Statistical mechanics-based method to extract atomic distance-dependent potentials from protein structures

Assembly of Protein Complexes in and on the Membrane with Predicted Spatial Arrangement Constraints

Membrane proteins play crucial roles in various cellular processes, and their interactions with other proteins in and on the membrane are essential for their proper functioning. While an increasing number of structures of more membrane proteins are being determined, the available structure data is still sparse. To gain insights into the mechanisms of membrane protein complexes, computational docking methods are necessary due to the challenge of experimental determination. Here, we introduce Mem-LZerD, a rigid-body membrane docking algorithm designed to take advantage of modern membrane modeling and protein docking techniques to facilitate the docking of membrane protein complexes. Mem-LZerD is based on the LZerD protein docking algorithm, which has been constantly among the top servers in many rounds of CAPRI protein docking assessment. By employing a combination of geometric hashing, newly constrained by the predicted membrane height and tilt angle, and model scoring accounting for the energy of membrane insertion, we demonstrate the capability of Mem-LZerD to model diverse membrane protein-protein complexes. Mem-LZerD successfully performed unbound docking on 13 of 21 (61.9%) transmembrane complexes in an established benchmark, more than shown by previous approaches. It was additionally tested on new datasets of 44 transmembrane complexes and 92 peripheral membrane protein complexes, of which it successfully modeled 35 (79.5%) and 15 (16.3%) complexes respectively. When non-blind orientations of peripheral targets were included, the number of successes increased to 54 (58.7%). We further demonstrate that Mem-LZerD produces complex models which are suitable for molecular dynamics simulation. Mem-LZerD is made available at https://lzerd.kiharalab.org.

Assembly of Protein Complexes In and On the Membrane with Predicted Spatial Arrangement Constraints

Membrane proteins play crucial roles in various cellular processes, and their interactions with other proteins in and on the membrane are essential for their proper functioning. While an increasing number of structures of more membrane proteins are being determined, the available structure data is still sparse. To gain insights into the mechanisms of membrane protein complexes, computational docking methods are necessary due to the challenge of experimental determination. Here, we introduce Mem-LZerD, a rigid-body membrane docking algorithm designed to take advantage of modern membrane modeling and protein docking techniques to facilitate the docking of membrane protein complexes. Mem-LZerD is based on the LZerD protein docking algorithm, which has been constantly among the top servers in many rounds of CAPRI protein docking assessment. By employing a combination of geometric hashing, newly constrained by the predicted membrane height and tilt angle, and model scoring accounting for the energy of membrane insertion, we demonstrate the capability of Mem-LZerD to model diverse membrane protein-protein complexes. Mem-LZerD successfully performed unbound docking on 13 of 21 (61.9%) transmembrane complexes in an established benchmark, more than shown by previous approaches. It was additionally tested on new datasets of 44 transmembrane complexes and 92 peripheral membrane protein complexes, of which it successfully modeled 35 (79.5%) and 15 (16.3%) complexes respectively. When non-blind orientations of peripheral targets were included, the number of successes increased to 54 (58.7%). We further demonstrate that Mem-LZerD produces complex models which are suitable for molecular dynamics simulation. Mem-LZerD is made available at https://lzerd.kiharalab.org.

Discriminating physiological from non-physiological interfaces in structures of protein complexes: A community-wide study

Reliably scoring and ranking candidate models of protein complexes and assigning their oligomeric state from the structure of the crystal lattice represent outstanding challenges. A community-wide effort was launched to tackle these challenges. The latest resources on protein complexes and interfaces were exploited to derive a benchmark dataset consisting of 1677 homodimer protein crystal structures, including a balanced mix of physiological and non-physiological complexes. The non-physiological complexes in the benchmark were selected to bury a similar or larger interface area than their physiological counterparts, making it more difficult for scoring functions to differentiate between them. Next, 252 functions for scoring protein-protein interfaces previously developed by 13 groups were collected and evaluated for their ability to discriminate between physiological and non-physiological complexes. A simple consensus score generated using the best performing score of each of the 13 groups, and a cross-validated Random Forest (RF) classifier were created. Both approaches showed excellent performance, with an area under the Receiver Operating Characteristic (ROC) curve of 0.93 and 0.94, respectively, outperforming individual scores developed by different groups. Additionally, AlphaFold2 engines recalled the physiological dimers with significantly higher accuracy than the non-physiological set, lending support to the reliability of our benchmark dataset annotations. Optimizing the combined power of interface scoring functions and evaluating it on challenging benchmark datasets appears to be a promising strategy.

