Backbone-dependent Rotamer Library Research Articles

PocketOptimizer 2.0: A modular framework for computer-aided ligand-binding design.

The ability to design customized proteins to perform specific tasks is of great interest. We are particularly interested in the design of sensitive and specific small molecule ligand-binding proteins for biotechnological or biomedical applications. Computational methods can narrow down the immense combinatorial space to find the best solution and thus provide starting points for experimental procedures. However, success rates strongly depend on accurate modeling and energetic evaluation. Not only intra- but also intermolecular interactions have to be considered. To address this problem, we developed PocketOptimizer, a modular computational protein design pipeline, that predicts mutations in the binding pockets of proteins to increase affinity for a specific ligand. Its modularity enables users to compare different combinations of force fields, rotamer libraries, and scoring functions. Here, we present a much-improved version--PocketOptimizer 2.0. We implemented a cleaner user interface, an extended architecture with more supported tools, such as force fields and scoring functions, a backbone-dependent rotamer library, as well as different improvements in the underlying algorithms. Version 2.0 was tested against a benchmark of design cases and assessed in comparison to the first version. Our results show how newly implemented features such as the new rotamer library can lead to improved prediction accuracy. Therefore, we believe that PocketOptimizer 2.0, with its many new and improved functionalities, provides a robust and versatile environment for the design of small molecule-binding pockets in proteins. It is widely applicable and extendible due to its modular framework. PocketOptimizer 2.0 can be downloaded at https://github.com/Hoecker-Lab/pocketoptimizer.

A backbone-dependent rotamer library with high (ϕ, ψ) coverage using metadynamics simulations.

Backbone-dependent rotamer libraries are commonly used to assign the side chain dihedral angles of amino acids when modeling protein structures. Most rotamer libraries are created by curating protein crystal structure data and using various methods to extrapolate the existing data to cover all possible backbone conformations. However, these rotamer libraries may not be suitable for modeling the structures of cyclic peptides and other constrained peptides because these molecules frequently sample backbone conformations rarely seen in the crystal structures of linear proteins. To provide backbone-dependent side chain information beyond the α-helix, β-sheet, and PPII regions, we used explicit-solvent metadynamics simulations of model dipeptides to create a new rotamer library that has high coverage in the (ϕ, ψ) space. Furthermore, this approach can be applied to build high-coverage rotamer libraries for noncanonical amino acids. The resulting Metadynamics of Dipeptides for Rotamer Distribution (MEDFORD) rotamer library predicts the side chain conformations of high-resolution protein crystal structures with similar accuracy (~80%) to a state-of-the-art rotamer library. Our ability to test the accuracy of MEDFORD at predicting the side chain dihedral angles of amino acids in noncanonical backbone conformation is restricted by the limited structural data available for cyclic peptides. For the cyclic peptide data that are currently available, MEDFORD and the state-of-the-art rotamer library perform comparably. However, the two rotamer libraries indeed make different rotamer predictions in noncanonical (ϕ, ψ) regions. For noncanonical amino acids, the MEDFORD rotamer library predicts the χ1 values with approximately 75% accuracy.

Cost-Effective Potential for Accurate Polarizable Embedding Calculations in Protein Environments.

The fragment-based polarizable embedding (PE) model combined with an appropriate electronic structure method constitutes a highly efficient and accurate multiscale approach for computing spectroscopic properties of a central moiety including effects from its molecular environment through an embedding potential. There is, however, a comparatively high computational overhead associated with the computation of the embedding potential, which is derived from first-principles calculations on individual fragments of the environment. To reduce the computational cost associated with the calculation of embedding potential parameters, we developed a set of amino acid-specific transferable parameters tailored for large-scale PE-based calculations that include proteins. The amino acid-based parameters are obtained by simultaneously fitting to a set of reference electric potentials based on structures derived from a backbone-dependent rotamer library. The developed cost-effective polarizable protein potential (CP3) consists of atom-centered charges and isotropic dipole-dipole polarizabilities of the standard amino acids. In terms of reproduction of electric potentials, the CP3 is shown to perform consistently and with acceptable accuracy across both small tripeptide test systems and larger proteins. We show, through applications on realistic protein systems, that acceptable accuracy can be obtained by using a pure CP3 representation of the protein environment, thus altogether omitting the cost associated with the calculation of embedding potential parameters. High accuracy comparable to that of the full fragment-based approach can be achieved through a mixed description where the CP3 is used only to describe amino acids beyond a threshold distance from the central quantum part.

