Protein Side-chain Packing Research Articles

Invariant point message passing for protein side chain packing.

Protein side chain packing (PSCP) is a fundamental problem in the field of protein engineering, as high-confidence and low-energy conformations of amino acid side chains are crucial for understanding (and designing) protein folding, protein-protein interactions, and protein-ligand interactions. Traditional PSCP methods (such as the Rosetta Packer) often rely on a library of discrete side chain conformations, or rotamers, and a forcefield to guide the structure to low-energy conformations. Recently, deep learning (DL) based methods (such as DLPacker, AttnPacker, and DiffPack) have demonstrated state-of-the-art predictions and speed in the PSCP task. Building off the success of geometric graph neural networks for protein modeling, we present the Protein Invariant Point Packer (PIPPack) which effectively processes local structural and sequence information to produce realistic, idealized side chain coordinates using -angle distribution predictions and geometry-aware invariant point message passing (IPMP). On a test set of ∼1400 high-quality protein chains, PIPPack is highly competitive with other state-of-the-art PSCP methods in rotamer recovery and per-residue RMSD but is significantly faster.

De novo prediction of explicit water molecule positions by a novel algorithm within the protein design software MUMBO

By mediating interatomic interactions, water molecules play a major role in protein–protein, protein–DNA and protein–ligand interfaces, significantly affecting affinity and specificity. This notwithstanding, explicit water molecules are usually not considered in protein design software because of high computational costs. To challenge this situation, we analyzed the binding characteristics of 60,000 waters from high resolution crystal structures and used the observed parameters to implement the prediction of water molecules in the protein design and side chain-packing software MUMBO. To reduce the complexity of the problem, we incorporated water molecules through the solvation of rotamer pairs instead of relying on solvated rotamer libraries. Our validation demonstrates the potential of our algorithm by achieving recovery rates of 67% for bridging water molecules and up to 86% for fully coordinated waters. The efficacy of our algorithm is highlighted further by the prediction of 3 different proteinligand complexes. Here, 91% of water-mediated interactions between protein and ligand are correctly predicted. These results suggest that the new algorithm could prove highly beneficial for structure-based protein design, particularly for the optimization of ligand-binding pockets or protein–protein interfaces.

ZetaDesign: an end-to-end deep learning method for protein sequence design and side-chain packing.

Computational protein design has been demonstrated to be the most powerful tool in the last few years among protein designing and repacking tasks. In practice, these two tasks are strongly related but often treated separately. Besides, state-of-the-art deep-learning-based methods cannot provide interpretability from an energy perspective, affecting the accuracy of the design. Here we propose a new systematic approach, including both a posterior probability and a joint probability parts, to solve the two essential questions once for all. This approach takes the physicochemical property of amino acids into consideration and uses the joint probability model to ensure the convergence between structure and amino acid type. Our results demonstrated that this method could generate feasible, high-confidence sequences with low-energy side conformations. The designed sequences can fold into target structures with high confidence and maintain relatively stable biochemical properties. The side chain conformation has a significantly lower energy landscape without delegating to a rotamer library or performing the expensive conformational searches. Overall, we propose an end-to-end method that combines the advantages of both deep learning and energy-based methods. The design results of this model demonstrate high efficiency, and precision, as well as a low energy state and good interpretability.

An end-to-end deep learning method for protein side-chain packing and inverse folding

Protein side-chain packing (PSCP), the task of determining amino acid side-chain conformations given only backbone atom positions, has important applications to protein structure prediction, refinement, and design. Many methods have been proposed to tackle this problem, but their speed or accuracy is still unsatisfactory. To address this, we present AttnPacker, a deep learning (DL) method for directly predicting protein side-chain coordinates. Unlike existing methods, AttnPacker directly incorporates backbone 3D geometry to simultaneously compute all side-chain coordinates without delegating to a discrete rotamer library or performing expensive conformational search and sampling steps. This enables a significant increase in computational efficiency, decreasing inference time by over 100× compared to the DL-based method DLPacker and physics-based RosettaPacker. Tested on the CASP13 and CASP14 native and nonnative protein backbones, AttnPacker computes physically realistic side-chain conformations, reducing steric clashes and improving both rmsd and dihedral accuracy compared to state-of-the-art methods SCWRL4, FASPR, RosettaPacker, and DLPacker. Different from traditional PSCP approaches, AttnPacker can also codesign sequences and side chains, producing designs with subnative Rosetta energy and high in silico consistency.

