The key role of atom types, reference states, and interaction cutoff radii in the knowledge-based method: new variational approach

We present a variational method to derive knowledge-based potentials. The method is based on an optimization procedure of objective variables: atom types, reference states, and interaction cutoff radii. We suggest and apply new unsymmetrical reference states. The cutoff radii and atom types are optimized to improve docking accuracy of the corresponding potentials. The atom types are varied along an atom type tree, with 6 root and 49 top atom types, and the set of 18 optimal atom types is obtained. We demonstrate strong dependence between the choice of atom types and the docking accuracy of the potentials derived with these atom types. The averaged root-mean square deviations (RMSDs) of the ligand docked positions relative to the experimentally determined positions decrease when the elements C, N, O are split into the optimal types.     

DARS (Decoys As the Reference State) potentials for protein-protein docking

Decoys As the Reference State (DARS) is a simple and natural approach to the construction of structure-based intermolecular potentials. The idea is generating a large set of docked conformations with good shape complementarity but without accounting for atom types, and using the frequency of interactions extracted from these decoys as the reference state. In principle, the resulting potential is ideal for finding near-native conformations among structures obtained by docking, and can be combined with other energy terms to be used directly in docking calculations. We investigated the performance of various DARS versions for docking enzyme-inhibitor, antigen-antibody, and other type of complexes. For enzyme-inhibitor pairs, DARS provides both excellent discrimination and docking results, even with very small decoy sets. For antigen-antibody complexes, DARS is slightly better than a number of interaction potentials tested, but results are worse than for enzyme-inhibitor complexes. With a few exceptions, the DARS docking results are also good for the other complexes, despite poor discrimination, and we show that the latter is not a correct test for docking accuracy. The analysis of interactions in antigen-antibody pairs reveals that, in constructing pairwise potentials for such complexes, one should account for the asymmetry of hydrophobic patches on the two sides of the interface. Similar asymmetry does occur in the few other complexes with poor DARS docking results.     

A knowledge-based forcefield for protein-protein interface design

A distance-dependent knowledge-based potential for protein-protein interactions is derived and tested for application in protein design. Information on residue type specific C(alpha) and C(beta) pair distances is extracted from complex crystal structures in the Protein Data Bank and used in the form of radial distribution functions. The use of only backbone and C(beta) position information allows generation of relative protein-protein orientation poses with minimal sidechain information. Further coarse-graining can be done simply in the same theoretical framework to give potentials for residues of known type interacting with unknown type, as in a one-sided interface design problem. Both interface design via pose generation followed by sidechain repacking and localized protein-protein docking tests are performed on 39 nonredundant antibody-antigen complexes for which crystal structures are available. As reference, Lennard-Jones potentials, unspecific for residue type and biasing toward varying degrees of residue pair separation are used as controls. For interface design, the knowledge-based potentials give the best combination of consistently designable poses, low RMSD to the known structure, and more tightly bound interfaces with no added computational cost. 77% of the poses could be designed to give complexes with negative free energies of binding. Generally, larger interface separation promotes designability, but weakens the binding of the resulting designs. A localized docking test shows that the knowledge-based nature of the potentials improves performance and compares respectably with more sophisticated all-atoms potentials.     

General and targeted statistical potentials for protein-ligand interactions

We present a novel atom-atom potential derived from a database of protein-ligand complexes. First, we clarify the similarities and differences between two statistical potentials described in the literature, PMF and Drugscore. We highlight shortcomings caused by an important factor unaccounted for in their reference states, and describe a new potential, which we name the Astex Statistical Potential (ASP). ASP's reference state considers the difference in exposure of protein atom types towards ligand binding sites. We show that this new potential predicts binding affinities with an accuracy similar to that of Goldscore and Chemscore. We investigate the influence of the choice of reference state by constructing two additional statistical potentials that differ from ASP only in this respect. The reference states in these two potentials are defined along the lines of Drugscore and PMF. In docking experiments, the potential using the new reference state proposed for ASP gives better success rates than when these literature reference states were used; a success rate similar to the established scoring functions Goldscore and Chemscore is achieved with ASP. This is the case both for a large, general validation set of protein-ligand structures and for small test sets of actives against four pharmaceutically relevant targets. Virtual screening experiments for these targets show less discrimination between the different reference states in terms of enrichment. In addition, we describe how statistical potentials can be used in the construction of targeted scoring functions. Examples are given for cdk2, using four different targeted scoring functions, biased towards increasingly large target-specific databases. Using these targeted scoring functions, docking success rates as well as enrichments are significantly better than for the general ASP scoring function. Results improve with the number of structures used in the construction of the target scoring functions, thus illustrating that these targeted ASP potentials can be continuously improved as new structural data become available.     

