New computational method for prediction of interacting protein loop regions

Flexible loop regions of proteins play a crucial role in many biological functions such as protein–ligand recognition, enzymatic catalysis, and protein–protein association. To date, most computational methods that predict the conformational states of loops only focus on individual loop regions. However, loop regions are often spatially in close proximity to one another and their mutual interactions stabilize their conformations. We have developed a new method, titled CorLps, capable of simultaneously predicting such interacting loop regions. First, an ensemble of individual loop conformations is generated for each loop region. The members of the individual ensembles are combined and are accepted or rejected based on a steric clash filter. After a subsequent side‐chain optimization step, the resulting conformations of the interacting loops are ranked by the statistical scoring function DFIRE that originated from protein structure prediction. Our results show that predicting interacting loops with CorLps is superior to sequential prediction of the two interacting loop regions, and our method is comparable in accuracy to single loop predictions. Furthermore, improved predictive accuracy of the top‐ranked solution is achieved for 12‐residue length loop regions by diversifying the initial pool of individual loop conformations using a quality threshold clustering algorithm. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Toward high‐resolution homology modeling of antibody Fv regions and application to antibody–antigen docking

High‐resolution homology models are useful in structure‐based protein engineering applications, especially when a crystallographic structure is unavailable. Here, we report the development and implementation of RosettaAntibody, a protocol for homology modeling of antibody variable regions. The protocol combines comparative modeling of canonical complementarity determining region (CDR) loop conformations and de novo loop modeling of CDR H3 conformation with simultaneous optimization of V_L‐V_H rigid‐body orientation and CDR backbone and side‐chain conformations. The protocol was tested on a benchmark of 54 antibody crystal structures. The median root mean square deviation (rmsd) of the antigen binding pocket comprised of all the CDR residues was 1.5 Å with 80% of the targets having an rmsd lower than 2.0 Å. The median backbone heavy atom global rmsd of the CDR H3 loop prediction was 1.6, 1.9, 2.4, 3.1, and 6.0 Å for very short (4–6 residues), short (7–9), medium (10–11), long (12–14) and very long (17–22) loops, respectively. When the set of ten top‐scoring antibody homology models are used in local ensemble docking to antigen, a moderate‐to‐high accuracy docking prediction was achieved in seven of fifteen targets. This success in computational docking with high‐resolution homology models is encouraging, but challenges still remain in modeling antibody structures for sequences with long H3 loops. This first large‐scale antibody–antigen docking study using homology models reveals the level of “functional accuracy” of these structural models toward protein engineering applications. Proteins 2009; 74:497–514. © 2008 Wiley‐Liss, Inc.     

Prediction of structures of zinc‐binding proteins through explicit modeling of metal coordination geometry

Metal ions play an essential role in stabilizing protein structures and contributing to protein function. Ions such as zinc have well‐defined coordination geometries, but it has not been easy to take advantage of this knowledge in protein structure prediction efforts. Here, we present a computational method to predict structures of zinc‐binding proteins given knowledge of the positions of zinc‐coordinating residues in the amino acid sequence. The method takes advantage of the “atom‐tree” representation of molecular systems and modular architecture of the Rosetta3 software suite to incorporate explicit metal ion coordination geometry into previously developed de novo prediction and loop modeling protocols. Zinc cofactors are tethered to their interacting residues based on coordination geometries observed in natural zinc‐binding proteins. The incorporation of explicit zinc atoms and their coordination geometry in both de novo structure prediction and loop modeling significantly improves sampling near the native conformation. The method can be readily extended to predict protein structures bound to other metal and/or small chemical cofactors with well‐defined coordination or ligation geometry.     

