Derivation of protein-specific pair potentials based on weak sequence fragment similarity

A method is presented for the derivation of knowledge-based pair potentials that corrects for the various compositions of different proteins. The resulting statistical pair potential is more specific than that derived from previous approaches as assessed by gapless threading results. Additionally, a methodology is presented that interpolates between statistical potentials when no homologous examples to the protein of interest are in the structural database used to derive the potential, to a Go-like potential (in which native interactions are favorable and all nonnative interactions are not) when homologous proteins are present. For cases in which no protein exceeds 30% sequence identity, pairs of weakly homologous interacting fragments are employed to enhance the specificity of the potential. In gapless threading, the mean z score increases from -10.4 for the best statistical pair potential to -12.8 when the local sequence similarity, fragment-based pair potentials are used. Examination of the ab initio structure prediction of four representative globular proteins consistently reveals a qualitative improvement in the yield of structures in the 4 to 6 A rmsd from native range when the fragment-based pair potential is used relative to that when the quasichemical pair potential is employed. This suggests that such protein-specific potentials provide a significant advantage relative to generic quasichemical potentials.     

On the design and analysis of protein folding potentials

Pairwise interaction models to recognize native folds are designed and analyzed. Different sets of parameters are considered but the focus was on 20 x 20 contact matrices. Simultaneous solution of inequalities and minimization of the variance of the energy find matrices that recognize exactly the native folds of 572 sequences and structures from the protein data bank (PDB). The set includes many homologous pairs, which present a difficult recognition problem. Significant recognition ability is recovered with a small number of parameters (e.g., the H/P model). However, full recognition requires a complete set of amino acids. In addition to structures from the PDB, a folding program (MONSSTER) was used to generate decoy structures for 75 proteins. It is impossible to recognize all the native structures of the extended set by contact potentials. We therefore searched for a new functional form. An energy function U, which is based on a sum of general pairwise interactions limited to a resolution of 1 angstrom, is considered. This set was infeasible too. We therefore conjecture that it is not possible to find a folding potential, resolved to 1 angstrom, which is a sum of pair interactions.     

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 simple Cα-SC potential with higher accuracy for protein fold recognition

In this paper, an improved C_α-SC energy potential designed for protein fold recognition was reported. It consists of three extremely simple interaction terms which are supposed to be the dominant interactions in protein folding: residue-residue contact, hydrophobicity and pseudodihedral potentials. The potential function only contains 210 contacts, one hydrophobic and one torsion parameters, which have been optimized using an interior point algorithm of linear programming. Tests of the derived potential function on commonly used decoy sets illustrate that it outperforms most of the existing coarse-grained potentials in terms of its capabilities in recognizing native structures and consistency in achieving high Z-scores across decoy sets, and it has almost equivalent performance to the potentials which considered complex intra-molecular interactions. The results show that our scoring function is a generally prospective potential for protein structure prediction and modeling with regard to its recognition and computation efficacy.     

Optimized distance‐dependent atom‐pair‐based potential DOOP for protein structure prediction

The DOcking decoy‐based Optimized Potential (DOOP) energy function for protein structure prediction is based on empirical distance‐dependent atom‐pair interactions. To optimize the atom‐pair interactions, native protein structures are decomposed into polypeptide chain segments that correspond to structural motives involving complete secondary structure elements. They constitute near native ligand–receptor systems (or just pairs). Thus, a total of 8609 ligand–receptor systems were prepared from 954 selected proteins. For each of these hypothetical ligand–receptor systems, 1000 evenly sampled docking decoys with 0–10 Å interface root‐mean‐square‐deviation (iRMSD) were generated with a method used before for protein–protein docking. A neural network‐based optimization method was applied to derive the optimized energy parameters using these decoys so that the energy function mimics the funnel‐like energy landscape for the interaction between these hypothetical ligand–receptor systems. Thus, our method hierarchically models the overall funnel‐like energy landscape of native protein structures. The resulting energy function was tested on several commonly used decoy sets for native protein structure recognition and compared with other statistical potentials. In combination with a torsion potential term which describes the local conformational preference, the atom‐pair‐based potential outperforms other reported statistical energy functions in correct ranking of native protein structures for a variety of decoy sets. This is especially the case for the most challenging ROSETTA decoy set, although it does not take into account side chain orientation‐dependence explicitly. The DOOP energy function for protein structure prediction, the underlying database of protein structures with hypothetical ligand–receptor systems and their decoys are freely available at http://agknapp.chemie.fu‐berlin.de/doop/ . Proteins 2015; 83:881–890. © 2015 Wiley Periodicals, Inc.     

