REMO: A new protocol to refine full atomic protein models from C‐alpha traces by optimizing hydrogen‐bonding networks

Protein structure prediction approaches usually perform modeling simulations based on reduced representation of protein structures. For biological utilizations, it is an important step to construct full atomic models from the reduced structure decoys. Most of the current full atomic model reconstruction procedures have defects which either could not completely remove the steric clashes among backbone atoms or generate final atomic models with worse topology similarity relative to the native structures than the reduced models. In this work, we develop a new protocol, called REMO, to generate full atomic protein models by optimizing the hydrogen‐bonding network with basic fragments matched from a newly constructed backbone isomer library of solved protein structures. The algorithm is benchmarked on 230 nonhomologous proteins with reduced structure decoys generated by I‐TASSER simulations. The results show that REMO has a significant ability to remove steric clashes, and meanwhile retains good topology of the reduced model. The hydrogen‐bonding network of the final models is dramatically improved during the procedure. The REMO algorithm has been exploited in the recent CASP8 experiment which demonstrated significant improvements of the I‐TASSER models in both atomic‐level structural refinement and hydrogen‐bonding network construction. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

Application of biasing‐potential replica‐exchange simulations for loop modeling and refinement of proteins in explicit solvent

Comparative or homology modeling of a target protein based on sequence similarity to a protein with known structure is widely used to provide structural models of proteins. Depending on the target‐template similarity these model structures may contain regions of limited structural accuracy. In principle, molecular dynamics (MD) simulations can be used to refine protein model structures and also to model loop regions that connect structurally conserved regions but it is limited by the currently accessible simulation time scales. A recently developed biasing potential replica exchange (BP‐REMD) method was used to refine loops and complete decoy protein structures at atomic resolution including explicit solvent. In standard REMD simulations several replicas of a system are run in parallel at different temperatures allowing exchanges at preset time intervals. In a BP‐REMD simulation replicas are controlled by various levels of a biasing potential to reduce the energy barriers associated with peptide backbone dihedral transitions. The method requires much fewer replicas for efficient sampling compared with T‐REMD. Application of the approach to several protein loops indicated improved conformational sampling of backbone dihedral angle of loop residues compared to conventional MD simulations. BP‐REMD refinement simulations on several test cases starting from decoy structures deviating significantly from the native structure resulted in final structures in much closer agreement with experiment compared to conventional MD simulations. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Protein structure refinement by optimization

Knowledge‐based protein potentials are simplified potentials designed to improve the quality of protein models, which is important as more accurate models are more useful for biological and pharmaceutical studies. Consequently, knowledge‐based potentials often are designed to be efficient in ordering a given set of deformed structures denoted decoys according to how close they are to the relevant native protein structure. This, however, does not necessarily imply that energy minimization of this potential will bring the decoys closer to the native structure. In this study, we introduce an iterative strategy to improve the convergence of decoy structures. It works by adding energy optimized decoys to the pool of decoys used to construct the next and improved knowledge‐based potential. We demonstrate that this strategy results in significantly improved decoy convergence on Titan high resolution decoys and refinement targets from Critical Assessment of protein Structure Prediction competitions. Our potential is formulated in Cartesian coordinates and has a fixed backbone potential to restricts motions to be close to those of a dihedral model, a fixed hydrogen‐bonding potential and a variable coarse grained carbon alpha potential consisting of a pair potential and a novel solvent potential that are b‐spline based as we use explicit gradient and Hessian for efficient energy optimization. Proteins 2015; 83:1616–1624. © 2015 Wiley Periodicals, Inc.     

