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.     

Distinguish protein decoys by using a scoring function based on a new AMBER force field, short molecular dynamics simulations, and the generalized born solvent model

Recent works have shown the ability of physics-based potentials (e.g., CHARMM and OPLS-AA) and energy minimization to differentiate the native protein structures from large ensemble of non-native structures. In this study, we extended previous work by other authors and developed an energy scoring function using a new set of AMBER parameters (also recently developed in our laboratory) in conjunction with molecular dynamics and the Generalized Born solvent model. We evaluated the performance of our new scoring function by examining its ability to distinguish between the native and decoy protein structures. Here we present a systematic comparison of our results with those obtained with use of other physics-based potentials by previous authors. A total of 7 decoy sets, 117 protein sequences, and more than 41,000 structures were evaluated. The results of our study showed that our new scoring function represents a significant improvement over previously published physics-based scoring functions.     

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.     

Information‐theoretic analysis of the reference state in contact potentials used for protein structure prediction

Using information‐theoretic concepts, we examine the role of the reference state, a crucial component of empirical potential functions, in protein fold recognition. We derive an information‐based connection between the probability distribution functions of the reference state and those that characterize the decoy set used in threading. In examining commonly used contact reference states, we find that the quasi‐chemical approximation is informatically superior to other variant models designed to include characteristics of real protein chains, such as finite length and variable amino acid composition from protein to protein. We observe that in these variant models, the total divergence, the operative function that quantifies discrimination, decreases along with threading performance. We find that any amount of nativeness encoded in the reference state model does not significantly improve threading performance. A promising avenue for the development of better potentials is suggested by our information‐theoretic analysis of the action of contact potentials on individual protein sequences. Our results show that contact potentials perform better when the compositional properties of the data set used to derive the score function probabilities are similar to the properties of the sequence of interest. Results also suggest to use only sequences of similar composition in deriving contact potentials, to tailor the contact potential specifically for a test sequence. Proteins 2010. © 2009 Wiley‐Liss, Inc.     

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/.     

Distance-scaled,finite ideal-gas reference state improves structure-derived potentials of mean force for structure selection and stability prediction

The distance-dependent structure-derived potentials developed so far all employed a reference state that can be characterized as a residue (atom)-averaged state. Here, we establish a new reference state called the distance-scaled, finite ideal-gas reference (DFIRE) state. The reference state is used to construct a residue-specific all-atom potential of mean force from a database of 1011 nonhomologous (less than 30% homology) protein structures with resolution less than 2 A. The new all-atom potential recognizes more native proteins from 32 multiple decoy sets, and raises an average Z-score by 1.4 units more than two previously developed, residue-specific, all-atom knowledge-based potentials. When only backbone and C(beta) atoms are used in scoring, the performance of the DFIRE-based potential, although is worse than that of the all-atom version, is comparable to those of the previously developed potentials on the all-atom level. In addition, the DFIRE-based all-atom potential provides the most accurate prediction of the stabilities of 895 mutants among three knowledge-based all-atom potentials. Comparison with several physical-based potentials is made.     

The use of soluble protein structures in modeling helical proteins in a layered membrane

Major advances have been made in the prediction of soluble protein structures, led by the knowledge-based modeling methods that extract useful structural trends from known protein structures and incorporate them into scoring functions. The same cannot be reported for the class of transmembrane proteins, primarily due to the lack of high-resolution structural data for transmembrane proteins, which render many of the knowledge-based method unreliable or invalid. We have developed a method that harnesses the vast structural knowledge available in soluble protein data for use in the modeling of transmembrane proteins. At the core of the method, a set of transmembrane protein decoy sets that allow us to filter and train features recognized from soluble proteins for transmembrane protein modeling into a set of scoring functions. We have demonstrated that structures of soluble proteins can provide significant insight into transmembrane protein structures. A complementary novel two-stage modeling/selection process that mimics the two-stage helical membrane protein folding was developed. Combined with the scoring function, the method was successfully applied to model 5 transmembrane proteins. The root mean square deviations of the predicted models ranged from 5.0 to 8.8?Å to the native structures.     

Absolute quality evaluation of protein model structures using statistical potentials with respect to the native and reference states

In protein structure prediction, it is crucial to evaluate the degree of native-likeness of given model structures. Statistical potentials extracted from protein structure data sets are widely used for such quality assessment problems, but they are only applicable for comparing different models of the same protein. Although various other methods, such as machine learning approaches, were developed to predict the absolute similarity of model structures to the native ones, they required a set of decoy structures in addition to the model structures. In this paper, we tried to reformulate the statistical potentials as absolute quality scores, without using the information from decoy structures. For this purpose, we regarded the native state and the reference state, which are necessary components of statistical potentials, as the good and bad standard states, respectively, and first showed that the statistical potentials can be regarded as the state functions, which relate a model structure to the native and reference states. Then, we proposed a standardized measure of protein structure, called native-likeness, by interpolating the score of a model structure between the native and reference state scores defined for each protein. The native-likeness correlated with the similarity to the native structures and discriminated the native structures from the models, with better accuracy than the raw score. Our results show that statistical potentials can quantify the native-like properties of protein structures, if they fully utilize the statistical information obtained from the data set.     

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.     