An iterative knowledge-based scoring function for protein-protein recognition

Using an efficient iterative method, we have developed a distance-dependent knowledge-based scoring function to predict protein-protein interactions. The function, referred to as ITScore-PP, was derived using the crystal structures of a training set of 851 protein-protein dimeric complexes containing true biological interfaces. The key idea of the iterative method for deriving ITScore-PP is to improve the interatomic pair potentials by iteration, until the pair potentials can distinguish true binding modes from decoy modes for the protein-protein complexes in the training set. The iterative method circumvents the challenging reference state problem in deriving knowledge-based potentials. The derived scoring function was used to evaluate the ligand orientations generated by ZDOCK 2.1 and the native ligand structures on a diverse set of 91 protein-protein complexes. For the bound test cases, ITScore-PP yielded a success rate of 98.9% if the top 10 ranked orientations were considered. For the more realistic unbound test cases, the corresponding success rate was 40.7%. Furthermore, for faster orientational sampling purpose, several residue-level knowledge-based scoring functions were also derived following the similar iterative procedure. Among them, the scoring function that uses the side-chain center of mass (SCM) to represent a residue, referred to as ITScore-PP(SCM), showed the best performance and yielded success rates of 71.4% and 30.8% for the bound and unbound cases, respectively, when the top 10 orientations were considered. ITScore-PP was further tested using two other published protein-protein docking decoy sets, the ZDOCK decoy set and the RosettaDock decoy set. In addition to binding mode prediction, the binding scores predicted by ITScore-PP also correlated well with the experimentally determined binding affinities, yielding a correlation coefficient of R = 0.71 on a test set of 74 protein-protein complexes with known affinities. ITScore-PP is computationally efficient. The average run time for ITScore-PP was about 0.03 second per orientation (including optimization) on a personal computer with 3.2 GHz Pentium IV CPU and 3.0 GB RAM. The computational speed of ITScore-PP(SCM) is about an order of magnitude faster than that of ITScore-PP. ITScore-PP and/or ITScore-PP(SCM) can be combined with efficient protein docking software to study protein-protein recognition.     

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.     

Nonplanar DNA Base Pairs

Abstract

Three-dimensional structures of a representative set of more than 30 hydrogen-bonded nucleic acids base pairs have been studied by reliable ab initio quantum mechanical methods. We show that many hydrogen-bonded nucleic acid base pairs are intrinsically nonplanar, mainly due to the partial sp³ hybridization of nitrogen atoms of their amino groups and secondary electrostatic interactions. This finding extends the variability of intermolecular interactions of DNA bases in that i) flexibility of the base pairs is larger than has been assumed before, and ii) attractive proton-proton acceptor interactions oriented out of the base pair plane are allowed. For example, all four G…A mismatch base pairs are propeller twisted, and the energy preferences for the nonplanar structures range from less than 0.1 kcal/mol to 1.8 kcal/mol. We predict that nonplanarity of the amino group of guanine in the G(anti)…A(anti) pair of the ApG step of the d(CCAAGATTGG)₂ crystal structure is an important stabilizing factor that improves the energy of this structure by almost 3 kcal/mol. Currently used empirical potentials are not accurate enough to properly cover the interactions associated with amino-group and base-pair nonplanarity.     

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.     

