Protein Loop Modeling Research Articles

Highly Accurate and Efficient Deep Learning Paradigm for Full-Atom Protein Loop Modeling with KarmaLoop.

Protein loop modeling is a challenging yet highly nontrivial task in protein structure prediction. Despite recent progress, existing methods including knowledge-based, abinitio, hybrid, and deep learning (DL) methods fall substantially short of either atomic accuracy or computational efficiency. To overcome these limitations, we present KarmaLoop, a novel paradigm that distinguishes itself as the first DL method centered on full-atom (encompassing both backbone and side-chain heavy atoms) protein loop modeling. Our results demonstrate that KarmaLoop considerably outperforms conventional and DL-based methods of loop modeling in terms of both accuracy and efficiency, with the average RMSDs of 1.77 and 1.95 Å for the CASP13+14 and CASP15 benchmark datasets, respectively, and manifests at least 2 orders of magnitude speedup in general compared with other methods. Consequently, our comprehensive evaluations indicate that KarmaLoop provides a state-of-the-art DL solution for protein loop modeling, with the potential to hasten the advancement of protein engineering, antibody-antigen recognition, and drug design.

Ab Initio Prediction of 3-D Conformations for Protein Long Loops with High Accuracy and Applications to Antibody CDRH3 Modeling.

Residue-level potentials of mean force were widely used for protein backbone refinements to avoid simultaneous sampling of side-chain conformations. The interaction energy between the reduced side chains and backbone atoms was not considered explicitly. In this study, we developed novel methods to calculate the residue-atom interaction energy in combination with atomic and residue-level terms. The parameters were optimized step by step to remove the overcounting or overlap problem between different energy terms. The mixing energy functions were then used to evaluate the generated backbone conformations at the initial sampling stage of protein loop modeling (OSCAR-loop), including the interaction energy between the reduced loop residues and full atoms of the protein framework. The accuracies of top-ranked decoys were 1.18 and 2.81 Å for 8-residue and 12-residue loops, respectively. We then selected diverse decoys for side-chain modeling, backbone refinement, and energy minimization. The procedure was repeated multiple times to select one prediction with the lowest energy. Consequently, we obtained an accuracy of 0.74 Å for a prevailing test set of 12-residue loops, compared with >1.4 Å reported by other researchers. The OSCAR-loop was also effective for modeling the H3 loops of antibody complementary determining regions (CDRs) in the crystal environment. The prediction accuracy of OSCAR-loop (1.74 Å) was better than the accuracy of the Rosetta NGK method (3.11 Å) or those achieved by deep learning methods (>2.2 Å) for the CDRH3 loops of 49 targets in the Rosetta antibody benchmark. The performance of OSCAR-loop in a model environment was also discussed.

Comprehensive assessment of protein loop modeling programs on large-scale datasets: prediction accuracy and efficiency.

Protein loops play a critical role in the dynamics of proteins and are essential for numerous biological functions, and various computational approaches to loop modeling have been proposed over the past decades. However, a comprehensive understanding of the strengths and weaknesses of each method is lacking. In this work, we constructed two high-quality datasets (i.e. the General dataset and the CASP dataset) and systematically evaluated the accuracy and efficiency of 13 commonly used loop modeling approaches from the perspective of loop lengths, protein classes and residue types. The results indicate that the knowledge-based method FREAD generally outperforms the other tested programs in most cases, but encountered challenges when predicting loops longer than 15 and 30 residues on the CASP and General datasets, respectively. The ab initio method Rosetta NGK demonstrated exceptional modeling accuracy for short loops with four to eight residues and achieved the highest success rate on the CASP dataset. The well-known AlphaFold2 and RoseTTAFold require more resources for better performance, but they exhibit promise for predicting loops longer than 16 and 30 residues in the CASP and General datasets. These observations can provide valuable insights for selecting suitable methods for specific loop modeling tasks and contribute to future advancements in the field.

Distance geometry and protein loop modeling.

Due to the role of loops in protein function, loop modeling is an important problem in computational biology. We present a new approach to loop modeling based on a combinatorial version of distance geometry, where the search space of the associated problem is represented by a binary tree and a branch-and-prune method is defined to explore it, following an atomic ordering previously given. This ordering is used to calculate the coordinates of atoms from the positions of its predecessors. In addition to the theoretical development, computational results are presented to illustrate the advantage of the proposed method, compared with another approach of the literature. Our algorithm is freely available at https://github.com/michaelsouza/bpl.

Protein Loop Modeling using Deep Neural Networks Enhanced by Reinforcement Learning

Protein Loop Modeling using Deep Neural Networks Enhanced by Reinforcement Learning

New Deep Learning Methods for Protein Loop Modeling.

