All‐atom chain‐building by optimizing MODELLER energy function using conformational space annealing

We have investigated the effect of rigorous optimization of the MODELLER energy function for possible improvement in protein all‐atom chain‐building. For this we applied the global optimization method called conformational space annealing (CSA) to the standard MODELLER procedure to achieve better energy optimization than what MODELLER provides. The method, which we call MODELLERCSA , is tested on two benchmark sets. The first is the 298 proteins taken from the HOMSTRAD multiple alignment set. By simply optimizing the MODELLER energy function, we observe significant improvement in side‐chain modeling, where MODELLERCSA provides about 10.7% (14.5%) improvement for χ₁ (χ₁ + χ₂) accuracy compared to the standard MODELLER modeling. The improvement of backbone accuracy by MODELLERCSA is shown to be less prominent, and a similar improvement can be achieved by simply generating many standard MODELLER models and selecting lowest energy models. However, the level of side‐chain modeling accuracy by MODELLERCSA could not be matched either by extensive MODELLER strategies, side‐chain remodeling by SCWRL3, or copying unmutated rotamers. The identical procedure was successfully applied to 100 CASP7 template base modeling domains during the prediction season in a blind fashion, and the results are included here for comparison. From this study, we observe a good correlation between the MODELLER energy and the side‐chain accuracy. Our findings indicate that, when a good alignment between a target protein and its templates is provided, thorough optimization of the MODELLER energy function leads to accurate all‐atom models. Proteins 2009. © 2008 Wiley‐Liss, Inc.     

Prediction of the folding of short polypeptide segments by uniform conformational sampling

A procedure, CONGEN, for uniformly sampling the conformational spaceof short polypeptide segments in proteins has been implemented. Because thetime required for this sampling grows exponentially with the number of residues, parameters are introduced to limit the conformational space that has to be explored. This is done by the use of the empirical energy function ofCHARMM [B. R. Brooks, R. E. Bruccoleri, B. D. Olafson, D. J. States, S. Swaminathan and M. Karplus (1983) J. Comput. Chem. 4 , 187-217] and truncating the search when conformations of grossly unfavorable energy are sampled. Tests are made to determine control parameters that optimize the search without excluding important configurations. When applied to known protein structures, the resulting procedure is generally capable of generating conformations where the lowest energy conformation matches the known structure within a rms deviation of 1 Å.     

Building proteins from C alpha coordinates using the dihedral probability grid Monte Carlo method.

Dihedral probability grid Monte Carlo (DPG-MC) is a general-purpose method of conformational sampling that can be applied to many problems in peptide and protein modeling. Here we present the DPG-MC method and apply it to predicting complete protein structures from C alpha coordinates. This is useful in such endeavors as homology modeling, protein structure prediction from lattice simulations, or fitting protein structures to X-ray crystallographic data. It also serves as an example of how DPG-MC can be applied to systems with geometric constraints. The conformational propensities for individual residues are used to guide conformational searches as the protein is built from the amino-terminus to the carboxyl-terminus. Results for a number of proteins show that both the backbone and side chain can be accurately modeled using DPG-MC. Backbone atoms are generally predicted with RMS errors of about 0.5 A (compared to X-ray crystal structure coordinates) and all atoms are predicted to an RMS error of 1.7 A or better.     

Conformational States of the Water-Soluble Fragment of Cytochrome b5. I. pH-Induced Denaturation

Cytochrome b ₅ is a membrane protein that comprises two fragments: one is water-soluble and heme-containing, and the other is hydrophobic and membrane-embedded. The function of electron transfer is performed by the former whose crystal structure is known; however, its conformational states when in the membrane field and interacting with other proteins are still to be studied. Previously, we proposed water–alcohol mixtures for modeling the effect of membrane surface on proteins, and used this approach to study the conformational behavior of positively charged cytochrome c as well as relatively neutral retinol-binding protein also functioning in the field of a negatively charged membrane. The current study describes the conformational behavior of the negatively charged water-soluble fragment of cytochrome b ₅ as dependent on pH. Decreasing pH was shown to transform the fragment state from native to intermediate, similar to the molten globule reported earlier for other proteins in aqueous solutions: at pH 3.0, the fragment preserved a pronounced secondary structure and compactness but lost its rigid tertiary structure. A possible role of this intermediate state in cytochrome b ₅ functioning is discussed.     