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.     

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.     

Reduced C(beta) statistical potentials can outperform all-atom potentials in decoy identification

We developed a series of statistical potentials to recognize the native protein from decoys, particularly when using only a reduced representation in which each side chain is treated as a single C(beta) atom. Beginning with a highly successful all-atom statistical potential, the Discrete Optimized Protein Energy function (DOPE), we considered the implications of including additional information in the all-atom statistical potential and subsequently reducing to the C(beta) representation. One of the potentials includes interaction energies conditional on backbone geometries. A second potential separates sequence local from sequence nonlocal interactions and introduces a novel reference state for the sequence local interactions. The resultant potentials perform better than the original DOPE statistical potential in decoy identification. Moreover, even upon passing to a reduced C(beta) representation, these statistical potentials outscore the original (all-atom) DOPE potential in identifying native states for sets of decoys. Interestingly, the backbone-dependent statistical potential is shown to retain nearly all of the information content of the all-atom representation in the C(beta) representation. In addition, these new statistical potentials are combined with existing potentials to model hydrogen bonding, torsion energies, and solvation energies to produce even better performing potentials. The ability of the C(beta) statistical potentials to accurately represent protein interactions bodes well for computational efficiency in protein folding calculations using reduced backbone representations, while the extensions to DOPE illustrate general principles for improving knowledge-based potentials.     

Predicting transmembrane helix pair configurations with knowledge-based distance-dependent pair potentials

As a first step toward a novel de novo structure prediction approach for alpha-helical membrane proteins, we developed coarse-grained knowledge-based potentials to score the mutual configuration of transmembrane (TM) helices. Using a comprehensive database of 71 known membrane protein structures, pairwise potentials depending solely on amino acid types and distances between C(alpha)-atoms were derived. To evaluate the potentials, they were used as an objective function for the rigid docking of 442 TM helix pairs. This is by far the largest test data set reported to date for that purpose. After clustering 500 docking runs for each pair and considering the largest cluster, we found solutions with a root mean squared (RMS) deviation <2 A for about 30% of all helix pairs. Encouragingly, if only clusters that contain at least 20% of all decoys are considered, a success rate >71% (with a RMS deviation <2 A) is obtained. The cluster size thus serves as a measure of significance to identify good docking solutions. In a leave-one-protein-family-out cross-validation study, more than 2/3 of the helix pairs were still predicted with an RMS deviation <2.5 A (if only clusters that contain at least 20% of all decoys are considered). This demonstrates the predictive power of the potentials in general, although it is advisable to further extend the knowledge base to derive more robust potentials in the future. When compared to the scoring function of Fleishman and Ben-Tal, a comparable performance is found by our cross-validated potentials. Finally, well-predicted "anchor helix pairs" can be reliably identified for most of the proteins of the test data set. This is important for an extension of the approach towards TM helix bundles because these anchor pairs will act as "nucleation sites" to which more helices will be added subsequently, which alleviates the sampling problem.     

PIPER: an FFT-based protein docking program with pairwise potentials

The Fast Fourier Transform (FFT) correlation approach to protein-protein docking can evaluate the energies of billions of docked conformations on a grid if the energy is described in the form of a correlation function. Here, this restriction is removed, and the approach is efficiently used with pairwise interaction potentials that substantially improve the docking results. The basic idea is approximating the interaction matrix by its eigenvectors corresponding to the few dominant eigenvalues, resulting in an energy expression written as the sum of a few correlation functions, and solving the problem by repeated FFT calculations. In addition to describing how the method is implemented, we present a novel class of structure-based pairwise intermolecular potentials. The DARS (Decoys As the Reference State) potentials are extracted from structures of protein-protein complexes and use large sets of docked conformations as decoys to derive atom pair distributions in the reference state. The current version of the DARS potential works well for enzyme-inhibitor complexes. With the new FFT-based program, DARS provides much better docking results than the earlier approaches, in many cases generating 50% more near-native docked conformations. Although the potential is far from optimal for antibody-antigen pairs, the results are still slightly better than those given by an earlier FFT method. The docking program PIPER is freely available for noncommercial applications.     