Improving the orientation‐dependent statistical potential using a reference state

Statistical potentials are frequently engaged in the protein structural prediction and protein folding for conformational evaluation. Theoretically, to describe the many‐body effect, pairwise interaction between two atom groups should be corrected by their relative geometric orientation. The potential functions developed by this means are called orientation‐dependent statistical potentials and have exhibited substantially improved performance. However, none of the currently available orientation‐dependent statistical potentials use any reference state, which has been proven to greatly enhance the power of distance‐dependent statistical potentials in numerous previous studies. In this work, we designed a reasonable reference state for the orientation‐dependent statistical potentials: using the average geometric relationship between atom pairs in known structures by neglecting their residue identities. The statistical potential developed using this reference state (called ORDER_AVE) prevails most available rival potentials in a series of tests on the decoy sets, although the information of side chain atoms (except the β‐carbon) is absent in its construction. Proteins 2014; 82:2383–2393. © 2014 Wiley Periodicals, Inc.     

DOCKGROUND protein-protein docking decoy set

A protein-protein docking decoy set is built for the Dockground unbound benchmark set. The GRAMM-X docking scan was used to generate 100 non-native and at least one near-native match per complex for 61 complexes. The set is a publicly available resource for the development of scoring functions and knowledge-based potentials for protein docking methodologies. AVAILABILITY: The decoys are freely available for download at http://dockground.bioinformatics.ku.edu/UNBOUND/decoy/decoy.php     

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.     

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 free-rotating and self-avoiding chain model for deriving statistical potentials based on protein structures

Statistical potentials have been widely used in protein studies despite the much-debated theoretical basis. In this work, we have applied two physical reference states for deriving the statistical potentials based on protein structure features to achieve zero interaction and orthogonalization. The free-rotating chain-based potential applies a local free-rotating chain reference state, which could theoretically be described by the Gaussian distribution. The self-avoiding chain-based potential applies a reference state derived from a database of artificial self-avoiding backbones generated by Monte Carlo simulation. These physical reference states are independent of known protein structures and are based solely on the analytical formulation or simulation method. The new potentials performed better and yielded higher Z-scores and success rates compared to other statistical potentials. The end-to-end distance distribution produced by the self-avoiding chain model was similar to the distance distribution of protein atoms in structure database. This fact may partly explain the basis of the reference states that depend on the atom pair frequency observed in the protein database. The current study showed that a more physical reference model improved the performance of statistical potentials in protein fold recognition, which could also be extended to other types of applications.     

Predicting protein complex geometries with a neural network

A major challenge of the protein docking problem is to define scoring functions that can distinguish near‐native protein complex geometries from a large number of non‐native geometries (decoys) generated with noncomplexed protein structures (unbound docking). In this study, we have constructed a neural network that employs the information from atom‐pair distance distributions of a large number of decoys to predict protein complex geometries. We found that docking prediction can be significantly improved using two different types of polar hydrogen atoms. To train the neural network, 2000 near‐native decoys of even distance distribution were used for each of the 185 considered protein complexes. The neural network normalizes the information from different protein complexes using an additional protein complex identity input neuron for each complex. The parameters of the neural network were determined such that they mimic a scoring funnel in the neighborhood of the native complex structure. The neural network approach avoids the reference state problem, which occurs in deriving knowledge‐based energy functions for scoring. We show that a distance‐dependent atom pair potential performs much better than a simple atom‐pair contact potential. We have compared the performance of our scoring function with other empirical and knowledge‐based scoring functions such as ZDOCK 3.0, ZRANK, ITScore‐PP, EMPIRE, and RosettaDock. In spite of the simplicity of the method and its functional form, our neural network‐based scoring function achieves a reasonable performance in rigid‐body unbound docking of proteins. Proteins 2010. © 2009 Wiley‐Liss, Inc.     

Potentials of mean force for protein structure prediction vindicated, formalized and generalized

Understanding protein structure is of crucial importance in science, medicine and biotechnology. For about two decades, knowledge-based potentials based on pairwise distances--so-called "potentials of mean force" (PMFs)--have been center stage in the prediction and design of protein structure and the simulation of protein folding. However, the validity, scope and limitations of these potentials are still vigorously debated and disputed, and the optimal choice of the reference state--a necessary component of these potentials--is an unsolved problem. PMFs are loosely justified by analogy to the reversible work theorem in statistical physics, or by a statistical argument based on a likelihood function. Both justifications are insightful but leave many questions unanswered. Here, we show for the first time that PMFs can be seen as approximations to quantities that do have a rigorous probabilistic justification: they naturally arise when probability distributions over different features of proteins need to be combined. We call these quantities "reference ratio distributions" deriving from the application of the "reference ratio method." This new view is not only of theoretical relevance but leads to many insights that are of direct practical use: the reference state is uniquely defined and does not require external physical insights; the approach can be generalized beyond pairwise distances to arbitrary features of protein structure; and it becomes clear for which purposes the use of these quantities is justified. We illustrate these insights with two applications, involving the radius of gyration and hydrogen bonding. In the latter case, we also show how the reference ratio method can be iteratively applied to sculpt an energy funnel. Our results considerably increase the understanding and scope of energy functions derived from known biomolecular 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.     

Comparison between Generalized-Born and Poisson–Boltzmann methods in physics-based scoring functions for protein structure prediction

Continuum solvent models such as Generalized-Born and Poisson–Boltzmann methods hold the promise to treat solvation effect efficiently and to enable rapid scoring of protein structures when they are combined with physics-based energy functions. Yet, direct comparison of these two approaches on large protein data set is lacking. Building on our previous work with a scoring function based on a Generalized-Born (GB) solvation model, and short molecular-dynamics simulations, we further extended the scoring function to compare with the MM-PBSA method to treat the solvent effect. We benchmarked this scoring function against seven publicly available decoy sets. We found that, somewhat surprisingly, the results of MM-PBSA approach are comparable to the previous GB-based scoring function. We also discussed the effect to the scoring function accuracy due to presence of large ligands and ions in some native structures of the decoy sets.