Homology modeling in a dynamical world

A key concept in template‐based modeling (TBM) is the high correlation between sequence and structural divergence, with the practical consequence that homologous proteins that are similar at the sequence level will also be similar at the structural level. However, conformational diversity of the native state will reduce the correlation between structural and sequence divergence, because structural variation can appear without sequence diversity. In this work, we explore the impact that conformational diversity has on the relationship between structural and sequence divergence. We find that the extent of conformational diversity can be as high as the maximum structural divergence among families. Also, as expected, conformational diversity impairs the well‐established correlation between sequence and structural divergence, which is nosier than previously suggested. However, we found that this noise can be resolved using a priori information coming from the structure‐function relationship. We show that protein families with low conformational diversity show a well‐correlated relationship between sequence and structural divergence, which is severely reduced in proteins with larger conformational diversity. This lack of correlation could impair TBM results in highly dynamical proteins. Finally, we also find that the presence of order/disorder can provide useful beforehand information for better TBM performance.     

Bioactive conformations of peptides and mimetics as milestones in drug design: Investigation of NK1 receptor antagonists

Summary Nine potent and selective substance P receptor antagonists (NK₁ ^-) were analyzed with respect to their conformational space, with the aim to suggest probable conformations adopted at the receptor site and superposition rules for each structure (pharmacophore mapping). Key atoms within the ligands as well as receptor site points were considered in order to identify acceptable solutions (DISCO program). The results obtained allowed the suggestion or probable peptidic pharmacophores based on the structure of 1 (FK888). This knowledge was used to search commercial databases. The number and diversity of known retrieved NK₁ antagonists allowed a general evaluation of the proposed pharmacophores. Moreover, a search in our proprietary database detected a short peptide with modest affinity but high selectivity for the NK₁ receptor. The combination of molecular modeling with database searches is useful in a strategy aiming to develop new NK₁ antagonists starting from existing knowledge.     

A hybrid NMR/SAXS‐based approach for discriminating oligomeric protein interfaces using Rosetta

Oligomeric proteins are important targets for structure determination in solution. While in most cases the fold of individual subunits can be determined experimentally, or predicted by homology‐based methods, protein–protein interfaces are challenging to determine de novo using conventional NMR structure determination protocols. Here we focus on a member of the bet‐V1 superfamily, Aha1 from Colwellia psychrerythraea. This family displays a broad range of crystallographic interfaces none of which can be reconciled with the NMR and SAXS data collected for Aha1. Unlike conventional methods relying on a dense network of experimental restraints, the sparse data are used to limit conformational search during optimization of a physically realistic energy function. This work highlights a new approach for studying minor conformational changes due to structural plasticity within a single dimeric interface in solution. Proteins 2015; 83:309–317. © 2014 Wiley Periodicals, Inc.     

Refinement of protein termini in template-based modeling using conformational space annealing

The rapid increase in the number of experimentally determined protein structures in recent years enables us to obtain more reliable protein tertiary structure models than ever by template-based modeling. However, refinement of template-based models beyond the limit available from the best templates is still needed for understanding protein function in atomic detail. In this work, we develop a new method for protein terminus modeling that can be applied to refinement of models with unreliable terminus structures. The energy function for terminus modeling consists of both physics-based and knowledge-based potential terms with carefully optimized relative weights. Effective sampling of both the framework and terminus is performed using the conformational space annealing technique. This method has been tested on a set of termini derived from a nonredundant structure database and two sets of termini from the CASP8 targets. The performance of the terminus modeling method is significantly improved over our previous method that does not employ terminus refinement. It is also comparable or superior to the best server methods tested in CASP8. The success of the current approach suggests that similar strategy may be applied to other types of refinement problems such as loop modeling or secondary structure rearrangement.     

Application of a directed conformational search for generating 3-D coordinates for protein structures from alpha-carbon coordinates.

A directed conformational search algorithm using the program CONGEN (ref. 3), which samples backbone conformers, is described. The search technique uses information from the partially built structures to direct the search process and is tested on the problem of generating a full set of backbone Cartesian coordinates given only alpha-carbon coordinates. The method has been tested on six proteins of known structure, varying in size and classification, and was able to generate the original backbone coordinates with RMSs ranging from 0.30-0.87A for the alpha-carbons and 0.5-0.99A RMSs for the backbone atoms. Cis peptide linkages were also correctly identified. The procedure was also applied to two proteins available with only alpha-carbon coordinates in the Brookhaven Protein Data Bank; thioredoxin (SRX) and triacylglycerol acylhydrolase (TGL). All-atom models are proposed for the backbone of both these proteins. In addition, the technique was applied to randomized coordinates of flavodoxin to assess the effects of irregularities in the data on the final RMS. This study represents the first time a deterministic conformational search was used on such a large scale.     

