Rapid Protein Side-Chain Packing via Tree Decomposition

How hydrophobicity, side chains, and salt affect the dimensions of disordered proteins

Despite the generally accepted role of the hydrophobic effect as the driving force for folding, many intrinsically disordered proteins (IDPs), including those with hydrophobic content typical of foldable proteins, behave nearly as self-avoiding random walks (SARWs) under physiological conditions. Here, we tested how temperature and ionic conditions influence the dimensions of the N-terminal domain of pertactin (PNt), an IDP with an amino acid composition typical of folded proteins. While PNt contracts somewhat with temperature, it nevertheless remains expanded over 10-58°C, with a Flory exponent, ν, >0.50. Both low and high ionic strength also produce contraction in PNt, but this contraction is mitigated by reducing charge segregation. With 46% glycine and low hydrophobicity, the reduced form of snow flea anti-freeze protein (red-sfAFP) is unaffected by temperature and ionic strength and persists as a near-SARW, ν ~ 0.54, arguing that the thermal contraction of PNt is due to stronger interactions between hydrophobic side chains. Additionally, red-sfAFP is a proxy for the polypeptide backbone, which has been thought to collapse in water. Increasing the glycine segregation in red-sfAFP had minimal effect on ν. Water remained a good solvent even with 21 consecutive glycine residues (ν > 0.5), and red-sfAFP variants lacked stable backbone hydrogen bonds according to hydrogen exchange. Similarly, changing glycine segregation has little impact on ν in other glycine-rich proteins. These findings underscore the generality that many disordered states can be expanded and unstructured, and that the hydrophobic effect alone is insufficient to drive significant chain collapse for typical protein sequences.

Tree diet: reducing the treewidth to unlock FPT algorithms in RNA bioinformatics

Hard graph problems are ubiquitous in Bioinformatics, inspiring the design of specialized Fixed-Parameter Tractable algorithms, many of which rely on a combination of tree-decomposition and dynamic programming. The time/space complexities of such approaches hinge critically on low values for the treewidth tw of the input graph. In order to extend their scope of applicability, we introduce the Tree-Diet problem, i.e. the removal of a minimal set of edges such that a given tree-decomposition can be slimmed down to a prescribed treewidth \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$tw'$$\end{document}tw′. Our rationale is that the time gained thanks to a smaller treewidth in a parameterized algorithm compensates the extra post-processing needed to take deleted edges into account. Our core result is an FPT dynamic programming algorithm for Tree-Diet, using \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^{O(tw)}n$$\end{document}2O(tw)n time and space. We complement this result with parameterized complexity lower-bounds for stronger variants (e.g., NP-hardness when \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$tw'$$\end{document}tw′ or \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$tw-tw'$$\end{document}tw-tw′ is constant). We propose a prototype implementation for our approach which we apply on difficult instances of selected RNA-based problems: RNA design, sequence-structure alignment, and search of pseudoknotted RNAs in genomes, revealing very encouraging results. This work paves the way for a wider adoption of tree-decomposition-based algorithms in Bioinformatics.

ProMod3-A versatile homology modelling toolbox

Computational methods for protein structure modelling are routinely used to complement experimental structure determination, thus they help to address a broad spectrum of scientific questions in biomedical research. The most accurate methods today are based on homology modelling, i.e. detecting a homologue to the desired target sequence that can be used as a template for modelling. Here we present a versatile open source homology modelling toolbox as foundation for flexible and computationally efficient modelling workflows. ProMod3 is a fully scriptable software platform that can perform all steps required to generate a protein model by homology. Its modular design aims at fast prototyping of novel algorithms and implementing flexible modelling pipelines. Common modelling tasks, such as loop modelling, sidechain modelling or generating a full protein model by homology, are provided as production ready pipelines, forming the starting point for own developments and enhancements. ProMod3 is the central software component of the widely used SWISS-MODEL web-server.

Ambiguity Coding Allows Accurate Inference of Evolutionary Parameters from Alignments in an Aggregated State-Space

How can we best learn the history of a protein’s evolution? Ideally, a model of sequence evolution should capture both the process that generates genetic variation and the functional constraints determining which changes are fixed. However, in practical terms the most suitable approach may simply be the one that combines the convenience of easily available input data with the ability to return useful parameter estimates. For example, we might be interested in a measure of the strength of selection (typically obtained using a codon model) or an ancestral structure (obtained using structural modeling based on inferred amino acid sequence and side chain configuration).