The nature of intermolecular interactions between aromatic amino acid residues

The nature of intermolecular interactions between aromatic amino acid residues has been investigated by a combination of molecular dynamics and ab initio methods. The potential energy surface of various interacting pairs, including tryptophan, phenilalanine, and tyrosine, was scanned for determining all the relevant local minima by a combined molecular dynamics and conjugate gradient methodology with the AMBER force field. For each of these minima, single-point correlated ab initio calculations of the binding energy were performed. The agreement between empirical force field and ab initio binding energies of the minimum energy structures is excellent. Aromatic-aromatic interactions can be rationalized on the basis of electrostatic and van der Waals interactions, whereas charge transfer or polarization phenomena are small for all intermolecular complexes and, particularly, for stacked structures. Proteins 2002;48:117-125.     

What is the best reference state for designing statistical atomic potentials in protein structure prediction?

Many statistical potentials were developed in last two decades for protein folding and protein structure recognition. The major difference of these potentials is on the selection of reference states to offset sampling bias. However, since these potentials used different databases and parameter cutoffs, it is difficult to judge what the best reference states are by examining the original programs. In this study, we aim to address this issue and evaluate the reference states by a unified database and programming environment. We constructed distance-specific atomic potentials using six widely-used reference states based on 1022 high-resolution protein structures, which are applied to rank modeling in six sets of structure decoys. The reference state on random-walk chain outperforms others in three decoy sets while those using ideal-gas, quasi-chemical approximation and averaging sample stand out in one set separately. Nevertheless, the performance of the potentials relies on the origin of decoy generations and no reference state can clearly outperform others in all decoy sets. Further analysis reveals that the statistical potentials have a contradiction between the universality and pertinence, and optimal reference states should be extracted based on specific application environments and decoy spaces.     

Contribution of cation-pi interactions to the stability of protein-DNA complexes

Cation-pi interactions between an aromatic ring and a positive charge located above it have proven to be important in protein structures and biomolecule associations. Here, the role of these interactions at the interface of protein-DNA complexes is investigated, by means of ab initio quantum mechanics energy calculations and X-ray structure analyses. Ab initio energy calculations indicate that Na ions and DNA bases can form stable cation-pi complexes, whose binding strength strongly depends on the type of base, on the position of the Na ion, and whether the base is isolated or included in a double-stranded B-DNA. A survey of protein-DNA complex structures using appropriate geometrical criteria revealed cation-pi interactions in 71% of the complexes. More than half of the cation-pi pairs involve arginine residues, about one-third asparagine or glutamine residues that only carry a partial charge, and one-seventh lysine residues. The most frequently observed pair, which is also the most stable as monitored by ab initio energy calculations, is arginine- guanine. Arginine-adenine interactions are also favorable in general, although to a lesser extent, whereas those with thymine and cytosine are not. Our calculations show that the major contribution to cation-pi interactions with DNA bases is of electrostatic nature. These interactions often occur concomitantly with hydrogen bonds with adjacent bases; their strength is estimated to be from three to four times lower than that of hydrogen bonds. Finally, the role of cation-pi interactions in the stability and specificity of protein-DNA complexes is discussed.     

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.     

