Discrimination of native loop conformations in membrane proteins: decoy library design and evaluation of effective energy scoring functions

The recent determination of crystal structures for several important membrane proteins opens the way for comparative modeling of their membrane-spanning regions. However, the ability to predict correctly the structures of loop regions, which may be critical, for example, in ligand binding, remains a considerable challenge. To meet this challenge, accurate scoring methods have to discriminate between candidate conformations of an unknown loop structure. Some success in loop prediction has been reported for globular proteins; however, the proximity of membrane protein loops to the lipid bilayer casts doubt on the applicability of the same scoring methods to this problem. In this work, we develop "decoy libraries" of non-native folds generated, using the structures of two membrane proteins, with molecular dynamics and Monte Carlo techniques over a range of temperatures. We introduce a new approach for decoy library generation by constructing a flat distribution of conformations covering a wide range of Calpha-root-mean-square deviation (RMSD) from the native structure; this removes possible bias in subsequent scoring stages. We then score these decoy conformations with effective energy functions, using increasingly more cpu-intensive implicit solvent models, including (1) simple Coulombic electrostatics with constant or distance-dependent dielectrics; (2) atomic solvation parameters; (3) the effective energy function (EEF1) of Lazaridis and Karplus; (4) generalized Born/Analytical Continuum Solvent; and (5) finite-difference Poisson-Boltzmann energy functions. We show that distinction of native-like membrane protein loops may be achieved using effective energies with the assumption of a homogenous environment; thus, the absence of the adjacent lipid bilayer does not affect the scoring ability. In particular, the Analytical Continuum Solvent and finite-difference Poisson-Boltzmann energy functions are seen to be the most powerful scoring functions. Interestingly, the use of the uncharged states of ionizable sidechains is shown to aid prediction, particularly for the simplest energy functions.     

The energy computation paradox and ab initio protein folding

The routine prediction of three-dimensional protein structure from sequence remains a challenge in computational biochemistry. It has been intuited that calculated energies from physics-based scoring functions are able to distinguish native from nonnative folds based on previous performance with small proteins and that conformational sampling is the fundamental bottleneck to successful folding. We demonstrate that as protein size increases, errors in the computed energies become a significant problem. We show, by using error probability density functions, that physics-based scores contain significant systematic and random errors relative to accurate reference energies. These errors propagate throughout an entire protein and distort its energy landscape to such an extent that modern scoring functions should have little chance of success in finding the free energy minima of large proteins. Nonetheless, by understanding errors in physics-based score functions, they can be reduced in a post-hoc manner, improving accuracy in energy computation and fold discrimination.     

Fast de novo discovery of low‐energy protein loop conformations

In the prediction of protein structure from amino acid sequence, loops are challenging regions for computational methods. Since loops are often located on the protein surface, they can have significant roles in determining protein functions and binding properties. Loop prediction without the aid of a structural template requires extensive conformational sampling and energy minimization, which are computationally difficult. In this article we present a new de novo loop sampling method, the Parallely filtered Energy Targeted All‐atom Loop Sampler (PETALS) to rapidly locate low energy conformations. PETALS explores both backbone and side‐chain positions of the loop region simultaneously according to the energy function selected by the user, and constructs a nonredundant ensemble of low energy loop conformations using filtering criteria. The method is illustrated with the DFIRE potential and DiSGro energy function for loops, and shown to be highly effective at discovering conformations with near‐native (or better) energy. Using the same energy function as the DiSGro algorithm, PETALS samples conformations with both lower RMSDs and lower energies. PETALS is also useful for assessing the accuracy of different energy functions. PETALS runs rapidly, requiring an average time cost of 10 minutes for a length 12 loop on a single 3.2 GHz processor core, comparable to the fastest existing de novo methods for generating an ensemble of conformations. Proteins 2017; 85:1402–1412. © 2017 Wiley Periodicals, Inc.     

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.     

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.     

Distance geometry generates native-like folds for small helical proteins using the consensus distances of predicted protein structures.

For successful ab initio protein structure prediction, a method is needed to identify native-like structures from a set containing both native and non-native protein-like conformations. In this regard, the use of distance geometry has shown promise when accurate inter-residue distances are available. We describe a method by which distance geometry restraints are culled from sets of 500 protein-like conformations for four small helical proteins generated by the method of Simons et al. (1997). A consensus-based approach was applied in which every inter-Calpha distance was measured, and the most frequently occurring distances were used as input restraints for distance geometry. For each protein, a structure with lower coordinate root-mean-square (RMS) error than the mean of the original set was constructed; in three cases the topology of the fold resembled that of the native protein. When the fold sets were filtered for the best scoring conformations with respect to an all-atom knowledge-based scoring function, the remaining subset of 50 structures yielded restraints of higher accuracy. A second round of distance geometry using these restraints resulted in an average coordinate RMS error of 4.38 A.     

