Conformational subspace in simulation of early-stage protein folding

A probability calculus was used to simulate the early stages of protein folding in ab initio structure prediction. The probabilities of particular phi and psi angles for each of 20 amino acids as they occur in crystal forms of proteins were used to calculate the amount of information necessary for the occurrence of given phi and psi angles to be predicted. It was found that the amount of information needed to predict phi and psi angles with 5 degrees precision is much higher than the amount of information actually carried by individual amino acids in the polypeptide chain. To handle this problem, a limited conformational space for the preliminary search for optimal polypeptide structure is proposed based on a simplified geometrical model of the polypeptide chain and on the probability calculus. These two models, geometric and probabilistic, based on different sources, yield a common conclusion concerning how a limited conformational space can represent an early stage of polypeptide chain-folding simulation. The ribonuclease molecule was used to test the limited conformational space as a tool for modeling early-stage folding.     

Unit-vector RMS (URMS) as a tool to analyze molecular dynamics trajectories

The Unit-vector RMS (URMS) is a new technique to compare protein chains and to detect similarities of chain segments. It is limited to comparison of C(alpha) chains. However, it has a number of unique features that include exceptionally weak dependence on the length of the chain and efficient detection of substructure similarities. Two molecular dynamics simulations of proteins in the neighborhood of their native states are used to test the performance of the URMS. The first simulation is of a solvated myoglobin and the second is of the protein MHC. In accord with previous studies the secondary structure elements (helices or sheets) are found to be moving relatively rigidly among flexible loops. In addition to these tests, folding trajectories of C peptides are analyzed, revealing a folding nucleus of seven amino acids.     

Conformation biases of amino acids based on tripeptide microenvironment from PDB database

We have constructed a bank (FTTP) of tendentious factors of three states of three-peptide units from PDB database based on conformational dihedral angle library and demonstrated that amino acid biases toward protein secondary structure are present in natural protein sequences. Our research results reveal that 20 standard amino acids fall into three groups: nine residues inclined to alpha-helix with a common character (e.g. direct side chain aliphatic residues or positive/negative charged residues) arrange in three grades, viz EA, QKRLD, and MN, in turn; seven residues are apt to beta-strand with 2'-branched side chain aliphatic residues or benzyl-included residues, namely PV, IYTC, and F, in three ranks; and four residues SHWG show a double tendency to both alpha and beta. Noticeably, proline has the strongest ability to form extended conformation, especially the Re value up to 9.5298 at position 3 (Table 3). Thus, biases of codons show an evident tendency in protein folding, where GC-rich codons are mainly in charge of forming contracted conformation, especially the codon's first letter plays a dominant role in translating the genomic GC signature into protein sequences and structures. So, biases of amino acids will play an important role in protein folding, folding codons, refining domain, structure prediction, and structural genomics/proteomics.     

Cooperativity in two-state protein folding kinetics

We present a solvable model that predicts the folding kinetics of two-state proteins from their native structures. The model is based on conditional chain entropies. It assumes that folding processes are dominated by small-loop closure events that can be inferred from native structures. For CI2, the src SH3 domain, TNfn3, and protein L, the model reproduces two-state kinetics, and it predicts well the average Phi-values for secondary structures. The barrier to folding is the formation of predominantly local structures such as helices and hairpins, which are needed to bring nonlocal pairs of amino acids into contact.     

Native geometry and the dynamics of protein folding

In this paper, we investigate the role of native geometry on the kinetics of protein folding based on simple lattice models and Monte Carlo simulations. Results obtained within the scope of the Miyazawa-Jernigan indicate the existence of two dynamical folding regimes depending on the protein chain length. For chains larger than 80 amino acids, the folding performance is sensitive to the native state's conformation. Smaller chains, with less than 80 amino acids, fold via two-state kinetics and exhibit a significant correlation between the contact order parameter and the logarithmic folding times. In particular, chains with N=48 amino acids were found to belong to two broad classes of folding, characterized by different cooperativity, depending on the contact order parameter. Preliminary results based on the Go model show that the effect of long-range contact interaction strength in the folding kinetics is largely dependent on the native state's geometry.     

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.     