Free energies of protein decoys provide insight into determinants of protein stability

We have calculated the stability of decoy structures of several proteins (from the CASP3 models and the Park and Levitt decoy set) relative to the native structures. The calculations were performed with the force field-consistent ES/IS method, in which an implicit solvent (IS) model is used to calculate the average solvation free energy for snapshots from explicit simulations (ESs). The conformational free energy is obtained by adding the internal energy of the solute from the ESs and an entropic term estimated from the covariance positional fluctuation matrix. The set of atomic Born radii and the cavity-surface free energy coefficient used in the implicit model has been optimized to be consistent with the all-atom force field used in the ESs (cedar/gromos with simple point charge (SPC) water model). The decoys are found to have a consistently higher free energy than that of the native structure; the gap between the native structure and the best decoy varies between 10 and 15 kcal/mole, on the order of the free energy difference that typically separates the native state of a protein from the unfolded state. The correlation between the free energy and the extent to which the decoy structures differ from the native (as root mean square deviation) is very weak; hence, the free energy is not an accurate measure for ranking the structurally most native-like structures from among a set of models. Analysis of the energy components shows that stability is attained as a result of three major driving forces: (1) minimum size of the protein-water surface interface; (2) minimum total electrostatic energy, which includes solvent polarization; and (3) minimum protein packing energy. The detailed fit required to optimize the last term may underlie difficulties encountered in recovering the native fold from an approximate decoy or model structure.     

Structure refinement of membrane proteins via molecular dynamics simulations

A refinement protocol based on physics‐based techniques established for water soluble proteins is tested for membrane protein structures. Initial structures were generated by homology modeling and sampled via molecular dynamics simulations in explicit lipid bilayer and aqueous solvent systems. Snapshots from the simulations were selected based on scoring with either knowledge‐based or implicit membrane‐based scoring functions and averaged to obtain refined models. The protocol resulted in consistent and significant refinement of the membrane protein structures similar to the performance of refinement methods for soluble proteins. Refinement success was similar between sampling in the presence of lipid bilayers and aqueous solvent but the presence of lipid bilayers may benefit the improvement of lipid‐facing residues. Scoring with knowledge‐based functions (DFIRE and RWplus) was found to be as good as scoring using implicit membrane‐based scoring functions suggesting that differences in internal packing is more important than orientations relative to the membrane during the refinement of membrane protein homology models.     

How well can we predict native contacts in proteins based on decoy structures and their energies?

One strategy for ab initio protein structure prediction is to generate a large number of possible structures (decoys) and select the most fitting ones based on a scoring or free energy function. The conformational space of a protein is huge, and chances are rare that any heuristically generated structure will directly fall in the neighborhood of the native structure. It is desirable that, instead of being thrown away, the unfitting decoy structures can provide insights into native structures so prediction can be made progressively. First, we demonstrate that a recently parameterized physics-based effective free energy function based on the GROMOS96 force field and a generalized Born/surface area solvent model is, as several other physics-based and knowledge-based models, capable of distinguishing native structures from decoy structures for a number of widely used decoy databases. Second, we observe a substantial increase in correlations of the effective free energies with the degree of similarity between the decoys and the native structure, if the similarity is measured by the content of native inter-residue contacts in a decoy structure rather than its root-mean-square deviation from the native structure. Finally, we investigate the possibility of predicting native contacts based on the frequency of occurrence of contacts in decoy structures. For most proteins contained in the decoy databases, a meaningful amount of native contacts can be predicted based on plain frequencies of occurrence at a relatively high level of accuracy. Relative to using plain frequencies, overwhelming improvements in sensitivity of the predictions are observed for the 4_state_reduced decoy sets by applying energy-dependent weighting of decoy structures in determining the frequency. There, approximately 80% native contacts can be predicted at an accuracy of approximately 80% using energy-weighted frequencies. The sensitivity of the plain frequency approach is much lower (20% to 40%). Such improvements are, however, not observed for the other decoy databases. The rationalization and implications of the results are discussed.     