Toward the Accuracy and Speed of Protein Side-Chain Packing: ASystematic Study on Rotamer Libraries.

Protein rotamers refer to the conformational isomers taken by the side-chains of amino acids to accommodate specific structural folding environments. Since accurate modeling of atomic interactions is difficult, rotamer information collected from experimentally solved protein structures is often used to guide side-chain packing in protein folding and sequence design studies. Many rotamer libraries have been built in the literature but there is little quantitative guidance on which libraries should be chosen for different structural modeling studies. Here, we performed a comparative study of six widely used rotamer libraries and systematically examined their suitability for protein folding and sequence design in four aspects: (1) side-chain match accuracy, (2) side-chain conformation prediction, (3) de novo protein sequence design, and (4) computational time cost. We demonstrated that, compared to the backbone-dependent rotamer libraries (BBDRLs), the backbone-independent rotamer libraries (BBIRLs) generated conformations that more closely matched the native conformations due to the larger number of rotamers in the local rotamer search spaces. However, more practically, using an optimized physical energy function incorporated into a simulated annealing Monte Carlo searching scheme, we showed that utilization of the BBDRLs could result in higher accuracies in side-chain prediction and higher sequence recapitulation rates in protein design experiments. Detailed data analyses showed that the major advantage of BBDRLs lies in the energy term derived from the rotamer probabilities that are associated with the individual backbone torsion angle subspaces. This term is important for distinguishing between amino acid identities as well as the rotamer conformations of an amino acid. Meanwhile, the backbone torsion angle subspace-specific rotamer search drastically speeds up the searching time, despite the significantly larger number of total rotamers in the BBDRLs. These results should provide important guidance for the development and selection of rotamer libraries for practical protein design and structure prediction studies.

Antibody side chain conformations are position-dependent.

Side chain prediction is an integral component of computational antibody design and structure prediction. Current antibody modelling tools use backbone-dependent rotamer libraries with conformations taken from general proteins. Here we present our antibody-specific rotamer library, where rotamers are binned according to their immunogenetics (IMGT) position, rather than their local backbone geometry. We find that for some amino acid types at certain positions, only a restricted number of side chain conformations are ever observed. Using this information, we are able to reduce the breadth of the rotamer sampling space. Based on our rotamer library, we built a side chain predictor, position-dependent antibody rotamer swapper (PEARS). On a blind test set of 95 antibody model structures, PEARS had the highest average χ1 and χ1+2 accuracy (78.7% and 64.8%) compared to three leading backbone-dependent side chain predictors. Our use of IMGT position, rather than backbone ϕ/ψ, meant that PEARS was more robust to errors in the backbone of the model structure. PEARS also achieved the lowest number of side chain-side chain clashes. PEARS is freely available as a web application at http://opig.stats.ox.ac.uk/webapps/pears.

Assessing the capability of in silico mutation protocols for predicting the finite temperature conformation of amino acids.

Mutation protocols are a key tool in computational biophysics for modelling unknown side chain conformations. In particular, these protocols are used to generate the starting structures for molecular dynamics simulations. The accuracy of the initial side chain and backbone placement is crucial to obtain a stable and quickly converging simulation. In this work, we assessed the performance of several mutation protocols in predicting the most probable conformer observed in finite temperature molecular dynamics simulations for a set of protein-peptide crystals differing only by single-point mutations in the peptide sequence. Our results show that several programs which predict well the crystal conformations fail to predict the most probable finite temperature configuration. Methods relying on backbone-dependent rotamer libraries have, in general, a better performance, but even the best protocol fails in predicting approximately 30% of the mutations.

New Dynamic Rotamer Libraries: Data-Driven Analysis of Side-Chain Conformational Propensities

Most rotamer libraries are generated from subsets of the PDB and do not fully represent the conformational scope of protein side chains. Previous attempts to rectify this sparse coverage of conformational space have involved application of weighting and smoothing functions. We resolve these limitations by using physics-based molecular dynamics simulations to determine more accurate frequencies of rotameric states. This work forms part of our Dynameomics initiative and uses a set of 807 proteins selected to represent 97% of known autonomous protein folds, thereby eliminating the bias toward common topologies found within the PDB. Our Dynameomics derived rotamer libraries encompass 4.8 × 10(9) rotamers, sampled from at least 51,000 occurrences of each of 93,642 residues. Here, we provide a backbone-dependent rotamer library, based on secondary structure ϕ/ψ regions, and an update to our 2011 backbone-independent library that addresses the doubling of our dataset since its original publication.

