High–quality protein backbone reconstruction from alpha carbons using Gaussian mixture models

Coarse‐grained protein structure models offer increased efficiency in structural modeling, but these must be coupled with fast and accurate methods to revert to a full‐atom structure. Here, we present a novel algorithm to reconstruct mainchain models from C traces. This has been parameterized by fitting Gaussian mixture models (GMMs) to short backbone fragments centered on idealized peptide bonds. The method we have developed is statistically significantly more accurate than several competing methods, both in terms of RMSD values and dihedral angle differences. The method produced Ramachandran dihedral angle distributions that are closer to that observed in real proteins and better Phaser molecular replacement log‐likelihood gains. Amino acid residue sidechain reconstruction accuracy using SCWRL4 was found to be statistically significantly correlated to backbone reconstruction accuracy. Finally, the PD2 method was found to produce significantly lower energy full‐atom models using Rosetta which has implications for multiscale protein modeling using coarse‐grained models. A webserver and C++ source code is freely available for noncommercial use from: http://www.sbg.bio.ic.ac.uk/phyre2/PD2_ca2main/ . © 2013 Wiley Periodicals, Inc.     

Identifying and reducing error in cluster‐expansion approximations of protein energies

Protein design involves searching a vast space for sequences that are compatible with a defined structure. This can pose significant computational challenges. Cluster expansion is a technique that can accelerate the evaluation of protein energies by generating a simple functional relationship between sequence and energy. The method consists of several steps. First, for a given protein structure, a training set of sequences with known energies is generated. Next, this training set is used to expand energy as a function of clusters consisting of single residues, residue pairs, and higher order terms, if required. The accuracy of the sequence‐based expansion is monitored and improved using cross‐validation testing and iterative inclusion of additional clusters. As a trade‐off for evaluation speed, the cluster‐expansion approximation causes prediction errors, which can be reduced by including more training sequences, including higher order terms in the expansion, and/or reducing the sequence space described by thecluster expansion. This article analyzes the sources of error and introduces a method whereby accuracy can be improved by judiciously reducing the described sequence space. The method is applied to describe the sequence–stability relationship for several protein structures: coiled‐coil dimers and trimers, a PDZ domain, and T4 lysozyme as examples with computationally derived energies, and SH3 domains in amphiphysin‐1 and endophilin‐1 as examples where the expanded pseudo‐energies are obtained from experiments. Our open‐source software package Cluster Expansion Version 1.0 allows users to expand their own energy function of interest and thereby apply cluster expansion to custom problems in protein design. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Backbone building from quadrilaterals: a fast and accurate algorithm for protein backbone reconstruction from alpha carbon coordinates

In this contribution, we present an algorithm for protein backbone reconstruction that comprises very high computational efficiency with high accuracy. Reconstruction of the main chain atomic coordinates from the alpha carbon trace is a common task in protein modeling, including de novo structure prediction, comparative modeling, and processing experimental data. The method employed in this work follows the main idea of some earlier approaches to the problem. The details and careful design of the present approach are new and lead to the algorithm that outperforms all commonly used earlier applications. BBQ (Backbone Building from Quadrilaterals) program has been extensively tested both on native structures as well as on near-native decoy models and compared with the different available existing methods. Obtained results provide a comprehensive benchmark of existing tools and evaluate their applicability to a large scale modeling using a reduced representation of protein conformational space. The BBQ package is available for downloading from our website at http://biocomp.chem.uw.edu.pl/services/BBQ/. This webpage also provides a user manual that describes BBQ functions in detail.     

ProteinUnet—An efficient alternative to SPIDER3‐single for sequence‐based prediction of protein secondary structures

Predicting protein function and structure from sequence remains an unsolved problem in bioinformatics. The best performing methods rely heavily on evolutionary information from multiple sequence alignments, which means their accuracy deteriorates for sequences with a few homologs, and given the increasing sequence database sizes requires long computation times. Here, a single‐sequence‐based prediction method is presented, called ProteinUnet, leveraging an U‐Net convolutional network architecture. It is compared to SPIDER3‐Single model, based on long short‐term memory‐bidirectional recurrent neural networks architecture. Both methods achieve similar results for prediction of secondary structures (both three‐ and eight‐state), half‐sphere exposure, and contact number, but ProteinUnet has two times fewer parameters, 17 times shorter inference time, and can be trained 11 times faster. Moreover, ProteinUnet tends to be better for short sequences and residues with a low number of local contacts. Additionally, the method of loss weighting is presented as an effective way of increasing accuracy for rare secondary structures.     

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.     