FASPR: an open-source tool for fast and accurate protein side-chain packing.

Protein structure and function are essentially determined by how the side-chain atoms interact with each other. Thus, accurate protein side-chain packing (PSCP) is a critical step toward protein structure prediction and protein design. Despite the importance of the problem, however, the accuracy and speed of current PSCP programs are still not satisfactory. We present FASPR for fast and accurate PSCP by using an optimized scoring function in combination with a deterministic searching algorithm. The performance of FASPR was compared with four state-of-the-art PSCP methods (CISRR, RASP, SCATD and SCWRL4) on both native and non-native protein backbones. For the assessment on native backbones, FASPR achieved a good performance by correctly predicting 69.1% of all the side-chain dihedral angles using a stringent tolerance criterion of 20°, compared favorably with SCWRL4, CISRR, RASP and SCATD which successfully predicted 68.8%, 68.6%, 67.8% and 61.7%, respectively. Additionally, FASPR achieved the highest speed for packing the 379 test protein structures in only 34.3 s, which was significantly faster than the control methods. For the assessment on non-native backbones, FASPR showed an equivalent or better performance on I-TASSER predicted backbones and the backbones perturbed from experimental structures. Detailed analyses showed that the major advantage of FASPR lies in the optimal combination of the dead-end elimination and tree decomposition with a well optimized scoring function, which makes FASPR of practical use for both protein structure modeling and protein design studies. The web server, source code and datasets are freely available at https://zhanglab.ccmb.med.umich.edu/FASPR and https://github.com/tommyhuangthu/FASPR. Supplementary data are available at Bioinformatics online.

Toward the Accuracy and Speed of Protein Side-Chain Packing: ASystematic Study on Rotamer Libraries.

Protein rotamers refer to the conformational isomers taken by the side-chains of amino acids to accommodate specific structural folding environments. Since accurate modeling of atomic interactions is difficult, rotamer information collected from experimentally solved protein structures is often used to guide side-chain packing in protein folding and sequence design studies. Many rotamer libraries have been built in the literature but there is little quantitative guidance on which libraries should be chosen for different structural modeling studies. Here, we performed a comparative study of six widely used rotamer libraries and systematically examined their suitability for protein folding and sequence design in four aspects: (1) side-chain match accuracy, (2) side-chain conformation prediction, (3) de novo protein sequence design, and (4) computational time cost. We demonstrated that, compared to the backbone-dependent rotamer libraries (BBDRLs), the backbone-independent rotamer libraries (BBIRLs) generated conformations that more closely matched the native conformations due to the larger number of rotamers in the local rotamer search spaces. However, more practically, using an optimized physical energy function incorporated into a simulated annealing Monte Carlo searching scheme, we showed that utilization of the BBDRLs could result in higher accuracies in side-chain prediction and higher sequence recapitulation rates in protein design experiments. Detailed data analyses showed that the major advantage of BBDRLs lies in the energy term derived from the rotamer probabilities that are associated with the individual backbone torsion angle subspaces. This term is important for distinguishing between amino acid identities as well as the rotamer conformations of an amino acid. Meanwhile, the backbone torsion angle subspace-specific rotamer search drastically speeds up the searching time, despite the significantly larger number of total rotamers in the BBDRLs. These results should provide important guidance for the development and selection of rotamer libraries for practical protein design and structure prediction studies.

Scoring of Side-Chain Packings: An Analysis of Weight Factors and Molecular Dynamics Structures.

The protein side-chain packing problem (PSCPP) is a central task in computational protein design. The problem is usually modeled as a combinatorial optimization problem, which consists of searching for a set of rotamers, from a given rotamer library, that minimizes a scoring function (SF). The SF is a weighted sum of terms, that can be decomposed in physics-based and knowledge-based terms. Although there are many methods to obtain approximate solutions for this problem, all of them have similar performances and there has not been a significant improvement in recent years. Studies on protein structure prediction and protein design revealed the limitations of current SFs to achieve further improvements for these two problems. In the same line, a recent work reported a similar result for the PSCPP. In this work, we ask whether or not this negative result regarding further improvements in performance is due to (i) an incorrect weighting of the SFs terms or (ii) the constrained conformation resulting from the protein crystallization process. To analyze these questions, we (i) model the PSCPP as a bi-objective combinatorial optimization problem, optimizing, at the same time, the two most important terms of two SFs of state-of-the-art algorithms and (ii) performed a preprocessing relaxation of the crystal structure through molecular dynamics to simulate the protein in the solvent and evaluated the performance of these two state-of-the-art SFs under these conditions. Our results indicate that (i) no matter what combination of weight factors we use the current SFs will not lead to better performances and (ii) the evaluated SFs will not be able to improve performance on relaxed structures. Furthermore, the experiments revealed that the SFs and the methods are biased toward crystallized structures.