A distance‐ and orientation‐dependent energy function of amino acid key blocks

Blocks are the selected portions of amino acids. They have been used effectively to represent amino acids in distinguishing the native conformation from the decoys. Although many statistical energy functions exist, most of them rely on the distances between two or more amino acids. In this study, the authors have developed a pairwise energy function “DOKB” that is both distance and orientation dependent, and it is based on the key blocks that bias the distal ends of side chains. The results suggest that both the distance and the orientation are needed to distinguish the fine details of the packing geometry. DOKB appears to perform well in recognizing native conformations when compared with six other energy functions. Highly packed clusters play important roles in stabilizing the structure. The investigation about the highly packed clusters at the residue level suggests that certain residue pairs in a low‐energy region have lower probability to appear in the highly packed clusters than in the entire protein. The cluster energy term appears to significantly improve the recognition of the native conformations in ig_structal decoy set, in which more highly packed clusters are contained than in other decoy sets. © 2013 Wiley Periodicals, Inc. Biopolymers 101: 681–692, 2014.     

An improved protein decoy set for testing energy functions for protein structure prediction

We have improved the original Rosetta centroid/backbone decoy set by increasing the number of proteins and frequency of near native models and by building on sidechains and minimizing clashes. The new set consists of 1,400 model structures for 78 different and diverse protein targets and provides a challenging set for the testing and evaluation of scoring functions. We evaluated the extent to which a variety of all-atom energy functions could identify the native and close-to-native structures in the new decoy sets. Of various implicit solvent models, we found that a solvent-accessible surface area-based solvation provided the best enrichment and discrimination of close-to-native decoys. The combination of this solvation treatment with Lennard Jones terms and the original Rosetta energy provided better enrichment and discrimination than any of the individual terms. The results also highlight the differences in accuracy of NMR and X-ray crystal structures: a large energy gap was observed between native and non-native conformations for X-ray structures but not for NMR structures.     

Template‐free protein structure prediction and quality assessment with an all‐atom free‐energy model

Biophysical forcefields have contributed less than originally anticipated to recent progress in protein structure prediction. Here, we have investigated the selectivity of a recently developed all‐atom free‐energy forcefield for protein structure prediction and quality assessment (QA). Using a heuristic method, but excluding homology, we generated decoy‐sets for all targets of the CASP7 protein structure prediction assessment with <150 amino acids. The decoys in each set were then ranked by energy in short relaxation simulations and the best low‐energy cluster was submitted as a prediction. For four of nine template‐free targets, this approach generated high‐ranking predictions within the top 10 models submitted in CASP7 for the respective targets. For these targets, our de‐novo predictions had an average GDT_S score of 42.81, significantly above the average of all groups. The refinement protocol has difficulty for oligomeric targets and when no near‐native decoys are generated in the decoy library. For targets with high‐quality decoy sets the refinement approach was highly selective. Motivated by this observation, we rescored all server submissions up to 200 amino acids using a similar refinement protocol, but using no clustering, in a QA exercise. We found an excellent correlation between the best server models and those with the lowest energy in the forcefield. The free‐energy refinement protocol may thus be an efficient tool for relative QA and protein structure prediction. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

Early events in protein folding: Is there something more than hydrophobic burst?

The presence of native contacts in the denatured state of many proteins suggests that elements of the biologically active structure of these molecules are formed during the initial stage of the folding process. The rapidity with which these events take place makes it difficult to study them in vitro, but, by the same token, suitable for studies in silico. With the help of all-atom, explicit solvent, molecular dynamics simulations we have followed in time, starting from elongated structureless conformations, the early events in the folding of src-SH3 domain and of proteins G, L, and CI2. It is observed that within the first 50 ns two important events take place, essentially independent of each other: hydrophobic collapse and formation of a few selected native contacts. The same contacts are also found in simulations carried out in the presence of guanidinium chloride in order to reproduce the conditions used to characterize experimentally the denatured state and testify to the fact that these contacts are to be considered a resilient characterizing property of the denaturated state.     

Sampling of near-native protein conformations during protein structure refinement using a coarse-grained model, normal modes, and molecular dynamics simulations

Protein structure refinement from comparative models with the goal of predicting structures at near-experimental accuracy remains an unsolved problem. Structure refinement might be achieved with an iterative protocol where the most native-like structure from a set of decoys generated from an initial model in one cycle is used as the starting structure for the next cycle. Conformational sampling based on the coarse-grained SICHO model, atomic level of detail molecular dynamics simulations, and normal-mode analysis is compared in the context of such a protocol. All of the sampling methods can achieve significant refinement close to experimental structures, although the distribution of structures and the ability to reach native-like structures differs greatly. Implications for the practical application of such sampling methods and the requirements for scoring functions in an iterative refinement protocol are analyzed in the context of theoretical predictions for the distribution of protein-like conformations with a random sampling protocol.     

