RankViaContact: ranking and visualization of amino acid contacts

SUMMARY: RankViaContact is a web service for calculation of residue-residue contact energies in proteins based on a coarse-grained model, and for visualization of interactions. The service provides information about ranked contact energies of residues, coordination numbers and the relative solvent accessibility of selected residues, as well as sequence and structure information. The program can be used to design stabilizing mutations, to analyze residue-residue contacts and to study the consequences of mutations. AVAILABILITY: http://bioinf.uta.fi/Rank.htm.     

Prediction of contact numbers of amino acid residues using a neural network regression algorithm

The profile of contact numbers of amino acid residues in proteins contains important information about the protein structure and is connected with the accessibility of residues to solvent. Here we propose a method for predicting the profile of contact numbers of residues in protein from its amino acid sequence. The method is based on regression using a neural network algorithm. The algorithm predicts two types of profiles, namely, the total number of contacts and the number of close contacts with the neighbors in the chain. The Pearson coefficient of correlation between the actual and predicted values of total contact numbers amounted to 0.526–0.703. As for the number of close contacts, this coefficient was higher (0.662–0.743) for all the considered threshold contact distances (6, 8, 10, and 12 Å). The program for prediction of contact numbers CONNP is available at http://wwwmgs2.bionet.nsc.ru/reloaded.     

Prediction of contact numbers of amino acid residues using a neural network regression algorithm

The profile of contact numbers of amino acid residues in proteins contains important information about the protein structure and is connected with the accessibility of residues to solvent. Here we propose a method for predicting the profile of contact numbers of residues in protein from its amino acid sequence. The method is based on regression using a neural network algorithm. The algorithm predicts two types of profiles, namely, the total number of contacts and the number of close contacts with the neighbors in the chain. The Pearson coefficient of correlation between the actual and predicted values of total contact numbers amounted to 0.526–0.703. As for the number of close contacts, this coefficient was higher (0.662–0.743) for all the considered threshold contact distances (6, 8, 10, and 12 Å). The program for prediction of contact numbers CONNP is available at http://wwwmgs2.bionet.nsc.ru/reloaded.

     

New surface contacts formed upon reductive lysine methylation: Improving the probability of protein crystallization

Surface lysine methylation (SLM) is a technique for improving the rate of success of protein crystallization by chemically methylating lysine residues. The exact mechanism by which SLM enhances crystallization is still not clear. To study these mechanisms, and to analyze the conditions where SLM will provide the optimal benefits for rescuing failed crystallization experiments, we compared 40 protein structures containing N,N-dimethyl-lysine (dmLys) to a nonredundant set of 18,972 nonmethylated structures from the PDB. By measuring the relative frequency of intermolecular contacts (where contacts are defined as interactions between the residues in proximity with a distance of 3.5 Å or less) of basic residues in the methylated versus nonmethylated sets, dmLys-Glu contacts are seen more frequently than Lys-Glu contacts. Based on observation of the 10 proteins with both native and methylated structures, we propose that the increased rate of contact for dmLys-Glu is due to both a slight increase in the number of amine-carboxyl H-bonds and to the formation of methyl C–H···O interactions. By comparing the relative contact frequencies of dmLys with other residues, the mechanism by which methylation of lysines improves the formation of crystal contacts appears to be similar to that of Lys to Arg mutation. Moreover, analysis of methylated structures with the surface entropy reduction (SER) prediction server suggests that in many cases SLM of predicted SER sites may contribute to improved crystallization. Thus, tools that analyze protein sequences and mark residues for SER mutation may identify proteins with good candidate sites for SLM.     

An algorithm to parse segment packing in predicted protein contact maps

Background

The analysis of correlation in alignments generates a matrix of predicted contacts between positions in the structure and while these can arise for many reasons, the simplest explanation is that the pair of residues are in contact in a three-dimensional structure and are affecting each others selection pressure. To analyse these data, A dynamic programming algorithm was developed for parsing secondary structure interactions in predicted contact maps.