Protein side-chain packing problem: is there still room for improvement?

The protein side-chain packing problem (PSCPP) is an important subproblem of both protein structure prediction and protein design. During the past two decades, a large number of methods have been proposed to tackle this problem. These methods consist of three main components: a rotamer library, a scoring function and a search strategy. The average overall accuracy level obtained by these methods is approximately 87%. Whether a better accuracy level could be achieved remains to be answered. To address this question, we calculated the maximum accuracy level attainable using a simple rotamer library, independently of the energy function or the search method. Using 2883 different structures from the Protein Data Bank, we compared this accuracy level with the accuracy level of five state-of-the-art methods. These comparisons indicated that, for buried residues in the protein, we are already close to the best possible accuracy results. In addition, for exposed residues, we found that a significant gap exists between the possible improvement and the maximum accuracy level achievable with current methods. After determining that an improvement is possible, the next step is to understand what limitations are preventing us from obtaining such an improvement. Previous works on protein structure prediction and protein design have shown that scoring function inaccuracies may represent the main obstacle to achieving better results for these problems. To show that the same is true for the PSCPP, we evaluated the quality of two scoring functions used by some state-of-the-art algorithms. Our results indicate that neither of these scoring functions can guide the search method correctly, thereby reinforcing the idea that efforts to solve the PSCPP must also focus on developing better scoring functions.

Necessity of high-resolution for coarse-grained modeling of flexible proteins.

The popular MARTINI coarse-grained (CG) force field requires the protein structure to be fixed, and is unsuitable for simulating dynamic processes such as protein folding. Here, we examine the feasibility of developing a flexible protein model within the MARTINI framework. The results demonstrate that the MARTINI CG scheme does not properly describe the volume and packing of protein backbone and side chains and leads to excessive collapse without structural restraints in explicit CG water. Combining atomistic protein representation with the MARTINI CG solvent, such as in the PACE model, dramatically improves description of flexible protein conformations. Yet, the CG solvent is insufficient to capture the conformational dependence of protein-solvent interactions, and PACE is unable to properly model context dependent conformational transitions. Taken together, high physical resolution at or near the atomistic level is likely necessary for flexible protein models with explicit, microscopic solvents, and the coarse-graining needs to focus on possible simplification in interaction potentials. © 2016 Wiley Periodicals, Inc.

Dead-End Elimination with a Polarizable Force Field Repacks PCNA Structures

A balance of van der Waals, electrostatic, and hydrophobic forces drive the folding and packing of protein side chains. Although such interactions between residues are often approximated as being pairwise additive, in reality, higher-order many-body contributions that depend on environment drive hydrophobic collapse and cooperative electrostatics. Beginning from dead-end elimination, we derive the first algorithm, to our knowledge, capable of deterministic global repacking of side chains compatible with many-body energy functions. The approach is applied to seven PCNA x-ray crystallographic data sets with resolutions 2.5–3.8 Å (mean 3.0 Å) using an open-source software. While PDB_REDO models average an Rfree value of 29.5% and MOLPROBITY score of 2.71 Å (77th percentile), dead-end elimination with the polarizable AMOEBA force field lowered Rfree by 2.8–26.7% and improved mean MOLPROBITY score to atomic resolution at 1.25 Å (100th percentile). For structural biology applications that depend on side-chain repacking, including x-ray refinement, homology modeling, and protein design, the accuracy limitations of pairwise additivity can now be eliminated via polarizable or quantum mechanical potentials.