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.     

Decoys 'R' Us: a database of incorrect conformations to improve protein structure prediction

The development of an energy or scoring function for protein structure prediction is greatly enhanced by testing the function on a set of computer-generated conformations (decoys) to determine whether it can readily distinguish native-like conformations from nonnative ones. We have created "Decoys 'R' Us," a database containing many such sets of conformations, to provide a resource that allows scoring functions to be improved.     

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.     

Progress and challenges in high-resolution refinement of protein structure models

Achieving atomic level accuracy in de novo structure prediction presents a formidable challenge even in the context of protein models with correct topologies. High-resolution refinement is a fundamental test of force field accuracy and sampling methodology, and its limited success in both comparative modeling and de novo prediction contexts highlights the limitations of current approaches. We constructed four tests to identify bottlenecks in our current approach and to guide progress in this challenging area. The first three tests showed that idealized native structures are stable under our refinement simulation conditions and that the refinement protocol can significantly decrease the root mean square deviation (RMSD) of perturbed native structures. In the fourth test we applied the refinement protocol to de novo models and showed that accurate models could be identified based on their energies, and in several cases many of the buried side chains adopted native-like conformations. We also showed that the differences in backbone and side-chain conformations between the refined de novo models and the native structures are largely localized to loop regions and regions where the native structure has unusual features such as rare rotamers or atypical hydrogen bonding between beta-strands. The refined de novo models typically have higher energies than refined idealized native structures, indicating that sampling of local backbone conformations and side-chain packing arrangements in a condensed state is a primary obstacle.     

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.     

DockRank: Ranking docked conformations using partner‐specific sequence homology‐based protein interface prediction

Selecting near‐native conformations from the immense number of conformations generated by docking programs remains a major challenge in molecular docking. We introduce DockRank, a novel approach to scoring docked conformations based on the degree to which the interface residues of the docked conformation match a set of predicted interface residues. DockRank uses interface residues predicted by partner‐specific sequence homology‐based protein–protein interface predictor (PS‐HomPPI), which predicts the interface residues of a query protein with a specific interaction partner. We compared the performance of DockRank with several state‐of‐the‐art docking scoring functions using Success Rate (the percentage of cases that have at least one near‐native conformation among the top m conformations) and Hit Rate (the percentage of near‐native conformations that are included among the top m conformations). In cases where it is possible to obtain partner‐specific (PS) interface predictions from PS‐HomPPI, DockRank consistently outperforms both (i) ZRank and IRAD, two state‐of‐the‐art energy‐based scoring functions (improving Success Rate by up to 4‐fold); and (ii) Variants of DockRank that use predicted interface residues obtained from several protein interface predictors that do not take into account the binding partner in making interface predictions (improving success rate by up to 39‐fold). The latter result underscores the importance of using partner‐specific interface residues in scoring docked conformations. We show that DockRank, when used to re‐rank the conformations returned by ClusPro, improves upon the original ClusPro rankings in terms of both Success Rate and Hit Rate. DockRank is available as a server at http://einstein.cs.iastate.edu/DockRank/ . Proteins 2014; 82:250–267. © 2013 Wiley Periodicals, Inc.     

Predicting protein complex geometries with a neural network

A major challenge of the protein docking problem is to define scoring functions that can distinguish near‐native protein complex geometries from a large number of non‐native geometries (decoys) generated with noncomplexed protein structures (unbound docking). In this study, we have constructed a neural network that employs the information from atom‐pair distance distributions of a large number of decoys to predict protein complex geometries. We found that docking prediction can be significantly improved using two different types of polar hydrogen atoms. To train the neural network, 2000 near‐native decoys of even distance distribution were used for each of the 185 considered protein complexes. The neural network normalizes the information from different protein complexes using an additional protein complex identity input neuron for each complex. The parameters of the neural network were determined such that they mimic a scoring funnel in the neighborhood of the native complex structure. The neural network approach avoids the reference state problem, which occurs in deriving knowledge‐based energy functions for scoring. We show that a distance‐dependent atom pair potential performs much better than a simple atom‐pair contact potential. We have compared the performance of our scoring function with other empirical and knowledge‐based scoring functions such as ZDOCK 3.0, ZRANK, ITScore‐PP, EMPIRE, and RosettaDock. In spite of the simplicity of the method and its functional form, our neural network‐based scoring function achieves a reasonable performance in rigid‐body unbound docking of proteins. Proteins 2010. © 2009 Wiley‐Liss, Inc.     