Folding simulations of Trp‐cage mini protein in explicit solvent using biasing potential replica‐exchange molecular dynamics simulations

Replica exchange molecular dynamics (RexMD) simulations are frequently used for studying structure formation and dynamics of peptides and proteins. A significant drawback of standard temperature RexMD is, however, the rapid increase of the replica number with increasing system size to cover a desired temperature range. A recently developed Hamiltonian RexMD method has been used to study folding of the Trp‐cage protein. It employs a biasing potential that lowers the backbone dihedral barriers and promotes peptide backbone transitions along the replica coordinate. In two independent applications of the biasing potential RexMD method including explicit solvent and starting from a completely unfolded structure the formation of near‐native conformations was observed after 30–40 ns simulation time. The conformation representing the most populated cluster at the final simulation stage had a backbone root mean square deviation of ～1.3 Å from the experimental structure. This was achieved with a very modest number of five replicas making it well suited for peptide and protein folding and refinement studies including explicit solvent. In contrast, during five independent continuous 70 ns molecular dynamics simulations formation of collapsed states but no near native structure formation was observed. The simulations predict a largely collapsed state with a significant helical propensity for the helical domain of the Trp‐cage protein already in the unfolded state. Hydrogen bonded bridging water molecules were identified that could play an active role by stabilizing the arrangement of the helical domain with respect to the rest of the chain already in intermediate states of the protein. Proteins 2009. © 2008 Wiley‐Liss, Inc.     

Distinguishing native conformations of proteins from decoys with an effective free energy estimator based on the OPLS all-atom force field and the Surface Generalized Born solvent model

Protein decoy data sets provide a benchmark for testing scoring functions designed for fold recognition and protein homology modeling problems. It is commonly believed that statistical potentials based on reduced atomic models are better able to discriminate native-like from misfolded decoys than scoring functions based on more detailed molecular mechanics models. Recent benchmark tests on small data sets, however, suggest otherwise. In this work, we report the results of extensive decoy detection tests using an effective free energy function based on the OPLS all-atom (OPLS-AA) force field and the Surface Generalized Born (SGB) model for the solvent electrostatic effects. The OPLS-AA/SGB effective free energy is used as a scoring function to detect native protein folds among a total of 48,832 decoys for 32 different proteins from Park and Levitt's 4-state-reduced, Levitt's local-minima, Baker's ROSETTA all-atom, and Skolnick's decoy sets. Solvent electrostatic effects are included through the Surface Generalized Born (SGB) model. All structures are locally minimized without restraints. From an analysis of the individual energy components of the OPLS-AA/SGB energy function for the native and the best-ranked decoy, it is determined that a balance of the terms of the potential is responsible for the minimized energies that most successfully distinguish the native from the misfolded conformations. Different combinations of individual energy terms provide less discrimination than the total energy. The results are consistent with observations that all-atom molecular potentials coupled with intermediate level solvent dielectric models are competitive with knowledge-based potentials for decoy detection and protein modeling problems such as fold recognition and homology modeling.     

Prediction,refinement, and persistency of transmembrane helix dimers in lipid bilayers using implicit and explicit solvent/lipid representations: Microsecond molecular dynamics simulations of ErbB1/B2 and EphA1

