Configurational-bias sampling technique for predicting side-chain conformations in proteins

Prediction of side-chain conformations is an important component of several biological modeling applications. In this work, we have developed and tested an advanced Monte Carlo sampling strategy for predicting side-chain conformations. Our method is based on a cooperative rearrangement of atoms that belong to a group of neighboring side-chains. This rearrangement is accomplished by deleting groups of atoms from the side-chains in a particular region, and regrowing them with the generation of trial positions that depends on both a rotamer library and a molecular mechanics potential function. This method allows us to incorporate flexibility about the rotamers in the library and explore phase space in a continuous fashion about the primary rotamers. We have tested our algorithm on a set of 76 proteins using the all-atom AMBER99 force field and electrostatics that are governed by a distance-dependent dielectric function. When the tolerance for correct prediction of the dihedral angles is a <20 degrees deviation from the native state, our prediction accuracies for chi1 are 83.3% and for chi1 and chi2 are 65.4%. The accuracies of our predictions are comparable to the best results in the literature that often used Hamiltonians that have been specifically optimized for side-chain packing. We believe that the continuous exploration of phase space enables our method to overcome limitations inherent with using discrete rotamers as trials.     

Effective scoring function for protein sequence design

We have developed an effective scoring function for protein design. The atomic solvation parameters, together with the weights of energy terms, were optimized so that residues corresponding to the native sequence were predicted with low energy in the training set of 28 protein structures. The solvation energy of non-hydrogen-bonded hydrophilic atoms was considered separately and expressed in a nonlinear way. As a result, our scoring function predicted native residues as the most favorable in 59% of the total positions in 28 proteins. We then tested the scoring function by comparing the predicted stability changes for 103 T4 lysozyme mutants with the experimental values. The correlation coefficients were 0.77 for surface mutations and 0.71 for all mutations. Finally, the scoring function combined with Monte Carlo simulation was used to predict favorable sequences on a fixed backbone. The designed sequences were similar to the natural sequences of the family to which the template structure belonged. The profile of the designed sequences was helpful for identification of remote homologues of the native sequence.     

Improved side-chain prediction accuracy using an ab initio potential energy function and a very large rotamer library

Accurate prediction of the placement and comformations of protein side chains given only the backbone trace has a wide range of uses in protein design, structure prediction, and functional analysis. Prediction has most often relied on discrete rotamer libraries so that rapid fitness of side-chain rotamers can be assessed against some scoring function. Scoring functions are generally based on experimental parameters from small-molecule studies or empirical parameters based on determined protein structures. Here, we describe the NCN algorithm for predicting the placement of side chains. A predominantly first-principles approach was taken to develop the potential energy function incorporating van der Waals and electrostatics based on the OPLS parameters, and a hydrogen bonding term. The only empirical knowledge used is the frequency of rotameric states from the PDB. The rotamer library includes nearly 50,000 rotamers, and is the most extensive discrete library used to date. Although the computational time tends to be longer than most other algorithms, the overall accuracy exceeds all algorithms in the literature when placing rotamers on an accurate backbone trace. Considering only the most buried residues, 80% of the total residues tested, the placement accuracy reaches 92% for chi(1), and 83% for chi(1 + 2), and an overall RMS deviation of 1 A. Additionally, we show that if information is available to restrict chi(1) to one rotamer well, then this algorithm can generate structures with an average RMS deviation of 1.0 A for all heavy side-chains atoms and a corresponding overall chi(1 + 2) accuracy of 85.0%.     

Threading without optimizing weighting factors for scoring function

Optimizing weighting factors for a linear combination of terms in a scoring function is a crucial step for success in developing a threading algorithm. Usually weighting factors are optimized to yield the highest success rate on a training dataset, and the determined constant values for the weighting factors are used for any target sequence. Here we explore completely different approaches to handle weighting factors for a scoring function of threading. Throughout this study we use a model system of gapless threading using a scoring function with two terms combined by a weighting factor, a main chain angle potential and a residue contact potential. First, we demonstrate that the optimal weighting factor for recognizing the native structure differs from target sequence to target sequence. Then, we present three novel threading methods which circumvent training dataset-based weighting factor optimization. The basic idea of the three methods is to employ different weighting factor values and finally select a template structure for a target sequence by examining characteristics of the distribution of scores computed by using the different weighting factor values. Interestingly, the success rate of our approaches is comparable to the conventional threading method where the weighting factor is optimized based on a training dataset. Moreover, when the size of the training set available for the conventional threading method is small, our approach often performs better. In addition, we predict a target-specific weighting factor optimal for a target sequence by an artificial neural network from features of the target sequence. Finally, we show that our novel methods can be used to assess the confidence of prediction of a conventional threading with an optimized constant weighting factor by considering consensus prediction between them. Implication to the underlined energy landscape of protein folding is discussed.     