Fast Protein Loop Sampling and Structure Prediction Using Distance-Guided Sequential Chain-Growth Monte Carlo Method

Loops in proteins are flexible regions connecting regular secondary structures. They are often involved in protein functions through interacting with other molecules. The irregularity and flexibility of loops make their structures difficult to determine experimentally and challenging to model computationally. Conformation sampling and energy evaluation are the two key components in loop modeling. We have developed a new method for loop conformation sampling and prediction based on a chain growth sequential Monte Carlo sampling strategy, called Distance-guided Sequential chain-Growth Monte Carlo (DiSGro). With an energy function designed specifically for loops, our method can efficiently generate high quality loop conformations with low energy that are enriched with near-native loop structures. The average minimum global backbone RMSD for 1,000 conformations of 12-residue loops is Å, with a lowest energy RMSD of Å, and an average ensemble RMSD of Å. A novel geometric criterion is applied to speed up calculations. The computational cost of generating 1,000 conformations for each of the x loops in a benchmark dataset is only about cpu minutes for 12-residue loops, compared to ca cpu minutes using the FALCm method. Test results on benchmark datasets show that DiSGro performs comparably or better than previous successful methods, while requiring far less computing time. DiSGro is especially effective in modeling longer loops (– residues).     

Loop prediction for a GPCR homology model: Algorithms and results

We present loop structure prediction results of the intracellular and extracellular loops of four G‐protein‐coupled receptors (GPCRs): bovine rhodopsin (bRh), the turkey β1‐adrenergic (β1Ar), the human β2‐adrenergic (β2Ar) and the human A2a adenosine receptor (A2Ar) in perturbed environments. We used the protein local optimization program, which builds thousands of loop candidates by sampling rotamer states of the loops' constituent amino acids. The candidate loops are discriminated between with our physics‐based, all‐atom energy function, which is based on the OPLS force field with implicit solvent and several correction terms. For relevant cases, explicit membrane molecules are included to simulate the effect of the membrane on loop structure. We also discuss a new sampling algorithm that divides phase space into different regions, allowing more thorough sampling of long loops that greatly improves results. In the first half of the paper, loop prediction is done with the GPCRs' transmembrane domains fixed in their crystallographic positions, while the loops are built one‐by‐one. Side chains near the loops are also in non‐native conformations. The second half describes a full homology model of β2Ar using β1Ar as a template. No information about the crystal structure of β2Ar was used to build this homology model. We are able to capture the architecture of short loops and the very long second extracellular loop, which is key for ligand binding. We believe this the first successful example of an RMSD validated, physics‐based loop prediction in the context of a GPCR homology model. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

Large loop conformation sampling using the activation relaxation technique, ART-nouveau method

We present an adaptation of the ART-nouveau energy surface sampling method to the problem of loop structure prediction. This method, previously used to study protein folding pathways and peptide aggregation, is well suited to the problem of sampling the conformation space of large loops by targeting probable folding pathways instead of sampling exhaustively that space. The number of sampled conformations needed by ART nouveau to find the global energy minimum for a loop was found to scale linearly with the sequence length of the loop for loops between 8 and about 20 amino acids. Considering the linear scaling dependence of the computation cost on the loop sequence length for sampling new conformations, we estimate the total computational cost of sampling larger loops to scale quadratically compared to the exponential scaling of exhaustive search methods.     

Antibodies as a model system for comparative model refinement

Predicting the conformations of loops is a critical aspect of protein comparative (homology) modeling. Despite considerable advances in developing loop prediction algorithms, refining loops in homology models remains challenging. In this work, we use antibodies as a model system to investigate strategies for more robustly predicting loop conformations when the protein model contains errors in the conformations of side chains and protein backbone surrounding the loop in question. Specifically, our test system consists of partial models of antibodies in which the “scaffold” (i.e., the portion other than the complementarity determining region, CDR, loops) retains native backbone conformation, whereas the CDR loops are predicted using a combination of knowledge‐based modeling (H1, H2, L1, L2, and L3) and ab initio loop prediction (H3). H3 is the most variable of the CDRs. Using a previously published method, a test set of 10 shorter H3 loops (5–7 residues) are predicted to an average backbone (N? Cα? C? O) RMSD of 2.7 Å while 11 longer loops (8–9 residues) are predicted to 5.1 Å, thus recapitulating the difficulties in refining loops in models. By contrast, in control calculations predicting the same loops in crystal structures, the same method reconstructs the loops to an average of 0.5 and 1.4 Å for the shorter and longer loops, respectively. We modify the loop prediction method to improve the ability to sample near‐native loop conformations in the models, primarily by reducing the sensitivity of the sampling to the loop surroundings, and allowing the other CDR loops to optimize with the H3 loop. The new method improves the average accuracy significantly to 1.3 Å RMSD and 3.1 Å RMSD for the shorter and longer loops, respectively. Finally, we present results predicting 8–10 residue loops within complete comparative models of five nonantibody proteins. While anecdotal, these mixed, full‐model results suggest our approach is a promising step toward more accurately predicting loops in homology models. Furthermore, while significant challenges remain, our method is a potentially useful tool for predicting antibody structures based on a known Fv scaffold. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Ab initio structure prediction of the antibody hypervariable H3 loop