Analyses on hydrophobicity and attractiveness of all‐atom distance‐dependent potentials

Accurate model evaluation is a crucial step in protein structure prediction. For this purpose, statistical potentials, which evaluate a model structure based on the observed atomic distance frequencies in comparison with those in reference states, have been widely used. The reference state is a virtual state where all of the atomic interactions are turned off, and it provides a standard to measure the observed frequencies. In this study, we examined seven all‐atom distance‐dependent potentials with different reference states. As results, we observed that the variations of atom pair composition and those of distance distributions in the reference states produced systematic changes in the hydrophobic and attractive characteristics of the potentials. The performance evaluations with the CASP7 structures indicated that the preference of hydrophobic interactions improved the correlation between the energy and the GDT‐TS score, but decreased the Z‐score of the native structure. The attractiveness of potential improved both the correlation and Z‐score for template‐based modeling targets, but the benefit was smaller in free modeling targets. These results indicated that the performances of the potentials were more strongly influenced by their characteristics than by the accuracy of the definitions of the reference states.     

Evolutionary potentials: structure specific knowledge-based potentials exploiting the evolutionary record of sequence homologs

We introduce a new type of knowledge-based potentials for protein structure prediction, called 'evolutionary potentials', which are derived using a single experimental protein structure and all three-dimensional models of its homologous sequences. The new potentials have been benchmarked against other knowledge-based potentials, resulting in a significant increase in accuracy for model assessment. In contrast to standard knowledge-based potentials, we propose that evolutionary potentials capture key determinants of thermodynamic stability and specific sequence constraints required for fast folding.     

A protein-specifically adapted scoring function for the reranking of docking solutions

In this work, we developed a protein-specifically adapted scoring function and applied it to the reranking of protein-protein docking solutions generated with a conventional docking program. The approach was validated using experimentally determined structures of the bacterial HPr-protein in complex with four structurally nonhomologous binding partners as an example. A sufficiently large data basis for the generation of protein-specifically adapted pair potentials was generated by modeling all orthologous complexes for each type of interaction resulting in a total of 224 complexes. The parameters for potential generation were systematically varied and resulted in a total of 66,132 different scoring functions that were tested for their ability of successful reranking of 1000 docking solutions generated from modeled structures of the unbound binding partners. Parameters that proved critical for the generation of good scoring functions were the distance cutoff used for the generation of the pair potential, and an additional cutoff that allows a proper weighting of conserved and nonconserved contacts in the interface. Compared to the original scoring function, application of this novel type of scoring functions resulted in a significant accumulation of acceptable docking solutions within the first 10 ranks. Depending on the type of complex investigated one to five acceptable complex geometries are found among the 10 highest-ranked solutions and for three of the four systems tested, an acceptable solution was placed on the first rank.     

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.     

Evaluating mixture models for building RNA knowledge-based potentials

Ribonucleic acid (RNA) molecules play important roles in a variety of biological processes. To properly function, RNA molecules usually have to fold to specific structures, and therefore understanding RNA structure is vital in comprehending how RNA functions. One approach to understanding and predicting biomolecular structure is to use knowledge-based potentials built from experimentally determined structures. These types of potentials have been shown to be effective for predicting both protein and RNA structures, but their utility is limited by their significantly rugged nature. This ruggedness (and hence the potential's usefulness) depends heavily on the choice of bin width to sort structural information (e.g. distances) but the appropriate bin width is not known a priori. To circumvent the binning problem, we compared knowledge-based potentials built from inter-atomic distances in RNA structures using different mixture models (Kernel Density Estimation, Expectation Minimization and Dirichlet Process). We show that the smooth knowledge-based potential built from Dirichlet process is successful in selecting native-like RNA models from different sets of structural decoys with comparable efficacy to a potential developed by spline-fitting - a commonly taken approach - to binned distance histograms. The less rugged nature of our potential suggests its applicability in diverse types of structural modeling.     