But what if data in the relevant state-space are not readily available? We show that it is possible to obtain accurate estimates of the outputs of interest using an established method for handling missing data. Encoding observed characters in an alignment as ambiguous representations of characters in a larger state-space allows the application of models with the desired features to data that lack the resolution that is normally required. This strategy is viable because the evolutionary path taken through the observed space contains information about states that were likely visited in the “unseen” state-space. To illustrate this, we consider two examples with amino acid sequences as input. We show that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$$\omega$$\end{document}, a parameter describing the relative strength of selection on nonsynonymous and synonymous changes, can be estimated in an unbiased manner using an adapted version of a standard 61-state codon model. Using simulated and empirical data, we find that ancestral amino acid side chain configuration can be inferred by applying a 55-state empirical model to 20-state amino acid data. Where feasible, combining inputs from both ambiguity-coded and fully resolved data improves accuracy. Adding structural information to as few as 12.5% of the sequences in an amino acid alignment results in remarkable ancestral reconstruction performance compared to a benchmark that considers the full rotamer state information. These examples show that our methods permit the recovery of evolutionary information from sequences where it has previously been inaccessible. [Ancestral reconstruction; natural selection; protein structure; state-spaces; substitution models.]

Computational reconstruction of atomistic protein structures from coarse-grained models

Three-dimensional protein structures, whether determined experimentally or theoretically, are often too low resolution. In this mini-review, we outline the computational methods for protein structure reconstruction from incomplete coarse-grained to all atomistic models. Typical reconstruction schemes can be divided into four major steps. Usually, the first step is reconstruction of the protein backbone chain starting from the C-alpha trace. This is followed by side-chains rebuilding based on protein backbone geometry. Subsequently, hydrogen atoms can be reconstructed. Finally, the resulting all-atom models may require structure optimization. Many methods are available to perform each of these tasks. We discuss the available tools and their potential applications in integrative modeling pipelines that can transfer coarse-grained information from computational predictions, or experiment, to all atomistic structures.

OPUS-Rota2: An Improved Fast and Accurate Side-Chain Modeling Method

Side-chain modeling plays a critical role in protein structure prediction. However, in many current methods, balancing the speed and accuracy is still challenging. In this paper, on the basis of our previous work OPUS-Rota (Protein Sci. 2008, 17, 1576-1585), we introduce a new side-chain modeling method, OPUS-Rota2, which is tested on both a 65-protein test set (DB65) in the OPUS-Rota paper and a 379-protein test set (DB379) in the SCWRL4 paper. If the main chain is native, OPUS-Rota2 is more accurate than OPUS-Rota, SCWRL4, and OSCAR-star but slightly less accurate than OSCAR-o. Also, if the main chain is non-native, OPUS-Rota2 is more accurate than any other method. Moreover, OPUS-Rota2 is significantly faster than any other method, in particular, 2 orders of magnitude faster than OSCAR-o. Thus, the combination of higher accuracy and speed of OPUS-Rota2 in modeling side chains on both the native and non-native main chains makes OPUS-Rota2 a very useful tool in protein structure modeling.

SWISS-MODEL: homology modelling of protein structures and complexes

Homology modelling has matured into an important technique in structural biology, significantly contributing to narrowing the gap between known protein sequences and experimentally determined structures. Fully automated workflows and servers simplify and streamline the homology modelling process, also allowing users without a specific computational expertise to generate reliable protein models and have easy access to modelling results, their visualization and interpretation. Here, we present an update to the SWISS-MODEL server, which pioneered the field of automated modelling 25 years ago and been continuously further developed. Recently, its functionality has been extended to the modelling of homo- and heteromeric complexes. Starting from the amino acid sequences of the interacting proteins, both the stoichiometry and the overall structure of the complex are inferred by homology modelling. Other major improvements include the implementation of a new modelling engine, ProMod3 and the introduction a new local model quality estimation method, QMEANDisCo. SWISS-MODEL is freely available at https://swissmodel.expasy.org.

Modeling of Protein Tertiary and Quaternary Structures Based on Evolutionary Information

Proteins are subject to evolutionary forces that shape their three-dimensional structure to meet specific functional demands. The knowledge of the structure of a protein is therefore instrumental to gain information about the molecular basis of its function. However, experimental structure determination is inherently time consuming and expensive, making it impossible to follow the explosion of sequence data deriving from genome-scale projects. As a consequence, computational structural modeling techniques have received much attention and established themselves as a valuable complement to experimental structural biology efforts. Among these, comparative modeling remains the method of choice to model the three-dimensional structure of a protein when homology to a protein of known structure can be detected.The general strategy consists of using experimentally determined structures of proteins as templates for the generation of three-dimensional models of related family members (targets) of which the structure is unknown. This chapter provides a description of the individual steps needed to obtain a comparative model using SWISS-MODEL, one of the most widely used automated servers for protein structure homology modeling.