Antibodies have the capability of binding a wide range of antigens due to the diversity of the six loops constituting the complementarity determining region (CDR). Among the six loops, the H3 loop is the most diverse in structure, length, and sequence identity. Prediction of the three‐dimensional structures of antibodies, especially the CDR loops, is an important step in the computational design and engineering of novel antibodies for improved affinity and specificity. Although it has been demonstrated that the conformation of the five non‐H3 loops can be accurately predicted by comparing their sequences against databases of canonical loop conformations, no such connection has been established for H3 loops. In this work, we present the results for ab initio structure prediction of the H3 loop using conformational sampling and energy calculations with the program Prime on a dataset of 53 loops ranging in length from 4 to 22 residues. When the prediction is performed in the crystal environment and including symmetry mates, the median backbone root mean square deviation (RMSD) is 0.5 Å to the crystal structure, with 91% of cases having an RMSD of less than 2.0 Å. When the prediction is performed in a noncrystallographic environment, where the scaffold is constructed by swapping the H3 loops between homologous antibodies, 70% of cases have an RMSD below 2.0 Å. These results show promise for ab initio loop predictions applied to modeling of antibodies. © 2012 Wiley Periodicals, Inc.     

Monte Carlo replica‐exchange based ensemble docking of protein conformations

A replica‐exchange Monte Carlo (REMC) ensemble docking approach has been developed that allows efficient exploration of protein–protein docking geometries. In addition to Monte Carlo steps in translation and orientation of binding partners, possible conformational changes upon binding are included based on Monte Carlo selection of protein conformations stored as ordered pregenerated conformational ensembles. The conformational ensembles of each binding partner protein were generated by three different approaches starting from the unbound partner protein structure with a range spanning a root mean square deviation of 1–2.5 Å with respect to the unbound structure. Because MC sampling is performed to select appropriate partner conformations on the fly the approach is not limited by the number of conformations in the ensemble compared to ensemble docking of each conformer pair in ensemble cross docking. Although only a fraction of generated conformers was in closer agreement with the bound structure the REMC ensemble docking approach achieved improved docking results compared to REMC docking with only the unbound partner structures or using docking energy minimization methods. The approach has significant potential for further improvement in combination with more realistic structural ensembles and better docking scoring functions. Proteins 2017; 85:924–937. © 2016 Wiley Periodicals, Inc.     

Protein Loop Modeling Using a New Hybrid Energy Function and Its Application to Modeling in Inaccurate Structural Environments

Protein loop modeling is a tool for predicting protein local structures of particular interest, providing opportunities for applications involving protein structure prediction and de novo protein design. Until recently, the majority of loop modeling methods have been developed and tested by reconstructing loops in frameworks of experimentally resolved structures. In many practical applications, however, the protein loops to be modeled are located in inaccurate structural environments. These include loops in model structures, low-resolution experimental structures, or experimental structures of different functional forms. Accordingly, discrepancies in the accuracy of the structural environment assumed in development of the method and that in practical applications present additional challenges to modern loop modeling methods. This study demonstrates a new strategy for employing a hybrid energy function combining physics-based and knowledge-based components to help tackle this challenge. The hybrid energy function is designed to combine the strengths of each energy component, simultaneously maintaining accurate loop structure prediction in a high-resolution framework structure and tolerating minor environmental errors in low-resolution structures. A loop modeling method based on global optimization of this new energy function is tested on loop targets situated in different levels of environmental errors, ranging from experimental structures to structures perturbed in backbone as well as side chains and template-based model structures. The new method performs comparably to force field-based approaches in loop reconstruction in crystal structures and better in loop prediction in inaccurate framework structures. This result suggests that higher-accuracy predictions would be possible for a broader range of applications. The web server for this method is available at http://galaxy.seoklab.org/loop with the PS2 option for the scoring function.     