All‐atom simulations are carried out on ErbB1/B2 and EphA1 transmembrane helix dimers in lipid bilayers starting from their solution/DMPC bicelle NMR structures. Over the course of microsecond trajectories, the structures remain in close proximity to the initial configuration and satisfy the majority of experimental tertiary contact restraints. These results further validate CHARMM protein/lipid force fields and simulation protocols on Anton. Separately, dimer conformations are generated using replica exchange in conjunction with an implicit solvent and lipid representation. The implicit model requires further improvement, and this study investigates whether lengthy all‐atom molecular dynamics simulations can alleviate the shortcomings of the initial conditions. The simulations correct many of the deficiencies. For example, excessive helix twisting is eliminated over a period of hundreds of nanoseconds. The helix tilt, crossing angles, and dimer contacts approximate those of the NMR‐derived structure, although the detailed contact surface remains off‐set for one of two helices in both systems. Hence, even microsecond simulations are not long enough for extensive helix rotations. The alternate structures can be rationalized with reference to interaction motifs and may represent still sought after receptor states that are important in ErbB1/B2 and EphA1 signaling. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

Self‐guided Langevin dynamics study of regulatory interactions in NtrC

Multiple self‐guided Langevin dynamics (SGLD) simulations were performed to examine structural and dynamical properties of the receiver domain of nitrogen regulatory protein C (NtrC^r). SGLD and MD simulations of the phosphorylated active form structure suggest a mostly stable but broad structural ensemble of this protein. The finite difference Poisson–Boltzmann calculations of the pK_a values of the active site residues suggest an increase in the pK_a of His‐84 on phosphorylation of Asp‐54. In SGLD simulations of the phosphorylated active form with charged His‐84, the average position of the regulatory helix α4 is found closer to the starting structure than in simulations with the neutral His‐84. To model the transition pathway, the phosphate group was removed from the simulations. After 7 ns of simulations, the regulatory helix α4 was found approximately halfway between positions in the NMR structures of the active and inactive forms. Removal of the phosphate group stimulated loss of helix α4, suggesting that the pathway of conformational transition may involve partial unfolding mechanism. The study illustrates the potential utility of the SGLD method in studies of the coupling between ligand binding and conformational transitions. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

Native fold and docking pose discrimination by the same residue‐based scoring function

Structure prediction and quality assessment are crucial steps in modeling native protein conformations. Statistical potentials are widely used in related algorithms, with different parametrizations typically developed for different contexts such as folding protein monomers or docking protein complexes. Here, we describe BACH‐SixthSense, a single residue‐based statistical potential that can be successfully employed in both contexts. BACH‐SixthSense shares the same approach as BACH, a knowledge‐based potential originally developed to score monomeric protein structures. A term that penalizes steric clashes as well as the distinction between polar and apolar sidechain‐sidechain contacts are crucial novel features of BACH‐SixthSense. The performance of BACH‐SixthSense in discriminating correctly the native structure among a competing set of decoys is significantly higher than other state‐of‐the‐art scoring functions, that were specifically trained for a single context, for both monomeric proteins (QMEAN, Rosetta, RF_CB_SRS_OD, benchmarked on CASP targets) and protein dimers (IRAD, Rosetta, PIE*PISA, HADDOCK, FireDock, benchmarked on 14 CAPRI targets). The performance of BACH‐SixthSense in recognizing near‐native docking poses within CAPRI decoy sets is good as well. Proteins 2015; 83:621–630. © 2015 Wiley Periodicals, Inc.     

Analysis of anisotropic side-chain packing in proteins and application to high-resolution structure prediction

pi-pi, Cation-pi, and hydrophobic packing interactions contribute specificity to protein folding and stability to the native state. As a step towards developing improved models of these interactions in proteins, we compare the side-chain packing arrangements in native proteins to those found in compact decoys produced by the Rosetta de novo structure prediction method. We find enrichments in the native distributions for T-shaped and parallel offset arrangements of aromatic residue pairs, in parallel stacked arrangements of cation-aromatic pairs, in parallel stacked pairs involving proline residues, and in parallel offset arrangements for aliphatic residue pairs. We then investigate the extent to which the distinctive features of native packing can be explained using Lennard-Jones and electrostatics models. Finally, we derive orientation-dependent pi-pi, cation-pi and hydrophobic interaction potentials based on the differences between the native and compact decoy distributions and investigate their efficacy for high-resolution protein structure prediction. Surprisingly, the orientation-dependent potential derived from the packing arrangements of aliphatic side-chain pairs distinguishes the native structure from compact decoys better than the orientation-dependent potentials describing pi-pi and cation-pi interactions.     