Results

The non-local nature of the constraints required an iterated approach (using a “frozen approximation”) but with good starting definitions, a single pass was usually sufficient. The method was shown to be effective when applied to the transmembrane class of protein and error tolerant even when the signal becomes degraded. In the globular class of protein, where the extent of interactions are more limited and more complex, the algorithm still behaved well, classifying most of the important interactions correctly in both a small and a large test case. For the larger protein, this involved examples of the algorithm apportioning parts of a single large secondary structure element between two different interactions.

Conclusions

It is expected that the method will be useful as a pre-processor to coarse-grained modelling methods to extend the range of protein tertiary structure prediction to larger proteins or to data that is currently too ’noisy’ to be used by current residue-based methods.

     

Effect of short- and long-range interactions on protein folding

The relative importance of short- and long-range interactions is examined using a Monte Carlo simulation of protein folding on bovine pancreatic trypsin inhibitor. The model of the protein and the interaction energies were parametrized using X-ray structures of 30 native proteins. A nearest neighbor Ising model is used to determine the conformational state at each stage of the Monte Carlo procedure. Long-range interactions are simulated by contact free energies which become effective as two residues, separated by four or more residues along the chain, approach each other, and by disulfide-bond energies. Short-range interactions for residues separated by one, two, or three residues along the chain are also modeled by contact free energies and by -helical hydrogen bonds. A hard-sphere model is used to represent repulsive interactions. The ratios of short- to long-range interactions studied are 1:1, 2:1, 1:2, 0:1, and 1:0; e.g., for the 2:1 ratio, short-range interactions are weighted twice as much as long-range interactions, and for the 1:0 ratio, long-range interactions are omitted. For each ratio of short- to long-range interactions, a native conformation is found by a Monte Carlo procedure, a segment of 11 residues (residue numbers 1–11) is then rotated away from the rest of the molecule [breaking the 5–55 native disulfide bond, and moving this segment so that the distance between the sulfur atoms of the 5 and 55 cystine side chains (averaged for all native conformations) increases from 3.9 to 7.3 Å], and the Monte Carlo simulation is carried out (allowing the conformation of the whole molecule to change) until equilibrium is attained. For each ratio, the refolded conformation is compared to the native one using triangular distance maps and differential geometry distance criteria. With ratios of short- to long-range interaction energies of 1:1 and 0:1, the native disulfide bond could be re-formed; with ratios of 2:1 and 1:2 it did not; and with the 1:0 ratio, even a stable native conformation was not achieved. Therefore, long-range interactions (in addition to short-range ones) are required to bring remote parts of the protein together and to stabilize its native conformation.NIH Postdoctoral Fellow, 1977–1978.     

Validity of Gō models: comparison with a solvent-shielded empirical energy decomposition

Do Gō-type model potentials provide a valid approach for studying protein folding? They have been widely used for this purpose because of their simplicity and the speed of simulations based on their use. The essential assumption in such models is that only contact interactions existing in the native state determine the energy surface of a polypeptide chain, even for non-native configurations sampled along folding trajectories. Here we use an all-atom molecular mechanics energy function to investigate the adequacy of Gō-type potentials. We show that, although the contact approximation is accurate, non-native contributions to the energy can be significant. The assumed relation between residue-residue interaction energies and the number of contacts between them is found to be only approximate. By contrast, individual residue energies correlate very well with the number of contacts. The results demonstrate that models based on the latter should give meaningful results (e.g., as used to interpret phi values), whereas those that depend on the former are only qualitative, at best.     

A New Method to Characterize Hydrophobic Organization of Proteins: Application to Rational Protein Engineering of Barnase