Computational protein structure prediction is a long-standing challenge in bioinformatics. In the process of predicting protein 3D structures, it is common that parts of an experimental structure are missing or parts of a predicted structure need to be remodeled. The process of predicting local protein structures of particular regions is called loop modeling. In this paper, five new loop modeling methods based on machine learning techniques, called NearLooper, ConLooper, ResLooper, HyLooper1, and HyLooper2 are proposed. NearLooper is based on the nearest neighbor technique. ConLooper applies deep convolutional neural networks to predict ${\mathrm{C}}_{{{\alpha }}}$Cα atoms distance matrix as an orientation-independent representation of protein structure. ResLooper uses residual neural networks instead of deep convolutional neural networks. HyLooper1 combines the results of NearLooper and ConLooper while HyLooper2 combines NearLooper and ResLooper. Three commonly used benchmarks for loop modeling are used to compare the performance between these methods and existing state-of-the-art methods. The experiment results show promising performance in which our best method improves existing state-of-the-art methods by 28 and 54 percent of average RMSD on two datasets while being comparable on the other one.

Protein Loop Structure Prediction Using Conformational Space Annealing.

We have developed a protein loop structure prediction method by combining a new energy function, which we call EPLM (energy for protein loop modeling), with the conformational space annealing (CSA) global optimization algorithm. The energy function includes stereochemistry, dynamic fragment assembly, distance-scaled finite ideal gas reference (DFIRE), and generalized orientation- and distance-dependent terms. For the conformational search of loop structures, we used the CSA algorithm, which has been quite successful in dealing with various hard global optimization problems. We assessed the performance of EPLM with two widely used loop-decoy sets, Jacobson and RAPPER, and compared the results against the DFIRE potential. The accuracy of model selection from a pool of loop decoys as well as de novo loop modeling starting from randomly generated structures was examined separately. For the selection of a nativelike structure from a decoy set, EPLM was more accurate than DFIRE in the case of the Jacobson set and had similar accuracy in the case of the RAPPER set. In terms of sampling more nativelike loop structures, EPLM outperformed EDFIRE for both decoy sets. This new approach equipped with EPLM and CSA can serve as the state-of-the-art de novo loop modeling method.

Protein Structure Classification and Loop Modeling Using Multiple Ramachandran Distributions

Recently, the study of protein structures using angular representations has attracted much attention among structural biologists. The main challenge is how to efficiently model the continuous conformational space of the protein structures based on the differences and similarities between different Ramachandran plots. Despite the presence of statistical methods for modeling angular data of proteins, there is still a substantial need for more sophisticated and faster statistical tools to model the large-scale circular datasets. To address this need, we have developed a nonparametric method for collective estimation of multiple bivariate density functions for a collection of populations of protein backbone angles. The proposed method takes into account the circular nature of the angular data using trigonometric spline which is more efficient compared to existing methods. This collective density estimation approach is widely applicable when there is a need to estimate multiple density functions from different populations with common features. Moreover, the coefficients of adaptive basis expansion for the fitted densities provide a low-dimensional representation that is useful for visualization, clustering, and classification of the densities. The proposed method provides a novel and unique perspective to two important and challenging problems in protein structure research: structure-based protein classification and angular-sampling-based protein loop structure prediction.

Computational Models of Interacting Loop Regions in pH-Dependent Gating of OmpG

Outer membrane protein G (OmpG), a monomeric beta-barrel membrane protein, has the potential to be used as a nano-sensor device. To achieve this goal, it is important to understand OmpG's ion current conducting properties. Previous studies have demonstrated pH-dependent gating, namely, current flow through the porin decreases as the pH decreases. While it is thought that loop regions have strong influence on the OmpG gating state, there is uncertainty on the mechanism that induces the functional switch as the pH is altered. Based on the DiSGro method of protein loop modeling, we extensively sample the three-dimensional conformations of multiple interacting loop regions of OmpG at various pH levels. Specifically, 10,000 loop samples are generated at pH 5 and pH 7 for each of 6 mutant OmpG variants and the wild type. These loops are used to study the conformations of mutant OmpG variants with experimentally observed differences in gating properties.

Collective Estimation of Multiple Bivariate Density Functions With Application to Angular-Sampling-Based Protein Loop Modeling

This article develops a method for simultaneous estimation of density functions for a collection of populations of protein backbone angle pairs using a data-driven, shared basis that is constructed by bivariate spline functions defined on a triangulation of the bivariate domain. The circular nature of angular data is taken into account by imposing appropriate smoothness constraints across boundaries of the triangles. Maximum penalized likelihood is used to fit the model and an alternating blockwise Newton-type algorithm is developed for computation. A simulation study shows that the collective estimation approach is statistically more efficient than estimating the densities individually. The proposed method was used to estimate neighbor-dependent distributions of protein backbone dihedral angles (i.e., Ramachandran distributions). The estimated distributions were applied to protein loop modeling, one of the most challenging open problems in protein structure prediction, by feeding them into an angular-sampling-based loop structure prediction framework. Our estimated distributions compared favorably to the Ramachandran distributions estimated by fitting a hierarchical Dirichlet process model; and in particular, our distributions showed significant improvements on the hard cases where existing methods do not work well.

