Database-derived potentials dependent on protein size for in silico folding and design

Knowledge-based potentials are widely used in simulations of protein folding, structure prediction, and protein design. Their advantages include limited computational requirements and the ability to deal with low-resolution protein models compatible with long-scale simulations. Their drawbacks comprehend their dependence on specific features of the dataset from which they are derived, such as the size of the proteins it contains, and their physical meaning is still a subject of debate. We address these issues by probing the theoretical validity of these potentials as mean-force potentials that take the solvent implicitly into account and involve entropic contributions due to atomic degrees of freedom and solvation. The dependence on the size of the system is checked on distance-dependent amino acid pair potentials, derived from six protein structure sets containing proteins of increasing length N. For large inter-residue distances, they are found to display the theoretically predicted 1/N behavior weighted by a factor depending on the boundaries and the compressibility of the system. For short distances, different trends are observed according to the nature of the residue pairs and their ability to form, for example, electrostatic, cation-pi or pi-pi interactions, or hydrophobic packing. The results of this analysis are used to devise a novel protein size-dependent distance potential, which displays an improved performance in discriminating native sequence-structure matches among decoy models.     

OPUS-PSP: an orientation-dependent statistical all-atom potential derived from side-chain packing

Here we report an orientation-dependent statistical all-atom potential derived from side-chain packing, named OPUS-PSP. It features a basis set of 19 rigid-body blocks extracted from the chemical structures of all 20 amino acid residues. The potential is generated from the orientation-specific packing statistics of pairs of those blocks in a non-redundant structural database. The purpose of such an approach is to capture the essential elements of orientation dependence in molecular packing interactions. Tests of OPUS-PSP on commonly used decoy sets demonstrate that it significantly outperforms most of the existing knowledge-based potentials in terms of both its ability to recognize native structures and consistency in achieving high Z-scores across decoy sets. As OPUS-PSP excludes interactions among main-chain atoms, its success highlights the crucial importance of side-chain packing in forming native protein structures. Moreover, OPUS-PSP does not explicitly include solvation terms, and thus the potential should perform well when the solvation effect is difficult to determine, such as in membrane proteins. Overall, OPUS-PSP is a generally applicable potential for protein structure modeling, especially for handling side-chain conformations, one of the most difficult steps in high-accuracy protein structure prediction and refinement.     

Extracting the excitonic Hamiltonian of the Fenna-Matthews-Olson complex using three-dimensional third-order electronic spectroscopy

An accurate scoring function is a key component for successful protein structure prediction. To address this important unsolved problem, we develop a generalized orientation and distance-dependent all-atom statistical potential. The new statistical potential, generalized orientation-dependent all-atom potential (GOAP), depends on the relative orientation of the planes associated with each heavy atom in interacting pairs. GOAP is a generalization of previous orientation-dependent potentials that consider only representative atoms or blocks of side-chain or polar atoms. GOAP is decomposed into distance- and angle-dependent contributions. The DFIRE distance-scaled finite ideal gas reference state is employed for the distance-dependent component of GOAP. GOAP was tested on 11 commonly used decoy sets containing 278 targets, and recognized 226 native structures as best from the decoys, whereas DFIRE recognized 127 targets. The major improvement comes from decoy sets that have homology-modeled structures that are close to native (all within ∼4.0 Å) or from the ROSETTA ab initio decoy set. For these two kinds of decoys, orientation-independent DFIRE or only side-chain orientation-dependent RWplus performed poorly. Although the OPUS-PSP block-based orientation-dependent, side-chain atom contact potential performs much better (recognizing 196 targets) than DFIRE, RWplus, and dDFIRE, it is still ∼15% worse than GOAP. Thus, GOAP is a promising advance in knowledge-based, all-atom statistical potentials. GOAP is available for download at http://cssb.biology.gatech.edu/GOAP.     