Computational Feasibility of an Exhaustive Search of Side-Chain Conformations in Protein-Protein Docking

Protein-protein docking procedures typically perform the global scan of the proteins relative positions, followed by the local refinement of the putative matches. Because of the size of the search space, the global scan is usually implemented as rigid-body search, using computationally inexpensive intermolecular energy approximations. An adequate refinement has to take into account structural flexibility. Since the refinement performs conformational search of the interacting proteins, it is extremely computationally challenging, given the enormous amount of the internal degrees of freedom. Different approaches limit the search space by restricting the search to the side chains, rotameric states, coarse-grained structure representation, principal normal modes, and so on. Still, even with the approximations, the refinement presents an extreme computational challenge due to the very large number of the remaining degrees of freedom. Given the complexity of the search space, the advantage of the exhaustive search is obvious. The obstacle to such search is computational feasibility. However, the growing computational power of modern computers, especially due to the increasing utilization of Graphics Processing Unit (GPU) with large amount of specialized computing cores, extends the ranges of applicability of the brute-force search methods. This proof-of-concept study demonstrates computational feasibility of an exhaustive search of side-chain conformations in protein pocking. The procedure, implemented on the GPU architecture, was used to generate the optimal conformations in a large representative set of protein-protein complexes. © 2018 Wiley Periodicals, Inc.

Protein structure prediction

Predicting 3D structure of protein from its amino acid sequence is one of the most important unsolved problems in biophysics and computational biology. This paper attempts to give a comprehensive introduction of the most recent effort and progress on protein structure prediction. Following the general flowchart of structure prediction, related concepts and methods are presented and discussed. Moreover, brief introductions are made to several widely-used prediction methods and the community-wide critical assessment of protein structure prediction (CASP) experiments.

SPIDR: small-molecule peptide-influenced drug repurposing

Background

Conventional de novo drug design is costly and time consuming, making it accessible to only the best resourced research organizations. An emergent approach to new drug development is drug repurposing, in which compounds that have already gone through some level of clinical testing are examined for efficacy against diseases divergent than their original application. Repurposing of existing drugs circumvents the time and considerable cost of early stages of drug development, and can be accelerated by using software to screen existing chemical databases to identify suitable drug candidates.

Results

Small-molecule Peptide-Influenced Drug Repurposing (SPIDR) was developed to identify small molecule drugs that target a specific receptor by exploring the conformational binding space of peptide ligands. SPIDR was tested using the potent and selective 16-amino acid peptide α-conotoxin MII ligand and the α₃β₂-nicotinic acetylcholine receptor (nAChR) isoform. SPIDR incorporates a genetic algorithm-based, heuristic search procedure, which was used to explore the ligand binding domain of the α₃β₂-nAChR isoform using a library consisting of 640,000 α-conotoxin MII peptide analogs. The peptides that exhibited the highest affinity for α₃β₂-nAChR were used as models for a small-molecule structure similarity search of the PubChem Compound database. SPIDR incorporates the SimSearcher utility, which generates shape distribution signatures of molecules and employs multi-level K-means clustering to insure fast database queries. SPIDR identified non-peptide drugs with estimated binding affinities nearly double that of the native α-conotoxin MII peptide.

Conclusions

SPIDR has been generalized and integrated into DockoMatic v 2.1. This software contains an intuitive graphical interface for peptide mutant screening workflow and facilitates mapping, clustering, and searching of local molecular databases, making DockoMatic a valuable tool for researchers in drug design and repurposing.

Electronic supplementary material

The online version of this article (10.1186/s12859-018-2153-y) contains supplementary material, which is available to authorized users.

A critical analysis of computational protein design with sparse residue interaction graphs

Protein design algorithms enumerate a combinatorial number of candidate structures to compute the Global Minimum Energy Conformation (GMEC). To efficiently find the GMEC, protein design algorithms must methodically reduce the conformational search space. By applying distance and energy cutoffs, the protein system to be designed can thus be represented using a sparse residue interaction graph, where the number of interacting residue pairs is less than all pairs of mutable residues, and the corresponding GMEC is called the sparse GMEC. However, ignoring some pairwise residue interactions can lead to a change in the energy, conformation, or sequence of the sparse GMEC vs. the original or the full GMEC. Despite the widespread use of sparse residue interaction graphs in protein design, the above mentioned effects of their use have not been previously analyzed. To analyze the costs and benefits of designing with sparse residue interaction graphs, we computed the GMECs for 136 different protein design problems both with and without distance and energy cutoffs, and compared their energies, conformations, and sequences. Our analysis shows that the differences between the GMECs depend critically on whether or not the design includes core, boundary, or surface residues. Moreover, neglecting long-range interactions can alter local interactions and introduce large sequence differences, both of which can result in significant structural and functional changes. Designs on proteins with experimentally measured thermostability show it is beneficial to compute both the full and the sparse GMEC accurately and efficiently. To this end, we show that a provable, ensemble-based algorithm can efficiently compute both GMECs by enumerating a small number of conformations, usually fewer than 1000. This provides a novel way to combine sparse residue interaction graphs with provable, ensemble-based algorithms to reap the benefits of sparse residue interaction graphs while avoiding their potential inaccuracies.