Abstract

We present a new algorithm for characterization of protein spatial structure basing on the molecular hydrophobicity potential approach. The method is illustrated by the analysis of three-dimensional structure of barnase and barnase-barstar complex. Current approach enables identification of amino acid residues situated in unfavorable environment (these residues may be “active” for binding), and to map quantitatively hydrophobic, hydrophilic and unfavorable hydrophobic-hydrophilic intra-and inter-molecular contacts involving backbone and side-chain segments of amino acid residues. Calculation of individual contributions of amino acid residues to such contacts permits identification of structurally-important residues. The contact plots obtained with molecular hydrophobicity potential calculations, provide easy rules to choose sites for mutations, which can increase a strength of intra- or inter-molecular hydrophobic interactions. The unfavorable hydrophobic-hydrophilic contact can be mutated to favorable hydrophobic, and already existing weak hydrophobic contact can be strengthen by increasing hydrophobicity of residues in contact. Basing on the analysis of the contact plots, we suggest several mutations of barnase which are supposed to increase intramolecular hydrophobic interactions, and thus might lead to increased stability of the protein. Part of these mutations was studied previously experimentally, and indeed stabilized barnase. The other of predicted mutations were not studied experimentally yet. Several new mutations of barnase and barstar are also proposed to enhance the hydrophobic interactions on their binding interface.     

Amino acid empirical contact energy definitions for fold recognition in the space of contact maps

Background  

Contradicting evidence has been presented in the literature concerning the effectiveness of empirical contact energies for fold recognition. Empirical contact energies are calculated on the basis of information available from selected protein structures, with respect to a defined reference state, according to the quasi-chemical approximation. Protein-solvent interactions are estimated from residue solvent accessibility.     

Extracting contact energies from protein structures: A study using a simplified model

In this study, we exploited an elementary 2-dimensional square lattice model of HP polymers to test the premise of extracting contact energies from protein structures. Given a set of prespecified energies for H–H, H–P, and P–P contacts, all possible sequences of various lengths were exhaustively enumerated to find sequences that have unique lowest-energy conformations. The lowest-energy structures (or native structures) of such (native) sequences were used to extract contact energies using the Miyazawa-Jernigan procedure and here-defined reference state. The relative magnitudes of the original energies were restored reasonably well, but the extracted contact energies were independent of the absolute magnitudes of the initial energies. We turned to a more detailed characterization of the energy landscapes of the native sequences in light of a new theoretical framework on protein folding. Foldability of such sequences imposes two limits on the absolute value of the prespecified energies: a lower bound entailed by the minimum requirement for thermodynamic stability and an upper bound associated with the entrapment of the chain to local minima. We found that these two limits confine the prespecified energy values to a rather narrow range which, surprisingly, also contains the extracted energies in all the cases examined. These results indicate that the quasi-chemical approximation can be used to connect quantitatively the occurrence of various residue–residue contacts in an ensemble of native structures with the energies of the contacts. More importantly, they suggest that the extracted contact energies do contain information on structural stability and can be used to estimate actual structural energetics. This study also encourages the use of structure-derived contact energies in threading. The finding that there is a rather narrow range of energies that are optimal for folding a sequence also cautions the use of arbitrary energy Hamiltonion in minimal folding models. Proteins 31:299–308, 1998. © 1998 Wiley-Liss, Inc.     

Probing the structure of complex macromolecular interactions by homolog specificity scanning: the P1 and P7 plasmid partition systems.

The P1 plasmid partition locus, P1 par, actively distributes plasmid copies to Escherichia coli daughter cells. It encodes two DNA sites and two proteins, ParA and ParB. Plasmid P7 uses a similar system, but the key macromolecular interactions are species specific. Homolog specificity scanning (HSS) exploits such specificities to map critical contact points between component macromolecules. The ParA protein contacts the par operon operator for operon autoregulation, and the ParB contacts the parS partition site during partition. Here, we refine the mapping of these contacts and extend the use of HSS to map protein-protein contacts. We found that ParB participates in autoregulation at the operator site by making a specific contact with ParA. Similarly, ParA acts in partition by making a specific contact with ParB bound at parS. Both these interactions involve contacts between a C-terminal region of ParA and the extreme N-terminus of ParB. As a single type of ParA-ParB complex appears to be involved in recognizing both DNA sites, the operator and the parS sites may both be occupied by a single protein complex during partition. The general HSS strategy may aid in solving the three-dimensional structures of large complexes of macromolecules.     