BCL::Fold - De Novo Prediction of Complex and Large Protein Topologies by Assembly of Secondary Structure Elements

Computational de novo protein structure prediction is limited to small proteins of simple topology. The present work explores an approach to extend beyond the current limitations through assembling protein topologies from idealized α-helices and β-strands. The algorithm performs a Monte Carlo Metropolis simulated annealing folding simulation. It optimizes a knowledge-based potential that analyzes radius of gyration, β-strand pairing, secondary structure element (SSE) packing, amino acid pair distance, amino acid environment, contact order, secondary structure prediction agreement and loop closure. Discontinuation of the protein chain favors sampling of non-local contacts and thereby creation of complex protein topologies. The folding simulation is accelerated through exclusion of flexible loop regions further reducing the size of the conformational search space. The algorithm is benchmarked on 66 proteins with lengths between 83 and 293 amino acids. For 61 out of these proteins, the best SSE-only models obtained have an RMSD100 below 8.0 Å and recover more than 20% of the native contacts. The algorithm assembles protein topologies with up to 215 residues and a relative contact order of 0.46. The method is tailored to be used in conjunction with low-resolution or sparse experimental data sets which often provide restraints for regions of defined secondary structure.     

Direct correlation between proteins' folding rates and their amino acid compositions: an ab initio folding rate prediction

Discovering the mechanism of protein folding, in molecular biology, is a great challenge. A key step to this end is to find factors that correlate with protein folding rates. Over the past few years, many empirical parameters, such as contact order, long-range order, total contact distance, secondary structure contents, have been developed to reflect the correlation between folding rates and protein tertiary or secondary structures. However, the correlation between proteins' folding rates and their amino acid compositions has not been explored. In the present work, we examined systematically the correlation between proteins' folding rates and their amino acid compositions for two-state and multistate folders and found that different amino acids contributed differently to the folding progress. The relation between the amino acids' molecular weight and degeneracy and the folding rates was examined, and the role of hydrophobicity in the protein folding process was also inspected. As a consequence, a new indicator called composition index was derived, which takes no structure factors into account and is merely determined by the amino acid composition of a protein. Such an indicator is found to be highly correlated with the protein's folding rate (r > 0.7). From the results of this work, three points of concluding remarks are evident. (1) Two-state folders and multistate folders have different rate-determining amino acids. (2) The main determining information of a protein's folding rate is largely reflected in its amino acid composition. (3) Composition index may be the best predictor for an ab initio protein folding rate prediction directly from protein sequence from the standpoint of practical application.     

未折叠蛋白质的普遍初始热力学亚稳态

探索和理解蛋白质折叠问题一直是分子生物学、结构生物学和生物物理学的终极挑战.未折叠的蛋白质应该存在一种普遍初始热力学亚稳态,否则无法解释蛋白质是如何在剧烈的热振动干扰下完成快速精确折叠的.本文通过分析水溶液环境和蛋白质折叠的相关性,揭示了一种由水分子屏蔽效应引起的未折叠蛋白质的普遍初始热力学亚稳态,该亚稳态的存在是水溶液环境中水分子的物理性质决定,并赋予未折叠蛋白质抵抗热扰动和避免错误折叠的能力.我们通过研究已发表的实验数据和建立分子模型,找到了该初始热力学亚稳态存在的相关证据,并推测了该亚稳态导致蛋白质精确折叠的相关物理学机制.     

Single amino acid substitutions globally suppress the folding defects of temperature-sensitive folding mutants of phage P22 coat protein.

The amino acid sequence of a polypeptide defines both the folding pathway and the final three-dimensional structure of a protein. Eighteen amino acid substitutions have been identified in bacteriophage P22 coat protein that are defective in folding and cause their folding intermediates to be substrates for GroEL and GroES. These temperature-sensitive folding (tsf) substitutions identify amino acids that are critical for directing the folding of coat protein. Additional amino acid residues that are critical to the folding process of P22 coat protein were identified by isolating second site suppressors of the tsf coat proteins. Suppressor substitutions isolated from the phage carrying the tsf coat protein substitutions included global suppressors, which are substitutions capable of alleviating the folding defects of numerous tsf coat protein mutants. In addition, potential global and site-specific suppressors were isolated, as well as a group of same site amino acid substitutions that had a less severe phenotype than the tsf parent. The global suppressors were located at positions 163, 166, and 170 in the coat protein sequence and were 8-190 amino acid residues away from the tsf parent. Although the folding of coat proteins with tsf amino acid substitutions was improved by the global suppressor substitutions, GroEL remained necessary for folding. Therefore, we believe that the global suppressor sites identify a region that is critical to the folding of coat protein.     