Optimized distance‐dependent atom‐pair‐based potential DOOP for protein structure prediction

The DOcking decoy‐based Optimized Potential (DOOP) energy function for protein structure prediction is based on empirical distance‐dependent atom‐pair interactions. To optimize the atom‐pair interactions, native protein structures are decomposed into polypeptide chain segments that correspond to structural motives involving complete secondary structure elements. They constitute near native ligand–receptor systems (or just pairs). Thus, a total of 8609 ligand–receptor systems were prepared from 954 selected proteins. For each of these hypothetical ligand–receptor systems, 1000 evenly sampled docking decoys with 0–10 Å interface root‐mean‐square‐deviation (iRMSD) were generated with a method used before for protein–protein docking. A neural network‐based optimization method was applied to derive the optimized energy parameters using these decoys so that the energy function mimics the funnel‐like energy landscape for the interaction between these hypothetical ligand–receptor systems. Thus, our method hierarchically models the overall funnel‐like energy landscape of native protein structures. The resulting energy function was tested on several commonly used decoy sets for native protein structure recognition and compared with other statistical potentials. In combination with a torsion potential term which describes the local conformational preference, the atom‐pair‐based potential outperforms other reported statistical energy functions in correct ranking of native protein structures for a variety of decoy sets. This is especially the case for the most challenging ROSETTA decoy set, although it does not take into account side chain orientation‐dependence explicitly. The DOOP energy function for protein structure prediction, the underlying database of protein structures with hypothetical ligand–receptor systems and their decoys are freely available at http://agknapp.chemie.fu‐berlin.de/doop/ . Proteins 2015; 83:881–890. © 2015 Wiley Periodicals, Inc.     

SVR_CAF: An integrated score function for detecting native protein structures among decoys

An accurate score function for detecting the most native‐like models among a huge number of decoy sets is essential to the protein structure prediction. In this work, we developed a novel integrated score function (SVR_CAF) to discriminate native structures from decoys, as well as to rank near‐native structures and select best decoys when native structures are absent. SVR_CAF is a machine learning score, which incorporates the contact energy based score ( C E_score), amino acid network based score ( A AN_score), and the fast Fourier transform based score ( F FT_score). The score function was evaluated with four decoy sets for its discriminative ability and it shows higher overall performance than the state‐of‐the‐art score functions. Proteins 2014; 82:556–564. © 2013 Wiley Periodicals, Inc.     

IRECS: a new algorithm for the selection of most probable ensembles of side-chain conformations in protein models

We introduce a new algorithm, IRECS (Iterative REduction of Conformational Space), for identifying ensembles of most probable side-chain conformations for homology modeling. On the basis of a given rotamer library, IRECS ranks all side-chain rotamers of a protein according to the probability with which each side chain adopts the respective rotamer conformation. This ranking enables the user to select small rotamer sets that are most likely to contain a near-native rotamer for each side chain. IRECS can therefore act as a fast heuristic alternative to the Dead-End-Elimination algorithm (DEE). In contrast to DEE, IRECS allows for the selection of rotamer subsets of arbitrary size, thus being able to define structure ensembles for a protein. We show that the selection of more than one rotamer per side chain is generally meaningful, since the selected rotamers represent the conformational space of flexible side chains. A knowledge-based statistical potential ROTA was constructed for the IRECS algorithm. The potential was optimized to discriminate between side-chain conformations of native and rotameric decoys of protein structures. By restricting the number of rotamers per side chain to one, IRECS can optimize side chains for a single conformation model. The average accuracy of IRECS for the chi1 and chi1+2 dihedral angles amounts to 84.7% and 71.6%, respectively, using a 40 degrees cutoff. When we compared IRECS with SCWRL and SCAP, the performance of IRECS was comparable to that of both methods. IRECS and the ROTA potential are available for download from the URL http://irecs.bioinf.mpi-inf.mpg.de.