A rotamer library to enable modeling and design of peptoid foldamers.

Peptoids are a family of synthetic oligomers composed of N-substituted glycine units. Along with other “foldamer” systems, peptoid oligomer sequences can be predictably designed to form a variety of stable secondary structures. It is not yet evident if foldamer design can be extended to reliably create tertiary structure features that mimic more complex biomolecular folds and functions. Computational modeling and prediction of peptoid conformations will likely play a critical role in enabling complex biomimetic designs. We introduce a computational approach to provide accurate conformational and energetic parameters for peptoid side chains needed for successful modeling and design. We find that peptoids can be described by a “rotamer” treatment, similar to that established for proteins, in which the peptoid side chains display rotational isomerism to populate discrete regions of the conformational landscape. Because of the insufficient number of solved peptoid structures, we have calculated the relative energies of side-chain conformational states to provide a backbone-dependent (BBD) rotamer library for a set of 54 different peptoid side chains. We evaluated two rotamer library development methods that employ quantum mechanics (QM) and/or molecular mechanics (MM) energy calculations to identify side-chain rotamers. We show by comparison to experimental peptoid structures that both methods provide an accurate prediction of peptoid side chain placements in folded peptoid oligomers and at protein interfaces. We have incorporated our peptoid rotamer libraries into ROSETTA, a molecular design package previously validated in the context of protein design and structure prediction.

Design of a Rotamer Library for Coarse-Grained Models in Protein-Folding Simulations

Rotamer libraries usually contain geometric information to trace an amino acid side chain, atom by atom, onto a protein backbone. These libraries have been widely used in protein design, structure refinement and prediction, homology modeling, and X-ray and NMR structure validation. However, they usually present too much information and are not always fully compatible with the coarse-grained models of the protein geometry that are frequently used to tackle the protein-folding problem through molecular simulation. In this work, we introduce a new backbone-dependent rotamer library for side chains compatible with low-resolution models in polypeptide chains. We have dispensed with an atomic description of proteins, representing each amino acid side chain by its geometric center (or centroid). The resulting rotamers have been estimated from a statistical analysis of a large structural database consisting of high-resolution X-ray protein structures. As additional information, each rotamer includes the frequency with which it has been found during the statistical analysis. More importantly, the library has been designed with a careful control to ensure that the vast majority of side chains in protein structures (at least 95% of residues) are properly represented. We have tested our library using an independent set of proteins, and our results support a good correlation between the reconstructed centroids from our rotamer library and those in the experimental structures. This new library can serve to improve the definition of side chain centroids in coarse-grained models, avoiding at the same time an excessive additional complexity in a geometric model for the polypeptide chain.

Examination of Mechanism of N-Acetyl-1-d-myo-inosityl-2-amino-2-deoxy-α-d-glucopyranoside Deacetylase (MshB) Reveals Unexpected Role for Dynamic Tyrosine

Actinomycetes are a group of gram-positive bacteria that includes pathogenic mycobacterial species, such as Mycobacterium tuberculosis. These organisms do not have glutathione and instead utilize the small molecule mycothiol (MSH) as their primary reducing agent and for the detoxification of xenobiotics. Due to these important functions, enzymes involved in MSH biosynthesis and MSH-dependent detoxification are targets for drug development. The metal-dependent deacetylase N-acetyl-1-D-myo-inosityl-2-amino-2-deoxy-α-D-glucopyranoside deacetylase (MshB) catalyzes the hydrolysis of N-acetyl-1-D-myo-inosityl-2-amino-2-deoxy-α-D-glucopyranoside to form 1-D-myo-inosityl-2-amino-2-deoxy-α-D-glucopyranoside and acetate in MSH biosynthesis. Herein we examine the chemical mechanism of MshB. We demonstrate that the side chains of Asp-15, Tyr-142, His-144, and Asp-146 are important for catalytic activity. We show that NaF is an uncompetitive inhibitor of MshB, consistent with a metal-water/hydroxide functioning as the reactive nucleophile in the catalytic mechanism. We have previously shown that MshB activity has a bell-shaped dependence on pH with pK(a) values of ∼7.3 and 10.5 (Huang, X., Kocabas, E. and Hernick, M. (2011) J. Biol. Chem. 286, 20275-20282). Mutagenesis experiments indicate that the observed pK(a) values reflect ionization of Asp-15 and Tyr-142, respectively. Together, findings from our studies suggest that MshB functions through a general acid-base pair mechanism with the side chain of Asp-15 functioning as the general base catalyst and His-144 serving as the general acid catalyst, whereas the side chain of Tyr-142 probably assists in polarizing substrate/stabilizing the oxyanion intermediate. Additionally, our results indicate that Tyr-142 is a dynamic side chain that plays key roles in catalysis, modulating substrate binding, chemistry, and product release.