Computational structure-based protein design algorithms have successfully redesigned proteins to fold and bind target substrates in vitro, and even in vivo. Because the complexity of a computational design increases dramatically with the number of mutable residues, many design algorithms employ cutoffs (distance or energy) to neglect some pairwise residue interactions, thereby reducing the effective search space and computational cost. However, the energies neglected by such cutoffs can add up, which may have nontrivial effects on the designed sequence and its function. To study the effects of using cutoffs on protein design, we computed the optimal sequence both with and without cutoffs, and showed that neglecting long-range interactions can significantly change the computed conformation and sequence. Designs on proteins with experimentally measured thermostability showed the benefits of computing the optimal sequences (and their conformations), both with and without cutoffs, efficiently and accurately. Therefore, we also showed that a provable, ensemble-based algorithm can efficiently compute the optimal conformation and sequence, both with and without applying cutoffs, by enumerating a small number of conformations, usually fewer than 1000. This provides a novel way to combine cutoffs with provable, ensemble-based algorithms to reap the computational efficiency of cutoffs while avoiding their potential inaccuracies.

Using kernelized partial canonical correlation analysis to study directly coupled side chains and allostery in small G proteins

Motivation: Inferring structural dependencies among a protein’s side chains helps us understand their coupled motions. It is known that coupled fluctuations can reveal pathways of communication used for information propagation in a molecule. Side-chain conformations are commonly represented by multivariate angular variables, but existing partial correlation methods that can be applied to this inference task are not capable of handling multivariate angular data. We propose a novel method to infer direct couplings from this type of data, and show that this method is useful for identifying functional regions and their interactions in allosteric proteins.

Results: We developed a novel extension of canonical correlation analysis (CCA), which we call ‘kernelized partial CCA’ (or simply KPCCA), and used it to infer direct couplings between side chains, while disentangling these couplings from indirect ones. Using the conformational information and fluctuations of the inactive structure alone for allosteric proteins in the Ras and other Ras-like families, our method identified allosterically important residues not only as strongly coupled ones but also in densely connected regions of the interaction graph formed by the inferred couplings. Our results were in good agreement with other empirical findings. By studying distinct members of the Ras, Rho and Rab sub-families, we show further that KPCCA was capable of inferring common allosteric characteristics in the small G protein super-family.

Availability and implementation:https://github.com/lsgh/ismb15

Contact:lsoltang@uwaterloo.ca

The impact of side-chain packing on protein docking refinement

We study the impact of optimizing the side-chain positions in the interface region between two proteins during the process of binding. Mathematically, the problem is similar to side-chain prediction, which has been extensively explored in the process of protein structure prediction. The protein-protein docking application, however, has a number of characteristics that necessitate different algorithmic and implementation choices. In this work, we implement a distributed approximate algorithm that can be implemented on multiprocessor architectures and enables a trade-off between accuracy and running speed. We report computational results on benchmarks of enzyme-inhibitor and other types of complexes, establishing that the side-chain flexibility our algorithm introduces substantially improves the performance of docking protocols. Furthermore, we establish that the inclusion of unbound side-chain conformers in the side-chain positioning problem is critical in these performance improvements. The code is available to the community under open source license.

LoopWeaver: loop modeling by the weighted scaling of verified proteins

Modeling loops is a necessary step in protein structure determination, even with experimental nuclear magnetic resonance (NMR) data, it is widely known to be difficult. Database techniques have the advantage of producing a higher proportion of predictions with subangstrom accuracy when compared with ab initio techniques, but the disadvantage of also producing a higher proportion of clashing or highly inaccurate predictions. We introduce LoopWeaver, a database method that uses multidimensional scaling to achieve better, clash-free placement of loops obtained from a database of protein structures. This allows us to maintain the above-mentioned advantage while avoiding the disadvantage. Test results show that we achieve significantly better results than all other methods, including Modeler, Loopy, SuperLooper, and Rapper, before refinement. With refinement, our results (LoopWeaver and Loopy consensus) are better than ROSETTA, with 0.42 Å RMSD on average for 206 length 6 loops, 0.64 Å local RMSD for 168 length 7 loops, 0.81Å RMSD for 117 length 8 loops, and 0.98 Å RMSD for length 9 loops, while ROSETTA has 0.55, 0.79, 1.16, 1.42, respectively, at the same average time limit (3 hours). When we allow ROSETTA to run for over a week, it approaches, but does not surpass, our accuracy.

Modeling of protein side-chain conformations with RASP

Modeling of side-chain conformations on a fixed protein backbone, also called side-chain packing, plays an important role in protein structure prediction, protein design, molecular docking, and functional analysis. RASP, or RApid Side-chain Predictor, is a recently developed program that can model protein side-chain conformations with both high accuracy and high speed. Moreover, it can generate structures with few atomic clashes. This chapter first provides a brief introduction to the principle and performances of the RASP package. Then details on how to use RASP programs to predict protein side-chain conformations are elaborated. Finally, it describes case studies for structure refinement in homology modeling and residue substitution.