The jigsaw puzzle model: search for conformational specificity in protein interiors

The jigsaw puzzle model postulates that the predominant factor relating primary sequence to three-dimensional fold lies in the stereospecific packing of interdigitating side-chains within densely packed protein interiors. An attempt has been made to check the validity of the model by means of a surface complementarity function. Out of a database of 100 highly resolved protein structures the contacts between buried hydrophobic residues (Leu, Ile, Val, Phe) and their neighbours have been categorized in terms of the extent of side-chain surface area involved in a contact (overlap) and their steric fit (Sm). The results show that the majority of contacts between a buried residue and its immediate neighbours (side-chains) are of high steric fit and in the case of extended overlap at least one of the angular parameters characterizing interresidue geometry to have pronounced deviation from a random distribution, estimated by chi(2). The calculations thus tend to support the "jigsaw puzzle" model in that 75-85% of the contacts involving hydrophobic residues are of high surface complementarity, which, coupled to high overlap, exercise fairly stringent constraints over the possible geometrical orientations between interacting residues. These constraints manifest in simple patterns in the distributions of orientational angles. Approximately 60-80% of the buried side-chain surface packs against neighbouring side-chains, the rest interacting with main-chain atoms. The latter partition of the surface maintains an equally high steric fit (relative to side-chain contacts) emphasizing a non-trivial though secondary role played by main-chain atoms in interior packing. The majority of this class of contacts, though of high complementarity, is of reduced overlap. All residues whether hydrophobic or polar/charged show similar surface complementarity measures upon burial, indicating comparable competence of all amino acids in packing effectively with their atomic environments. The specificity thus appears to be distributed over the entire network of contacts within proteins. The study concludes with a proposal to classify contacts as specific and non-specific (based on overlap and fit), with the former perhaps contributing more to the specificity between sequence and fold than the latter.     

Molecular basis of co-operativity in protein folding. III. Structural identification of cooperative folding units and folding intermediates.

The hierarchical partition function formalism for protein folding developed earlier has been extended through the use of three-dimensional polar and apolar contact plots. For each amino acid residue in the protein, these plots indicate the apolar and polar surfaces that are buried from the solvent, the identity of all amino acid residues that contribute to this shielding, and the magnitude of their contributions. These contact plots are then used to examine the distribution of the free energy of stabilization throughout the protein molecule. Analysis of these data allows identification of co-operative folding units and their hierarchical levels, and the identification of partially folded intermediates with a significant probability of being populated. The overall folding/unfolding thermodynamics of 12 globular proteins, for which crystallographic and experimental thermodynamics are available, is predicted within error. An energetic classification of partially folded intermediates is presented and the results compared to those cases for which structural and thermodynamic experimental information is available. Four different types of partially folded states and their structural energies are considered. (1) Local intermediates, in which only a local region of the protein loses secondary and tertiary interactions, while the rest of the protein remains intact. (2) Global intermediates, corresponding to the standard molten globule definition, in which significant secondary structure is maintained but native-like tertiary structure contacts are disrupted. (3) Extended intermediates characterized by the existence of secondary structure elements (e.g. alpha-helices) exposed to solvent. (4) Folding intermediates in proteins with two structural domains. The structure and energetics of folding intermediates of apo-myoglobin, alpha-lactalbumin, phosphoglycerate kinase and arabinose-binding protein are considered in detail.     

Equilibrium folding and unfolding pathways for a model protein

The folding–unfolding process of reduced bovine pancreatic trypsin inhibitor was investigated with an idealized model employing approximate free energies. The protein is regarded to consist of only C^α and C^β atoms. The backbone dihedral angles are the only conformational variables and are permitted to take discrete values at every 10°. Intraresidue energies consist of two terms: an empirical part taken from the observed frequency distributions of (?,ψ) and an additional favorable energy assigned to the native conformation of each residue. Interresidue interactions are simplified by assuming that there is an attractive energy operative only between residue pairs in close contact in the native structure. A total of 230,000 molecular conformations, with no atomic overlaps, ranging from the native state to the denatured state, are randomly generated by changing the sampling bias. Each conformation is classified according to its conformational energy, F; a conformational entropy, S(F) is estimated for each value of F from the number of samples. The dependence of S(F) on energy reveals that the folding–unfolding transition for this idealized model is an “all-or-none” type; this is attributable to the specific long-range interactions. Interresidue contact probabilities, averaged over samples representing various stages of folding, serve to characterize folding intermediates. Most probable equilibrium pathways for the folding–unfolding transition are constructed by connecting conformationally similar intermediates. The specific details obtained for bovine pancreatic trypsin inhibitor are as follows: (1) Folding begins with the appearance of nativelike medium-range contacts at a β-turn and at the α-helix. (2) These grow to include the native pair of interacting β-strands. This state includes intact regular secondary conformations, as well as the interstrand sheet contacts, and corresponds to an activated state with the highest free energy on the pathway. (3) Additional native long-range contacts are completely formed either toward the amino terminus or toward the carboxyl terminus. (4) In a final step, the missing contacts appear. Although these folding pathways for this model are not consistent with experimental reports, it does indicate multiple folding pathways. The method is general and can be applied to any set of calculated conformational energies and furthermore permits investigation of gross folding features.     