A protein-dependent side-chain rotamer library

BackgroundProtein side-chain packing problem has remained one of the key open problems in bioinformatics. The three main components of protein side-chain prediction methods are a rotamer library, an energy function and a search algorithm. Rotamer libraries summarize the existing knowledge of the experimentally determined structures quantitatively. Depending on how much contextual information is encoded, there are backbone-independent rotamer libraries and backbone-dependent rotamer libraries. Backbone-independent libraries only encode sequential information, whereas backbone-dependent libraries encode both sequential and locally structural information. However, side-chain conformations are determined by spatially local information, rather than sequentially local information. Since in the side-chain prediction problem, the backbone structure is given, spatially local information should ideally be encoded into the rotamer libraries.MethodsIn this paper, we propose a new type of backbone-dependent rotamer library, which encodes structural information of all the spatially neighboring residues. We call it protein-dependent rotamer libraries. Given any rotamer library and a protein backbone structure, we first model the protein structure as a Markov random field. Then the marginal distributions are estimated by the inference algorithms, without doing global optimization or search. The rotamers from the given library are then re-ranked and associated with the updated probabilities.ResultsExperimental results demonstrate that the proposed protein-dependent libraries significantly outperform the widely used backbone-dependent libraries in terms of the side-chain prediction accuracy and the rotamer ranking ability. Furthermore, without global optimization/search, the side-chain prediction power of the protein-dependent library is still comparable to the global-search-based side-chain prediction methods.

SIDEpro: A novel machine learning approach for the fast and accurate prediction of side‐chain conformations

Accurate protein side-chain conformation prediction is crucial for protein modeling and existing methods for the task are widely used; however, faster and more accurate methods are still required. Here we present a new machine learning approach to the problem where an energy function for each rotamer in a structure is computed additively over pairs of contacting atoms. A family of 156 neural networks indexed by amino acid and contacting atom types is used to compute these rotamer energies as a function of atomic contact distances. Although direct energy targets are not available for training, the neural networks can still be optimized by converting the energies to probabilities and optimizing these probabilities using Markov Chain Monte Carlo methods. The resulting predictor SIDEpro makes predictions by initially setting the rotamer probabilities for each residue from a backbone-dependent rotamer library, then iteratively updating these probabilities using the trained neural networks. After convergences of the probabilities, the side-chains are set to the highest probability rotamer. Finally, a post processing clash reduction step is applied to the models. SIDEpro represents a significant improvement in speed and a modest, but statistically significant, improvement in accuracy when compared with the state-of-the-art for rapid side-chain prediction method SCWRL4 on the following datasets: (1) 379 protein test set of SCWRL4; (2) 94 proteins from CASP9; (3) a set of seven large protein-only complexes; and (4) a ribosome with and without the RNA. Using the SCWRL4 test set, SIDEpro's accuracy (χ(1) 86.14%, χ(1+2) 74.15%) is slightly better than SCWRL4-FRM (χ(1) 85.43%, χ(1+2) 73.47%) and it is 7.0 times faster. On the same test set SIDEpro is clearly more accurate than SCWRL4-rigid rotamer model (RRM) (χ(1) 84.15%, χ(1+2) 71.24%) and 2.4 times faster. Evaluation on the additional test sets yield similar accuracy results with SIDEpro being slightly more accurate than SCWRL4-flexible rotamer model (FRM) and clearly more accurate than SCWRL4-RRM; however, the gap in CPU time is much more significant when the methods are applied to large protein complexes. SIDEpro is part of the SCRATCH suite of predictors and available from: http://scratch.proteomics.ics.uci.edu/.

