Prediction of the location of structural domains in globular proteins

The location of structural domains in proteins is predicted from the amino acid sequence, based on the analysis of a computed contact map for the protein, the average distance map (ADM). Interactions between residues i and j in a protein are subdivided into several ranges, according to the separation |i-j| in the amino acid sequence. Within each range, average spatial distances between every pair of amino acid residues are computed from a data base of known protein structures. Infrequently occurring pairs are omitted as being statistically insignificant. The average distances are used to construct a predicted ADM. The ADM is analyzed for the occurrence of regions with high densities of contacts (compact regions). Locations of rapid changes of density between various parts of the map are determined by the use of scanning plots of contact densities. These locations serve to pinpoint the distribution of compact regions. This distribution, in turn, is used to predict boundaries of domains in the protein. The technique provides an objective method for the location of domains both on a contact map derived from a known three-dimensional protein structure, the real distance map (RDM), and on an ADM. While most other published methods for the identification of domains locate them in the known three-dimensional structure of a protein, the technique presented here also permits the prediction of domains in proteins of unknown spatial structure, as the construction of the ADM for a given protein requires knowledge of only its amino acid sequence.     

A study of the occurrence of regulator secondary structures in globular proteins

The distribution of regular secondary structures, viz. α-helices and β-strands, along the length of over 70 properties whose secondary structural details have been reported, has been analysed. The occurrence of these regular structures tends to be a maximum at the N- and C-termini. Our analysis suggests that both these free ends could possibly serve as nucleating centers for secondary structures and could play an important role in the folding of proteins.     

Outlining folding nuclei in globular proteins

Our theoretical approach for prediction of folding/unfolding nuclei in three-dimensional protein structures is based on a search for free energy saddle points on networks of protein unfolding pathways. Under some approximations, this search is performed rapidly by dynamic programming and results in prediction of Phi values, which can be compared with those found experimentally. In this study, we optimize some details of the model (specifically, hydrogen atoms are taken into account in addition to heavy atoms), and compare the theoretically obtained and experimental Phi values (which characterize involvement of residues in folding nuclei) for all 17 proteins, where Phi values are now known for many residues. We show that the model provides good Phi value predictions for proteins whose structures have been determined by X-ray analysis (the average correlation coefficient is 0.65), with a more limited success for proteins whose structures have been determined by NMR techniques only (the average correlation coefficient is 0.34), and that the transition state free energies computed from the same model are in a good anticorrelation with logarithms of experimentally measured folding rates at mid-transition (the correlation coefficient is -0.73).     

Distance-constraint approach to higher-order structures of globular proteins with empirically determined distances between amino acid residues

An analysis of higher-order structures of globular proteins by means of a distance-constraint approach is presented. Conformations are generated for each of 21 test proteins of small and medium sizes by optimizing an objective functionf=w _ij(d _ij–d _ij)², whered _ij is a distance between residuesi andj in a calculated conformation, d _ij is an assigned distance to the (ij) pair of residues which is determined based on the statistics of known three-dimensional structures of 14 proteins in the earlier study, andw _ij is a weighting factor. d _ij involves information about hydrophobicity and hydrophilicity of each amino acid residue and about connectivity of a polypeptide chain. In these calculations, only the amino acid sequence is used as input data specific to a calculated protein. With respect to higher-order structures regenerated in the optimized conformations, the following properties are analyzed: (a) N14 of a residue, defined as the number of residues surrounding the residue located within a sphere of radius of 14 Å; (b) root-mean-square differences of the global and local conformations from the corresponding X-ray conformations; (c) distance profiles in the short and medium ranges; and (d) distance maps. The effects of supplementary information about locations of secondary structures and disulfide bonds are also examined to discuss the potential ability of this methodology to predict the three-dimensional structures of globular proteins.     

Understanding the determinants of stability and folding of small globular proteins from their energetics

The results of minimal model calculations indicate that the stability and the kinetic accessibility of the native state of small globular proteins are controlled by few "hot" sites. By means of molecular dynamics simulations around the native conformation, which describe the protein and the surrounding solvent at the all-atom level, an accurate and compact energetic map of the native state of the protein is generated. This map is further simplified by means of an eigenvalue decomposition. The components of the eigenvector associated with the lowest eigenvalue indicate which hot sites are likely to be responsible for the stability and for the rapid folding of the protein. The comparison of the results of the model with the findings of mutagenesis experiments performed for four small proteins show that the eigenvalue decomposition method is able to identify between 60% and 80% of these (hot) sites.     