Measurements of protein sequence-structure correlations

Correlations between protein structures and amino acid sequences are widely used for protein structure prediction. For example, secondary structure predictors generally use correlations between a secondary structure sequence and corresponding primary structure sequence, whereas threading algorithms and similar tertiary structure predictors typically incorporate interresidue contact potentials. To investigate the relative importance of these sequence-structure interactions, we measured the mutual information among the primary structure, secondary structure and side-chain surface exposure, both for adjacent residues along the amino acid sequence and for tertiary structure contacts between residues distantly separated along the backbone. We found that local interactions along the amino acid chain are far more important than non-local contacts and that correlations between proximate amino acids are essentially uninformative. This suggests that knowledge-based contact potentials may be less important for structure predication than is generally believed.     

Identifying sequence-structure pairs undetected by sequence alignments

We examine how effectively simple potential functions previously developed can identify compatibilities between sequences and structures of proteins for database searches. The potential function consists of pairwise contact energies, repulsive packing potentials of residues for overly dense arrangement and short-range potentials for secondary structures, all of which were estimated from statistical preferences observed in known protein structures. Each potential energy term was modified to represent compatibilities between sequences and structures for globular proteins. Pairwise contact interactions in a sequence-structure alignment are evaluated in a mean field approximation on the basis of probabilities of site pairs to be aligned. Gap penalties are assumed to be proportional to the number of contacts at each residue position, and as a result gaps will be more frequently placed on protein surfaces than in cores. In addition to minimum energy alignments, we use probability alignments made by successively aligning site pairs in order by pairwise alignment probabilities. The results show that the present energy function and alignment method can detect well both folds compatible with a given sequence and, inversely, sequences compatible with a given fold, and yield mostly similar alignments for these two types of sequence and structure pairs. Probability alignments consisting of most reliable site pairs only can yield extremely small root mean square deviations, and including less reliable pairs increases the deviations. Also, it is observed that secondary structure potentials are usefully complementary to yield improved alignments with this method. Remarkably, by this method some individual sequence-structure pairs are detected having only 5-20% sequence identity.     

All-atom contact potential approach to protein thermostability analysis

In this paper we use all-atom potential energy to define and analyze the inter-residue contacts in mesophilic and thermophilic proteins. Fifteen families of proteins are selected and each family has two representative proteins with greatly different preferred environmental temperatures. We find that both the number and energy of the contacts defined in this way show stronger correlations with the preferred temperatures of proteins than other factors used before. We also find that the charged-polar and charged-nonpolar residue contacts not only have larger contact numbers but also have lower single contact energies. Furthermore, the most important is that most of the thermophilic proteins have more charged-polar and charged-nonpolar residue contacts than their mesophilic counterparts. This suggests that they may play an important role in the thermostability of proteins, except usual charged-charged and nonpolar-nonpolar residue contacts. Charged residues may exert their profound influence by forming contacts not only with other charged residues but also with polar or nonpolar residues, thus further increasing the strength of contact network and then the thermostability of proteins.     