Protein Structure Idealization: How accurately is it possible to model protein structures with dihedral angles?

Previous studies show that the same type of bond lengths and angles fit Gaussian distributions well with small standard deviations on high resolution protein structure data. The mean values of these Gaussian distributions have been widely used as ideal bond lengths and angles in bioinformatics. However, we are not aware of any research done to evaluate how accurately we can model protein structures with dihedral angles and ideal bond lengths and angles.

Here, we introduce the protein structure idealization problem. We focus on the protein backbone structure idealization. We describe a fast O(nm/ε) dynamic programming algorithm to find an idealized protein backbone structure that is approximately optimal according to our scoring function. The scoring function evaluates not only the free energy, but also the similarity with the target structure. Thus, the idealized protein structures found by our algorithm are guaranteed to be protein-like and close to the target protein structure.

We have implemented our protein structure idealization algorithm and idealized the high resolution protein structures with low sequence identities of the CULLPDB_PC30_RES1.6_R0.25 data set. We demonstrate that idealized backbone structures always exist with small changes and significantly better free energy. We also applied our algorithm to refine protein pseudo-structures determined in NMR experiments.

RASP: rapid modeling of protein side chain conformations

MOTIVATION

Modeling of side chain conformations constitutes an indispensable effort in protein structure modeling, protein-protein docking and protein design. Thanks to an intensive attention to this field, many of the existing programs can achieve reasonably good and comparable prediction accuracy. Moreover, in our previous work on CIS-RR, we argued that the prediction with few atomic clashes can complement the current existing methods for subsequent analysis and refinement of protein structures. However, these recent efforts to enhance the quality of predicted side chains have been accompanied by a significant increase of computational cost.

RESULTS

In this study, by mainly focusing on improving the speed of side chain conformation prediction, we present a RApid Side-chain Predictor, called RASP. To achieve a much faster speed with a comparable accuracy to the best existing methods, we not only employ the clash elimination strategy of CIS-RR, but also carefully optimize energy terms and integrate different search algorithms. In comprehensive benchmark testings, RASP is over one order of magnitude faster (~ 40 times over CIS-RR) than the recently developed methods, while achieving comparable or even better accuracy.

DockoMatic: automated peptide analog creation for high throughput virtual screening

The purpose of this manuscript is threefold: (1) to describe an update to DockoMatic that allows the user to generate cyclic peptide analog structure files based on protein database (pdb) files, (2) to test the accuracy of the peptide analog structure generation utility, and (3) to evaluate the high throughput capacity of DockoMatic. The DockoMatic graphical user interface interfaces with the software program Treepack to create user defined peptide analogs. To validate this approach, DockoMatic produced cyclic peptide analogs were tested for three-dimensional structure consistency and binding affinity against four experimentally determined peptide structure files available in the Research Collaboratory for Structural Bioinformatics database. The peptides used to evaluate this new functionality were alpha-conotoxins ImI, PnIA, and their published analogs. Peptide analogs were generated by DockoMatic and tested for their ability to bind to X-ray crystal structure models of the acetylcholine binding protein originating from Aplysia californica. The results, consisting of more than 300 simulations, demonstrate that DockoMatic predicts the binding energy of peptide structures to within 3.5 kcal mol(-1), and the orientation of bound ligand compares to within 1.8 Å root mean square deviation for ligand structures as compared to experimental data. Evaluation of high throughput virtual screening capacity demonstrated that Dockomatic can collect, evaluate, and summarize the output of 10,000 AutoDock jobs in less than 2 hours of computational time, while 100,000 jobs requires approximately 15 hours and 1,000,000 jobs is estimated to take up to a week.

Improved side-chain modeling by coupling clash-detection guided iterative search with rotamer relaxation

MOTIVATION

Side-chain modeling has seen wide applications in computational structure biology. Most of the popular side-chain modeling programs explore the conformation space using discrete rigid rotamers for speed and efficiency. However, in the tightly packed environments of protein interiors, these methods will inherently lead to atomic clashes and hinder the prediction accuracy.

RESULTS

We present a side-chain modeling method (CIS-RR), which couples a novel clash-detection guided iterative search (CIS) algorithm with continuous torsion space optimization of rotamers (RR). Benchmark testing shows that compared with the existing popular side-chain modeling methods, CIS-RR removes atomic clashes much more effectively and achieves comparable or even better prediction accuracy while having comparable computational cost. We believe that CIS-RR could be a useful method for accurate side-chain modeling.

AVAILABILITY

CIS-RR is available to non-commercial users at our website: http://jianglab.ibp.ac.cn/lims/cisrr/cisrr.html.