Lattice simulations of cotranslational folding of single domain proteins

We use lattice protein models and Monte Carlo simulations to study cotranslational folding of small single domain proteins. We show that the assembly of native structure begins during late extrusion stages, but final formation of native state occurs during de novo folding, when all residues are extruded. There are three main results in our study. First, for the sequences displaying two-state refolding mechanism de novo cotranslational folding pathway differs from that sampled in in vitro refolding. The change in folding pathways is due to partial assembly of native interactions during extrusion that results in different starting conditions for in vitro refolding and for de novo cotranslational folding. For small single domain proteins cotranslational folding is slower than in vitro refolding, but is generally fast enough to be completed before the release from a ribosome. Second, we found that until final stages of biosynthesis cotranslational folding is essentially equilibrium. This observation is explained by low stability of structured states for partially extruded chains. Finally, our data suggest that the proteins, which refold in vitro slowly via intermediates, complete their de novo folding after the release from a ribosome. Comparison of our lattice cotranslational simulations with recent experimental and computational studies is discussed.     

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.     

Principal eigenvector of contact matrices and hydrophobicity profiles in proteins

With the aim of studying the relationship between protein sequences and their native structures, we adopted vectorial representations for both sequence and structure. The structural representation was based on the principal eigenvector of the fold's contact matrix (PE). As has been recently shown, the latter encodes sufficient information for reconstructing the whole contact matrix. The sequence was represented through a hydrophobicity profile (HP), using a generalized hydrophobicity scale that we obtained from the principal eigenvector of a residue-residue interaction matrix, and denoted as interactivity scale. Using this novel scale, we defined the optimal HP of a protein fold, and, by means of stability arguments, predicted to be strongly correlated with the PE of the fold's contact matrix. This prediction was confirmed through an evolutionary analysis, which showed that the PE correlates with the HP of each individual sequence adopting the same fold and, even more strongly, with the average HP of this set of sequences. Thus, protein sequences evolve in such a way that their average HP is close to the optimal one, implying that neutral evolution can be viewed as a kind of motion in sequence space around the optimal HP. Our results indicate that the correlation coefficient between N-dimensional vectors constitutes a natural metric in the vectorial space in which we represent both protein sequences and protein structures, which we call vectorial protein space. In this way, we define a unified framework for sequence-to-sequence, sequence-to-structure and structure-to-structure alignments. We show that the interactivity scale is nearly optimal both for the comparison of sequences to sequences and sequences to structures.     

Structural mobility and transformations in globular proteins

Journal of Biosciences - Although globular proteins are endowed with well defined three-dimensional structures, they exhibit substantial mobility within the framework of the given three-dimensional...     

Ramachandran maps for side chains in globular proteins

The Ramachandran plot for backbone ϕ,ψ-angles in a blocked monopeptide has played a central role in understanding protein structure. Curiously, a similar analysis for side chain χ-angles has been comparatively neglected. Instead, efforts have focused on compiling various types of side chain libraries extracted from proteins of known structure. Departing from this trend, the following analysis presents backbone-based maps of side chains in blocked monopeptides. As in the original ϕ,ψ-plot, these maps are derived solely from hard-sphere steric repulsion. Remarkably, the side chain biases exhibit marked similarities to corresponding biases seen in high-resolution protein structures. Consequently, some of the entropic cost for side chain localization in proteins is prepaid prior to the onset of folding events because conformational bias is built into the chain at the covalent level. Furthermore, side chain conformations are seen to experience fewer steric restrictions for backbone conformations in either the α or β basins, those map regions where repetitive ϕ,ψ-angles result in α-helices or strands of β-sheet, respectively. Here, these α and β basins are entropically favored for steric reasons alone; a blocked monopeptide is too short to accommodate the peptide hydrogen bonds that stabilize repetitive secondary structure. Thus, despite differing energetics, α/β-basins are favored for both monopeptides and repetitive secondary structure, underpinning an energetically unfrustrated compatibility between these two levels of protein structure.     