Necessity of High Physical Resolution in the Development of Flexible Coarse-Grained Protein Models

The Martini force field is a one of the most widely used coarse-grained (CG) model. An important strength of the Martini force field is that it includes explicit, microscopic representation of solvent, which allows proper description of the context-dependence of protein-protein interactions. However, in the Martini force field the secondary structures of the protein are fixed, which makes it is unsuitable for simulating dynamic processes such as protein folding and membrane insertion. In this work, we examine the possibility of developing a flexible protein model within the Martini CG framework, such as by supplementing the force field with Go-like potentials. It was found the current Martini CG representation of proteins was insufficient to support a flexible model. The model does not provide a sufficient resolution to properly describe the volume and packing of protein backbone and sidechains. The interior voids resulting from improper packing would lead to excessive structural collapse in absence of structural restraints. Along this line, we further examined the PACE model, where an atomistic protein model is deployed in the Martini solvent. The results suggest that, while atomistic protein representation does dramatically improve the ability to describe specific protein-protein interactions, the low physical resolution of the Martini water molecules does not allow sufficient discrimination of various open and compact conformational states. As a result, PACE is not capable of describing context dependent protein structure transition, such as helical transition induced by membrane absorption and/or insertion. In conclusion, high physical resolution is likely necessary for developing flexible protein models and the coarse-graining needs to focus on exploiting possible simplification of interaction potentials.

Improved packing of protein side chains with parallel ant colonies

IntroductionThe accurate packing of protein side chains is important for many computational biology problems, such as ab initio protein structure prediction, homology modelling, and protein design and ligand docking applications. Many of existing solutions are modelled as a computational optimisation problem. As well as the design of search algorithms, most solutions suffer from an inaccurate energy function for judging whether a prediction is good or bad. Even if the search has found the lowest energy, there is no certainty of obtaining the protein structures with correct side chains.MethodsWe present a side-chain modelling method, pacoPacker, which uses a parallel ant colony optimisation strategy based on sharing a single pheromone matrix. This parallel approach combines different sources of energy functions and generates protein side-chain conformations with the lowest energies jointly determined by the various energy functions. We further optimised the selected rotamers to construct subrotamer by rotamer minimisation, which reasonably improved the discreteness of the rotamer library.ResultsWe focused on improving the accuracy of side-chain conformation prediction. For a testing set of 442 proteins, 87.19% of and 77.11% of angles were predicted correctly within 40° of the X-ray positions. We compared the accuracy of pacoPacker with state-of-the-art methods, such as CIS-RR and SCWRL4. We analysed the results from different perspectives, in terms of protein chain and individual residues. In this comprehensive benchmark testing, 51.5% of proteins within a length of 400 amino acids predicted by pacoPacker were superior to the results of CIS-RR and SCWRL4 simultaneously. Finally, we also showed the advantage of using the subrotamers strategy. All results confirmed that our parallel approach is competitive to state-of-the-art solutions for packing side chains.ConclusionsThis parallel approach combines various sources of searching intelligence and energy functions to pack protein side chains. It provides a frame-work for combining different inaccuracy/usefulness objective functions by designing parallel heuristic search algorithms.

A protein-dependent side-chain rotamer library

BackgroundProtein side-chain packing problem has remained one of the key open problems in bioinformatics. The three main components of protein side-chain prediction methods are a rotamer library, an energy function and a search algorithm. Rotamer libraries summarize the existing knowledge of the experimentally determined structures quantitatively. Depending on how much contextual information is encoded, there are backbone-independent rotamer libraries and backbone-dependent rotamer libraries. Backbone-independent libraries only encode sequential information, whereas backbone-dependent libraries encode both sequential and locally structural information. However, side-chain conformations are determined by spatially local information, rather than sequentially local information. Since in the side-chain prediction problem, the backbone structure is given, spatially local information should ideally be encoded into the rotamer libraries.MethodsIn this paper, we propose a new type of backbone-dependent rotamer library, which encodes structural information of all the spatially neighboring residues. We call it protein-dependent rotamer libraries. Given any rotamer library and a protein backbone structure, we first model the protein structure as a Markov random field. Then the marginal distributions are estimated by the inference algorithms, without doing global optimization or search. The rotamers from the given library are then re-ranked and associated with the updated probabilities.ResultsExperimental results demonstrate that the proposed protein-dependent libraries significantly outperform the widely used backbone-dependent libraries in terms of the side-chain prediction accuracy and the rotamer ranking ability. Furthermore, without global optimization/search, the side-chain prediction power of the protein-dependent library is still comparable to the global-search-based side-chain prediction methods.

