Limited conformational space for early-stage protein folding simulation

MOTIVATION: The problem of early-stage protein folding is critical for protein structure prediction. The model presented introduces a common definition of protein structures which may be treated as the possible in silico early-stage form of the polypeptide chain. Limitation of the conformational space to the ellipse path on the Ramachandran map was tested as a possible sub-space to represent the early-stage structure for simulation of protein folding. The proposed conformational sub-space was developed on the basis of the backbone conformation, with side-chain interactions excluded. RESULTS: The ellipse-path-limited conformation of BPTI was created using the criterion of shortest distance between Phi, Psi angles in native form of protein and the Phi, Psi angles belonging to the ellipse. No knots were observed in the structure created according to ellipse-path conformational sub-space. The energy minimization procedure applied to ellipse-path derived conformation directed structural changes toward the native form of the protein with SS-bonds system introduced to the procedure. AVAILABILITY: Program 'Ellipse' to create the ellipse-path derived structure available on request: myroterm@cyf-kr.edu.pl     

Lysozyme folded in silico according to the limited conformational sub-space

The conformational sub-space oriented on early-stage protein folding is applied to lysozyme folding. The part of the Ramachandran map distinguished on the basis of a geometrical model of the polypeptide chain limited to the mutual orientation of the peptide bond planes is shown to deliver the initial structure of the polypeptide for the energy minimization procedure in the ab initio model of protein folding prediction. Two forms of energy minimization and molecular dynamics simulation procedures were applied to the assumed early-stage protein folding of lysozyme. One of them included the disulphide bond system and the other excluded it. The post-energy-minimization and post-dynamics structures were compared using RMS-D and non-bonding contact maps to estimate the degree of approach to the native, target structure of the protein molecule obtained using the limited conformational sub-space for the early stage of folding.     

Lysozyme Folded In Silico According to the Limited Conformational Sub-space

Abstract

The conformational sub-space oriented on early-stage protein folding is applied to lysozyme folding. The part of the Ramachandran map distinguished on the basis of a geometrical model of the polypeptide chain limited to the mutual orientation of the peptide bond planes is shown to deliver the initial structure of the polypeptide for the energy minimization procedure in the ab initio model of protein folding prediction. Two forms of energy minimization and molecular dynamics simulation procedures were applied to the assumed early-stage protein folding of lysozyme. One of them included the disulphide bond system and the other excluded it. The post-energy-minimization and post-dynamics structures were compared using RMS-D and non-bonding contact maps to estimate the degree of approach to the native, target structure of the protein molecule obtained using the limited conformational sub-space for the early stage of folding.     

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.     

Characterization of the nonregular regions of proteins by a contortion index

Nonstructured regions in proteins that provide the link between two regular structured regions play a significant role in maintaining the scaffold of the protein. Not only do they act as connectors between two regular secondary structural elements of proteins but they also provide the necessary turn or reversal in the polypeptide chain. This incorporates flexibility in the structure. Thus an understanding of the structural aspects of the nonregular regions is necessary to have a better insight into these features. We can assume the nonregular region to be a contorted polypeptide segment tethered by regular secondary structured regions at both ends. To describe the undulating nature of the nonregular regions, we introduce a parameter called the "contortion index." This index describes how tortuously the region is organized. Our analysis shows that the contortion index is related to other physicochemical parameters and can be used to characterize the nonregular regions of proteins.     

A simple topological representation of protein structure: implications for new, fast, and robust structural classification

A topological representation of proteins is developed that makes use of two metrics: the Euclidean metric for identifying natural nearest neighboring residues via the Delaunay tessellation in Cartesian space and the distance between residues in sequence space. Using this representation, we introduce a quantitative and computationally inexpensive method for the comparison of protein structural topology. The method ultimately results in a numerical score quantifying the distance between proteins in a heuristically defined topological space. The properties of this scoring scheme are investigated and correlated with the standard Calpha distance root-mean-square deviation measure of protein similarity calculated by rigid body structural alignment. The topological comparison method is shown to have a characteristic dependence on protein conformational differences and secondary structure. This distinctive behavior is also observed in the comparison of proteins within families of structural relatives. The ability of the comparison method to successfully classify proteins into classes, superfamilies, folds, and families that are consistent with standard classification methods, both automated and human-driven, is demonstrated. Furthermore, it is shown that the scoring method allows for a fine-grained classification on the family, protein, and species level that agrees very well with currently established phylogenetic hierarchies. This fine classification is achieved without requiring visual inspection of proteins, sequence analysis, or the use of structural superimposition methods. Implications of the method for a fast, automated, topological hierarchical classification of proteins are discussed.     