Improved prediction of protein side-chain conformations with SCWRL4

Determination of side-chain conformations is an important step in protein structure prediction and protein design. Many such methods have been presented, although only a small number are in widespread use. SCWRL is one such method, and the SCWRL3 program (2003) has remained popular because of its speed, accuracy, and ease-of-use for the purpose of homology modeling. However, higher accuracy at comparable speed is desirable. This has been achieved in a new program SCWRL4 through: (1) a new backbone-dependent rotamer library based on kernel density estimates; (2) averaging over samples of conformations about the positions in the rotamer library; (3) a fast anisotropic hydrogen bonding function; (4) a short-range, soft van der Waals atom-atom interaction potential; (5) fast collision detection using k-discrete oriented polytopes; (6) a tree decomposition algorithm to solve the combinatorial problem; and (7) optimization of all parameters by determining the interaction graph within the crystal environment using symmetry operators of the crystallographic space group. Accuracies as a function of electron density of the side chains demonstrate that side chains with higher electron density are easier to predict than those with low-electron density and presumed conformational disorder. For a testing set of 379 proteins, 86% of chi(1) angles and 75% of chi(1+2) angles are predicted correctly within 40 degrees of the X-ray positions. Among side chains with higher electron density (25-100th percentile), these numbers rise to 89 and 80%. The new program maintains its simple command-line interface, designed for homology modeling, and is now available as a dynamic-linked library for incorporation into other software programs.

Optimization techniques in molecular structure and function elucidation

This paper discusses recent optimization approaches to the protein side-chain prediction problem, protein structural alignment, and molecular structure determination from X-ray diffraction measurements. The machinery employed to solve these problems has included algorithms from linear programming, dynamic programming, combinatorial optimization, and mixed-integer nonlinear programming. Many of these problems are purely continuous in nature. Yet, to this date, they have been approached mostly via combinatorial optimization algorithms that are applied to discrete approximations. The main purpose of the paper is to offer an introduction and motivate further systems approaches to these problems.

Principles of flexible protein-protein docking

Treating flexibility in molecular docking is a major challenge in cell biology research. Here we describe the background and the principles of existing flexible protein-protein docking methods, focusing on the algorithms and their rational. We describe how protein flexibility is treated in different stages of the docking process: in the preprocessing stage, rigid and flexible parts are identified and their possible conformations are modeled. This preprocessing provides information for the subsequent docking and refinement stages. In the docking stage, an ensemble of pre-generated conformations or the identified rigid domains may be docked separately. In the refinement stage, small-scale movements of the backbone and side-chains are modeled and the binding orientation is improved by rigid-body adjustments. For clarity of presentation, we divide the different methods into categories. This should allow the reader to focus on the most suitable method for a particular docking problem.

Free energy estimates of all-atom protein structures using generalized belief propagation

We present a technique for approximating the free energy of protein structures using generalized belief propagation (GBP). The accuracy and utility of these estimates are then demonstrated in two different application domains. First, we show that the entropy component of our free energy estimates can useful in distinguishing native protein structures from decoys-structures with similar internal energy to that of the native structure, but otherwise incorrect. Our method is able to correctly identify the native fold from among a set of decoys with 87.5% accuracy over a total of 48 different immunoglobulin folds. The remaining 12.5% of native structures are ranked among the top four of all structures. Second, we show that our estimates of DeltaDeltaG upon mutation upon mutation for three different data sets have linear correlations of 0.63-0.70 with experimental measurements and statistically significant p-values. Together, these results suggest that GBP is an effective means for computing free energy in all-atom models of protein structures. GBP is also efficient, taking a few minutes to run on a typical sized protein, further suggesting that GBP may be an attractive alternative to more costly molecular dynamic simulations for some tasks.

Fast procedure for reconstruction of full-atom protein models from reduced representations

We introduce PULCHRA, a fast and robust method for the reconstruction of full-atom protein models starting from a reduced protein representation. The algorithm is particularly suitable as an intermediate step between coarse-grained model-based structure prediction and applications requiring an all-atom structure, such as molecular dynamics, protein-ligand docking, structure-based function prediction, or assessment of quality of the predicted structure. The accuracy of the method was tested on a set of high-resolution crystallographic structures as well as on a set of low-resolution protein decoys generated by a protein structure prediction algorithm TASSER. The method is implemented as a standalone program that is available for download from http://cssb.biology.gatech.edu/skolnick/files/PULCHRA.