Genetic algorithm with alternating selection pressure for protein side-chain packing and p K(a) prediction

The prediction of protein side-chain conformation is central for understanding protein functions. Side-chain packing is a sub-problem of protein folding and its computational complexity has been shown to be NP-hard. We investigated the capabilities of a hybrid (genetic algorithm/simulated annealing) technique for side-chain packing and for the generation of an ensemble of low energy side-chain conformations. Our method first relies on obtaining a near-optimal low energy protein conformation by optimizing its amino-acid side-chains. Upon convergence, the genetic algorithm is allowed to undergo forward and “backward” evolution by alternating selection pressures between minimal and higher energy setpoints. We show that this technique is very efficient for obtaining distributions of solutions centered at any desired energy from the minimum. We outline the general concepts of our evolutionary sampling methodology using three different alternating selective pressure schemes. Quality of the method was assessed by using it for protein p K(a) prediction.

Explicit Orientation Dependence in Empirical Potentials and Its Significance to Side-Chain Modeling

Protein structure modeling and prediction have important applications throughout the biological sciences, from the design of pharmaceuticals to the elucidation of enzyme mechanisms. At the core of most protein modeling is an energy function, the minimum of which represents the free energy "cost" for forming a correct protein structure. The most commonly used energy functions are knowledge-based statistical potential functions; that is, they are empirically derived from statistical analysis of a set of high-resolution protein structures. When that kind of potential function is constructed, the anisotropic orientation dependence between the interacting groups is a critical component for accurately representing key molecular interactions, such as those involved in protein side-chain packing. In the literature, however, many potential functions are limited in their ability to describe orientation dependence. In all-atom potentials, they typically ignore heterogeneous chemical-bond connectivity. In coarse-grained potentials, such as (semi)-residue-based potentials, the simplified representation of residues often reduces the sensitivity of the potential to side-chain orientation. Recently, in an effort to maximally capture the orientation dependence in side-chain interactions, a new type of all-atom statistical potential was developed: OPUS-PSP (potential derived from side-chain packing). The key feature of this potential is its explicit description of orientation dependence in molecular interactions, which is achieved with a basis set of 19 rigid-body blocks extracted from the chemical structures of 20 amino acid residues. This basis set is specifically designed to maximally capture the essential elements of orientation dependence in molecular packing interactions. The potential is constructed from the orientation-specific packing statistics of pairs of those blocks in a nonredundant structural database. On decoy set tests, OPUS-PSP significantly outperforms most of the existing knowledge-based potentials in terms of both its ability to recognize native structures and its consistency in achieving high Z scores across decoy sets. The application of OPUS-PSP to conformational modeling of side chains has led to another method, called OPUS-Rota. In terms of combined speed and accuracy, OPUS-Rota outperforms all of the other methods in modeling side-chain conformation. In this Account, we briefly outline the basic scheme of the OPUS-PSP potential and its application to side-chain modeling via OPUS-Rota. Future perspectives on the modeling of orientation dependence are also discussed. The computer programs for OPUS-PSP and OPUS-Rota can be downloaded at http://sigler.bioch.bcm.tmc.edu/MaLab . They are free for academic users.

Sublinear time width-bounded separators and their application to the protein side-chain packing problem

Given d>2 and a set of n grid points Q in ℜ d , we design a randomized algorithm that finds a w-wide separator, which is determined by a hyper-plane, in $O(n^{2\over d}\log n)$ sublinear time such that Q has at most $({d\over d+1}+o(1))n$ points on either side of the hyper-plane, and at most $c_{d}wn^{d-1\over d}$ points within $\frac{w}{2}$ distance to the hyper-plane, where c d is a constant for fixed d. In particular, c 3=1.209. To our best knowledge, this is the first sublinear time algorithm for finding geometric separators. Our 3D separator is applied to derive an algorithm for the protein side-chain packing problem, which improves and simplifies the previous algorithm of Xu (Research in computational molecular biology, 9th annual international conference, pp. 408–422, 2005).