Modeling protein-nucleic acid complexes with extremely large conformational changes using Flex-LZerD

Proteins and nucleic acids are key components in many processes in living cells, and interactions between proteins and nucleic acids are often crucial pathway components. In many cases, large flexibility of proteins as they interact with nucleic acids is key to their function. To understand the mechanisms of these processes, it is necessary to consider the 3D atomic structures of such protein-nucleic acid complexes. When such structures are not yet experimentally determined, protein docking can be used to computationally generate useful structure models. However, such docking has long had the limitation that the consideration of flexibility is usually limited to small movements or to small structures. We previously developed a method of flexible protein docking which could model ordered proteins which undergo large-scale conformational changes, which we also showed was compatible with nucleic acids. Here, we elaborate on the ability of that pipeline, Flex-LZerD, to model specifically interactions between proteins and nucleic acids, and demonstrate that Flex-LZerD can model more interactions and types of conformational change than previously shown.

Critical Assessment of Methods for Predicting the 3D Structure of Proteins and Protein Complexes

Advances in a scientific discipline are often measured by small, incremental steps. In this review, we report on two intertwined disciplines in the protein structure prediction field, modeling of single chains and modeling of complexes, that have over decades emulated this pattern, as monitored by the community-wide blind prediction experiments CASP and CAPRI. However, over the past few years, dramatic advances were observed for the accurate prediction of single protein chains, driven by a surge of deep learning methodologies entering the prediction field. We review the mainscientific developments that enabled these recent breakthroughs and feature the important role of blind prediction experiments in building up and nurturing the structure prediction field. We discuss how the new wave of artificial intelligence-based methods is impacting the fields of computational and experimental structural biology and highlight areas in which deep learning methods are likely to lead to future developments, provided that major challenges are overcome.

Pairwise and Multi-chain Protein Docking Enhanced Using LZerD Web Server

Interactions of proteins with other macromolecules have important structural and functional roles in the basic processes of living cells. To understand and elucidate the mechanisms of interactions, it is important to know the 3D structures of the complexes. Proteomes contain numerous protein-protein complexes, for which experimentally determined structures often do not exist. Computational techniques can be a practical alternative to obtain useful complex structure models. Here, we present a web server that provides access to the LZerD and Multi-LZerD protein docking tools, which can perform both pairwise and multi-chain docking. The web server is user-friendly, with options to visualize the distribution and structures of binding poses of top-scoring models. The LZerD web server is available at https://lzerd.kiharalab.org . This chapter dictates the algorithm and step-by-step procedure to model the monomeric structures with AttentiveDist, and also provides the detail of pairwise LZerD docking, and multi-LZerD. This also provided case studies for each of the three modules.

Domain-Based Protein Docking with Extremely Large Conformational Changes

Proteins are key components in many processes in living cells, and physical interactions with other proteins and nucleic acids often form key parts of their functions. In many cases, large flexibility of proteins as they interact is key to their function. To understand the mechanisms of these processes, it is necessary to consider the 3D structures of such protein complexes. When such structures are not yet experimentally determined, protein docking has long been present to computationally generate useful structure models. However, protein docking has long had the limitation that the consideration of flexibility is usually limited to very small movements or very small structures. Methods have been developed which handle minor flexibility via normal mode or other structure sampling, but new methods are required to model ordered proteins which undergo large-scale conformational changes to elucidate their function at the molecular level. Here, we present Flex-LZerD, a framework for docking such complexes. Via partial assembly multidomain docking and an iterative normal mode analysis admitting curvilinear motions, we demonstrate the ability to model the assembly of a variety of protein-protein and protein-nucleic acid complexes.