Amino acid sequence predicts folding rate for middle-size two-state proteins

The significant correlation between protein folding rates and the sequence-predicted secondary structure suggests that folding rates are largely determined by the amino acid sequence. Here, we present a method for predicting the folding rates of proteins from sequences using the intrinsic properties of amino acids, which does not require any information on secondary structure prediction and structural topology. The contribution of residue to the folding rate is expressed by the residue's Omega value. For a given residue, its Omega depends on the amino acid properties (amino acid rigidity and dislike of amino acid for secondary structures). Our investigation achieves 82% correlation with folding rates determined experimentally for simple, two-state proteins studied until the present, suggesting that the amino acid sequence of a protein is an important determinant of the protein-folding rate and mechanism.     

Characterization of the amino acid contribution to the folding degree of proteins

The folding degree index (Estrada, Bioinformatics 2002;18:697-704) is extended to account for the contribution of amino acids to folding. First, the mathematical formalism for extending the folding degree index is presented. Then, the amino acid contributions to folding degree of several proteins are used to analyze its relation to secondary structure. The possibilities of using these contributions in helping or checking the assignation of secondary structure to amino acids are also introduced. The influence of external factors to the amino acids contribution to folding degree is studied through the temperature effect on ribonuclease A. Finally, the analysis of 3D protein similarity through the use of amino acid contributions to folding degree is studied by selecting a series of lysozymes. These results are compared to that obtained by sequence alignment (2D similarity) and 3D superposition of the structures, showing the uniqueness of the current approach.     

Reduced alphabet for protein folding prediction

What are the key building blocks that would have been needed to construct complex protein folds? This is an important issue for understanding protein folding mechanism and guiding de novo protein design. Twenty naturally occurring amino acids and eight secondary structures consist of a 28‐letter alphabet to determine folding kinetics and mechanism. Here we predict folding kinetic rates of proteins from many reduced alphabets. We find that a reduced alphabet of 10 letters achieves good correlation with folding rates, close to the one achieved by full 28‐letter alphabet. Many other reduced alphabets are not significantly correlated to folding rates. The finding suggests that not all amino acids and secondary structures are equally important for protein folding. The foldable sequence of a protein could be designed using at least 10 folding units, which can either promote or inhibit protein folding. Reducing alphabet cardinality without losing key folding kinetic information opens the door to potentially faster machine learning and data mining applications in protein structure prediction, sequence alignment and protein design. Proteins 2015; 83:631–639. © 2015 Wiley Periodicals, Inc.     

Folding type-specific secondary structure propensities of amino acids,derived from α-helical, β-sheet, α/β, and α+β proteins of known structures

Folding type-specific secondary structure propensities of 20 naturally occurring amino acids have been derived from α-helical, β-sheet, α/β, and α+β proteins of known structures. These data show that each residue type of amino acids has intrinsic propensities in different regions of secondary structures for different folding types of proteins. Each of the folding types shows markedly different rank ordering, indicating folding type-specific effects on the secondary structure propensities of amino acids. Rigorous statistical tests have been made to validate the folding type-specific effects. It should be noted that α and β proteins have relatively small α-helices and β-strands forming propensities respectively compared with those of α+β and α/β proteins. This may suggest that, with more complex architectures than α and β proteins, α+β and α/β proteins require larger propensities to distinguish from interacting α-helices and β-strands. Our finding of folding type-specific secondary structure propensities suggests that sequence space accessible to each folding type may have differing features. Differing sequence space features might be constrained by topological requirement for each of the folding types. Almost all strong β-sheet forming residues are hydrophobic in character regardless of folding types, thus suggesting the hydrophobicities of side chains as a key determinant of β-sheet structures. In contrast, conformational entropy of side chains is a major determinant of the helical propensities of amino acids, although other interactions such as hydrophobicities and charged interactions cannot be neglected. These results will be helpful to protein design, class-based secondary structure prediction, and protein folding. © 1998 John Wiley & Sons, Inc. Biopoly 45: 35–49, 1998     

Are the same or different amino acid residues responsible for correct and incorrect protein folding?

It has been shown for 20 proteins that amino acid residues included into the protein folding nucleus, determined experimentally, are often involved in the theoretically determined amyloidogenic fragments. For 18 proteins, Φ-values indicative of the extent of residue involvement into the folding nucleus are on average higher for amino acid residues within amyloidogenic regions. Amyloidogenic fragments were predicted for 20 proteins by two methods chosen from four on the basis of comparison of prediction of amyloidogenic regions known from experimental data. Since theoretical folding nuclei are detected by the protein three-dimensional structure and amyloidogenic regions by the protein chain primary structure, the detected regularity makes possible predictions of folding nucleation sites on the basis of amino acid sequence.     