A consistent set of statistical potentials for quantifying local side-chain and backbone interactions

The frequencies of occurrence of atom arrangements in high-resolution protein structures provide some of the most accurate quantitative measures of interaction energies in proteins. In this report we extend our development of a consistent set of statistical potentials for quantifying local interactions between side-chains and the polypeptide backbone, as well as nearby side-chains. Starting with phi/psi/chi1 propensities that select for optimal interactions of the 20 amino acid side-chains with the 2 flanking peptide bonds, the following 3 new terms are added: (1) a distance-dependent interaction between the side-chain at i and the carbonyl oxygens and amide protons of the peptide units at i +/- 2, i +/- 3, and i +/- 4; (2) a distance-dependent interaction between the side-chain at position i and side-chains at positions i + 1 through i + 4; and (3) an orientation-dependent interaction between the side-chain at position i and side-chains at i + 1 through i + 4. The relative strengths of these 4 pseudo free energy terms are estimated by the average information content of each scoring matrix and by assessing their performance in a simple fragment threading test. They vary from -0.4 - -0.5 kcal/mole per residue for phi/psi/chi1 propensities to a range of -0.15 - -0.6 kcal/mole per residue for each of the other 3 terms. The combined energy function, containing no interactions between atoms more than 4 residues apart, identifies the correct structural fragment for randomly selected 15 mers over 40% of the time, after searching through 232,000 alternative conformations. For 14 out of 20 sets of all-atom Rosetta decoys analyzed, the native structure has a combined score lower than any of the 1700-1900 decoy conformations. The ability of this energy function to detect energetically important details of local structure is demonstrated by its power to distinguish high-resolution crystal structures from NMR solution structures.     

An accurate, residue-level, pair potential of mean force for folding and binding based on the distance-scaled, ideal-gas reference state

Structure prediction on a genomic scale requires a simplified energy function that can efficiently sample the conformational space of polypeptide chains. A good energy function at minimum should discriminate native structures against decoys. Here, we show that a recently developed, residue-specific, all-atom knowledge-based potential (167 atomic types) based on distance-scaled, finite ideal-gas reference state (DFIRE-all-atom) can be substantially simplified to 20 residue types located at side-chain center of mass (DFIRE-SCM) without a significant change in its capability of structure discrimination. Using 96 standard multiple decoy sets, we show that there is only a small reduction (from 80% to 78%) in success rate of ranking native structures as the top 1. The success rate is higher than two previously developed, all-atom distance-dependent statistical pair potentials. Applied to structure selections of 21 docking decoys without modification, the DFIRE-SCM potential is 29% more successful in recognizing native complex structures than an all-atom statistical potential trained by a database of dimeric interfaces. The potential also achieves 92% accuracy in distinguishing true dimeric interfaces from artificial crystal interfaces. In addition, the DFIRE potential with the C(alpha) positions as the interaction centers recognizes 123 native structures out of a comprehensive 125-protein TOUCHSTONE decoy set in which each protein has 24,000 decoys with only C(alpha) positions. Furthermore, the performance by DFIRE-SCM on newly established 25 monomeric and 31 docking Rosetta-decoy sets is comparable to (or better than in the case of monomeric decoy sets) that of a recently developed, all-atom Rosetta energy function enhanced with an orientation-dependent hydrogen bonding potential.     

Multibody coarse-grained potentials for native structure recognition and quality assessment of protein models

Multibody potentials have been of much interest recently because they take into account three dimensional interactions related to residue packing and capture the cooperativity of these interactions in protein structures. Our goal was to combine long range multibody potentials and short range potentials to improve recognition of native structure among misfolded decoys. We optimized the weights for four-body nonsequential, four-body sequential, and short range potentials to obtain optimal model ranking results for threading and have compared these data against results obtained with other potentials (26 different coarse-grained potentials from the Potentials 'R'Us web server have been used). Our optimized multibody potentials outperform all other contact potentials in the recognition of the native structure among decoys, both for models from homology template-based modeling and from template-free modeling in CASP8 decoy sets. We have compared the results obtained for this optimized coarse-grained potentials, where each residue is represented by a single point, with results obtained by using the DFIRE potential, which takes into account atomic level information of proteins. We found that for all proteins larger than 80 amino acids our optimized coarse-grained potentials yield results comparable to those obtained with the atomic DFIRE potential.     

