MQAPsingle: A quasi single‐model approach for estimation of the quality of individual protein structure models

We present a Model Quality Assessment Program (MQAP), called MQAPsingle, for ranking and assessing the absolute global quality of single protein models. MQAPsingle is quasi single‐model MQAP, a method that combines advantages of both “pure” single‐model MQAPs and clustering MQAPs. This approach results in higher accuracy compared to the state‐of‐the‐art single‐model MQAPs. Notably, the prediction for a given model is the same regardless if this model is submitted to our server alone or together with other models. Proteins 2016; 84:1021–1028. © 2015 Wiley Periodicals, Inc.     

Improving the quality of protein structure models by selecting from alignment alternatives

Background  

In the area of protein structure prediction, recently a lot of effort has gone into the development of Model Quality Assessment Programs (MQAPs). MQAPs distinguish high quality protein structure models from inferior models. Here, we propose a new method to use an MQAP to improve the quality of models. With a given target sequence and template structure, we construct a number of different alignments and corresponding models for the sequence. The quality of these models is scored with an MQAP and used to choose the most promising model. An SVM-based selection scheme is suggested for combining MQAP partial potentials, in order to optimize for improved model selection.     

Toward the solution of the protein structure prediction problem

Since Anfinsen demonstrated that the information encoded in a protein’s amino acid sequence determines its structure in 1973, solving the protein structure prediction problem has been the Holy Grail of structural biology. The goal of protein structure prediction approaches is to utilize computational modeling to determine the spatial location of every atom in a protein molecule starting from only its amino acid sequence. Depending on whether homologous structures can be found in the Protein Data Bank (PDB), structure prediction methods have been historically categorized as template-based modeling (TBM) or template-free modeling (FM) approaches. Until recently, TBM has been the most reliable approach to predicting protein structures, and in the absence of reliable templates, the modeling accuracy sharply declines. Nevertheless, the results of the most recent community-wide assessment of protein structure prediction experiment (CASP14) have demonstrated that the protein structure prediction problem can be largely solved through the use of end-to-end deep machine learning techniques, where correct folds could be built for nearly all single-domain proteins without using the PDB templates. Critically, the model quality exhibited little correlation with the quality of available template structures, as well as the number of sequence homologs detected for a given target protein. Thus, the implementation of deep-learning techniques has essentially broken through the 50-year-old modeling border between TBM and FM approaches and has made the success of high-resolution structure prediction significantly less dependent on template availability in the PDB library.     

Improved estimation of structure predictor quality

Background  

Methods that can automatically assess the quality of computationally predicted protein structures are important, as they enable the selection of the most accurate structure from an ensemble of predictions. Assessment methods that determine the quality of a predicted structure by comparing it against the various structures predicted by different servers have been shown to outperform approaches that rely on the intrinsic characteristics of the structure itself.     

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.     

Toward the detection and validation of repeats in protein structure

We present a method called DAVROS to detect, localize, and validate repeating motifs in protein structure allowing for insertions and deletions. DAVROS uses the score matrix from a structural alignment program (SAP) to search for repeating motifs using an algorithm based on concepts from signal processing and the statistical properties of the alignments. The method was tested against a nonredundant Protein Data Bank, and each chain was assigned a score. For the top 50 chains ranked by score, 70% contain repeating motifs detected without error. These represent 14 types of fold covering alpha, beta, and alphabeta protein classes. A second data set comprising protein chains in different sequence families for triosephosphate isomerase (TIM) barrel, leucine-rich repeat (LRR), trefoil, and alpha-alpha barrel folds was used to assess the ability of DAVROS to detect all motifs within a specific fold. For the second test set, the percentage of motifs detected was highest for the LRR chains (88.7%) and least for the TIM barrels (60%). This variability results from the regularity of the LRR motif compared to the alphabeta units of the TIM barrel, which generally have many more indels. These reduce the strength of the repeat signal in the SAP matrix, making repeat detection more difficult.     