Folding of peptide fragments comprising the complete sequence of proteins. Models for initiation of protein folding. I. Myohemerythrin.

In an attempt to delineate potential folding initiation sites for different protein structural motifs, we have synthesized series of peptides that span the entire length of the polypeptide chain of two proteins, and examined their conformational preferences in aqueous solution using proton nuclear magnetic resonance and circular dichroism spectroscopy. We describe here the behavior of peptides derived from a simple four-helix bundle protein, myohemerythrin. The peptides correspond to the sequences of the four long helices (the A, B, C and D helices), the N- and C-terminal loops and the connecting sequences between the helices. The peptides corresponding to the helices of the folded protein all exhibit preferences for helix-like conformations in solution. The conformational ensembles of the A- and D-helix peptides contain ordered helical forms, as shown by extensive series of medium-range nuclear Overhauser effect connectivities, while the B- and C-helix peptides exhibit conformational preferences for nascent helix. All four peptides adopt ordered helical conformations in mixtures of trifluoroethanol and water. The terminal and interconnecting loop peptides also appear to contain appreciable populations of conformers with backbone phi and psi angles in the alpha-region and include highly populated hydrophobic cluster and/or turn conformations in some cases. Trifluoroethanol is unable to drive these peptides towards helical conformations. Overall, the peptide fragments of myohemerythrin have a marked preference towards secondary structure formation in aqueous solution. In contrast, peptide fragments derived from the beta-sandwich protein plastocyanin are relatively devoid of secondary structure in aqueous solution (see accompanying paper). These results suggest that the two different protein structural motifs may require different propensities for formation of local elements of secondary structure to initiate folding, and that there is a prepartitioning of conformational space determined by the local amino acid sequence that is different for the helical and beta-sandwich structural motifs.     

Preformed structural elements feature in partner recognition by intrinsically unstructured proteins

Intrinsically unstructured proteins (IUPs) are devoid of extensive structural order but often display signs of local and limited residual structure. To explain their effective functioning, we reasoned that such residual structure can be crucial in their interactions with their structured partner(s) in a way that preformed structural elements presage their final conformational state. To check this assumption, a database of 24 IUPs with known 3D structures in the bound state has been assembled and the distribution of secondary structure elements and backbone torsion angles have been analysed. The high proportion of residues in coil conformation and with phi, psi angles in the disallowed regions of the Ramachandran map compared to the reference set of globular proteins shows that IUPs are not fully ordered even in their bound form. To probe the effect of partner proteins on IUP folding, inherent conformational preferences of IUP sequences have been assessed by secondary structure predictions using the GOR, ALB and PROF algorithms. The accuracy of predicting secondary structure elements of IUPs is similar to that of their partner proteins and is significantly higher than the corresponding values for random sequences. We propose that strong conformational preferences mark regions in IUPs (mostly helices), which correspond to their final structural state, while regions with weak conformational preferences represent flexible linkers between them. In our interpretation, preformed elements could serve as initial contact points, the binding of which facilitates the reeling of the flexible regions onto the template. This finding implies that IUPs draw a functional advantage from preformed structural elements, as they enable their facile, kinetically and energetically less demanding, interaction with their physiological partner.     