Assessment of effects of experimental imprecision on optimized biochemical systems.

Metabolic pathways may be optimized with S-system models that prescribe profiles of control variables leading to optimal output while keeping metabolites and enzyme activities within predefined ranges. Monte Carlo simulations show how much the yield and the corresponding metabolite concentrations would be affected by inaccuracies in the experimental implementation of the prescribed profiles. For a recent model of citric acid production in Aspergillus niger, the yield is roughly normally distributed, whereas the distributions of metabolite concentrations differ greatly in shape and statistical characteristics. Even moderate inaccuracies may lead to constraint violations, which appear to be correlated with high logarithmic gains.     

Homology modeling by the ICM method

Five models have been built by the ICM method for the Comparative Modeling section of the Meeting on the Critical Assessment of Techniques for Protein Structure Prediction. The targets have homologous proteins with known three-dimensional structure with sequence identity ranging from 25 to 77%. After alignment of the target sequence with the related three-dimensional structure, the modeling procedure consists of two subproblems: side-chain prediction and loop prediction. The ICM method approaches these problems with the following steps: (1) a starting model is created based on the homologous structure with the conserved portion fixed and the noncon-served portion having standard covalent geometry and free torsion angles; (2) the Biased Probability Monte Carlo (BPMC) procedure is applied to search the subspaces of either all the nonconservative side-chain torsion angles or torsion angles in a loop backbone and surrounding side chains. A special algorithm was designed to generate low-energy loop deformations. The BPMC procedure globally optimizes the energy function consisting of ECEPP/3 and solvation energy terms. Comparison of the predictions with the NMR or crystallographic solutions reveals a high proportion of correctly predicted side chains. The loops were not correctly predicted because imprinted distortions of the backbone increased the energy of the near-native conformation and thus made the solution unrecognizable. Interestingly, the energy terms were found to be reliable and the sampling of conformational space sufficient. The implications of this finding for the strategies of future comparative modeling are discussed. © 1995 Wiley-Liss, Inc.     

Potential optimization for the calculation of shocked liquid nitromethane properties

We present the results of the optimization of a classical molecular force field used to calculate the properties of shocked nitromethane by Monte Carlo simulations. The optimization technique allows a good transferability of the potential parameters on a broad range of thermodynamic conditions (temperature and pressure) since a large variety of reference data can be used in the optimization procedure, including densities, vaporization enthalpies or pressures along the Hugoniot curve. Results of calculated properties of shocked nitromethane are in good agreement with experimental shock Hugoniot data, including temperature measurements of second shock Hugoniot.     

Functional group based Ligand binding affinity scoring function at atomic environmental level

Use of knowledge based scoring function (KBSF) for virtual screening and molecular docking has become an established method for drug discovery. Lack of a precise and reliable free energy function that describes several interactions including water-mediated atomic interaction between amino-acid residues and ligand makes distance based statistical measure as the only alternative. Till now all the distance based scoring functions in KBSF arena use atom singularity concept, which neglects the environmental effect of the atom under consideration. We have developed a novel knowledge-based statistical energy function for protein-ligand complexes which takes atomic environment in to account hence functional group as a singular entity. The proposed knowledge based scoring function is fast, simple to construct, easy to use and moreover it tackle the existing problem of handling molecular orientation in active site pocket. We have designed and used Functional group based Ligand retrieval (FBLR) system which can identify and detect the orientation of functional groups in ligand. This decoy searching was used to build the above KBSF to quantify the activity and affinity of high resolution protein-ligand complexes. We have proposed the probable use of these decoys in molecular build-up as a de-novo drug designing approach. We have also discussed the possible use of the said KSBF in pharmacophore fragment detection and pseudo center based fragment alignment procedure.     