Structure‐based redesign of proteins for minimal T‐cell epitope content

The protein universe displays a wealth of therapeutically relevant activities, but T‐cell driven immune responses to non‐“self” biological agents present a major impediment to harnessing the full diversity of these molecular functions. Mutagenic T‐cell epitope deletion seeks to mitigate the immune response, but can typically address only a small number of epitopes. Here, we pursue a “bottom‐up” approach that redesigns an entire protein to remain native‐like but contain few if any immunogenic epitopes. We do so by extending the Rosetta flexible‐backbone protein design software with an epitope scoring mechanism and appropriate constraints. The method is benchmarked with a diverse panel of proteins and applied to three targets of therapeutic interest. We show that the deimmunized designs indeed have minimal predicted epitope content and are native‐like in terms of various quality measures, and moreover that they display levels of native sequence recovery comparable to those of non‐deimmunized designs. © 2013 Wiley Periodicals, Inc.     

GRID: A high‐resolution protein structure refinement algorithm

The energy‐based refinement of protein structures generated by fold prediction algorithms to atomic‐level accuracy remains a major challenge in structural biology. Energy‐based refinement is mainly dependent on two components: (1) sufficiently accurate force fields, and (2) efficient conformational space search algorithms. Focusing on the latter, we developed a high‐resolution refinement algorithm called GRID. It takes a three‐dimensional protein structure as input and, using an all‐atom force field, attempts to improve the energy of the structure by systematically perturbing backbone dihedrals and side‐chain rotamer conformations. We compare GRID to Backrub, a stochastic algorithm that has been shown to predict a significant fraction of the conformational changes that occur with point mutations. We applied GRID and Backrub to 10 high‐resolution (≤ 2.8 Å) crystal structures from the Protein Data Bank and measured the energy improvements obtained and the computation times required to achieve them. GRID resulted in energy improvements that were significantly better than those attained by Backrub while expending about the same amount of computational resources. GRID resulted in relaxed structures that had slightly higher backbone RMSDs compared to Backrub relative to the starting crystal structures. The average RMSD was 0.25 ± 0.02 Å for GRID versus 0.14 ± 0.04 Å for Backrub. These relatively minor deviations indicate that both algorithms generate structures that retain their original topologies, as expected given the nature of the algorithms. © 2012 Wiley Periodicals, Inc.     

Flexible protein‐protein docking based on Best‐First search algorithm

We developed a new high resolution protein‐protein docking method based on Best‐First search algorithm that loosely imitates protein‐protein associations. The method operates in two stages: first, we perform a rigid search on the unbound proteins. Second, we search alternately on rigid and flexible degrees of freedom starting from multiple configurations from the rigid search. Both stages use heuristics added to the energy function, which causes the proteins to rapidly approach each other and remain adjacent, while optimizing on the energy. The method deals with backbone flexibility explicitly by searching over ensembles of conformations generated before docking. We ran the rigid docking stage on 66 complexes and grouped the results into four classes according to evaluation criteria used in Critical Assessment of Predicted Interactions (CAPRI; “high,” “medium,” “acceptable,” and “incorrect”). Our method found medium binding conformations for 26% of the complexes and acceptable for additional 44% among the top 10 configurations. Considering all the configurations, we found medium binding conformations for 55% of the complexes and acceptable for additional 39% of the complexes. Introducing side‐chains flexibility in the second stage improves the best found binding conformation but harms the ranking. However, introducing side‐chains and backbone flexibility improve both the best found binding conformation and the best found conformation in the top 10. Our approach is a basis for incorporating multiple flexible motions into protein‐protein docking and is of interest even with the current use of a simple energy function. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

A homology/ab initio hybrid algorithm for sampling near‐native protein conformations

One of the major challenges for protein tertiary structure prediction strategies is the quality of conformational sampling algorithms, which can effectively and readily search the protein fold space to generate near‐native conformations. In an effort to advance the field by making the best use of available homology as well as fold recognition approaches along with ab initio folding methods, we have developed Bhageerath‐H Strgen, a homology/ab initio hybrid algorithm for protein conformational sampling. The methodology is tested on the benchmark CASP9 dataset of 116 targets. In 93% of the cases, a structure with TM‐score ≥ 0.5 is generated in the pool of decoys. Further, the performance of Bhageerath‐H Strgen was seen to be efficient in comparison with different decoy generation methods. The algorithm is web enabled as Bhageerath‐H Strgen web tool which is made freely accessible for protein decoy generation ( http://www.scfbio‐iitd.res.in/software/Bhageerath‐HStrgen1.jsp ). © 2013 Wiley Periodicals, Inc.     