OPUS-Rota: a fast and accurate method for side-chain modeling

In this paper, we introduce a fast and accurate side-chain modeling method, named OPUS-Rota. In a benchmark comparison with the methods SCWRL, NCN, LGA, SPRUCE, Rosetta, and SCAP, OPUS-Rota is shown to be much faster than all the methods except SCWRL, which is comparably fast. In terms of overall chi (1) and chi (1+2) accuracies, however, OPUS-Rota is 5.4 and 8.8 percentage points better, respectively, than SCWRL. Compared with NCN, which has the best accuracy in the literature, OPUS-Rota is 1.6 percentage points better for overall chi (1+2) but 0.3 percentage points weaker for overall chi (1). Hence, our algorithm is much more accurate than SCWRL with similar execution speed, and it has accuracy comparable to or better than the most accurate methods in the literature, but with a runtime that is one or two orders of magnitude shorter. In addition, OPUS-Rota consistently outperforms SCWRL on the Wallner and Elofsson homology-modeling benchmark set when the sequence identity is greater than 40%. We hope that OPUS-Rota will contribute to high-accuracy structure refinement, and the computer program is freely available for academic users.

FireDock: a web server for fast interaction refinement in molecular docking

Structural details of protein–protein interactions are invaluable for understanding and deciphering biological mechanisms. Computational docking methods aim to predict the structure of a protein–protein complex given the structures of its single components. Protein flexibility and the absence of robust scoring functions pose a great challenge in the docking field. Due to these difficulties most of the docking methods involve a two-tier approach: coarse global search for feasible orientations that treats proteins as rigid bodies, followed by an accurate refinement stage that aims to introduce flexibility into the process. The FireDock web server, presented here, is the first web server for flexible refinement and scoring of protein–protein docking solutions. It includes optimization of side-chain conformations and rigid-body orientation and allows a high-throughput refinement. The server provides a user-friendly interface and a 3D visualization of the results. A docking protocol consisting of a global search by PatchDock and a refinement by FireDock was extensively tested. The protocol was successful in refining and scoring docking solution candidates for cases taken from docking benchmarks. We provide an option for using this protocol by automatic redirection of PatchDock candidate solutions to the FireDock web server for refinement. The FireDock web server is available at http://bioinfo3d.cs.tau.ac.il/FireDock/.

A historical perspective of template-based protein structure prediction

This chapter presents a broad and a historical overview of the problem of protein structure prediction. Different structure prediction methods, including homology modeling, fold recognition (FR)/protein threading, ab initio/de novo approaches, and hybrid techniques involving multiple types of approaches, are introduced in a historical context. The progress of the field as a whole, especially in the threading/FR area, as reflected by the CASP/CAFASP contests, is reviewed. At the end of the chapter, we discuss the challenging issues ahead in the field of protein structure prediction.

FireDock: fast interaction refinement in molecular docking

Here, we present FireDock, an efficient method for the refinement and rescoring of rigid-body docking solutions. The refinement process consists of two main steps: (1) rearrangement of the interface side-chains and (2) adjustment of the relative orientation of the molecules. Our method accounts for the observation that most interface residues that are important in recognition and binding do not change their conformation significantly upon complexation. Allowing full side-chain flexibility, a common procedure in refinement methods, often causes excessive conformational changes. These changes may distort preformed structural signatures, which have been shown to be important for binding recognition. Here, we restrict side-chain movements, and thus manage to reduce the false-positive rate noticeably. In the later stages of our procedure (orientation adjustments and scoring), we smooth the atomic radii. This allows for the minor backbone and side-chain movements and increases the sensitivity of our algorithm. FireDock succeeds in ranking a near-native structure within the top 15 predictions for 83% of the 30 enzyme-inhibitor test cases, and for 78% of the 18 semiunbound antibody-antigen complexes. Our refinement procedure significantly improves the ranking of the rigid-body PatchDock algorithm for these cases. The FireDock program is fully automated. In particular, to our knowledge, FireDock's prediction results are comparable to current state-of-the-art refinement methods while its running time is significantly lower. The method is available at http://bioinfo3d.cs.tau.ac.il/FireDock/.

A Parameterized Algorithm for Protein Structure Alignment

This paper proposes a parameterized polynomial time approximation scheme (PTAS) for aligning two protein structures, in the case where one protein structure is represented by a contact map graph and the other by a contact map graph or a distance matrix. If the sequential order of alignment is not required, the time complexity is polynomial in the protein size and exponential with respect to two parameters D(u)/D(l) and D(c)/D(l), which usually can be treated as constants. In particular, D(u) is the distance threshold determining if two residues are in contact or not, D(c) is the maximally allowed distance between two matched residues after two proteins are superimposed, and D(l) is the minimum inter-residue distance in a typical protein. This result clearly demonstrates that the computational hardness of the contact map based protein structure alignment problem is related not to protein size but to several parameters modeling the problem. The result is achieved by decomposing the protein structure using tree decomposition and discretizing the rigid-body transformation space. Preliminary experimental results indicate that on a Linux PC, it takes from ten minutes to one hour to align two proteins with approximately 100 residues.