An Energetic Representation of Protein Architecture that Is Independent of Primary and Secondary Structure

Protein fold classification often assumes that similarity in primary, secondary, or tertiary structure signifies a common evolutionary origin. However, when similarity is not obvious, it is sometimes difficult to conclude that particular proteins are completely unrelated. Clearly, a set of organizing principles that is independent of traditional classification could be valuable in linking different structural motifs and identifying common ancestry from seemingly disparate folds. Here, a four-dimensional ensemble-based energetic space spanned by a diverse set of proteins was defined and its characteristics were contrasted with those of Cartesian coordinate space. Eigenvector decomposition of this energetic space revealed the dominant physical processes contributing to the more or less stable regions of a protein. Unexpectedly, those processes were identical for proteins with different secondary structure content and were also identical among different amino-acid types. The implications of these results are twofold. First, it indicates that excited conformational states comprising the protein native state ensemble, largely invisible upon inspection of the high-resolution structure, are the major determinant of the energetic space. Second, it suggests that folds dissimilar in sequence or structure could nonetheless be energetically similar if their respective excited conformational states are considered, one example of which was observed in the N-terminal region of the Arc repressor switch mutant. Taken together, these results provide a surface area-based framework for understanding folds in energetic terms, a framework that may eventually yield a means of identifying common ancestry among structurally dissimilar proteins.     

Prediction of N-linked glycan branching patterns using artificial neural networks

A model was developed for novel prediction of N-linked glycan branching pattern classification for CHO-derived N-linked glycoproteins. The model consists of 30 independent recurrent neural networks and uses predicted quantities of secondary structure elements and residue solvent accessibility as an input vector. The model was designed to predict the major component of a heterogeneous mixture of CHO-derived glycoforms of a recombinant protein under normal growth conditions. Resulting glycosylation prediction is classified as either complex-type or high mannose. The incorporation of predicted quantities in the input vector allowed for theoretical mutant N-linked glycan branching predictions without initial experimental analysis of protein structures. Primary amino acid sequence data were effectively eliminated from the input vector space based on neural network prediction analyses. This provided further evidence that localized protein secondary structure elements and conformational structure may play more important roles in determining glycan branching patterns than does the primary sequence of a polypeptide. A confidence interval parameter was incorporated into the model to enable identification of false predictions. The model was further tested using published experimental results for mutants of the tissue-type plasminogen activator protein [J. Wilhelm, S.G. Lee, N.K. Kalyan, S.M. Cheng, F. Wiener, W. Pierzchala, P.P. Hung, Alterations in the domain structure of tissue-type plasminogen activator change the nature of asparagine glycosylation. Biotechnology (N.Y.) 8 (1990) 321-325].     

A rapid method for exploring the protein structure universe

We have developed an automatic protein fingerprinting method for the evaluation of protein structural similarities based on secondary structure element compositions, spatial arrangements, lengths, and topologies. This method can rapidly identify proteins sharing structural homologies as we demonstrate with five test cases: the globins, the mammalian trypsinlike serine proteases, the immunoglobulins, the cupredoxins, and the actinlike ATPase domain-containing proteins. Principal components analysis of the similarity distance matrix calculated from an all-by-all comparison of 1,031 unique chains in the Protein Data Bank has produced a distribution of structures within a high-dimensional structural space. Fifty percent of the variance observed for this distribution is bounded by six axes, two of which encode structural variability within two large families, the immunoglobulins and the trypsinlike serine proteases. Many aspects of the spatial distribution remain stable upon reduction of the database to 140 proteins with minimal family overlap. The axes correlated with specific structural families are no longer observed. A clear hierarchy of organization is seen in the arrangement of protein structures in the universe. At the highest level, protein structures populate regions corresponding to the all-alpha, all-beta, and alpha/beta superfamilies. Large protein families are arranged along family-specific axes, forming local densely populated regions within the space. The lowest level of organization is intrafamilial; homologous structures are ordered by variations in peripheral secondary structure elements or by conformational shifts in the tertiary structure.     