New energy terms for reduced protein models implemented in an off‐lattice force field

Parameterization and test calculations of a reduced protein model with new energy terms are presented. The new energy terms retain the steric properties and the most significant degrees of freedom of protein side chains in an efficient way using only one to three virtual atoms per amino acid residue. The energy terms are implemented in a force field containing predefined secondary structure elements as constraints, electrostatic interaction terms, and a solvent‐accessible surface area term to include the effect of solvation. In the force field the main‐chain peptide units are modeled as electric dipoles, which have constant directions in α‐helices and β‐sheets and variable conformation‐dependent directions in loops. Protein secondary structures can be readily modeled using these dipole terms. Parameters of the force field were derived using a large set of experimental protein structures and refined by minimizing RMS errors between the experimental structures and structures generated using molecular dynamics simulations. The final average RMS error was 3.7 Å for the main‐chain virtual atoms (C_α atoms) and 4.2 Å for all virtual atoms for a test set of 10 proteins with 58–294 amino acid residues. The force field was further tested with a substantially larger test set of 608 proteins yielding somewhat lower accuracy. The fold recognition capabilities of the force field were also evaluated using a set of 27,814 misfolded decoy structures. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1229–1242, 2001     

Local protein backbone folds determined by calculated NMR chemical shifts

NMR chemical shifts (CSs: δN(NH), δC(α), δC(β), δC', δH(NH), and δH(α)) were computed for the amino acid backbone conformers (α(L), β(L), γ(L), δ(L), ε(L), α(D), γ(D), δ(D), and ε(D) [Perczel et al., J Am Chem Soc 1991, 113, 6256]) modeled by oligoalanine structures. Topological differences of the extended fold were investigated on single β-strands, hairpins with type I and II β-turns, as well as double- and triple-stranded β-sheet models. The so-called "capping effect" was analyzed: residues at the termini of a homoconformer sequence unit usually have different CSs than the central residues of an adequately long homoconformer model. In heteroconformer sequences capping effect ruins the direct applicability of several chemical shift types (δH(NH), δC', and δN(NH)) for backbone structure determination of the parent residue. Experimental δH(α), δC(α), and δC(β) values retrieved from protein database are in good agreement with the relevant computed data in the case of the common backbone conformers (α(L), β(L), γ(L), and ε(L)), even though neighboring residue effects were not accounted for. Experimental and computed ΔδH(α)-ΔδC(α), ΔδH(α)-ΔδC(β), and ΔδC(α)-ΔδC(β) maps give qualitatively the same picture, that is, the positions of the backbone conformers relative to each other are very similar. This indicates that the H(α), C(α), and C(β) chemical shifts of alanine depend considerably on the backbone fold of the parent residue also in proteins. We provide tabulated CSs of the chiral amino acids that may predict the various structures of the residues.     

Fast and accurate methods for predicting short-range constraints in protein models

Protein modeling tools utilize many kinds of structural information that may be predicted from amino acid sequence of a target protein or obtained from experiments. Such data provide geometrical constraints in a modeling process. The main aim is to generate the best possible consensus structure. The quality of models strictly depends on the imposed conditions. In this work we present an algorithm, which predicts short-range distances between Cα atoms as well as a set of short structural fragments that possibly share structural similarity with a query sequence. The only input of the method is a query sequence profile. The algorithm searches for short protein fragments with high sequence similarity. As a result a statistics of distances observed in the similar fragments is returned. The method can be used also as a scoring function or a short-range knowledge-based potential based on the computed statistics.     

Controlled Expansion of a Strong‐Field Iron Nitride Cluster: Multi‐Site Ligand Substitution as a Strategy for Activating Interstitial Nitride Nucleophilicity

Multimetallic clusters have long been investigated as molecular surrogates for reactive sites on metal surfaces. In the case of the μ₄‐nitrido cluster [Fe₄(μ₄‐N)(CO)₁₂]^?, this analogy is limited owing to the electron‐withdrawing effect of carbonyl ligands on the iron nitride core. Described here is the synthesis and reactivity of [Fe₄(μ₄‐N)(CO)₈(CNAr^Mes2)₄]^?, an electron‐rich analogue of [Fe₄(μ₄‐N)(CO)₁₂]^?, where the interstitial nitride displays significant nucleophilicity. This characteristic enables rational expansion with main‐group and transition‐metal centers to yield unsaturated sites. The resulting clusters display surface‐like reactivity through coordination‐sphere‐dependent atom rearrangement and metal–metal cooperativity.     

CABS‐NMR—De novo tool for rapid global fold determination from chemical shifts,residual dipolar couplings and sparse methyl‐methyl noes