Andante: reducing side-chain rotamer search space during comparative modeling using environment-specific substitution probabilities

MOTIVATION

The accurate placement of side chains in computational protein modeling and design involves the searching of vast numbers of rotamer combinations.

RESULTS

We have applied the information contained within structurally aligned homologous families, in the form of conserved chi angle conservation rules, to the problem of the comparative modeling. This allows the accurate borrowing of entire side-chain conformations and/or the restriction to high probability rotamer bins. The application of these rules consistently reduces the number of rotamer combinations that need to be searched to trivial values and also reduces the overall side-chain root mean square deviation (rmsd) of the final model. The approach is complementary to current side-chain placement algorithms that use the decomposition of interacting clusters to increase the speed of the placement process.

Efficient parameterized algorithms for biopolymer structure-sequence alignment

Computational alignment of a biopolymer sequence (e.g., an RNA or a protein) to a structure is an effective approach to predict and search for the structure of new sequences. To identify the structure of remote homologs, the structure-sequence alignment has to consider not only sequence similarity, but also spatially conserved conformations caused by residue interactions and, consequently, is computationally intractable. It is difficult to cope with the inefficiency without compromising alignment accuracy, especially for structure search in genomes or large databases. This paper introduces a novel method and a parameterized algorithm for structure-sequence alignment. Both the structure and the sequence are represented as graphs, where, in general, the graph for a biopolymer structure has a naturally small tree width. The algorithm constructs an optimal alignment by finding in the sequence graph the maximum valued subgraph isomorphic to the structure graph. It has the computational time complexity O[k(t)N(2)] for the structure of N residues and its tree decomposition of width t. Parameter k, small in nature, is determined by a statistical cutoff for the correspondence between the structure and the sequence. This paper demonstrates a successful application of the algorithm to RNA structure search used for noncoding RNA identification. An application to protein threading is also discussed.

Residue-rotamer-reduction algorithm for the protein side-chain conformation problem

MOTIVATION

The protein side-chain conformation problem is a central problem in proteomics with wide applications in protein structure prediction and design. Computational complexity results show that the problem is hard to solve. Yet, instances from realistic applications are large and demand fast and reliable algorithms.

RESULTS

We propose a new global optimization algorithm, which for the first time integrates residue reduction and rotamer reduction techniques previously developed for the protein side-chain conformation problem. We show that the proposed approach simplifies dramatically the topology of the underlining residue graph. Computations show that our algorithm solves problems using only 1-10% of the time required by the mixed-integer linear programming approach available in the literature. In addition, on a set of hard side-chain conformation problems, our algorithm runs 2-78 times faster than SCWRL 3.0, which is widely used for solving these problems.

AVAILABILITY

The implementation is available as an online server at http://eudoxus.scs.uiuc.edu/r3.html

Efficient Parameterized Algorithm for Biopolymer Structure-Sequence Alignment

Computational alignment of a biopolymer sequence (e.g., an RNA or a protein) to a structure is an effective approach to predict and search for the structure of new sequences. To identify the structure of remote homologs, the structure-sequence alignment has to consider not only sequence similarity but also spatially conserved conformations caused by residue interactions, and consequently is computationally intractable. It is difficult to cope with the inefficiency without compromising alignment accuracy, especially for structure search in genomes or large databases.

This paper introduces a novel method and a parameterized algorithm for structure-sequence alignment. Both the structure and the sequence are represented as graphs, where in general the graph for a biopolymer structure has a naturally small tree width. The algorithm constructs an optimal alignment by finding in the sequence graph the maximum valued subgraph isomorphic to the structure graph. It has the computational time complexity O(k^tN²) for the structure of N residues and its tree decomposition of width t. The parameter k, small in nature, is determined by a statistical cutoff for the correspondence between the structure and the sequence. The paper demonstrates a successful application of the algorithm to developing a fast program for RNA structural homology search.

A tree-decomposition approach to protein structure prediction

This paper proposes a tree decomposition of protein structures, which can be used to efficiently solve two key subproblems of protein structure prediction: protein threading for backbone prediction and protein side-chain prediction. To develop a unified tree-decomposition based approach to these two subproblems, we model them as a geometric neighborhood graph labeling problem. Theoretically, we can have a low-degree polynomial time algorithm to decompose a geometric neighborhood graph G = (V, E) into components with size O(|V|((2/3))log|V|). The computational complexity of the tree-decomposition based graph labeling algorithms is O(|V|Delta(tw+1)) where Delta is the average number of possible labels for each vertex and tw( = O(|V|((2/3))log|V|)) the tree width of G. Empirically, tw is very small and the tree-decomposition method can solve these two problems very efficiently. This paper also compares the computational efficiency of the tree-decomposition approach with the linear programming approach to these two problems and identifies the condition under which the tree-decomposition approach is more efficient than the linear programming approach. Experimental result indicates that the tree-decomposition approach is more efficient most of the time.