On the Bioactive Conformation of a Small Peptide and its Set of Thermodynamically Accessible Conformations

Abstract

In order to investigate the relationship between the bioactive conformation of a peptide and its set of thermodynamically accessible structures in solution, the conformational profile of the tetrapeptide Ac-Pro-Ala-Pro-Tyr-OH was characterized by computational methods. Search of the conformational space was performed within the molecular mechanics framework using the AMBER4.0 force field with an effective dielectric constant of 80. Unique structures of the peptide were compared with its bioactive conformation for the protein Streptomyces griseus Protease A, as taken from the crystal structure of the enzyme-peptide complex. The results show that the bound conformation is close to one of the unique conformations characterized in the conformational search of the isolated peptide. Moreover, the lowest energy minimum characterized in the conformational search exhibits large deviations when compared to the bound conformation of the crystal structure.     

Simulated annealing with restrained molecular dynamics using a flexible restraint potential: theory and evaluation with simulated NMR constraints.

A new functional representation of NMR-derived distance constraints, the flexible restraint potential, has been implemented in the program CONGEN (Bruccoleri RE, Karplus M, 1987, Biopolymers 26:137-168) for molecular structure generation. In addition, flat-bottomed restraint potentials for representing dihedral angle and vicinal scalar coupling constraints have been introduced into CONGEN. An effective simulated annealing (SA) protocol that combines both weight annealing and temperature annealing is described. Calculations have been performed using ideal simulated NMR constraints, in order to evaluate the use of restrained molecular dynamics (MD) with these target functions as implemented in CONGEN. In this benchmark study, internuclear distance, dihedral angle, and vicinal coupling constant constraints were calculated from the energy-minimized X-ray crystal structure of the 46-amino acid polypeptide crambin (ICRN). Three-dimensional structures of crambin that satisfy these simulated NMR constraints were generated using restrained MD and SA. Polypeptide structures with extended backbone and side-chain conformations were used as starting conformations. Dynamical annealing calculations using extended starting conformations and assignments of initial velocities taken randomly from a Maxwellian distribution were found to adequately sample the conformational space consistent with the constraints. These calculations also show that loosened internuclear constraints can allow molecules to overcome local minima in the search for a global minimum with respect to both the NMR-derived constraints and conformational energy. This protocol and the modified version of the CONGEN program described here are shown to be reliable and robust, and are applicable generally for protein structure determination by dynamical simulated annealing using NMR data.     

Beyond rotamers: a generative,probabilistic model of side chains in proteins

Background  

Accurately covering the conformational space of amino acid side chains is essential for important applications such as protein design, docking and high resolution structure prediction. Today, the most common way to capture this conformational space is through rotamer libraries - discrete collections of side chain conformations derived from experimentally determined protein structures. The discretization can be exploited to efficiently search the conformational space. However, discretizing this naturally continuous space comes at the cost of losing detailed information that is crucial for certain applications. For example, rigorously combining rotamers with physical force fields is associated with numerous problems.     

Solution Structure of the HIV Protease Inhibitor Acetyl-pepstatin as Determined by NMR and Molecular Modeling

Abstract

The structure of acetyl-pepstatin has been investigated in solution by two-dimensional NMR spectroscopy and molecular modeling. The analysis of DQFCOSY, TOCSY and NOESY spectra lead to a full assignment of the NMR signals both in DMSO-d₆ and in TFE-d₃:H₂O 1:1. Interproton distances, dihedral angles and exchange regimes of NH or OH protons were derived from ROESY connectivities, coupling constants and temperature dependences of the chemical shifts, respectively. Molecular modeling using the NMR distance and dihedral angle constraints obtained in DMSO-d₆ yielded a model showing a well-defined structure for the N-terminal segment Ac-1 to Sta-4, but a flexible structure for the C-terminal segment. The structure was less defined in TFE-d₃:H₂O 1:1 and ¹³C T₁ measurements are indicative of higher mobility. Comparison of the NMR-determined solution structure of acetyl-pepstatin with its crystal structure when bound to HIV-1 protease shows that the conformation is more extended in the complex as a result of intermolecular interactions.     