A united residue force-field for calcium-protein interactions

United-residue potentials are derived for interactions of the calcium cation with polypeptide chains in energy-based prediction of protein structure with a united-residue (UNRES) force-field. Specific potentials were derived for the interaction of the calcium cation with the Asp, Glu, Asn, and Gln side chains and the peptide group. The analytical expressions for the interaction energies for each of these amino acids were obtained by averaging the electrostatic interaction energy, expressed by a multipole series over the dihedral angles not considered in the united-residue model, that is, the side-chain dihedral angles chi and the dihedral angles lambda for the rotation of peptide groups about the C(alpha)...C(alpha) virtual-bond axes. For the side-chains that do not interact favorably with calcium, simple excluded-volume potentials were introduced. The parameters of the potentials were obtained from ab initio quantum mechanical calculations of model systems at the Restricted Hartree-Fock (RHF) level with the 6-31G(d,p) basis set. The energy surfaces of pairs consisting of Ca(2+)-acetate, Ca(2+)-propionate, Ca(2+)-acetamide, Ca(2+)-propionamide, and Ca(2+)-N-methylacetamide systems (modeling the Ca(2+)-Asp(-), Ca(2+)-Glu(-), Ca(2+)-Asn, Ca(2+)-Gln, and Ca(2+)-peptide group interactions) at different distances and orientations were calculated. For each pair, the restricted free energy (RFE) surfaces were calculated by numerical integration over the degrees of freedom lost when switching from the all-atom model to the united-residue model. Finally, the analytical expressions for each pair were fitted to the RFE surfaces. This force-field was able to distinguish the EF-hand motif from all potential binding sites in the crystal structures of bovine alpha-lactalbumin, whiting parvalbumin, calbindin D9K, and apo-calbindin D9K.     

Accurate and efficient loop selections by the DFIRE-based all-atom statistical potential

The conformations of loops are determined by the water-mediated interactions between amino acid residues. Energy functions that describe the interactions can be derived either from physical principles (physical-based energy function) or statistical analysis of known protein structures (knowledge-based statistical potentials). It is commonly believed that statistical potentials are appropriate for coarse-grained representation of proteins but are not as accurate as physical-based potentials when atomic resolution is required. Several recent applications of physical-based energy functions to loop selections appear to support this view. In this article, we apply a recently developed DFIRE-based statistical potential to three different loop decoy sets (RAPPER, Jacobson, and Forrest-Woolf sets). Together with a rotamer library for side-chain optimization, the performance of DFIRE-based potential in the RAPPER decoy set (385 loop targets) is comparable to that of AMBER/GBSA for short loops (two to eight residues). The DFIRE is more accurate for longer loops (9 to 12 residues). Similar trend is observed when comparing DFIRE with another physical-based OPLS/SGB-NP energy function in the large Jacobson decoy set (788 loop targets). In the Forrest-Woolf decoy set for the loops of membrane proteins, the DFIRE potential performs substantially better than the combination of the CHARMM force field with several solvation models. The results suggest that a single-term DFIRE-statistical energy function can provide an accurate loop prediction at a fraction of computing cost required for more complicate physical-based energy functions. A Web server for academic users is established for loop selection at the softwares/services section of the Web site http://theory.med.buffalo.edu/.     

Distinguishing native conformations of proteins from decoys with an effective free energy estimator based on the OPLS all-atom force field and the Surface Generalized Born solvent model

Protein decoy data sets provide a benchmark for testing scoring functions designed for fold recognition and protein homology modeling problems. It is commonly believed that statistical potentials based on reduced atomic models are better able to discriminate native-like from misfolded decoys than scoring functions based on more detailed molecular mechanics models. Recent benchmark tests on small data sets, however, suggest otherwise. In this work, we report the results of extensive decoy detection tests using an effective free energy function based on the OPLS all-atom (OPLS-AA) force field and the Surface Generalized Born (SGB) model for the solvent electrostatic effects. The OPLS-AA/SGB effective free energy is used as a scoring function to detect native protein folds among a total of 48,832 decoys for 32 different proteins from Park and Levitt's 4-state-reduced, Levitt's local-minima, Baker's ROSETTA all-atom, and Skolnick's decoy sets. Solvent electrostatic effects are included through the Surface Generalized Born (SGB) model. All structures are locally minimized without restraints. From an analysis of the individual energy components of the OPLS-AA/SGB energy function for the native and the best-ranked decoy, it is determined that a balance of the terms of the potential is responsible for the minimized energies that most successfully distinguish the native from the misfolded conformations. Different combinations of individual energy terms provide less discrimination than the total energy. The results are consistent with observations that all-atom molecular potentials coupled with intermediate level solvent dielectric models are competitive with knowledge-based potentials for decoy detection and protein modeling problems such as fold recognition and homology modeling.     