Free energies for coarse-grained proteins by integrating multibody statistical contact potentials with entropies from elastic network models

We propose a novel method of calculation of free energy for coarse grained models of proteins by combining our newly developed multibody potentials with entropies computed from elastic network models of proteins. Multi-body potentials have been of much interest recently because they take into account three dimensional interactions related to residue packing and capture the cooperativity of these interactions in protein structures. Combining four-body non-sequential, four-body sequential and pairwise short range potentials with optimized weights for each term, our coarse-grained potential improved recognition of native structure among misfolded decoys, outperforming all other contact potentials for CASP8 decoy sets and performance comparable to the fully atomic empirical DFIRE potentials. By combing statistical contact potentials with entropies from elastic network models of the same structures we can compute free energy changes and improve coarse-grained modeling of protein structure and dynamics. The consideration of protein flexibility and dynamics should improve protein structure prediction and refinement of computational models. This work is the first to combine coarse-grained multibody potentials with an entropic model that takes into account contributions of the entire structure, investigating native-like decoy selection.     

Beta2-microglobulin amyloid fragment organization and morphology and its comparison to Abeta suggests that amyloid aggregation pathways are sequence specific

Beta2-microglobulin (beta2-m) can form dialysis-related amyloid deposits. The structure of a fragment of beta2-m (K3, Ser20-Lys41) in the oligomeric state has recently been solved. We modeled equilibrium structures of K3 oligomers with different organizations (single and double layers) and morphologies (linear-like and annular-like) for the wild-type and mutants using all-atom molecular dynamics (MD) simulations. We focused on the sheet-to-sheet association force, which is the key in the amyloid organization and morphology. For the linear-like morphology, we observed two stable organizations: (i) single-layered parallel-stranded beta-sheets and (ii) double-layered parallel-stranded antiparallel beta-sheets stacked perpendicular to the fibril axis through the hydrophobic N-terminal-N-terminal (NN) interface. No stable annular structures were observed. The structural instability of the annular morphology was mainly attributed to electrostatic repulsion of three negatively charged residues (Asp15, Glu17, and Asp19) projecting from the same beta-strand surface. Linear-like and annular-like double-layered oligomers with the NN interface are energetically more favorable than other oligomers with C-terminal-C-terminal (CC) or C-terminal-N-terminal (CN) interfaces, emphasizing the importance of hydrophobic interactions and side-chain packing in stabilizing these oligomers. Moreover, only linear-like structures, rather than annular structures, with parallel beta-strands and antiparallel beta-sheet arrangements are possible intermediate states for the K3 beta2-m amyloid fibrils in solution. Comparing the beta2-m fragment with Abeta indicates that while both adopt similar beta-strand-turn-beta-strand motifs, the final amyloid structures can be dramatically different in size, structure, and morphology due to differences in side-chain packing arrangements, intermolecular driving forces, sequence composition, and residue positions, suggesting that the mechanism leading to distinct morphologies and the aggregation pathways is sequence specific.     