Protein loop structure prediction with flexible stem geometries

The structure prediction of loops with flexible stem residues is addressed in this article. While the secondary structure of the stem residues is assumed to be known, the geometry of the protein into which the loop must fit is considered to be unknown in our methodology. As a consequence, the compatibility of the loop with the remainder of the protein is not used as a criterion to reject loop decoys. The loop structure prediction with flexible stems is more difficult than fitting loops into a known protein structure in that a larger conformational space has to be covered. The main focus of the study is to assess the precision of loop structure prediction if no information on the protein geometry is available. The proposed approach is based on (1) dihedral angle sampling, (2) structure optimization by energy minimization with a physically based energy function, (3) clustering, and (4) a comparison of strategies for the selection of loops identified in (3). Steps (1) and (2) have similarities to previous approaches to loop structure prediction with fixed stems. Step (3) is based on a new iterative approach to clustering that is tailored for the loop structure prediction problem with flexible stems. In this new approach, clustering is not only used to identify conformers that are likely to be close to the native structure, but clustering is also employed to identify far-from-native decoys. By discarding these decoys iteratively, the overall quality of the ensemble and the loop structure prediction is improved. Step (4) provides a comparative study of criteria for loop selection based on energy, colony energy, cluster density, and a hybrid criterion introduced here. The proposed method is tested on a large set of 3215 loops from proteins in the Pdb-Select25 set and to 179 loops from proteins from the Casp6 experiment.     

Protein loop modeling by using fragment assembly and analytical loop closure

Protein loops are often involved in important biological functions such as molecular recognition, signal transduction, or enzymatic action. The three dimensional structures of loops can provide essential information for understanding molecular mechanisms behind protein functions. In this article, we develop a novel method for protein loop modeling, where the loop conformations are generated by fragment assembly and analytical loop closure. The fragment assembly method reduces the conformational space drastically, and the analytical loop closure method finds the geometrically consistent loop conformations efficiently. We also derive an analytic formula for the gradient of any analytical function of dihedral angles in the space of closed loops. The gradient can be used to optimize various restraints derived from experiments or databases, for example restraints for preferential interactions between specific residues or for preferred backbone angles. We demonstrate that the current loop modeling method outperforms previous methods that employ residue‐based torsion angle maps or different loop closure strategies when tested on two sets of loop targets of lengths ranging from 4 to 12. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Long loop prediction using the protein local optimization program

We have developed an improved sampling algorithm and energy model for protein loop prediction, the combination of which has yielded the first methodology capable of achieving good results for the prediction of loop backbone conformations of 11 residue length or greater. Applied to our newly constructed test suite of 104 loops ranging from 11 to 13 residues, our method obtains average/median global backbone root-mean-square deviations (RMSDs) to the native structure (superimposing the body of the protein, not the loop itself) of 1.00/0.62 A for 11 residue loops, 1.15/0.60 A for 12 residue loops, and 1.25/0.76 A for 13 residue loops. Sampling errors are virtually eliminated, while energy errors leading to large backbone RMSDs are very infrequent compared to any previously reported efforts, including our own previous study. We attribute this success to both an improved sampling algorithm and, more critically, the inclusion of a hydrophobic term, which appears to approximately fix a major flaw in SGB solvation model that we have been employing. A discussion of these results in the context of the general question of the accuracy of continuum solvation models is presented.     