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.     

On the Importance of the Distance Measures Used to Train and Test Knowledge-Based Potentials for Proteins

Knowledge-based potentials are energy functions derived from the analysis of databases of protein structures and sequences. They can be divided into two classes. Potentials from the first class are based on a direct conversion of the distributions of some geometric properties observed in native protein structures into energy values, while potentials from the second class are trained to mimic quantitatively the geometric differences between incorrectly folded models and native structures. In this paper, we focus on the relationship between energy and geometry when training the second class of knowledge-based potentials. We assume that the difference in energy between a decoy structure and the corresponding native structure is linearly related to the distance between the two structures. We trained two distance-based knowledge-based potentials accordingly, one based on all inter-residue distances (PPD), while the other had the set of all distances filtered to reflect consistency in an ensemble of decoys (PPE). We tested four types of metric to characterize the distance between the decoy and the native structure, two based on extrinsic geometry (RMSD and GTD-TS*), and two based on intrinsic geometry (Q* and MT). The corresponding eight potentials were tested on a large collection of decoy sets. We found that it is usually better to train a potential using an intrinsic distance measure. We also found that PPE outperforms PPD, emphasizing the benefits of capturing consistent information in an ensemble. The relevance of these results for the design of knowledge-based potentials is discussed.     

Inter-residue interactions in protein folding and stability

During the process of protein folding, the amino acid residues along the polypeptide chain interact with each other in a cooperative manner to form the stable native structure. The knowledge about inter-residue interactions in protein structures is very helpful to understand the mechanism of protein folding and stability. In this review, we introduce the classification of inter-residue interactions into short, medium and long range based on a simple geometric approach. The features of these interactions in different structural classes of globular and membrane proteins, and in various folds have been delineated. The development of contact potentials and the application of inter-residue contacts for predicting the structural class and secondary structures of globular proteins, solvent accessibility, fold recognition and ab initio tertiary structure prediction have been evaluated. Further, the relationship between inter-residue contacts and protein-folding rates has been highlighted. Moreover, the importance of inter-residue interactions in protein-folding kinetics and for understanding the stability of proteins has been discussed. In essence, the information gained from the studies on inter-residue interactions provides valuable insights for understanding protein folding and de novo protein design.     

How well can we predict native contacts in proteins based on decoy structures and their energies?

One strategy for ab initio protein structure prediction is to generate a large number of possible structures (decoys) and select the most fitting ones based on a scoring or free energy function. The conformational space of a protein is huge, and chances are rare that any heuristically generated structure will directly fall in the neighborhood of the native structure. It is desirable that, instead of being thrown away, the unfitting decoy structures can provide insights into native structures so prediction can be made progressively. First, we demonstrate that a recently parameterized physics-based effective free energy function based on the GROMOS96 force field and a generalized Born/surface area solvent model is, as several other physics-based and knowledge-based models, capable of distinguishing native structures from decoy structures for a number of widely used decoy databases. Second, we observe a substantial increase in correlations of the effective free energies with the degree of similarity between the decoys and the native structure, if the similarity is measured by the content of native inter-residue contacts in a decoy structure rather than its root-mean-square deviation from the native structure. Finally, we investigate the possibility of predicting native contacts based on the frequency of occurrence of contacts in decoy structures. For most proteins contained in the decoy databases, a meaningful amount of native contacts can be predicted based on plain frequencies of occurrence at a relatively high level of accuracy. Relative to using plain frequencies, overwhelming improvements in sensitivity of the predictions are observed for the 4_state_reduced decoy sets by applying energy-dependent weighting of decoy structures in determining the frequency. There, approximately 80% native contacts can be predicted at an accuracy of approximately 80% using energy-weighted frequencies. The sensitivity of the plain frequency approach is much lower (20% to 40%). Such improvements are, however, not observed for the other decoy databases. The rationalization and implications of the results are discussed.