A Smoothed Backbone-Dependent Rotamer Library for Proteins Derived from Adaptive Kernel Density Estimates and Regressions

Rotamer libraries are used in protein structure determination, prediction, and design. The backbone-dependent rotamer library consists of rotamer frequencies, mean dihedral angles, and variances asa function of the backbone dihedral angles. Structure prediction and design methods that employ backbone flexibility would strongly benefit from smoothly varying probabilities and angles. A new version of thebackbone-dependent rotamer library has been developed using adaptive kernel density estimates for the rotamer frequencies and adaptive kernel regression for the mean dihedral angles and variances. This formulation allows for evaluation of the rotamer probabilities, mean angles, and variances asa smooth and continuous function of phi and psi. Continuous probability density estimates for the nonrotameric degrees of freedom of amides, carboxylates, and aromatic side chains have been modeled as a function of the backbone dihedrals and rotamers of the remaining degrees of freedom. New backbone-dependent rotamer libraries at varying levels of smoothing are available from http://dunbrack.fccc.edu.

Fleksy: a flexible approach to induced fit docking

Protein receptor rearrangements upon ligand binding are a major complicating factor in structure-based drug design. An accurate prediction of these so-called induced fit phenomena calls for ligand docking and virtual screening approaches capable of considering receptor flexibility. We present Fleksy [1], a flexible approach aimed at accurately positioning small molecule ligands into a protein receptor, while taking both ligand and receptor flexibility into account. Our method consists of an ensemble docking stage in which the ligand of interest is docked into a structural ensemble of receptor conformations, followed by a complex optimization stage during which both ligand and protein are allowed to move. Pivotal to our method is the use of receptor ensembles to describe protein flexibility. To construct these ensembles we use a backbone dependent rotamer library and implement the concept of interaction sampling. The latter allows for the evaluation of different orientations and, when relevant, different tautomers of ambivalent interaction partners in the binding site such as asparagine, glutamine and histidine side chains. The docking stage comprises an ensemble-based soft-docking experiment using FlexX-Ensemble [2], followed by an effective flexible receptor-ligand complex optimization using Yasara [3]. Ultimately Fleksy results in a set of receptor-ligand complexes ranked using a consensus scoring function which combines both docking scores and force field energies. Figure ​Figure11. Figure 1 Averaged over three cross-docking datasets, in total containing 35 different pharmaceutically relevant receptor-ligand complexes, Fleksy reproduces the observed binding mode within 2.0 A for 78% of the complexes. This compares favorably to the rigid receptor FlexX program [4] which on average reaches a success rate of 44% for these datasets.

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.

The Crystal Structure of Progesterone 5β-Reductase from Digitalis lanata Defines a Novel Class of Short Chain Dehydrogenases/Reductases

Progesterone 5beta-reductase (5beta-POR) catalyzes the stereospecific reduction of progesterone to 5beta-pregnane-3,20-dione and is a key enzyme in the biosynthetic pathway of cardenolides in Digitalis (foxglove) plants. Sequence considerations suggested that 5beta-POR is a member of the short chain dehydrogenase/reductase (SDR) family of proteins but at the same time revealed that the sequence motifs that in standard SDRs contain the catalytically important residues are missing. Here we present crystal structures of 5beta-POR from Digitalis lanata in complex with NADP(+) at 2.3A and without cofactor bound at 2.4A resolution together with a model of a ternary complex consisting of 5beta-POR, NADP(+), and progesterone. Indeed, 5beta-POR displays the fold of an extended SDR. The architecture of the active site is, however, unprecedented because none of the standard catalytic residues are structurally conserved. A tyrosine (Tyr-179) and a lysine residue (Lys-147) are present in the active site, but they are displayed from novel positions and are part of novel sequence motifs. Mutating Tyr-179 to either alanine or phenylalanine completely abolishes the enzymatic activity. We propose that the distinct topology reflects the fact that 5beta-POR reduces a conjugated double bond in a steroid substrate via a 1-4 addition mechanism and that this requires a repositioning of the catalytically important residues. Our observation that the sequence motifs that line the active site are conserved in a number of bacterial and plant enzymes of yet unknown function leads us to the proposition that 5beta-POR defines a novel class of SDRs.

A Flexible Approach to Induced Fit Docking

We present Fleksy, a new approach to consider both ligand and receptor flexibility in small molecule docking. Pivotal to our method is the use of a receptor ensemble to describe protein flexibility. To construct these ensembles, we use a backbone-dependent rotamer library and implement the concept of interaction sampling. The latter allows the evaluation of different orientations of ambivalent interaction partners. The docking stage consists of an ensemble-based soft-docking experiment using FlexX-Ensemble, followed by an effective flexible receptor-ligand complex optimization using Yasara. Fleksy produces a set of receptor-ligand complexes ranked using a consensus scoring function combining docking scores and force field energies. Averaged over three cross-docking datasets, containing 35 different receptor-ligand complexes in total, Fleksy reproduces the observed binding mode within 2.0 A for 78% of the complexes. This compares favorably to the rigid receptor FlexX program, which on average reaches a success rate of 44% for these datasets.