Determination of the conformation of folding initiation sites in proteins by computer simulation

Experimental evidence and theoretical models both suggest that protein folding begins by specific short regions of the polypeptide chain intermittently assuming conformations close to their final ones. The independent folding properties and small size of these folding initiation sites make them suitable subjects for computational methods aimed at deriving structure from sequence. We have used a torsion space Monte Carlo procedure together with an all-atom free energy function to investigate the folding of a set of such sites. The free energy function is derived by a potential of mean force analysis of experimental protein structures. The most important contributions to the total free energy are the local main chain electrostatics, main chain hydrogen bonds, and the burial of nonpolar area. Six proposed independent folding units and four control peptides 11–14 residues long have been investigated. Thirty Monte Carlo simulations were performed on each peptide, starting from different random conformations. Five of the six folding units adopted conformations close to the experimental ones in some of the runs. None of the controls did so, as expected. The generated conformations which are close to the experimental ones have among the lowest free energies encountered, although some less native like low free energy conformations were also found. The effectiveness of the method on these peptides, which have a wide variety of experimental conformations, is encouraging in two ways: First, it provides independent evidence that these regions of the sequences are able to adopt native like conformations early in folding, and therefore are most probably key components of the folding pathways. Second, it demonstrates that available simulation methods and free energy functions are able to produce reasonably accurate structures. Extensions of the methods to the folding of larger portions of proteins are suggested. © 1995 Wiley-Liss, Inc.     

Identifying folding nucleus based on residue contact networks of proteins

In the native structure of a protein, all the residues are tightly parked together in a specific order following its folding and every residue contacts with some spatially neighbor residues. A residue contact network can be constructed by defining the residues as nodes and the native contacts as edges. During the folding of small single-domain proteins, there is a set of contacts (or bonds), defined as the folding nucleus (FN), which is formed around the transition state, i.e., a rate-limiting barrier located at about the middle between the unfolded states and the native state on the free energy landscape. Such a FN plays an essential role in the folding dynamics and the residues, which form the related contacts called as folding nucleus residues (FNRs). In this work, the FNRs in proteins are identified by using quantities which characterize the topology of residue contact networks of proteins. By comparing the specificities of residues with the network quantities K(R), L(R), and D(R), up to 90% FNRs of six typical proteins found experimentally are identified. It is found that the FNRs behave the full-closeness centrals rather than degree or closeness centers in the residue contact network, implying that they are important to the folding cooperativity of proteins. Our study shows that the FNRs can be identified solely from the native structures of proteins based on the analysis of residue contact network without any knowledge of the transition state ensemble.     

Physical-chemical determinants of turn conformations in globular proteins

Globular proteins are assemblies of alpha-helices and beta-strands, interconnected by reverse turns and longer loops. Most short turns can be classified readily into a limited repertoire of discrete backbone conformations, but the physical-chemical determinants of these distinct conformational basins remain an open question. We investigated this question by exhaustive analysis of all backbone conformations accessible to short chain segments bracketed by either an alpha-helix or a beta-strand (i.e., alpha-segment-alpha, beta-segment-beta, alpha-segment-beta, and beta-segment-alpha) in a nine-state model. We find that each of these four secondary structure environments imposes its own unique steric and hydrogen-bonding constraints on the intervening segment, resulting in a limited repertoire of conformations. In greater detail, an exhaustive set of conformations was generated for short backbone segments having reverse-turn chain topology and bracketed between elements of secondary structure. This set was filtered, and only clash-free, hydrogen-bond-satisfied conformers having reverse-turn topology were retained. The filtered set includes authentic turn conformations, observed in proteins of known structure, but little else. In particular, over 99% of the alternative conformations failed to satisfy at least one criterion and were excluded from the filtered set. Furthermore, almost all of the remaining alternative conformations have close tolerances that would be too tight to accommodate side chains longer than a single beta-carbon. These results provide a molecular explanation for the observation that reverse turns between elements of regular secondary can be classified into a small number of discrete conformations.     

Hierarchical protein folding pathways: a computational study of protein fragments

We have previously presented a building block folding model. The model postulates that protein folding is a hierarchical top-down process. The basic unit from which a fold is constructed, referred to as a hydrophobic folding unit, is the outcome of combinatorial assembly of a set of "building blocks." Results obtained by the computational cutting procedure yield fragments that are in agreement with those obtained experimentally by limited proteolysis. Here we show that as expected, proteins from the same family give very similar building blocks. However, different proteins can also give building blocks that are similar in structure. In such cases the building blocks differ in sequence, stability, contacts with other building blocks, and in their 3D locations in the protein structure. This result, which we have repeatedly observed in many cases, leads us to conclude that while a building block is influenced by its environment, nevertheless, it can be viewed as a stand-alone unit. For small-sized building blocks existing in multiple conformations, interactions with sister building blocks in the protein will increase the population time of the native conformer. With this conclusion in hand, it is possible to develop an algorithm that predicts the building block assignment of a protein sequence whose structure is unknown. Toward this goal, we have created sequentially nonredundant databases of building block sequences. A protein sequence can be aligned against these, in order to be matched to a set of potential building blocks.     