RL-MLZerD: Multimeric protein docking using reinforcement learning

Numerous biological processes in a cell are carried out by protein complexes. To understand the molecular mechanisms of such processes, it is crucial to know the quaternary structures of the complexes. Although the structures of protein complexes have been determined by biophysical experiments at a rapid pace, there are still many important complex structures that are yet to be determined. To supplement experimental structure determination of complexes, many computational protein docking methods have been developed; however, most of these docking methods are designed only for docking with two chains. Here, we introduce a novel method, RL-MLZerD, which builds multiple protein complexes using reinforcement learning (RL). In RL-MLZerD a multi-chain assembly process is considered as a series of episodes of selecting and integrating pre-computed pairwise docking models in a RL framework. RL is effective in correctly selecting plausible pairwise models that fit well with other subunits in a complex. When tested on a benchmark dataset of protein complexes with three to five chains, RL-MLZerD showed better modeling performance than other existing multiple docking methods under different evaluation criteria, except against AlphaFold-Multimer in unbound docking. Also, it emerged that the docking order of multi-chain complexes can be naturally predicted by examining preferred paths of episodes in the RL computation.

Multi-level analysis of intrinsically disordered protein docking methods

Intrinsically Disordered Proteins (IDPs) are a class of proteins in which at least some region of the protein does not possess any stable structure in solution in the physiological condition but may adopt an ordered structure upon binding to a globular receptor. These IDP-receptor complexes are thus subject to protein complex modeling in which computational techniques are applied to accurately reproduce the IDP ligand-receptor interactions. This often exists in the form of protein docking, in which the 3D structures of both the subunits are known, but the position of the ligand relative to the receptor is not. Here, we evaluate the performance of three IDP-receptor modeling tools with metrics that characterize the IDP-receptor interface at various resolutions. We show that all three methods are able to properly identify the general binding site, as identified by lower resolution metrics, but begin to struggle with higher resolution metrics that capture biophysical interactions.

RNAStat: An Integrated Tool for Statistical Analysis of RNA 3D Structures

The 3D architectures of RNAs are essential for understanding their cellular functions. While an accurate scoring function based on the statistics of known RNA structures is a key component for successful RNA structure prediction or evaluation, there are few tools or web servers that can be directly used to make comprehensive statistical analysis for RNA 3D structures. In this work, we developed RNAStat, an integrated tool for making statistics on RNA 3D structures. For given RNA structures, RNAStat automatically calculates RNA structural properties such as size and shape, and shows their distributions. Based on the RNA structure annotation from DSSR, RNAStat provides statistical information of RNA secondary structure motifs including canonical/non-canonical base pairs, stems, and various loops. In particular, the geometry of base-pairing/stacking can be calculated in RNAStat by constructing a local coordinate system for each base. In addition, RNAStat also supplies the distribution of distance between any atoms to the users to help build distance-based RNA statistical potentials. To test the usability of the tool, we established a non-redundant RNA 3D structure dataset, and based on the dataset, we made a comprehensive statistical analysis on RNA structures, which could have the guiding significance for RNA structure modeling. The python code of RNAStat, the dataset used in this work, and corresponding statistical data files are freely available at GitHub (https://github.com/RNA-folding-lab/RNAStat).

rsRNASP: A residue-separation-based statistical potential for RNA 3D structure evaluation

Knowledge-based statistical potentials have been shown to be rather effective in protein 3-dimensional (3D) structure evaluation and prediction. Recently, several statistical potentials have been developed for RNA 3D structure evaluation, while their performances are either still at a low level for the test datasets from structure prediction models or dependent on the "black-box" process through neural networks. In this work, we have developed an all-atom distance-dependent statistical potential based on residue separation for RNA 3D structure evaluation, namely rsRNASP, which is composed of short- and long-ranged potentials distinguished by residue separation. The extensive examinations against available RNA test datasets show that rsRNASP has apparently higher performance than the existing statistical potentials for the realistic test datasets with large RNAs from structure prediction models, including the newly released RNA-Puzzles dataset, and is comparable to the existing top statistical potentials for the test datasets with small RNAs or near-native decoys. In addition, rsRNASP is superior to RNA3DCNN, a recently developed scoring function through 3D convolutional neural networks. rsRNASP and the relevant databases are available to the public.