Insights into protein-protein binding by binding free energy calculation and free energy decomposition for the Ras-Raf and Ras-RalGDS complexes

Absolute binding free energy calculations and free energy decompositions are presented for the protein-protein complexes H-Ras/C-Raf1 and H-Ras/RalGDS. Ras is a central switch in the regulation of cell proliferation and differentiation. In our study, we investigate the capability of the molecular mechanics (MM)-generalized Born surface area (GBSA) approach to estimate absolute binding free energies for the protein-protein complexes. Averaging gas-phase energies, solvation free energies, and entropic contributions over snapshots extracted from trajectories of the unbound proteins and the complexes, calculated binding free energies (Ras-Raf: -15.0(+/-6.3)kcal mol(-1); Ras-RalGDS: -19.5(+/-5.9)kcal mol(-1)) are in fair agreement with experimentally determined values (-9.6 kcal mol(-1); -8.4 kcal mol(-1)), if appropriate ionic strength is taken into account. Structural determinants of the binding affinity of Ras-Raf and Ras-RalGDS are identified by means of free energy decomposition. For the first time, computationally inexpensive generalized Born (GB) calculations are applied in this context to partition solvation free energies along with gas-phase energies between residues of both binding partners. For selected residues, in addition, entropic contributions are estimated by classical statistical mechanics. Comparison of the decomposition results with experimentally determined binding free energy differences for alanine mutants of interface residues yielded correlations with r(2)=0.55 and 0.46 for Ras-Raf and Ras-RalGDS, respectively. Extension of the decomposition reveals residues as far apart as 25A from the binding epitope that can contribute significantly to binding free energy. These "hotspots" are found to show large atomic fluctuations in the unbound proteins, indicating that they reside in structurally less stable regions. Furthermore, hotspot residues experience a significantly larger-than-average decrease in local fluctuations upon complex formation. Finally, by calculating a pair-wise decomposition of interactions, interaction pathways originating in the binding epitope of Raf are found that protrude through the protein structure towards the loop L1. This explains the finding of a conformational change in this region upon complex formation with Ras, and it may trigger a larger structural change in Raf, which is considered to be necessary for activation of the effector by Ras.     

Identification of amino acids involved in protein structural uniqueness: implication for de novo protein design

Structural uniqueness is characteristic of native proteins and is essential to express their biological functions. The major factors that bring about the uniqueness are specific interactions between hydrophobic residues and their unique packing in the protein core. To find the origin of the uniqueness in their amino acid sequences, we analyzed the distribution of the side chain rotational isomers (rotamers) of hydrophobic amino acids in protein tertiary structures and derived deltaS(contact), the conformational-entropy changes of side chains by residue-residue contacts in each secondary structure. The deltaS(contact) values indicate distinct tendencies of the residue pairs to restrict side chain conformation by inter-residue contacts. Of the hydrophobic residues in alpha-helices, aliphatic residues (Leu, Val, Ile) strongly restrict the side chain conformations of each other. In beta-sheets, Met is most strongly restricted by contact with Ile, whereas Leu, Val and Ile are less affected by other residues in contact than those in alpha-helices. In designed and native protein variants, deltaS(contact) was found to correlate with the folding-unfolding cooperativity. Thus, it can be used as a specificity parameter for designing artificial proteins with a unique structure.     

Propensities,probabilities, and the Boltzmann hypothesis

The relative strengths of interactions involving polypeptide chains can be estimated with reasonable accuracy with statistical potentials, free-energy functions derived from the frequency of occurrence of structural arrangements of residues or atoms in collections of protein structures. Recent published work has shown that the energetics of side-chain/backbone interactions can be modeled by the phi/psi propensities of the 20 amino acids. In this report, the more commonly used phi/psi probabilities are demonstrated to fail in evaluating the free energies of protein conformations because of an overriding preference for all helical structures. Comparison of the hypothetical reactions implied by these two different statistics-propensities versus probabilities-leads to the conclusion that the Boltzmann hypothesis may only be applicable for the calculation of statistical potentials after the starting conformation has been specified. This conclusion supports a simple conjecture: The surprising success of the Boltzmann hypothesis in explaining the energetics of protein structures is a direct consequence of a real equilibrium, one extending over evolutionary time that has maintained the stability of each protein within a narrow range of values.