High-Resolution Modeling of Transmembrane Helical Protein Structures from Distant Homologues

Eukaryotic transmembrane helical (TMH) proteins perform a wide diversity of critical cellular functions, but remain structurally largely uncharacterized and their high-resolution structure prediction is currently hindered by the lack of close structural homologues. To address this problem, we present a novel and generic method for accurately modeling large TMH protein structures from distant homologues exhibiting distinct loop and TMH conformations. Models of the adenosine A2AR and chemokine CXCR4 receptors were first ranked in GPCR-DOCK blind prediction contests in the receptor structure accuracy category. In a benchmark of 50 TMH protein homolog pairs of diverse topology (from 5 to 12 TMHs), size (from 183 to 420 residues) and sequence identity (from 15% to 70%), the method improves most starting templates, and achieves near-atomic accuracy prediction of membrane-embedded regions. Unlike starting templates, the models are of suitable quality for computer-based protein engineering: redesigned models and redesigned X-ray structures exhibit very similar native interactions. The method should prove useful for the atom-level modeling and design of a large fraction of structurally uncharacterized TMH proteins from a wide range of structural homologues.     

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.     

Simulated tempering yields insight into the low-resolution Rosetta scoring functions

Rosetta is a structure prediction package that has been employed successfully in numerous protein design and other applications.1 Previous reports have attributed the current limitations of the Rosetta de novo structure prediction algorithm to inadequate sampling, particularly during the low-resolution phase.2-5 Here, we implement the Simulated Tempering (ST) sampling algorithm67 in Rosetta to address this issue. ST is intended to yield canonical sampling by inducing a random walk in temperatures space such that broad sampling is achieved at high temperatures and detailed exploration of local free energy minima is achieved at low temperatures. ST should therefore visit basins in accordance with their free energies rather than their energies and achieve more global sampling than the localized scheme currently implemented in Rosetta. However, we find that ST does not improve structure prediction with Rosetta. To understand why, we carried out a detailed analysis of the low-resolution scoring functions and find that they do not provide a strong bias towards the native state. In addition, we find that both ST and standard Rosetta runs started from the native state are biased away from the native state. Although the low-resolution scoring functions could be improved, we propose that working entirely at full-atom resolution is now possible and may be a better option due to superior native-state discrimination at full-atom resolution. Such an approach will require more attention to the kinetics of convergence, however, as functions capable of native state discrimination are not necessarily capable of rapidly guiding non-native conformations to the native state.     

Evaluating CASP4 predictions with physical energy functions

Physical energy scoring functions based on implicit solvation models are tested by evaluating predictions from the most recent CASP4 competition. The best performing scoring functions are identified along with the best protocol for preparing structures before energies are evaluated. Ranking of structures with the best scoring functions is compared across CASP4 targets to establish when physical scoring functions can be expected to reliably distinguish structures that are most similar to the native fold in a set of misfolded or unfolded protein conformations. The results are used to interpret previous studies where scoring functions were tested on the standard decoy sets by Park, Levitt, and Baker. We show that the best physical scoring functions can be applied successfully in automated consensus scoring applications where a single best conformation has to be selected from a set of structures from different sources. Finally, the potential for better protein structure scoring functions is discussed with a suggestion for an empirically parameterized linear combination of energy components.     

Protein Structure Prediction and Design in a Biologically Realistic Implicit Membrane

Protein design is a powerful tool for elucidating mechanisms of function and engineering new therapeutics and nanotechnologies. Although soluble protein design has advanced, membrane protein design remains challenging because of difficulties in modeling the lipid bilayer. In this work, we developed an implicit approach that captures the anisotropic structure, shape of water-filled pores, and nanoscale dimensions of membranes with different lipid compositions. The model improves performance in computational benchmarks against experimental targets, including prediction of protein orientations in the bilayer, ΔΔG calculations, native structure discrimination, and native sequence recovery. When applied to de novo protein design, this approach designs sequences with an amino acid distribution near the native amino acid distribution in membrane proteins, overcoming a critical flaw in previous membrane models that were prone to generating leucine-rich designs. Furthermore, the proteins designed in the new membrane model exhibit native-like features including interfacial aromatic side chains, hydrophobic lengths compatible with bilayer thickness, and polar pores. Our method advances high-resolution membrane protein structure prediction and design toward tackling key biological questions and engineering challenges.     

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.