De novo backbone scaffolds for protein design

In recent years, there have been significant advances in the field of computational protein design including the successful computational design of enzymes based on backbone scaffolds from experimentally solved structures. It is likely that large‐scale sampling of protein backbone conformations will become necessary as further progress is made on more complicated systems. Removing the constraint of having to use scaffolds based on known protein backbones is a potential method of solving the problem. With this application in mind, we describe a method to systematically construct a large number of de novo backbone structures from idealized topological forms in a top–down hierarchical approach. The structural properties of these novel backbone scaffolds were analyzed and compared with a set of high‐resolution experimental structures from the protein data bank (PDB). It was found that the Ramachandran plot distribution and relative γ‐ and β‐turn frequencies were similar to those found in the PDB. The de novo scaffolds were sequence designed with RosettaDesign, and the energy distributions and amino acid compositions were comparable with the results for redesigned experimentally solved backbones. Proteins 2010. © 2009 Wiley‐Liss, Inc.     

The H3 loop of antibodies shows unique structural characteristics

The H3 loop in the Complementarity Determining Region of antibodies plays a key role in their ability to bind the diverse space of potential antigens. It is also exceptionally difficult to model computationally causing a significant hurdle for in silico development of antibody biotherapeutics. In this article, we show that most H3s have unique structural characteristics which may explain why they are so challenging to model. We found that over 75% of H3 loops do not have a sub‐Angstrom structural neighbor in the non‐antibody world. Also, in a comparison with a nonredundant set of all protein fragments over 30% of H3 loops have a unique structure, with the average for all of other loops being less than 3%. We further observed that this structural difference can be seen at the level of four residue fragments where H3 loops present numerous novel conformations, and also at the level of individual residues with Tyrosine and Glycine often found in energetically unfavorable conformations. Proteins 2017; 85:1311–1318. © 2017 Wiley Periodicals, Inc.     

A population-based evolutionary search approach to the multiple minima problem in de novo protein structure prediction

Background

Elucidating the native structure of a protein molecule from its sequence of amino acids, a problem known as de novo structure prediction, is a long standing challenge in computational structural biology. Difficulties in silico arise due to the high dimensionality of the protein conformational space and the ruggedness of the associated energy surface. The issue of multiple minima is a particularly troublesome hallmark of energy surfaces probed with current energy functions. In contrast to the true energy surface, these surfaces are weakly-funneled and rich in comparably deep minima populated by non-native structures. For this reason, many algorithms seek to be inclusive and obtain a broad view of the low-energy regions through an ensemble of low-energy (decoy) conformations. Conformational diversity in this ensemble is key to increasing the likelihood that the native structure has been captured.

Methods

We propose an evolutionary search approach to address the multiple-minima problem in decoy sampling for de novo structure prediction. Two population-based evolutionary search algorithms are presented that follow the basic approach of treating conformations as individuals in an evolving population. Coarse graining and molecular fragment replacement are used to efficiently obtain protein-like child conformations from parents. Potential energy is used both to bias parent selection and determine which subset of parents and children will be retained in the evolving population. The effect on the decoy ensemble of sampling minima directly is measured by additionally mapping a conformation to its nearest local minimum before considering it for retainment. The resulting memetic algorithm thus evolves not just a population of conformations but a population of local minima.

Results and conclusions

Results show that both algorithms are effective in terms of sampling conformations in proximity of the known native structure. The additional minimization is shown to be key to enhancing sampling capability and obtaining a diverse ensemble of decoy conformations, circumventing premature convergence to sub-optimal regions in the conformational space, and approaching the native structure with proximity that is comparable to state-of-the-art decoy sampling methods. The results are shown to be robust and valid when using two representative state-of-the-art coarse-grained energy functions.

     

Toward better refinement of comparative models: predicting loops in inexact environments

