of the chicken villin headpiece, an ultrafast-folding protein. Substitution of two buried lysine residues by norleucine residues stabilizes the protein by 1 kcal/mol and increases the folding rate sixfold, as measured by nanosecond laser T-jump. The folding rate at 300 K is (0.7 micros)(-1) with little or no temperature dependence, making this protein the first sub-microsecond folder, with a rate only twofold slower than the theoretically predicted speed limit. Using the 70 ns process to obtain the effective diffusion coefficient, the free energy barrier height is estimated from Kramers theory to be less than approximately 1 kcal/mol. X-ray crystallographic determination at 1A resolution shows no significant change in structure compared to the single-norleucine-substituted molecule and suggests that the increased stability is electrostatic in origin. The ultrafast folding rate, very accurate X-ray structure, and small size make this engineered villin subdomain an ideal system for simulation by atomistic molecular dynamics with explicit solvent.     

Evolution and similarity evaluation of protein structures in contact map space

Prediction of fold from amino acid sequence of a protein has been an active area of research in the past few years, but the limited accuracy of existing techniques emphasizes the need to develop newer approaches to tackle this task. In this study, we use contact map prediction as an intermediate step in fold prediction from sequence. Contact map is a reduced graph-theoretic representation of proteins that models the local and global inter-residue contacts in the structure. We start with a population of random contact maps for the protein sequence and "evolve" the population to a "high-feasibility" configuration using a genetic algorithm. A neural network is employed to assess the feasibility of contact maps based on their 4 physically relevant properties. We also introduce 5 parameters, based on algebraic graph theory and physical considerations, that can be used to judge the structural similarity between proteins through contact maps. To predict the fold of a given amino acid sequence, we predict a contact map that will sufficiently approximate the structure of the corresponding protein. Then we assess the similarity of this contact map with the representative contact map of each fold; the fold that corresponds to the closest match is our predicted fold for the input sequence. We have found that our feasibility measure is able to differentiate between feasible and infeasible contact maps. Further, this novel approach is able to predict the folds from sequences significantly better than a random predictor.     

Cover Image,Volume 87, Issue 7

Template-based modeling is considered as one of the most successful approaches for protein structure prediction. However, reliably and accurately selecting optimal template proteins from a library of known protein structures having similar folds as the target protein and making correct alignments between the target sequence and the template structures, a template-based modeling technique known as threading, remains challenging, particularly for non- or distantly-homologous protein targets. With the recent advancement in protein residue-residue contact map prediction powered by sequence co-evolution and machine learning, here we systematically analyze the effect of inclusion of residue-residue contact information in improving the accuracy and reliability of protein threading. We develop a new threading algorithm by incorporating various sequential and structural features, and subsequently integrate residue-residue contact information as an additional scoring term for threading template selection. We show that the inclusion of contact information attains statistically significantly better threading performance compared to a baseline threading algorithm that does not utilize contact information when everything else remains the same. Experimental results demonstrate that our contact based threading approach outperforms popular threading method MUSTER, contact-assisted ab initio folding method CONFOLD2, and recent state-of-the-art contact-assisted protein threading methods EigenTHREADER and map_align on several benchmarks. Our study illustrates that the inclusion of contact maps is a promising avenue in protein threading to ultimately help to improve the accuracy of protein structure prediction.     

Bicelle size modulates the rate of bacteriorhodopsin folding

The conformational equilibria of integral membrane proteins have proven extremely difficult to characterize within native lipid bilayers. To circumvent technical issues, investigations of the structure and stability of α‐helical membrane proteins are often carried out in mixed micelle or bicelle solvents that mimic the membrane and facilitate measurements of reversible folding. Under these conditions, the energetics of membrane protein folding are typically proportional to the mole fraction of an anionic detergent in the micelle. However, investigations of the folding and unfolding of bacteriorhodopsin (bR) surprisingly revealed that the folding rate is also highly sensitive to the bulk molar concentration of lipids and detergents. We show here that this rate enhancement coincides with changes in bicelle size and suggest this effect arises through restriction of the conformational search space during folding. In conjunction with previous mutagenic studies, these results provide additional evidence that a topological search limits the rate of bR folding. Furthermore, this finding provides insights into the manner by which micellar and bicellar environments influence the conformational stability of polytopic membrane proteins.     