Fast and accurate algorithms for protein side-chain packing

This article studies the protein side-chain packing problem using the tree-decomposition of a protein structure. To obtain fast and accurate protein side-chain packing, protein structures are modeled using a geometric neighborhood graph, which can be easily decomposed into smaller blocks. Therefore, the side-chain assignment of the whole protein can be assembled from the assignment of the small blocks. Although we will show that the side-chain packing problem is stillNP-hard, we can achieve a tree-decomposition-based globally optimal algorithm with time complexity ofO(Nnrottw+ 1)and several polynomial-time approximation schemes (PTAS), whereNis the number of residues contained in the protein,nrotthe average number of rotamers for each residue, andtw=O(N2/3logN) the treewidth of the protein structure graph. Experimental results indicate that after Goldstein dead-end elimination is conducted,nrotis very small andtwis equal to 3 or 4 most of the time. Based on the globally optimal algorithm, we developed a protein side-chain assignment program TreePack, which runs up to 90 times faster than SCWRL 3.0, a widely-used side-chain packing program, on some large test proteins in the SCWRL benchmark database and an average of five times faster on all the test proteins in this database. There are also some real-world instances that TreePack can solve but that SCWRL 3.0 cannot. The TreePack program is available at http://ttic.uchicago.edu/~jinbo/TreePack.htm.

PROTEIN SIDE-CHAIN PACKING PROBLEM: A MAXIMUM EDGE-WEIGHT CLIQUE ALGORITHMIC APPROACH

"Protein Side-chain Packing" has an ever-increasing application in the field of bio-informatics, dating from the early methods of homology modeling to protein design and to the protein docking. However, this problem is computationally known to be NP-hard. In this regard, we have developed a novel approach to solve this problem using the notion of a maximum edge-weight clique. Our approach is based on efficient reduction of protein side-chain packing problem to a graph and then solving the reduced graph to find the maximum clique by applying an efficient clique finding algorithm developed by our co-authors. Since our approach is based on deterministic algorithms in contrast to the various existing algorithms based on heuristic approaches, our algorithm guarantees of finding an optimal solution. We have tested this approach to predict the side-chain conformations of a set of proteins and have compared the results with other existing methods. We have found that our results are favorably comparable or better than the results produced by the existing methods. As our test set contains a protein of 494 residues, we have obtained considerable improvement in terms of size of the proteins and in terms of the efficiency and the accuracy of prediction.

Point matching under non-uniform distortions and protein side chain packing based on an efficient maximum clique algorithm.

We developed maximum clique-based algorithms for spot matching for two-dimensional gel electrophoresis images, protein structure alignment and protein side-chain packing, where these problems are known to be NP-hard. Algorithms based on direct reductions to the maximum clique can find optimal solutions for instances of size (the number of points or residues) up to 50-150 using a standard PC. We also developed pre-processing techniques to reduce the sizes of graphs. Combined with some heuristics, many realistic instances can be solved approximately.

Excluded volume in protein side-chain packing

The excluded volume occupied by protein side-chains and the requirement of high packing density in the protein interior should severely limit the number of side-chain conformations compatible with a given native backbone. To examine the relationship between side-chain geometry and side-chain packing, we use an all-atom Monte Carlo simulation to sample the large space of side-chain conformations. We study three models of excluded volume and use umbrella sampling to effectively explore the entire space. We find that while excluded volume constraints reduce the size of conformational space by many orders of magnitude, the number of allowed conformations is still large. An average repacked conformation has 20 % of its χ angles in a non-native state, a marked reduction from the expected 67 % in the absence of excluded volume. Interestingly, well-packed conformations with up to 50 % non-native χ angles exist. The repacked conformations have native packing density as measured by a standard Voronoi procedure. Entropy is distributed non-uniformly over positions, and we partially explain the observed distribution using rotamer probabilities derived from the Protein Data Bank database. In several cases, native rotamers that occur infrequently in the database are seen with high probability in our simulation, indicating that sequence-specific excluded volume interactions can stabilize rotamers that are rare for a given backbone. In spite of our finding that 65 % of the native rotamers and 85 % of χ 1 angles can be predicted correctly on the basis of excluded volume only, 95 % of positions can accommodate more than one rotamer in simulation. We estimate that, in order to quench the side-chain entropy observed in the presence of excluded volume interactions, other interactions (hydrophobic, polar, electrostatic) must provide an additional stabilization of at least 0.6 kT per residue in order to single out the native state.