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 Modeling with Optimized Backbone Potential Functions.

We represented protein backbone potential as a Fourier series. The parameters of the backbone dihedral potential were initialized to random values and optimized by Monte Carlo simulations so that generated native-like loop decoys had a lower energy than non-native decoys. The low energy regions of the optimized backbone potential were consistent with observed Ramachandran plots derived from crystal structures. The backbone potential was then used for the prediction of loop conformations (OSCAR-loop) combining with the previously described OSCAR force field, which has been shown to be very accurate in side chain modeling. As a result, the accuracy of OSCAR-loop was improved by local energy minimization based on the complete force field. The average accuracies were 0.40, 0.70, 1.10, 2.08, and 3.58 Å for 4, 6, 8, 10, and 12-residue loops, respectively, with each size being represented by 325 to 2809 targets. The accuracy was better than that of other loop modeling algorithms for short loops (<10 residues). For longer loops, the prediction accuracy was improved by concurrently sampling with a fragment-based method, Spanner. OSCAR-loop is available for download at http://sysimm.ifrec.osaka-u.ac.jp/OSCAR/ .

The FALC-Loop web server for protein loop modeling

The FALC-Loop web server provides an online interface for protein loop modeling by employing an ab initio loop modeling method called FALC (fragment assembly and analytical loop closure). The server may be used to construct loop regions in homology modeling, to refine unreliable loop regions in experimental structures or to model segments of designed sequences. The FALC method is computationally less expensive than typical ab initio methods because the conformational search space is effectively reduced by the use of fragments derived from a structure database. The analytical loop closure algorithm allows efficient search for loop conformations that fit into the protein framework starting from the fragment-assembled structures. The FALC method shows prediction accuracy comparable to other state-of-the-art loop modeling methods. Top-ranked model structures can be visualized on the web server, and an ensemble of loop structures can be downloaded for further analysis. The web server can be freely accessed at http://falc-loop.seoklab.org/.

Development of a new physics-based internal coordinate mechanics force field and its application to protein loop modeling.

We report the development of internal coordinate mechanics force field (ICMFF), new force field parameterized using a combination of experimental data for crystals of small molecules and quantum mechanics calculations. The main features of ICMFF include: (a) parameterization for the dielectric constant relevant to the condensed state (ε = 2) instead of vacuum, (b) an improved description of hydrogen-bond interactions using duplicate sets of van der Waals parameters for heavy atom-hydrogen interactions, and (c) improved backbone covalent geometry and energetics achieved using novel backbone torsional potentials and inclusion of the bond angles at the C(α) atoms into the internal variable set. The performance of ICMFF was evaluated through loop modeling simulations for 4-13 residue loops. ICMFF was combined with a solvent-accessible surface area solvation model optimized using a large set of loop decoys. Conformational sampling was carried out using the biased probability Monte Carlo method. Average/median backbone root-mean-square deviations of the lowest energy conformations from the native structures were 0.25/0.21 Å for four residues loops, 0.84/0.46 Å for eight residue loops, and 1.16/0.73 Å for 12 residue loops. To our knowledge, these results are significantly better than or comparable with those reported to date for any loop modeling method that does not take crystal packing into account. Moreover, the accuracy of our method is on par with the best previously reported results obtained considering the crystal environment. We attribute this success to the high accuracy of the new ICM force field achieved by meticulous parameterization, to the optimized solvent model, and the efficiency of the search method.

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.

A Probabilistic and Continuous Model of Protein Conformational Space for Template-Free Modeling

One of the major challenges with protein template-free modeling is an efficient sampling algorithm that can explore a huge conformation space quickly. The popular fragment assembly method constructs a conformation by stringing together short fragments extracted from the Protein Data Base (PDB). The discrete nature of this method may limit generated conformations to a subspace in which the native fold does not belong. Another worry is that a protein with really new fold may contain some fragments not in the PDB. This article presents a probabilistic model of protein conformational space to overcome the above two limitations. This probabilistic model employs directional statistics to model the distribution of backbone angles and 2(nd)-order Conditional Random Fields (CRFs) to describe sequence-angle relationship. Using this probabilistic model, we can sample protein conformations in a continuous space, as opposed to the widely used fragment assembly and lattice model methods that work in a discrete space. We show that when coupled with a simple energy function, this probabilistic method compares favorably with the fragment assembly method in the blind CASP8 evaluation, especially on alpha or small beta proteins. To our knowledge, this is the first probabilistic method that can search conformations in a continuous space and achieves favorable performance. Our method also generated three-dimensional (3D) models better than template-based methods for a couple of CASP8 hard targets. The method described in this article can also be applied to protein loop modeling, model refinement, and even RNA tertiary structure prediction.