Toward minimalist models of larger proteins: a ubiquitin-like protein

Our recently developed off-lattice bead model capable of simulating protein structures with mixed alpha/beta content has been extended to model the folding of a ubiquitin-like protein and provides a means for examining the more complex kinetics involved in the folding of larger proteins. Using trajectories generated from constant-temperature Langevin dynamics simulations and sampling with the multiple multi-histogram method over five-order parameters, we are able to characterize the free energy landscape for folding and find evidence for folding through compact intermediates. Our model reproduces the observation that the C-terminus loop structure in ubiquitin is the last to fold in the folding process and most likely plays a spectator role in the folding kinetics. The possibility of a productive metastable intermediate along the folding pathway consisting of collapsed states with no secondary structure, and of intermediates or transition structures involving secondary structural elements occurring early in the sequence, is also supported by our model. The kinetics of folding remain multi-exponential below the folding temperature, with glass-like kinetics appearing at T/T(f) approximately 0.86. This new physicochemical model, designed to be predictive, helps validate the value of modeling protein folding at this level of detail for genomic-scale studies, and motivates further studies of other protein topologies and the impact of more complex energy functions, such as the addition of solvation forces.     

Structural quality of unrefined models in protein docking

Structural characterization of protein‐protein interactions is essential for understanding life processes at the molecular level. However, only a fraction of protein interactions have experimentally resolved structures. Thus, reliable computational methods for structural modeling of protein interactions (protein docking) are important for generating such structures and understanding the principles of protein recognition. Template‐based docking techniques that utilize structural similarity between target protein‐protein interaction and cocrystallized protein‐protein complexes (templates) are gaining popularity due to generally higher reliability than that of the template‐free docking. However, the template‐based approach lacks explicit penalties for intermolecular penetration, as opposed to the typical free docking where such penalty is inherent due to the shape complementarity paradigm. Thus, template‐based docking models are commonly assumed to require special treatment to remove large structural penetrations. In this study, we compared clashes in the template‐based and free docking of the same proteins, with crystallographically determined and modeled structures. The results show that for the less accurate protein models, free docking produces fewer clashes than the template‐based approach. However, contrary to the common expectation, in acceptable and better quality docking models of unbound crystallographically determined proteins, the clashes in the template‐based docking are comparable to those in the free docking, due to the overall higher quality of the template‐based docking predictions. This suggests that the free docking refinement protocols can in principle be applied to the template‐based docking predictions as well. Proteins 2016; 85:39–45. © 2016 Wiley Periodicals, Inc.     

Local protein structure prediction using discriminative models

Background  

In recent years protein structure prediction methods using local structure information have shown promising improvements. The quality of new fold predictions has risen significantly and in fold recognition incorporation of local structure predictions led to improvements in the accuracy of results.     

Predicting absolute contact numbers of native protein structure from amino acid sequence

The contact number of an amino acid residue in a protein structure is defined by the number of C(beta) atoms around the C(beta) atom of the given residue, a quantity similar to, but different from, solvent accessible surface area. We present a method to predict the contact numbers of a protein from its amino acid sequence. The method is based on a simple linear regression scheme and predicts the absolute values of contact numbers. When single sequences are used for both parameter estimation and cross-validation, the present method predicts the contact numbers with a correlation coefficient of 0.555 on average. When multiple sequence alignments are used, the correlation increases to 0.627, which is a significant improvement over previous methods. In terms of discrete states prediction, the accuracies for 2-, 3-, and 10-state predictions are, respectively, 71.4%, 54.1%, and 18.9% with residue type-dependent unbiased thresholds, and 76.3%, 59.2%, and 21.8% with residue type-independent unbiased thresholds. The difference between accessible surface area and contact number from a prediction viewpoint and the application of contact number prediction to three-dimensional structure prediction are discussed.     

A resource for benchmarking the usefulness of protein structure models

ABSTRACT: BACKGROUND: Increasingly, biologists and biochemists use computational tools to design experiments to probe the function of proteins and/or to engineer them for a variety of different purposes. The most effective strategies rely on the knowledge of the three-dimensional structure of the protein of interest. However it is often the case that an experimental structure is not available and that models of different quality are used instead. On the other hand, the relationship between the quality of a model and its appropriate use is not easy to derive in general, and so far it has been analyzed in detail only for specific application RESULTS: This paper describes a database and related software tools that allow testing of a given structure based methods on models of a protein representing different levels of accuracy. The comparison of the results of a computational experiment on the experimental structure and on a set of its decoy models will allow developers and users to assess which is the specific threshold of accuracy required to perform the task effectively. CONCLUSIONS: The ModelDB server automatically builds decoy models of different accuracy for a given protein of known structure and provides a set of useful tools for their analysis. Pre-computed data for a non-redundant set of deposited protein structures are available for analysis and download in the ModelDB database.     