Analysis of topological and nontopological structural similarities in the PDB: New examples with old structures

We have developed a new method and program, SARF2, for fast comparison of protein structures, which can detect topological as well as nontopological similarities. The method searches for large ensembles of secondary structure elements, which are mutually compatible in two proteins. These ensembles consist of small fragments of C^α-trace, similarly arranged in three-dimensional space in two proteins, but not necessarily equally-ordered along the polypeptide chains. The program SARF2 is available for everyone through the World-Wide Web (WWW). We have performed an exhaustive pairwise comparison of all the entries from a recent issue of the Protein Data Bank (PDB) and report here on the results of an automated hierarchical cluster analysis. In addition, we report on several new cases of significant structural resemblance between proteins. To this end, a new definition of the significance of structural similarity is introduced, which effectively distinguishes the biologically meaningful equivalences from those occurring by chance. Analyzing the distribution of sequence similarity in significant structural matches, we show that sequence similarity as low as 20% in structurally-prealigned proteins can be a strong indication for the biological relevance of structural similarity. © 1996 Wiley-Liss, Inc.     

Peculiarities of secondary structure of serum albumin of some representatives of the animal kingdom

Methods of infrared (IR) spectroscopy and circular dichroism (CD) are suitable techniques for detection of proteins structural changes. These methods were used for determinating peculiarities of the secondary structure of serum albumins in some representatives of two classes of reptiles: Horsfield's tortoise (Testudo horsfieldi), water snake (Natrix tessellata) and grass snake (Natrix natrix) and birds: domestic goose (Anser anser), domestic chicken (Gallus domesticus), domestic duck (Anas platyrhyncha) and dove colored (Columba livia). An analysis of IR spectra and spectra obtained by the method of CD of serum albumins of both classes representatives revealed that beta-folding structure and alpha-helical sections that form the alpha-conformation play an important role in conformational structure formation of polypeptide chain and also disordered sites of molecules of these proteins. It was observed that certain redistribution depending on animals species exists, in the formation of secondary structure of serum albumins of the investigated representatives of reptiles and birds classes between the content of beta-folding structure, alpha-helical sections and disordered sites in molecules of these proteins.     

Dihedral angle preferences of amino acid residues forming various non-local interactions in proteins

In theory, a polypeptide chain can adopt a vast number of conformations, each corresponding to a set of backbone rotation angles. Many of these conformations are excluded due to steric overlaps. Ramachandran and coworkers were the first to look into this problem by plotting backbone dihedral angles in a two-dimensional plot. The conformational space in the Ramachandran map is further refined by considering the energetic contributions of various non-bonded interactions. Alternatively, the conformation adopted by a polypeptide chain may also be examined by investigating interactions between the residues. Since the Ramachandran map essentially focuses on local interactions (residues closer in sequence), out of interest, we have analyzed the dihedral angle preferences of residues that make non-local interactions (residues far away in sequence and closer in space) in the folded structures of proteins. The non-local interactions have been grouped into different types such as hydrogen bond, van der Waals interactions between hydrophobic groups, ion pairs (salt bridges), and ππ-stacking interactions. The results show the propensity of amino acid residues in proteins forming local and non-local interactions. Our results point to the vital role of different types of non-local interactions and their effect on dihedral angles in forming secondary and tertiary structural elements to adopt their native fold.     

Determination of the secondary structural elements of chicken liver fatty acid binding protein by two‐dimensional homonuclear NMR

A conformational study in solution of the fatty acid binding protein from chicken liver is presented. The nearly complete sequence‐specific ¹H resonance assignment was achieved from homonuclear two‐dimensional nmr experiments using a sample of native protein. The principal elements of secondary structure were identified: 10 antiparallel β‐strands and one helical segment followed by a turn comprising 5 residues. These elements correspond closely with those of the crystal structure of the related protein, and two new secondary structural features obtained from the nmr data are the β‐sheet conformation between the first and the last β‐strand in the protein sequence, as well as a helical loop at the N‐terminus of the polypeptide chain. © 1999 John Wiley & Sons, Inc. Biopoly 50: 1–11, 1999     

A comparison of the restrained molecular dynamics and distance geometry methods for determining three-dimensional structures of proteins on the basis of interproton distances

A direct comparison of the metric matrix distance geometry and restrained molecular dynamics methods for determining three-dimensional structures of proteins on the basis of interproton distances is presented using crambin as a model system. It is shown that both methods reproduce the overall features of the secondary and tertiary structure (shape and polypeptide fold). The region of conformational space sampled by the converged structures generated by the two methods is similar in size, and in both cases the converged structures are distributed about mean structures which are closer to the X-ray structure than any of the individual structures. The restrained molecular dynamics structures are superior to those obtained from distance geometry as regards local backbone conformation, side chain positions and non-bonding energies.     