Using a Hydrophobic Contact Potential to Evaluate Native and Near-native Folds Generated by Molecular Dynamics Simulations

There are several knowledge-based energy functions that can distinguish the native fold from a pool of grossly misfolded decoys for a given sequence of amino acids. These decoys, which are typically generated by mounting, or “threading”, the sequence onto the backbones of unrelated protein structures, tend to be non-compact and quite different from the native structure: the root-mean-squared (RMS) deviations from the native are commonly in the range of 15 to 20 Å. Effective energy functions should also demonstrate a similar recognition capability when presented with compact decoys that depart only slightly in conformation from the correct structure (i.e. those with RMS deviations of ∼5 Å or less). Recently, we developed a simple yet powerful method for native fold recognition based on the tendency for native folds to form hydrophobic cores. Our energy measure, which we call the hydrophobic fitness score, is challenged to recognize the native fold from 2000 near-native structures generated for each of five small monomeric proteins. First, 1000 conformations for each protein were generated by molecular dynamics simulation at room temperature. The average RMS deviation of this set of 5000 was 1.5 Å. A total of 323 decoys had energies lower than native; however, none of these had RMS deviations greater than 2 Å. Another 1000 structures were generated for each at high temperature, in which a greater range of conformational space was explored (4.3 Å average RMS deviation). Out of this set, only seven decoys were misrecognized. The hydrophobic fitness energy of a conformation is strongly dependent upon the RMS deviation. On average our potential yields energy values which are lowest for the population of structures generated at room temperature, intermediate for those produced at high temperature and highest for those constructed by threading methods. In general, the lowest energy decoy conformations have backbones very close to native structure. The possible utility of our method for screening backbone candidates for the purpose of modelling by side-chain packing optimization is discussed.     

A novel side-chain orientation dependent potential derived from random-walk reference state for protein fold selection and structure prediction

Background

An accurate potential function is essential to attack protein folding and structure prediction problems. The key to developing efficient knowledge-based potential functions is to design reference states that can appropriately counteract generic interactions. The reference states of many knowledge-based distance-dependent atomic potential functions were derived from non-interacting particles such as ideal gas, however, which ignored the inherent sequence connectivity and entropic elasticity of proteins.

Methodology

We developed a new pair-wise distance-dependent, atomic statistical potential function (RW), using an ideal random-walk chain as reference state, which was optimized on CASP models and then benchmarked on nine structural decoy sets. Second, we incorporated a new side-chain orientation-dependent energy term into RW (RWplus) and found that the side-chain packing orientation specificity can further improve the decoy recognition ability of the statistical potential.

Significance

RW and RWplus demonstrate a significantly better ability than the best performing pair-wise distance-dependent atomic potential functions in both native and near-native model selections. It has higher energy-RMSD and energy-TM-score correlations compared with other potentials of the same type in real-life structure assembly decoys. When benchmarked with a comprehensive list of publicly available potentials, RW and RWplus shows comparable performance to the state-of-the-art scoring functions, including those combining terms from multiple resources. These data demonstrate the usefulness of random-walk chain as reference states which correctly account for sequence connectivity and entropic elasticity of proteins. It shows potential usefulness in structure recognition and protein folding simulations. The RW and RWplus potentials, as well as the newly generated I-TASSER decoys, are freely available in http://zhanglab.ccmb.med.umich.edu/RW.     

Amino acid pairing preferences in parallel beta-sheets in proteins

Statistical approaches have been applied to examine amino acid pairing preferences within parallel beta-sheets. The main chain hydrogen bonding pattern in parallel beta-sheets means that, for each residue pair, only one of the residues is involved in main chain hydrogen bonding with the strand containing the partner residue. We call this the hydrogen bonded (HB) residue and the partner residue the non-hydrogen bonded (nHB) residue, and differentiate between the favorability of a pair and that of its reverse pair, e.g. Asn(HB)-Thr(nHB)versus Thr(HB)-Asn(nHB). Significantly (p < or = 0.000001) favoured pairings were rationalised using stereochemical arguments. For instance, Asn(HB)-Thr(nHB) and Arg(HB)-Thr(nHB) were favoured pairs, where the residues adopted favoured chi1 rotamer positions that allowed side-chain interactions to occur. In contrast, Thr(HB)-Asn(nHB) and Thr(HB)-Arg(nHB) were not significantly favoured, and could only form side-chain interactions if the residues involved adopted less favourable chi1 conformations. The favourability of hydrophobic pairs e.g. Ile(HB)-Ile(nHB), Val(HB)-Val(nHB) and Leu(HB)-Ile(nHB) was explained by the residues adopting their most preferred chi1 and chi2 conformations, which enabled them to form nested arrangements. Cysteine-cysteine pairs are significantly favoured, although these do not form intrasheet disulphide bridges. Interactions between positively and negatively charged residues were asymmetrically preferred: those with the negatively charged residue at the HB position were more favoured. This trend was accounted for by the presence of general electrostatic interactions, which, based on analysis of distances between charged atoms, were likely to be stronger when the negatively charged residue is the HB partner. The Arg(HB)-Asp(nHB) interaction was an exception to this trend and its favorability was rationalised by the formation of specific side-chain interactions. This research provides rules that could be applied to protein structure prediction, comparative modelling and protein engineering and design. The methods used to analyse the pairing preferences are automated and detailed results are available (http://www.rubic.rdg.ac.uk/betapairprefsparallel/).     