Beta-turn propensities as paradigms for the analysis of structural motifs to engineer protein stability.

The thermodynamic stability of a protein provides an experimental metric for the relationship of protein sequence and native structure. We have investigated an approach based on an analysis of the structural database for stability engineering of an immunoglobulin variable domain. The most frequently occurring residues in specific positions of beta-turn motifs were predicted to increase the folding stability of mutants that were constructed by site-directed mutagenesis. Even in positions in which different residues are conserved in immunoglobulin sequences, the predictions were confirmed. Frequently, mutants with increased beta-turn propensities display increased folding cooperativities, suggesting pronounced effects on the unfolded state independent of the expected effect on conformational entropy. We conclude that structural motifs with predominantly local interactions can serve as templates with which patterns of sequence preferences can be extracted from the database of protein structures. Such preferences can predict the stability effects of mutations for protein engineering and design.     

Improved Gō-like models demonstrate the robustness of protein folding mechanisms towards non-native interactions

The use of simple theoretical models has provided a considerable contribution to our present understanding of the means by which proteins adopt their native fold from the plethora of available unfolded states. A common assumption in building computationally tractable models has been the neglect of stabilizing non-native interactions in the class of models described as "Gō-like." The focus of this study is the characterization of the folding of a number of proteins via a Gō-like model, which aims to map a maximal amount of information reflecting the protein sequence onto a "minimalist" skeleton. This model is shown to contain sufficient information to reproduce the folding transition states of a number of proteins, including topologically analogous proteins that fold via different transition states. Remarkably, these models also demonstrate consistency with the general features of folding transition states thought to be stabilized by non-native interactions. This suggests that native interactions are the primary determinant of most protein folding transition states, and that non-native interactions lead only to local structural perturbations. A prediction is also included for an asymmetrical folding transition state of bacteriophage lambda protein W, which has yet to be subjected to experimental characterization.     

Water as a conformational editor in protein folding

As molecules approach one another in aqueous solution, desolvation free energy barriers to association are encountered. Experiments suggest these (de)solvation effects contribute to the free energy barriers separating the folded and unfolded states of protein molecules. To explore their influence on the energy landscapes of protein folding reactions, we have incorporated desolvation barriers into a semi-realistic, off-lattice protein model that uses a simplified physico-chemical force-field determined solely by the sequence of amino acids. Monte Carlo sampling techniques were used to study the effects on the thermodynamics and kinetics of folding of a number of systems, diverse in structure and sequence. In each case, desolvation barriers increase the stability of the native conformation and the cooperativity of the major folding/unfolding transition. The folding times of these systems are reduced significantly upon inclusion of desolvation barriers, demonstrating that the particulate nature of the solvent engenders a more defined route to the native fold.     

从氨基酸序列预测蛋白质折叠速率

蛋白质折叠速率预测是当今生物物理学最具挑战性的课题之一．近年来,许多科研工作者开展了大量的研究工作来探索折叠速率的决定因素,许多参数和方法被相继提出．但氨基酸残基间的相互作用、氨基酸的序列顺序等信息对折叠速率的影响从未被提及．采用伪氨基酸组成的方法提取氨基酸的序列顺序信息,利用蒙特卡洛方法选择最佳特征因子,建立线性回归模型进行折叠速率预测．该方法能在不需要任何(显示)结构信息的情况下,直接从蛋白质的氨基酸序列出发对折叠速率进行预测．在Jackknife交互检验方法的验证下,对含有99个蛋白质的数据集,发现折叠速率的预测值与实验值有很好的相关性,相关系数能达到0.81,预测误差仅为2.54．这一精度明显优于其他基于序列的方法,充分说明蛋白质的序列顺序信息是影响蛋白质折叠速率的重要因素．