Unbiased estimation of individual asymmetry

The importance of measurement error (ME) for the estimation of population level fluctuating asymmetry (FA) has long been recognized. At the individual level, however, this aspect has been studied in less detail. Recently, it has been shown that the random slopes of a mixed regression model can estimate individual asymmetry levels that are unbiased with respect to ME. Yet, recent studies have shown that such estimates may fail to reflect heterogeneity in these effects. In this note I show that this is not the case for the estimation of individual asymmetry. The random slopes adequately reflect between‐individual heterogeneity in the underlying developmental instability. Increased levels of ME resulted in, on average, lower estimates of individual asymmetry relative to the traditional unsigned asymmetry. This well‐known shrinkage effect in Bayesian analysis adequately corrected for ME and heterogeneity in ME resulting in unbiased estimates of individual asymmetry that were more closely correlated with the true underlying asymmetry.     

Stereochemical quality of protein structure coordinates.

Methods have been developed to assess the stereochemical quality of any protein structure both globally and locally using various criteria. Several parameters can be derived from the coordinates of a given structure. Global parameters include the distribution of phi, psi and chi 1 torsion angles, and hydrogen bond energies. There are clear correlations between these parameters and resolution; as the resolution improves, the distribution of the parameters becomes more clustered. These features show a broad distribution about ideal values derived from high-resolution structures. Some structures have tightly clustered distributions even at relatively low resolutions, while others show abnormal scatter though the data go to high resolution. Additional indicators of local irregularity include proline phi angles, peptide bond planarities, disulfide bond lengths, and their chi 3 torsion angles. These stereochemical parameters have been used to generate measures of stereochemical quality which provide a simple guide as to the reliability of a structure, in addition to the most important measures, resolution and R-factor. The parameters used in this evaluation are not novel, and are easily calculated from structure coordinates. A program suite is currently being developed which will quickly check a given structure, highlighting unusual stereochemistry and possible errors.     

Toward optimal fragment generations for ab initio protein structure assembly

Fragment assembly using structural motifs excised from other solved proteins has shown to be an efficient method for ab initio protein‐structure prediction. However, how to construct accurate fragments, how to derive optimal restraints from fragments, and what the best fragment length is are the basic issues yet to be systematically examined. In this work, we developed a gapless‐threading method to generate position‐specific structure fragments. Distance profiles and torsion angle pairs are then derived from the fragments by statistical consistency analysis, which achieved comparable accuracy with the machine‐learning‐based methods although the fragments were taken from unrelated proteins. When measured by both accuracies of the derived distance profiles and torsion angle pairs, we come to a consistent conclusion that the optimal fragment length for structural assembly is around 10, and at least 100 fragments at each location are needed to achieve optimal structure assembly. The distant profiles and torsion angle pairs as derived by the fragments have been successfully used in QUARK for ab initio protein structure assembly and are provided by the QUARK online server at http://zhanglab.ccmb. med.umich.edu/QUARK/ . Proteins 2013. © 2012 Wiley Periodicals, Inc.     

Least absolute deviation estimation for fractionally integrated autoregressive moving average time series models with conditional heteroscedasticity

We consider a unified least absolute deviation estimator forstationary and nonstationary fractionally integrated autoregressivemoving average models with conditional heteroscedasticity. Itsasymptotic normality is established when the second momentsof errors and innovations are finite. Several other alternativeestimators are also discussed and are shown to be less efficientand less robust than the proposed approach. A diagnostic tool,consisting of two portmanteau tests, is designed to check whetheror not the estimated models are adequate. The simulation experimentsgive further support to our model and the results for the absolutereturns of the Dow Jones Industrial Average Index daily closingprice demonstrate their usefulness in modelling time seriesexhibiting the features of long memory, conditional heteroscedasticityand heavy tails.