The formation of protein secondary structure. Its connection with amino acid sequence

Statistical analysis of the occurrence of tetrapeptides in 35 globular proteins was performed. It was found that the amino acids along the polypeptide chain are close to being randomly distributed and that the same tetrapeptide segments exist in different types of secondary structure. Therefore, a new method was proposed for locating 'microdomains' in protein interiors. Amino acid replacements in the hydrophobic core of six proteins were analyzed. The results show that the locations of amino acids belonging to defined microdomains are extremely conserved. It is suggested that the structures found may play a role as nucleation centers in protein folding.     

Backbones of folded proteins reveal novel invariant amino acid neighborhoods

Folding of naturally occurring proteins has eluded a universal molecular level explanation till date. Rather, there is an abundance of diverse views on dominant factors governing protein folding. Through rigorous analyses of several thousand crystal structures, we observe that backbones of folded proteins display some remarkable invariant features. Folded proteins are characterized by spatially well-defined, distance dependent, and universal, neighborhoods of amino acids which defy any of the conventionally prevalent views. These findings present a compelling case for a newer view of protein folding which takes into account solvent mediated and amino acid shape and size assisted optimization of the tertiary structure of the polypeptide chain to make a functional protein.     

Nature and distribution of sites of temperature-sensitive folding mutations in the gene for the P22 tailspike polypeptide chain

Temperature-sensitive folding (tsf) mutations in gene 9 of bacteriophage P22 interfere with the folding and association of the tailspike polypeptide chain at restrictive temperature. We report here the location and amino acid substitutions for 24 independent tsf mutants. The distribution of these and previously identified mutations is distinctly non-random; all of the 32 unambiguous sites of tsf mutations are located in the central 350 residues of the 666 residue tailspike polypeptide chain. No ts mutation has been found among the N-terminal 140 amino acids, and none among the C-terminal 170 amino acids. Since the physiological defect in these mutants is the destabilization of an early intermediate in the folding pathway, the localization of the mutants suggests that the central region of the chain is critical for formation or stabilization of this early intermediate. The majority of amino acids that served as sites for the tsf mutations were hydrophilic residues. Sixty percent of the replacements of these residues represented charge changes. This probably reflects the selection for mutant sites at the mature protein surface where the substitutions can be best tolerated without interfering with function. None of the sites of tsf mutations were at aromatic residues, and only one proline site was found. Substitutions at these residues may cause lethal folding defects which are not recovered as tsf mutants. The local sequences at tsf sites resemble those reported for turns. Structural studies identify beta-sheet as the dominant secondary structure. These mutations may disrupt the formation of conformational features of beta-sheets which are repeated, such as turns, associations between pairs of strands, or sheet/sheet packing interactions. Such a model accounts for the occurrence of tsf mutations with similar defective phenotypes at multiple positions along the chain.     

NMR and protein folding: equilibrium and stopped-flow studies.

NMR studies are now unraveling the structure of intermediates of protein folding using hydrogen-deuterium exchange methodologies. These studies provide information about the time dependence of formation of secondary structure. They require the ability to assign specific resonances in the NMR spectra to specific amide protons of a protein followed by experiments involving competition between folding and exchange reactions. Another approach is to use 19F-substituted amino acids to follow changes in side-chain environment upon folding. Current techniques of molecular biology allow assignments of 19F resonances to specific amino acids by site-directed mutagenesis. It is possible to follow changes and to analyze results from 19F spectra in real time using a stopped-flow device incorporated into the NMR spectrometer.     

Toward resolution of ambiguity for the unfolded state

The unfolded states in proteins and nucleic acids remain weakly understood despite their importance in folding processes; misfolding diseases (Parkinson's and Alzheimer's); natively unfolded proteins (as many as 30% of eukaryotic proteins, according to Fink); and the study of ribozymes. Research has been hindered by the inability to quantify the residual (native) structure present in an unfolded protein or nucleic acid. Here, a scaling model is proposed to quantify the molar degree of folding and the unfolded state. The model takes a global view of protein structure and can be applied to a number of analytic methods and to simulations. Three examples are given of application to small-angle scattering from pressure-induced unfolding of SNase, from acid-unfolded cytochrome c, and from folding of Azoarcus ribozyme. These examples quantitatively show three characteristic unfolded states for proteins, the statistical nature of a protein folding pathway, and the relationship between extent of folding and chain size during folding for charge-driven folding in RNA.