Assessing methods for identifying pair-wise atomic contacts across binding interfaces

An essential step in understanding the molecular basis of protein-protein interactions is the accurate identification of inter-protein contacts. We evaluate a number of common methods used in analyzing protein-protein interfaces: a Voronoi polyhedra-based approach, changes in solvent accessible surface area (DeltaSASA) and various radial cutoffs (closest atom, Cbeta, and centroid). First, we compared the Voronoi polyhedra-based analysis to the DeltaSASA and show that using Voronoi polyhedra finds knob-in-hole contacts. To assess the accuracy between the Voronoi polyhedra-based approach and the various radial cutoff methods, two sets of data were used: a small set of 75 experimental mutants and a larger one of 592 structures of protein-protein interfaces. In an assessment using the small set, the Voronoi polyhedra-based methods, a solvent accessible surface area method, and the closest atom radial method identified 100% of the direct contacts defined by mutagenesis data, but only the Voronoi polyhedra-based method found no false positives. The other radial methods were not able to find all of the direct contacts even using a cutoff of 9A. With the larger set of structures, we compared the overall number contacts using the Voronoi polyhedra-based method as a standard. All the radial methods using a 6-A cutoff identified more interactions, but these putative contacts included many false positives as well as missed many false negatives. While radial cutoffs are quicker to calculate as well as to implement, this result highlights why radial cutoff methods do not have the proper resolution to detail the non-homogeneous packing within protein interfaces, and suggests an inappropriate bias in pair-wise contact potentials. Of the radial cutoff methods, using the closest atom approach exhibits the best approximation to the more intensive Voronoi calculation. Our version of the Voronoi polyhedra-based method QContacts is available at .     

Molecular mechanical perspective on halogen bonding

The nature and strength of halogen bonding in halo molecule-Lewis base complexes were studied in terms of molecular mechanics using our recently developed positive extra-point (PEP) approach, in which the σ-hole on the halogen atom is represented by an extra point of positive charge. The contributions of the σ-hole (i.e., positively charged extra point) and the halogen atom to the strength of this noncovalent interaction were clarified using the atomic parameter contribution to the molecular interaction (APCtMI) approach. The molecular mechanical results revealed that the halogen bond is electrostatic and van der Waals in nature, and its strength depends on three types of interaction: (1) the attractive electrostatic interaction between the σ-hole and the Lewis base, (2) the repulsive electrostatic interaction between the negative halogen atom and the Lewis base, and (3) the repulsive/attractive van der Waals interactions between the halogen atom and the Lewis base. The strength of the halogen bond increases with increasing σ-hole size (i.e., magnitude of the extra-point charge) and increasing halogen atom size. The van der Waals interaction's contribution to the halogen bond strength is most favorable in chloro complexes, whereas the electrostatic interaction is dominant in iodo complexes. The idea that the chloromethane molecule can form a halogen bond with a Lewis base was revisited in terms of quantum mechanics and molecular mechanics. Although chloromethane does produce a positive region along the C-Cl axis, basis set superposition error corrected second-order M?ller-Plesset calculations showed that chloromethane-Lewis base complexes are unstable, producing halogen-Lewis base contacts longer than the sum of the van der Waals radii of the halogen and O/N atoms. Molecular mechanics using the APCtMI approach showed that electrostatic interactions between chloromethane and a Lewis base are unfavorable owing to the high negative charge on the chlorine atom, which overcomes the corresponding favorable van der Waals interactions.     

A pairwise residue contact area-based mean force potential for discrimination of native protein structure

Background  

Considering energy function to detect a correct protein fold from incorrect ones is very important for protein structure prediction and protein folding. Knowledge-based mean force potentials are certainly the most popular type of interaction function for protein threading. They are derived from statistical analyses of interacting groups in experimentally determined protein structures. These potentials are developed at the atom or the amino acid level. Based on orientation dependent contact area, a new type of knowledge-based mean force potential has been developed.     

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.