Network properties of protein-decoy structures

Convergence of the vast sequence space of proteins into a highly restricted fold/conformational space suggests a simple yet unique underlying mechanism of protein folding that has been the subject of much debate in the last several decades. One of the major challenges related to the understanding of protein folding or in silico protein structure prediction is the discrimination of non-native structures/decoys from the native structure. Applications of knowledge-based potentials to attain this goal have been extensively reported in the literature. Also, scoring functions based on accessible surface area and amino acid neighbourhood considerations were used in discriminating the decoys from native structures. In this article, we have explored the potential of protein structure network (PSN) parameters to validate the native proteins against a large number of decoy structures generated by diverse methods. We are guided by two principles: (a) the PSNs capture the local properties from a global perspective and (b) inclusion of non-covalent interactions, at all-atom level, including the side-chain atoms, in the network construction accommodates the sequence dependent features. Several network parameters such as the size of the largest cluster, community size, clustering coefficient are evaluated and scored on the basis of the rank of the native structures and the Z-scores. The network analysis of decoy structures highlights the importance of the global properties contributing to the uniqueness of native structures. The analysis also exhibits that the network parameters can be used as metrics to identify the native structures and filter out non-native structures/decoys in a large number of data-sets; thus also has a potential to be used in the protein ‘structure prediction’ problem.     

A novel hypothesis for the binding mode of HERG channel blockers

We present a new docking model for HERG channel blockade. Our new model suggests three key interactions such that (1) a protonated nitrogen of the channel blocker forms a hydrogen bond with the carbonyl oxygen of HERG residue T623; (2) an aromatic moiety of the channel blocker makes a pi-pi interaction with the aromatic ring of HERG residue Y652; and (3) a hydrophobic group of the channel blocker forms a hydrophobic interaction with the benzene ring of HERG residue F656. The previous model assumes two interactions such that (1) a protonated nitrogen of the channel blocker forms a cation-pi interaction with the aromatic ring of HERG residue Y652; and (2) a hydrophobic group of the channel blocker forms a hydrophobic interaction with the benzene ring of HERG residue F656. To test these models, we classified 69 known HERG channel blockers into eight binding types based on their plausible binding modes, and further categorized them into two groups based on the number of interactions our model would predict with the HERG channel (two or three). We then compared the pIC(50) value distributions between these two groups. If the old hypothesis is correct, the distributions should not differ between the two groups (i.e., both groups show only two binding interactions). If our novel hypothesis is correct, the distributions should differ between Groups 1 and 2. Consistent with our hypothesis, the two groups differed with regard to pIC(50), and the group having more predicted interactions with the HERG channel had a higher mean pIC(50) value. Although additional work will be required to further validate our hypothesis, this improved understanding of the HERG channel blocker binding mode may help promote the development of in silico predictions methods for identifying potential HERG channel blockers.     