Scrutiny of chain-length and N-terminal effects in α-helix folding: a molecular dynamics study on polyalanine peptides

Protein folding remains an unsolved problem as main-chain, side-chain, and solvent interactions remain entangled and have been hard to resolve. Polyalanines are promising models to analyze protein folding initiation and propagation structurally as well as energetically. In the present work, the effect of chain-length and N-terminal residue stereochemistry in polyalanine peptides are investigated for their role in the nucleation of α-helical conformation. The end-protected polyalanine peptides, tetra-alanine, Ac-^LAla₄-NHMe (Ia) and Ac-^DAla-^LAla₃-NHMe (Ib), hexa-alanine, Ac-^LAla₆-NHMe (IIa) and Ac-^DAla-^LAla₅-NHMe (IIb), and octa-alanine, Ac-^LAla₈-NHMe (IIIa) and Ac-^DAla-^LAla₇-NHMe (IIIb), are assessed as chain-length and stereochemical-structure perturbed models. The appreciable variations in the sampling of α-helical conformation, including a sampling of α-helix folds, due to the cooperative effect of chain-length and N-terminal residue stereochemistry have been noted. The electrostatics of α-helical conformation rather than the conformational entropy of the main-chain appear to be decisive in the initiation of α-helix folding. The results of the present work will enhance our understanding on the nucleation of α-helical conformation in short peptides and aid in the design of novel peptides with α-helical structure that can modulate disease-related protein–protein interactions.     

The Genetic Algorithm and the Conformational Search of Polypeptides and Proteins

Abstract

The genetic algorithm is a technique of function optimization derived from the principles of evolutionary theory. We have adapted it to perform conformational search on polypeptides and proteins. The algorithm was first tested on several small polypeptides and the 46 amino acid protein crambin under the AMBER potential energy function. The probable global minimum conformations of the polypeptides were located 90% of the time and a non-native conformation of crambin was located that was 150kcal/mol lower in potential energy than the minimized crystal structure conformation. Next, we used a knowledge-based potential function to predict the structures of melittin, pancreatic polypeptide, and crambin. A 2.31 Å ΔRMS conformation of melittin and a 5.33 Å ΔRMS conformation of pancreatic polypeptide were located by genetic algorithm-based conformational search under the knowledge-based potential function. Although the ΔRMS of pancreatic polypeptide was somewhat high, most of the secondary structure was correct. The secondary structure of crambin was predicted correctly, but the potential failed to promote packing interactions. Finally, we tested the packing aspects of our potential function by attempting to predict the tertiary structure of cytochrome b ₅₆₂ given correct secondary structure as a constraint. The final predicted conformation of cytochrome b ₅₆₂ was an almost completely extended continuous helix which indicated that the knowledge-based potential was useless for tertiary structure prediction. This work serves as a warning against testing potential functions designed for tertiary structure prediction on small proteins.     

Modeling of loops in protein structures

Comparative protein structure prediction is limited mostly by the errors in alignment and loop modeling. We describe here a new automated modeling technique that significantly improves the accuracy of loop predictions in protein structures. The positions of all nonhydrogen atoms of the loop are optimized in a fixed environment with respect to a pseudo energy function. The energy is a sum of many spatial restraints that include the bond length, bond angle, and improper dihedral angle terms from the CHARMM-22 force field, statistical preferences for the main-chain and side-chain dihedral angles, and statistical preferences for nonbonded atomic contacts that depend on the two atom types, their distance through space, and separation in sequence. The energy function is optimized with the method of conjugate gradients combined with molecular dynamics and simulated annealing. Typically, the predicted loop conformation corresponds to the lowest energy conformation among 500 independent optimizations. Predictions were made for 40 loops of known structure at each length from 1 to 14 residues. The accuracy of loop predictions is evaluated as a function of thoroughness of conformational sampling, loop length, and structural properties of native loops. When accuracy is measured by local superposition of the model on the native loop, 100, 90, and 30% of 4-, 8-, and 12-residue loop predictions, respectively, had <2 A RMSD error for the mainchain N, C(alpha), C, and O atoms; the average accuracies were 0.59 +/- 0.05, 1.16 +/- 0.10, and 2.61 +/- 0.16 A, respectively. To simulate real comparative modeling problems, the method was also evaluated by predicting loops of known structure in only approximately correct environments with errors typical of comparative modeling without misalignment. When the RMSD distortion of the main-chain stem atoms is 2.5 A, the average loop prediction error increased by 180, 25, and 3% for 4-, 8-, and 12-residue loops, respectively. The accuracy of the lowest energy prediction for a given loop can be estimated from the structural variability among a number of low energy predictions. The relative value of the present method is gauged by (1) comparing it with one of the most successful previously described methods, and (2) describing its accuracy in recent blind predictions of protein structure. Finally, it is shown that the average accuracy of prediction is limited primarily by the accuracy of the energy function rather than by the extent of conformational sampling.     