Clustering of protein structural fragments reveals modular building block approach of nature

Structures of peptide fragments drawn from a protein can potentially occupy a vast conformational continuum. We co-ordinatize this conformational space with the help of geometric invariants and demonstrate that the peptide conformations of the currently available protein structures are heavily biased in favor of a finite number of conformational types or structural building blocks. This is achieved by representing a peptides' backbone structure with geometric invariants and then clustering peptides based on closeness of the geometric invariants. This results in 12,903 clusters, of which 2207 are made up of peptides drawn from functionally and/or structurally related proteins. These are termed "functional" clusters and provide clues about potential functional sites. The rest of the clusters, including the largest few, are made up of peptides drawn from unrelated proteins and are termed "structural" clusters. The largest clusters are of regular secondary structures such as helices and beta strands as well as of beta hairpins. Several categories of helices and strands are discovered based on geometric differences. In addition to the known classes of loops, we discover several new classes, which will be useful in protein structure modeling. Our algorithm does not require assignment of secondary structure and, therefore, overcomes the limitations in loop classification due to ambiguity in secondary structure assignment at loop boundaries.     

Conformational properties of a peptide model for unfolded alpha-helices

Models of protein folding often hypothesize that the first step is local secondary structure formation. The assumption is that unfolded polypeptide chains possess an intrinsic propensity to form these local secondary structures. On the basis of this idea, it is tempting to model the local conformational properties of unfolded proteins using well-established residue secondary structure propensities, in particular, alpha-helix forming propensities. We have used spectroscopic methods to investigate the conformational behavior of a host-guest series of peptides designed to model unfolded alpha-helices. A suitable peptide model for unfolded alpha-helices was determined from studies of the length dependence of the conformational properties of alanine-based peptides. The chosen host peptide possessed a small, detectable, alpha-helix content. Substituting various representative guest residues into the central position of the host peptide at times changed the conformational behavior dramatically, and often in ways that could not be predicted from known alpha-helix forming propensities. The data presented can be used to rationalize some of these propensities. However, it is clear that secondary structure propensities cannot be used to predict the local conformational properties of unfolded proteins.     

Tipping the Scale from Disorder to Alpha-helix: Folding of Amphiphilic Peptides in the Presence of Macroscopic and Molecular Interfaces

Secondary amphiphilicity is inherent to the secondary structural elements of proteins. By forming energetically favorable contacts with each other these amphiphilic building blocks give rise to the formation of a tertiary structure. Small proteins and peptides, on the other hand, are usually too short to form multiple structural elements and cannot stabilize them internally. Therefore, these molecules are often found to be structurally ambiguous up to the point of a large degree of intrinsic disorder in solution. Consequently, their conformational preference is particularly susceptible to environmental conditions such as pH, salts, or presence of interfaces. In this study we use molecular dynamics simulations to analyze the conformational behavior of two synthetic peptides, LKKLLKLLKKLLKL (LK) and EAALAEALAEALAE (EALA), with built-in secondary amphiphilicity upon forming an alpha-helix. We use these model peptides to systematically study their aggregation and the influence of macroscopic and molecular interfaces on their conformational preferences. We show that the peptides are neither random coils in bulk water nor fully formed alpha helices, but adopt multiple conformations and secondary structure elements with short lifetimes. These provide a basis for conformation-selection and population-shift upon environmental changes. Differences in these peptides’ response to macroscopic and molecular interfaces (presented by an aggregation partner) can be linked to their inherent alpha-helical tendencies in bulk water. We find that the peptides’ aggregation behavior is also strongly affected by presence or absence of an interface, and rather subtly depends on their surface charge and hydrophobicity.