Physicochemical evaluation of protein folds predicted by threading

Protein structure prediction remains an unsolved problem. Since prediction of the native structure seems very difficult, one usually tries to predict the correct fold of a protein. Here the "fold" is defined by the approximate backbone structure of the protein. However, physicochemical factors that determine the correct fold are not well understood. It has recently been reported that molecular mechanics energy functions combined with effective solvent terms can discriminate the native structures from misfolded ones. Using such a physicochemical energy function, we studied the factors necessary for discrimination of correct and incorrect folds. We first selected correct and incorrect folds by a conventional threading method. Then, all-atom models of those folds were constructed by simply minimizing the atomic overlaps. The constructed correct model representing the native fold has almost the same backbone structure as the native structure but differs in side-chain packing. Finally, the energy values of the constructed models were compared with that of the experimentally determined native structure. The correct model as well as the native structure showed lower energy than misfolded models. However, a large energy gap was found between the native structure and the correct model. By decomposing the energy values into their components, it was found that solvent effects such as the hydrophobic interaction or solvent shielding and the Born energy stabilized the correct model rather than the native structure. The large energetic stabilization of the native structure was attained by specific side-chain packing. The stabilization by solvent effects is small compared to that by side-chain packing. Therefore, it is suggested that in order to confidently predict the correct fold of a protein, it is also necessary to predict correct side-chain packing.     

The dominant role of side-chain backbone interactions in structural realization of amino acid code. ChiRotor: a side-chain prediction algorithm based on side-chain backbone interactions

The basic differences between the 20 natural amino acid residues are due to differences in their side-chain structures. This characteristic design of protein building blocks implies that side-chain-side-chain interactions play an important, even dominant role in 3D-structural realization of amino acid codes. Here we present the results of a comparative analysis of the contributions of side-chain-side-chain (s-s) and side-chain-backbone (s-b) interactions to the stabilization of folded protein structures within the framework of the CHARMm molecular data model. Contrary to intuition, our results suggest that side-chain-backbone interactions play the major role in side-chain packing, in stabilizing the folded structures, and in differentiating the folded structures from the unfolded or misfolded structures, while the interactions between side chains have a secondary effect. An additional analysis of electrostatic energies suggests that combinatorial dominance of the interactions between opposite charges makes the electrostatic interactions act as an unspecific folding force that stabilizes not only native structure, but also compact random conformations. This observation is in agreement with experimental findings that, in the denatured state, the charge-charge interactions stabilize more compact conformations. Taking advantage of the dominant role of side-chain-backbone interactions in side-chain packing to reduce the combinatorial problem, we developed a new algorithm, ChiRotor, for rapid prediction of side-chain conformations. We present the results of a validation study of the method based on a set of high resolution X-ray structures.     

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.     

Desolvation and Development of Specific Hydrophobic Core Packing during Im7 Folding

Development of a tightly packed hydrophobic core drives the folding of water-soluble globular proteins and is a key determinant of protein stability. Despite this, there remains much to be learnt about how and when the hydrophobic core becomes desolvated and tightly packed during protein folding. We have used the bacterial immunity protein Im7 to examine the specificity of hydrophobic core packing during folding. This small, four-helix protein has previously been shown to fold via a compact three-helical intermediate state. Here, overpacking substitutions, in which residue side-chain size is increased, were used to examine the specificity and malleability of core packing in the folding intermediate and rate-limiting transition state. In parallel, polar groups were introduced into the Im7 hydrophobic core via Val→Thr or Phe→Tyr substitutions and used to determine the solvation status of core residues at different stages of folding. Over 30 Im7 variants were created allowing both series of substitutions to cover all regions of the protein structure. Φ-value analysis demonstrated that the major changes in Im7 core solvation occur prior to the population of the folding intermediate, with key regions involved in docking of the short helix III remaining solvent-exposed until after the rate-limiting transition state has been traversed. In contrast, overpacking core residues revealed that some regions of the native Im7 core are remarkably malleable to increases in side-chain volume. Overpacking residues in other regions of the Im7 core result in substantial (> 2.5 kJ mol^− 1) destabilisation of the native structure or even prevents efficient folding to the native state. This study provides new insights into Im7 folding; demonstrating that whilst desolvation occurs early during folding, adoption of a specifically packed core is achieved only at the very last step in the folding mechanism.     