Protein side‐chain modeling with a protein‐dependent optimized rotamer library

Despite years of effort, the problem of predicting the conformations of protein side chains remains a subject of inquiry. This problem has three major issues, namely defining the conformations that a side chain may adopt within a protein, developing a sampling procedure for generating possible side‐chain packings, and defining a scoring function that can rank these possible packings. To solve the former of these issues, most procedures rely on a rotamer library derived from databases of known protein structures. We introduce an alternative method that is free of statistics. We begin with a rotamer library that is based only on stereochemical considerations; this rotamer library is then optimized independently for each protein under study. We show that this optimization step restores the diversity of conformations observed in native proteins. We combine this protein‐dependent rotamer library (PDRL) method with the self‐consistent mean field (SCMF) sampling approach and a physics‐based scoring function into a new side‐chain prediction method, SCMF–PDRL. Using two large test sets of 831 and 378 proteins, respectively, we show that this new method compares favorably with competing methods such as SCAP, OPUS‐Rota, and SCWRL4 for energy‐minimized structures. Proteins 2014; 82:2000–2017. © 2014 Wiley Periodicals, Inc.     

Predicting structural effects in HIV-1 protease mutant complexes with flexible ligand docking and protein side-chain optimization

We present a computational approach for predicting structures of ligand-protein complexes and analyzing binding energy landscapes that combines Monte Carlo simulated annealing technique to determine the ligand bound conformation with the dead-end elimination algorithm for side-chain optimization of the protein active site residues. Flexible ligand docking and optimization of mobile protein side-chains have been performed to predict structural effects in the V32I/I47V/V82I HIV-1 protease mutant bound with the SB203386 ligand and in the V82A HIV-1 protease mutant bound with the A77003 ligand. The computational structure predictions are consistent with the crystal structures of these ligand-protein complexes. The emerging relationships between ligand docking and side-chain optimization of the active site residues are rationalized based on the analysis of the ligand-protein binding energy landscape. Proteins 33:295–310, 1998. © 1998 Wiley-Liss, 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.     

Sampling and scoring: A marriage made in heaven

Most structure prediction algorithms consist of initial sampling of the conformational space, followed by rescoring and possibly refinement of a number of selected structures. Here we focus on protein docking, and show that while decoupling sampling and scoring facilitates method development, integration of the two steps can lead to substantial improvements in docking results. Since decoupling is usually achieved by generating a decoy set containing both non‐native and near‐native docked structures, which can be then used for scoring function construction, we first review the roles and potential pitfalls of decoys in protein–protein docking, and show that some type of decoys are better than others for method development. We then describe three case studies showing that complete decoupling of scoring from sampling is not the best choice for solving realistic docking problems. Although some of the examples are based on our own experience, the results of the CAPRI docking and scoring experiments also show that performing both sampling and scoring generally yields better results than scoring the structures generated by all predictors. Next we investigate how the selection of training and decoy sets affects the performance of the scoring functions obtained. Finally, we discuss pathways to better alignment of the two steps, and show some algorithms that achieve a certain level of integration. Although we focus on protein–protein docking, our observations most likely also apply to other conformational search problems, including protein structure prediction and the docking of small molecules to proteins.Proteins 2013; 81:1874–1884. © 2013 Wiley Periodicals, Inc.     

Docking and scoring with alternative side-chain conformations

We describe a scoring and modeling procedure for docking ligands into protein models that have either modeled or flexible side-chain conformations. Our methodical contribution comprises a procedure for generating new potentials of mean force for the ROTA scoring function which we have introduced previously for optimizing side-chain conformations with the tool IRECS. The ROTA potentials are specially trained to tolerate small-scale positional errors of atoms that are characteristic of (i) side-chain conformations that are modeled using a sparse rotamer library and (ii) ligand conformations that are generated using a docking program. We generated both rigid and flexible protein models with our side-chain prediction tool IRECS and docked ligands to proteins using the scoring function ROTA and the docking programs FlexX (for rigid side chains) and FlexE (for flexible side chains). We validated our approach on the forty screening targets of the DUD database. The validation shows that the ROTA potentials are especially well suited for estimating the binding affinity of ligands to proteins. The results also show that our procedure can compensate for the performance decrease in screening that occurs when using protein models with side chains modeled with a rotamer library instead of using X-ray structures. The average runtime per ligand of our method is 168 seconds on an Opteron V20z, which is fast enough to allow virtual screening of compound libraries for drug candidates.     