Factors influencing accuracy of computer-built models: a study based on leucine zipper GCN4 structure.

A three-dimensional model of the leucine zipper GCN4 built from its amino acid sequence had been reported previously by us. When the two alternative x-ray structures of the GCN4 dimer became available, the root mean square (r.m.s.) shifts between our model and the structures were determined as approximately 2.7 A on all atoms. These values are similar to the r.m.s. shift of 2.8 A between the two GCN4 structures in the different crystal forms (C2 and P2(1)2(1)2(1)). CONGEN conformational searches were run to better understand the conditions that may determine the preference of different conformers in different environments and to test the sensitivity of our current modeling techniques. With a judicious choice of CONGEN search parameters, the backbone r.m.s. deviation improved to 0.8 A and 2.5 A on all atoms. The side-chain conformations of Val and Leu at the helical interface were well reproduced (1.2 A r.m.s.), and the large side-chain misplacements occurred with only a small number of charged amino acids and a tyrosine. Inclusion of the crystal environment (C2 symmetry), as a passive background, into the side-chain conformational search further improved the accuracy of the model to an r.m.s. deviation of 2.1 A. Conformational searches carried out in the two different crystal environments and employing the AMBER protein/DNA forcefield, as implemented in CONGEN, gave the r.m.s. values of 2.2 A (for the C2 symmetry) and 2.5 A (for the P2(1)2(1)2(1) symmetry). In the C2 symmetry crystal, as much as 40% of the surface of each dimer was involved in crystal contacts with other dimers, and the charged residues on the surface often interacted with immobilized water molecules. Thus, occasional large r.m.s. deviations between the model and the x-ray side chains were due to specific conditions that did not occur in solution.     

On the use of structural templates for high‐resolution docking

Reliable high‐resolution prediction of protein complex structures starting from the free monomers is a considerable challenge toward large‐scale mapping of the structural details of protein‐protein interactions. The current major bottleneck is to model the conformational changes of the monomer backbone upon binding. We evaluate the use of homolog structures as source for conformational diversity, within the framework of RosettaDock—a leading high‐resolution docking protocol. We find that the use of homolog templates can improve significantly the modeling of a complex structure, including known difficult cases. Several conformational changes however are not sampled by any of the templates, indicating the need for additional sources of conformational variability. Interestingly, the successful homolog templates are not restricted to a confined range of sequence identity, highlighting the importance of the backbone conformation rather than the sequence. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Criteria that discriminate between native proteins and incorrectly folded models

Various theoretical concepts, such as free energy potentials, electrostatic interaction potentials, atomic packing, solvent-exposed surface, and surface charge distribution, were tested for their ability to discriminate between native proteins and misfolded protein models. Misfolded models were constructed by introducing incorrect side chains onto polypeptide backbones: side chains of the alpha-helical hemerythrin were modeled on the beta-sheeted backbone of immunoglobulin VL domain, whereas those of the VL domain were similarly modeled on the hemerythrin backbone. CONGEN, a conformational space sampling program, was used to construct the side chains, in contrast to the previous work, where incorrect side chains were modeled in all trans conformations. Capability of the conformational search procedure to reproduce native conformations was gauged first by rebuilding (the correct) side chains in hemerythrin and the VL domain: constructs with r.m.s. differences from the x-ray side chains 2.2-2.4 A were produced, and many calculated conformations matched the native ones quite well. Incorrectly folded models were then constructed by the same conformational protocol applied to incorrect amino acid sequences. All CONGEN constructs, both correctly and incorrectly folded, were characterized by exceptionally small molecular surfaces and low potential energies. Surface charge density, atomic packing, and Coulomb formula-based electrostatic interactions of the misfolded structures and the correctly folded proteins were similar, and therefore of little interest for diagnosing incorrect folds. The following criteria clearly favored the native structures over the misfolded ones: 1) solvent-exposed side-chain nonpolar surface, 2) number of buried ionizable groups, and 3) empirical free energy functions that incorporate solvent effects.