Prediction of protein side-chain conformation by packing optimization

We have developed a rapid and completely automatic method for prediction of protein side-chain conformation, applying the simulated annealing algorithm to optimization of side-chain packing (van der Waals) interactions. The method directly attacks the combinatorial problem of simultaneously predicting many residues' conformation, solving in 8 to 12 hours problems for which the systematic search would require over 10(300) central processing unit years. Over a test set of nine proteins ranging in size from 46 to 323 residues, the program's predictions for side-chain atoms had a root-mean-square (r.m.s.) deviation of 1.77 A overall versus the native structures. More importantly, the predictions for core residues were especially accurate, with an r.m.s. value of 1.25 A overall: 80 to 90% of the large hydrophobic side-chains dominating the internal core were correctly predicted, versus 30 to 40% for most current methods. The predictions' main errors were in surface residues poorly constrained by packing and small residues with greater steric freedom and hydrogen bonding interactions, which were not included in the program's potential function. van der Waals interactions appear to be the supreme determinant of the arrangement of side-chains in the core, enforcing a unique allowed packing that in every case so far examined matches the native structure.     

Network properties of protein-decoy structures

Convergence of the vast sequence space of proteins into a highly restricted fold/conformational space suggests a simple yet unique underlying mechanism of protein folding that has been the subject of much debate in the last several decades. One of the major challenges related to the understanding of protein folding or in silico protein structure prediction is the discrimination of non-native structures/decoys from the native structure. Applications of knowledge-based potentials to attain this goal have been extensively reported in the literature. Also, scoring functions based on accessible surface area and amino acid neighbourhood considerations were used in discriminating the decoys from native structures. In this article, we have explored the potential of protein structure network (PSN) parameters to validate the native proteins against a large number of decoy structures generated by diverse methods. We are guided by two principles: (a) the PSNs capture the local properties from a global perspective and (b) inclusion of non-covalent interactions, at all-atom level, including the side-chain atoms, in the network construction accommodates the sequence dependent features. Several network parameters such as the size of the largest cluster, community size, clustering coefficient are evaluated and scored on the basis of the rank of the native structures and the Z-scores. The network analysis of decoy structures highlights the importance of the global properties contributing to the uniqueness of native structures. The analysis also exhibits that the network parameters can be used as metrics to identify the native structures and filter out non-native structures/decoys in a large number of data-sets; thus also has a potential to be used in the protein 'structure prediction' problem.     

The role of atomic level steric effects and attractive forces in protein folding

Protein folding into tertiary structures is controlled by an interplay of attractive contact interactions and steric effects. We investigate the balance between these contributions using structure‐based models using an all‐atom representation of the structure combined with a coarse‐grained contact potential. Tertiary contact interactions between atoms are collected into a single broad attractive well between the C^β atoms between each residue pair in a native contact. Through the width of these contact potentials we control their tolerance for deviations from the ideal structure and the spatial range of attractive interactions. In the compact native state dominant packing constraints limit the effects of a coarse‐grained contact potential. During folding, however, the broad attractive potentials allow an early collapse that starts before the native local structure is completely adopted. As a consequence the folding transition is broadened and the free energy barrier is decreased. Eventually two‐state folding behavior is lost completely for systems with very broad attractive potentials. The stabilization of native‐like residue interactions in non‐perfect geometries early in the folding process frequently leads to structural traps. Global mirror images are a notable example. These traps are penalized by the details of the repulsive interactions only after further collapse. Successful folding to the native state requires simultaneous guidance from both attractive and repulsive interactions. Proteins 2012. © 2011 Wiley Periodicals, Inc.