A combinatorial scoring function for protein–RNA docking

Protein–RNA docking is still an open question. One of the main challenges is to develop an effective scoring function that can discriminate near‐native structures from the incorrect ones. To solve the problem, we have constructed a knowledge‐based residue‐nucleotide pairwise potential with secondary structure information considered for nonribosomal protein–RNA docking. Here we developed a weighted combined scoring function RpveScore that consists of the pairwise potential and six physics‐based energy terms. The weights were optimized using the multiple linear regression method by fitting the scoring function to L_rmsd for the bound docking decoys from Benchmark II. The scoring functions were tested on 35 unbound docking cases. The results show that the scoring function RpveScore including all terms performs best. Also RpveScore was compared with the statistical mechanics‐based method derived potential ITScore‐PR, and the united atom‐based statistical potentials QUASI‐RNP and DARS‐RNP. The success rate of RpveScore is 71.6% for the top 1000 structures and the number of cases where a near‐native structure is ranked in top 30 is 25 out of 35 cases. For 32 systems (91.4%), RpveScore can find the binding mode in top 5 that has no lower than 50% native interface residues on protein and nucleotides on RNA. Additionally, it was found that the long‐range electrostatic attractive energy plays an important role in distinguishing near‐native structures from the incorrect ones. This work can be helpful for the development of protein–RNA docking methods and for the understanding of protein–RNA interactions. RpveScore program is available to the public at http://life.bjut.edu.cn/kxyj/kycg/2017116/14845362285362368_1.html Proteins 2017; 85:741–752. © 2016 Wiley Periodicals, Inc.     

Ab initio protein structure assembly using continuous structure fragments and optimized knowledge-based force field

Ab initio protein folding is one of the major unsolved problems in computational biology owing to the difficulties in force field design and conformational search. We developed a novel program, QUARK, for template-free protein structure prediction. Query sequences are first broken into fragments of 1-20 residues where multiple fragment structures are retrieved at each position from unrelated experimental structures. Full-length structure models are then assembled from fragments using replica-exchange Monte Carlo simulations, which are guided by a composite knowledge-based force field. A number of novel energy terms and Monte Carlo movements are introduced and the particular contributions to enhancing the efficiency of both force field and search engine are analyzed in detail. QUARK prediction procedure is depicted and tested on the structure modeling of 145 nonhomologous proteins. Although no global templates are used and all fragments from experimental structures with template modeling score >0.5 are excluded, QUARK can successfully construct 3D models of correct folds in one-third cases of short proteins up to 100 residues. In the ninth community-wide Critical Assessment of protein Structure Prediction experiment, QUARK server outperformed the second and third best servers by 18 and 47% based on the cumulative Z-score of global distance test-total scores in the FM category. Although ab initio protein folding remains a significant challenge, these data demonstrate new progress toward the solution of the most important problem in the field.     

Exact Simultaneous Comparisons with Control in an r × c Contingency Table

Let categorical data coming from a control group and (r - 1) treated groups be given in an r × c contingency table. A simultaneous test procedure of the (r - 1) hypotheses that the probabilities of all c categories do not differ between the i-th treated group and the control is derived. For small tables and small cell frequencies it is exactly performed by generation of all tables having the given marginal sums. If 2 categories or 2 groups only are given the asymptotic distribution of the test statistic is known; otherwise its distribution may be simulated if the computational expenditure of performing an exact test is too large. By means of a Monte Carlo study it is shown that this method meets its level more reliably and that it has a better power than others.     

Bayesian analysis of a time series of counts with covariates: an application to the control of an infectious disease

This paper presents a Bayesian analysis of a time series of counts to assess its dependence on an explanatory variable. The time series represented is the incidence of the infectious disease ESBL-producing Klebsiella pneumoniae in an Australian hospital and the explanatory variable is the number of grams of antibiotic (third generation) cephalosporin used during that time. We demonstrate that there is a statistically significant relationship between disease occurrence and use of the antibiotic, lagged by three months. The model used is a parameter-driven model in the form of a generalized linear mixed model. Comparison of models is made in terms of mean square error.