Recent development of nuclear magnetic resonance (NMR) techniques provided new types of structural restraints that can be successfully used in fast and low‐cost global protein fold determination. Here, we present CABS‐NMR, an efficient protein modeling tool, which takes advantage of such structural restraints. The restraints are converted from original NMR data to fit the coarse grained protein representation of the C‐Alpha‐Beta‐Side‐group (CABS) algorithm. CABS is a Monte Carlo search algorithm that uses a knowledge‐based force field. Its versatile structure enables a variety of protein‐modeling protocols, including purely de novo folding, folding guided by restraints derived from template structures or, structure assembly based on experimental data. In particular, CABS‐NMR uses the distance and angular restraints set derived from various NMR experiments. This new modeling technique was successfully tested in structure determination of 10 globular proteins of size up to 216 residues, for which sparse NMR data were available. Additional detailed analysis was performed for a S100A1 protein. Namely, we successfully predicted Nuclear Overhauser Effect signals on the basis of low‐energy structures obtained from chemical shifts by CABS‐NMR. It has been observed that utility of chemical shifts and other types of experimental data (i.e. residual dipolar couplings and methyl‐methyl Nuclear Overhauser Effect signals) in the presented modeling pipeline depends mainly on size of a protein and complexity of its topology. In this work, we have provided tools for either post‐experiment processing of various kinds of NMR data or fast and low‐cost structural analysis in the still challenging field of new fold predictions. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

Thermal expansion coefficient and bulk modulus of polyethylene closed‐cell foams

A regular Kelvin foam model was used to predict the linear thermal expansion coefficient and bulk modulus of crosslinked, closed‐cell, low‐density polyethylene (LDPE) foams from the polymer and gas properties. The materials used for the experimental measurements were crosslinked, had a uniform cell size, and were nearly isotropic. Young's modulus of biaxially oriented polyethylene was used for modeling the cell faces. The model underestimated the foam linear thermal expansion coefficient because it assumed that the cell faces were flat. However, scanning electron microscopy showed that some cell faces were crumpled as a result of foam processing. The measured bulk modulus, which was considerably smaller than the theoretical value, was used to estimate the linear thermal expansion coefficient of the LDPE foams. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3741–3749, 2004     

Structural informatics,modeling, and design with an open‐source Molecular Software Library (MSL)

We present the Molecular Software Library (MSL), a C++ library for molecular modeling. MSL is a set of tools that supports a large variety of algorithms for the design, modeling, and analysis of macromolecules. Among the main features supported by the library are methods for applying geometric transformations and alignments, the implementation of a rich set of energy functions, side chain optimization, backbone manipulation, calculation of solvent accessible surface area, and other tools. MSL has a number of unique features, such as the ability of storing alternative atomic coordinates (for modeling) and multiple amino acid identities at the same backbone position (for design). It has a straightforward mechanism for extending its energy functions and can work with any type of molecules. Although the code base is large, MSL was created with ease of developing in mind. It allows the rapid implementation of simple tasks while fully supporting the creation of complex applications. Some of the potentialities of the software are demonstrated here with examples that show how to program complex and essential modeling tasks with few lines of code. MSL is an ongoing and evolving project, with new features and improvements being introduced regularly, but it is mature and suitable for production and has been used in numerous protein modeling and design projects. MSL is open‐source software, freely downloadable at http://msl‐libraries.org . We propose it as a common platform for the development of new molecular algorithms and to promote the distribution, sharing, and reutilization of computational methods. © 2012 Wiley Periodicals, Inc.     

SSThread: Template‐free protein structure prediction by threading pairs of contacting secondary structures followed by assembly of overlapping pairs

Acquiring the three‐dimensional structure of a protein from its amino acid sequence alone, despite a great deal of work and significant progress on the subject, is still an unsolved problem. SSThread, a new template‐free algorithm is described here that consists of making several predictions of contacting pairs of α‐helices and β‐strands derived from a database of experimental structures using a knowledge‐based potential, secondary structure prediction, and contact map prediction followed by assembly of overlapping pair predictions to create an ensemble of core structure predictions whose loops are then predicted. In a set of seven CASP10 targets SSThread outperformed the two leading methods for two targets each. The targets were all β‐strand containing structures and most of them have a high relative contact order which demonstrates the advantages of SSThread. The primary bottlenecks based on sets of 74 and 21 test cases are the pair prediction and loop prediction stages. © 2014 Wiley Periodicals, Inc.     

High Accuracy of Karplus Equations for Relating Three‐Bond J Couplings to Protein Backbone Torsion Angles

³J_C′C′ and ³J_HNHα couplings are related to the intervening backbone torsion angle ${\varphi }$ by standard Karplus equations. Although these couplings are known to be affected by parameters other than ${\varphi }$ , including H‐bonding, valence angles and residue type, experimental results and quantum calculations indicate that the impact of these latter parameters is typically very small. The solution NMR structure of protein GB3, newly refined by using extensive sets of residual dipolar couplings, yields 50–60 % better Karplus equation agreement between ${\varphi }$ angles and experimental ³J_C′C′ and ³J_HNHα values than does the high‐resolution X‐ray structure. In intrinsically disordered proteins, ³J_C′C′ and ³J_HNHα couplings can be measured at even higher accuracy, and the impact of factors other than the intervening torsion angle on ³J will be smaller than in folded proteins, making these couplings exceptionally valuable reporters on the ensemble of ${\varphi }$ angles sampled by each residue.