Closing the side-chain gap in protein loop modeling

The success of structure-based drug design relies on accurate protein modeling where one of the key issues is the modeling and refinement of loops. This study takes a critical look at modeled loops, determining the effect of re-sampling side-chains after the loop conformation has been generated. The results are evaluated in terms of backbone and side-chain conformations with respect to the native loop. While models can contain loops with high quality backbone conformations, the side-chain orientations could be poor, and therefore unsuitable for ligand docking and structure-based design. In this study, we report on the ability to model loop side-chains accurately using a variety of commercially available algorithms that include rotamer libraries, systematic torsion scans and knowledge-based methods.

Modeling protein loops with knowledge-based prediction of sequence-structure alignment

As protein structure database expands, protein loop modeling remains an important and yet challenging problem. Knowledge-based protein loop prediction methods have met with two challenges in methodology development: (1) loop boundaries in protein structures are frequently problematic in constructing length-dependent loop databases for protein loop predictions; (2) knowledge-based modeling of loops of unknown structure requires both aligning a query loop sequence to loop templates and ranking the loop sequence-template matches. We developed a knowledge-based loop prediction method that circumvents the need of constructing hierarchically clustered length-dependent loop libraries. The method first predicts local structural fragments of a query loop sequence and then structurally aligns the predicted structural fragments to a set of non-redundant loop structural templates regardless of the loop length. The sequence-template alignments are then quantitatively evaluated with an artificial neural network model trained on a set of predictions with known outcomes. Prediction accuracy benchmarks indicated that the novel procedure provided an alternative approach overcoming the challenges of knowledge-based loop prediction. http://cmb.genomics.sinica.edu.tw

Rappertk: a versatile engine for discrete restraint-based conformational sampling of macromolecules

BackgroundMacromolecular structures are modeled by conformational optimization within experimental and knowledge-based restraints. Discrete restraint-based sampling generates high-quality structures within these restraints and facilitates further refinement in a continuous all-atom energy landscape. This approach has been used successfully for protein loop modeling, comparative modeling and electron density fitting in X-ray crystallography.ResultsHere we present a software toolkit (Rappertk) which generalizes discrete restraint-based sampling for use in structural biology. Modular design and multi-layered architecture enables Rappertk to sample conformations of any macromolecule at many levels of detail and within a variety of experimental restraints. Performance against a Cα-tracing benchmark shows that the efficiency has not suffered despite the overhead required by this flexibility. We demonstrate the toolkit's capabilities by building high-quality β-sheets and by introducing restraint-driven sampling. RNA sampling is demonstrated by rebuilding a protein-RNA interface. Ability to construct arbitrary ligands is used in sampling protein-ligand interfaces within electron density. Finally, secondary structure and shape information derived from EM are combined to generate multiple conformations of a protein consistent with the observed density.ConclusionThrough its modular design and ease of use, Rappertk enables exploration of a wide variety of interesting avenues in structural biology. This toolkit, with illustrative examples, is freely available to academic users from .

Minimalist explicit solvation models for surface loops in proteins.

We have performed molecular dynamics simulations of protein surface loops solvated by explicit water, where a prime focus of the study is the small numbers (e.g., ~100) of explicit water molecules employed. The models include only part of the protein (typically 500 - 1000 atoms), and the water molecules are restricted to a region surrounding the loop. In this study, the number of water molecules (N(w)) is systematically varied, and convergence with large N(w) is monitored to reveal N(w)(min), the minimum number required for the loop to exhibit realistic (fully hydrated) behavior. We have also studied protein surface coverage, as well as diffusion and residence times for water molecules as a function of N(w). A number of other modeling parameters are also tested. These include the number of environmental protein atoms explicitly considered in the model, as well as two ways to constrain the water molecules to the vicinity of the loop (where we find one of these methods to perform better when N(w) is small). The results (for RMSD and its fluctuations for four loops) are further compared to much larger, fully solvated systems (using ~10,000 water molecules under periodic boundary conditions and Ewald electrostatics), and to results for the GBSA implicit solvation model. We find that the loop backbone can stabilize with a surprisingly small number of water molecules (as low as 5 molecules per amino acid residue). The side chains of the loop require somewhat larger N(w), where the atomic fluctuations become too small if N(w) is further reduced. Thus, in general, we find adequate hydration to occur at roughly 12 water molecules per residue. This is an important result, because at this hydration level, computational times are comparable to those required for GBSA. Therefore these "minimalist explicit models" can provide a viable and potentially more accurate alternative. The importance of protein loop modeling is discussed in the context of these, and other, loop models, along with other challenges including the relevance of appropriate free energy simulation methodology for assessment of conformational stability.