The N-Acetyl-D-glucosaminylphosphatidylinositol De-N-acetylase of Glycosylphosphatidylinositol Biosynthesis Is a Zinc Metalloenzyme

The de-N-acetylation of N-acetyl-D-glucosaminylphosphatidylinositol (GlcNAc-PI) is the second step of mammalian and trypanosomal glycosylphosphatidylinositol biosynthesis. Glycosylphosphatidylinositol biosynthesis is essential for Trypanosoma brucei, the causative agent of African sleeping sickness, and GlcNAc-PI de-N-acetylase has previously been validated as a drug target. Inhibition of the trypanosome cell-free system and recombinant rat GlcNAc-PI de-N-acetylase by divalent metal cation chelators demonstrates that a tightly bound divalent metal cation is essential for activity. Reconstitution of metal-free GlcNAc-PI de-N-acetylase with divalent metal cations restores activity in the order Zn(2+) > Cu(2+) > Ni(2+) > Co(2+) > Mg(2+). Site-directed mutagenesis and homology modeling were used to identify active site residues and postulate a mechanism of action. The characterization of GlcNAc-PI de-N-acetylase as a zinc metalloenzyme will facilitate the rational design of anti-protozoan parasite drugs.

A graph-theory algorithm for rapid protein side-chain prediction.

Fast and accurate side-chain conformation prediction is important for homology modeling, ab initio protein structure prediction, and protein design applications. Many methods have been presented, although only a few computer programs are publicly available. The SCWRL program is one such method and is widely used because of its speed, accuracy, and ease of use. A new algorithm for SCWRL is presented that uses results from graph theory to solve the combinatorial problem encountered in the side-chain prediction problem. In this method, side chains are represented as vertices in an undirected graph. Any two residues that have rotamers with nonzero interaction energies are considered to have an edge in the graph. The resulting graph can be partitioned into connected subgraphs with no edges between them. These subgraphs can in turn be broken into biconnected components, which are graphs that cannot be disconnected by removal of a single vertex. The combinatorial problem is reduced to finding the minimum energy of these small biconnected components and combining the results to identify the global minimum energy conformation. This algorithm is able to complete predictions on a set of 180 proteins with 34342 side chains in <7 min of computer time. The total chi(1) and chi(1 + 2) dihedral angle accuracies are 82.6% and 73.7% using a simple energy function based on the backbone-dependent rotamer library and a linear repulsive steric energy. The new algorithm will allow for use of SCWRL in more demanding applications such as sequence design and ab initio structure prediction, as well addition of a more complex energy function and conformational flexibility, leading to increased accuracy.

The stability of transmembrane helices: A molecular dynamics study on the isolated helices of bacteriorhodopsin

Bacteriorhodopsin (bR) continues to be a proven testing ground for the study of integral membrane proteins (IMPs). It is important to study the stability of the individual helices of bR, as they are postulated to exist as independently stable transmembrane helices (TMHs) and also for their utility as templates for modeling other IMPs with the postulated seven-helix bundle topology. Toward this purpose, the seven helices of bR have been studied by molecular dynamics simulation in this study. The suitability of using the backbone-dependent rotamer library of side-chain conformations arrived at from the data base of globular protein structures in the case TMHs has been tested by another set of 7 helix simulations with the side-chain orientations taken from this library. The influence of the residue's net charge on the helix stability was examined by simulating the helices III, IV, and VI (from both of the above sets of helices) with zero net charge on the side chains. The results of these 20 simulations demonstrate in general the stability of the isolated helices of bR in conformity with the two-stage hypothesis of IMP folding. However, the helices I, II, V, and VII are more stable than the other three helices. The helical nature of certain regions of III, IV, and VI are influenced by factors such as the net charge and orientation of several residues. It is seen that the residues Arg, Lys, Asp, and Glu (charged residues), and Ser, Thr, Gly, and Pro, play a crucial role in the stability of the helices of bR. The backbone-dependent rotamer library for the side chains is found to be suitable for the study of TMHs in IMP.