Achieving atomic-level accuracy in comparative protein models is limited by our ability to refine the initial, homolog-derived model closer to the native state. Despite considerable effort, progress in developing a generalized refinement method has been limited. In contrast, methods have been described that can accurately reconstruct loop conformations in native protein structures. We hypothesize that loop refinement in homology models is much more difficult than loop reconstruction in crystal structures, in part, because side-chain, backbone, and other structural inaccuracies surrounding the loop create a challenging sampling problem; the loop cannot be refined without simultaneously refining adjacent portions. In this work, we single out one sampling issue in an artificial but useful test set and examine how loop refinement accuracy is affected by errors in surrounding side-chains. In 80 high-resolution crystal structures, we first perturbed 6-12 residue loops away from the crystal conformation, and placed all protein side chains in non-native but low energy conformations. Even these relatively small perturbations in the surroundings made the loop prediction problem much more challenging. Using a previously published loop prediction method, median backbone (N-Calpha-C-O) RMSD's for groups of 6, 8, 10, and 12 residue loops are 0.3/0.6/0.4/0.6 A, respectively, on native structures and increase to 1.1/2.2/1.5/2.3 A on the perturbed cases. We then augmented our previous loop prediction method to simultaneously optimize the rotamer states of side chains surrounding the loop. Our results show that this augmented loop prediction method can recover the native state in many perturbed structures where the previous method failed; the median RMSD's for the 6, 8, 10, and 12 residue perturbed loops improve to 0.4/0.8/1.1/1.2 A. Finally, we highlight three comparative models from blind tests, in which our new method predicted loops closer to the native conformation than first modeled using the homolog template, a task generally understood to be difficult. Although many challenges remain in refining full comparative models to high accuracy, this work offers a methodical step toward that goal.     

New efficient statistical sequence-dependent structure prediction of short to medium-sized protein loops based on an exhaustive loop classification.

A bank of 13,563 loops from three to eight amino acid residues long, representing motifs between two consecutive regular secondary structures, has been derived from protein structures presenting less than 95 % sequence identity. Statistical analyses of occurrences of conformations and residues revealed length-dependent over-representations of particular amino acids (glycine, proline, asparagine, serine, and aspartate) and conformations (alphaL, epsilon, betaPregions of the Ramachandran plot). A position-dependent distribution of these occurrences was observed for N and C-terminal residues, which are correlated to the nature of the flanking regions. Loops of the same length were clustered into statistically meaningful families on the basis of their backbone structures when placed in a common reference frame, independent of the flanks. These clusters present significantly different distributions of sequence, conformations, and endpoint residue Calphadistances. On the basis of the sequence-structure correlation of this clustering, an automatic loop modeling algorithm was developed. Based on the knowledge of its sequence and of its flank backbone structures each query loop is assigned to a family and target loop supports are selected in this family. The support backbones of these target loops are then adjusted on flanking structures by partial exploration of the conformational space. Loop closure is performed by energy minimization for each support and the final model is chosen among connected supports based upon energy criteria. The quality of the prediction is evaluated by the root-mean-square deviation (rmsd) between the final model and the native loops when the whole bank is re-attributed on itself with a Jackknife test. This average rmsd ranges from 1.1 A for three-residue loops to 3.8 A for eight-residue loops. A few poorly predicted loops are inescapable, considering the high level of diversity in loops and the lack of environment data. To overcome such modeling problems, a statistical reliability score was assigned for each prediction. This score is correlated to the quality of the prediction, in terms of rmsd, and thus improves the selection accuracy of the model. The algorithm efficiency was compared to CASP3 target loop predictions. Moreover, when tested on a test loop bank, this algorithm was shown to be robust when the loops are not precisely delimited, therefore proving to be a useful tool in practice for protein modeling.     

Loop modeling: Sampling, filtering, and scoring

We describe a fast and accurate protocol, LoopBuilder, for the prediction of loop conformations in proteins. The procedure includes extensive sampling of backbone conformations, side chain addition, the use of a statistical potential to select a subset of these conformations, and, finally, an energy minimization and ranking with an all-atom force field. We find that the Direct Tweak algorithm used in the previously developed LOOPY program is successful in generating an ensemble of conformations that on average are closer to the native conformation than those generated by other methods. An important feature of Direct Tweak is that it checks for interactions between the loop and the rest of the protein during the loop closure process. DFIRE is found to be a particularly effective statistical potential that can bias conformation space toward conformations that are close to the native structure. Its application as a filter prior to a full molecular mechanics energy minimization both improves prediction accuracy and offers a significant savings in computer time. Final scoring is based on the OPLS/SBG-NP force field implemented in the PLOP program. The approach is also shown to be quite successful in predicting loop conformations for cases where the native side chain conformations are assumed to be unknown, suggesting that it will prove effective in real homology modeling applications.