Information and redundancy in the burial folding code of globular proteins within a wide range of shapes and sizes

Recent ab initio folding simulations for a limited number of small proteins have corroborated a previous suggestion that atomic burial information obtainable from sequence could be sufficient for tertiary structure determination when combined to sequence‐independent geometrical constraints. Here, we use simulations parameterized by native burials to investigate the required amount of information in a diverse set of globular proteins comprising different structural classes and a wide size range. Burial information is provided by a potential term pushing each atom towards one among a small number L of equiprobable concentric layers. An upper bound for the required information is provided by the minimal number of layers L^min still compatible with correct folding behavior. We obtain L^min between 3 and 5 for seven small to medium proteins with 50 ≤ N_r ≤ 110 residues while for a larger protein with N_r = 141 we find that L ≥ 6 is required to maintain native stability. We additionally estimate the usable redundancy for a given L ≥ L^min from the burial entropy associated to the largest folding‐compatible fraction of “superfluous” atoms, for which the burial term can be turned off or target layers can be chosen randomly. The estimated redundancy for small proteins with L = 4 is close to 0.8. Our results are consistent with the above‐average quality of burial predictions used in previous simulations and indicate that the fraction of approachable proteins could increase significantly with even a mild, plausible, improvement on sequence‐dependent burial prediction or on sequence‐independent constraints that augment the detectable redundancy during simulations. Proteins 2016; 84:515–531. © 2016 Wiley Periodicals, Inc.     

Prediction of the initial folding sites and the entire folding processes for Ig-like beta-sandwich proteins

Describing the whole story of protein folding is currently the main enigmatic problem in molecular bioinformatics study. Protein folding mechanisms have been intensively investigated with experimental as well as simulation techniques. Since a protein folds into its specific 3D structure from a unique amino acid sequence, it is interesting to extract as much information as possible from the amino acid sequence of a protein. Analyses based on inter-residue average distance statistics and a coarse-grained Gō-model simulation were conducted on Ig and FN3 domains of a titin protein to decode the folding mechanisms from their sequence data and native structure data, respectively. The central region of all domains was predicted to be an initial folding unit, that is, stable in an early state of folding. This common feature coincides well with the experimental results and underscores the significance of the β-sandwich proteins' common structure, namely, the key strands for folding and the Greek-key motif, which is located in the central region. We confirmed that our sequence-based techniques were able to predict the initial folding event just next to the denatured state and that a 3D-based Gō-model simulation can be used to investigate the whole process of protein folding.     

Diversity in the disulfide folding pathways of cystine knot peptides

Summary The plant cyclotides are a fascinating family of circular proteins that contain a cyclic cystine knot motif (CCK). This unique family was discovered only recently but contains over 50 known sequences to date. Various biological activities are associated with these peptides including antimicrobial and insecticidal activity. The knotted topology and cyclic nature of the cyclotides poses interesting questions about the folding mechanisms and how the knotted arrangement of disulfide bonds is formed. Some studies have been performed on related inhibitor cystine knot (ICK) containing peptides, but little is known about the folding mechanisms of CCK molecules. We have examined the oxidative refolding and reductive unfolding of the prototypic member of the cyclotide family, kalata B1. Analysis of the rates of formation of the intermediates along the reductive unfolding pathway highlights the stability conferred by the cystine knot motif. Significant differences are observed between the folding of kalata B1 and an acyclic cystine knot protein, EETI-II, suggesting that the circular backbone has a significant influence in directing the folding pathway.     

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.     

Thermodynamic characterisation of two transition states along parallel protein folding pathways

Recent work has shown that a β-sandwich domain from the human muscle protein titin (TI I27) unfolds via more than one pathway, providing experimental evidence for a long-standing theoretical prediction in protein folding. Here we present a thermodynamic analysis of two transition states along different folding pathways for this protein. The unusual upwards curvature previously observed in the denaturant-dependent unfolding kinetics is increased at both high and low temperatures, indicating that the high denaturant pathway is becoming more accessible. The transition states in each pathway are structurally distinct and have very different heat capacities. Interestingly the nucleation-condensation pathway is dominant at all physiologically relevant temperatures, supporting the suggestion that pathways with diffuse rather than localised transition states have been selected for by evolution to prevent misfolding.