Prediction of protein assemblies, the next frontier: The CASP14-CAPRI experiment

We present the results for CAPRI Round 50, the fourth joint CASP-CAPRI protein assembly prediction challenge. The Round comprised a total of twelve targets, including six dimers, three trimers, and three higher-order oligomers. Four of these were easy targets, for which good structural templates were available either for the full assembly, or for the main interfaces (of the higher-order oligomers). Eight were difficult targets for which only distantly related templates were found for the individual subunits. Twenty-five CAPRI groups including eight automatic servers submitted ~1250 models per target. Twenty groups including six servers participated in the CAPRI scoring challenge submitted ~190 models per target. The accuracy of the predicted models was evaluated using the classical CAPRI criteria. The prediction performance was measured by a weighted scoring scheme that takes into account the number of models of acceptable quality or higher submitted by each group as part of their five top-ranking models. Compared to the previous CASP-CAPRI challenge, top performing groups submitted such models for a larger fraction (70-75%) of the targets in this Round, but fewer of these models were of high accuracy. Scorer groups achieved stronger performance with more groups submitting correct models for 70-80% of the targets or achieving high accuracy predictions. Servers performed less well in general, except for the MDOCKPP and LZERD servers, who performed on par with human groups. In addition to these results, major advances in methodology are discussed, providing an informative overview of where the prediction of protein assemblies currently stands.

LZerD webserver for pairwise and multiple protein-protein docking

Protein complexes are involved in many important processes in living cells. To understand the mechanisms of these processes, it is necessary to solve the 3D structures of the protein complexes. When protein complex structures have not yet been determined by experiment, protein-protein docking tools can be used to computationally model the structures of these complexes. Here, we present a webserver which provides access to LZerD and Multi-LZerD protein docking tools. The protocol provided by the server have performed consistently among the top in the CAPRI blind evaluation. LZerD docks pairs of structures, while Multi-LZerD can dock three or more structures simultaneously. LZerD uses a soft protein surface representation with 3D Zernike descriptors and explores the binding pose space using geometric hashing. Multi-LZerD performs multi-chain docking by combining pairwise solutions by LZerD. Both methods output full-atom docked models of the input proteins. Users can also input distance constraints between interacting or non-interacting residues as well as residues that locate at the interface or far from the interface. The webserver is equipped with a user-friendly panel that visualizes the distribution and structures of binding poses of top scoring models. The LZerD webserver is available at https://lzerd.kiharalab.org.

Self-Organized Morphology and Multiscale Structures of CoVE Proteins

Self-organizing structures of CoVE proteins have been investigated using a coarse-grained model in Monte Carlo simulations as a function of temperature (T) in a range covering the native (low T) to denatured (high T) phases. The presence of even a few chains accelerates the very slow dynamics of an otherwise free protein chain in the native phase. The radius of gyration depends nonmonotonically on temperature and increases with the protein concentration in both the native and denatured phase. The density of organized morphology over residue-to-sample length scales (λ) is quantified by an effective dimension (D) that varies between ~ 2 at high to ~ 3 at low temperatures at λ ~ R _g with an overall lower density (D ~ 2) on larger scales. The magnitude of D depends on temperature, length scale, and concentration of proteins, i.e., D ~ 3.2 at λ ~ R_g, D ~ 2.6 at λ > R _g, and D ~ 2.0 at λ ≫ R _g, at T = 0.024.

Scoring Functions for Protein-RNA Complex Structure Prediction: Advances, Applications, and Future Directions

Protein-RNA interaction is among the most essential of biological events in living cells, being involved in protein synthesizing, RNA processing and transport, DNA transcription, and regulation of gene expression, and many other critical bio-molecular activities. A thorough understanding of this interaction is of paramount importance in fundamental study of a variety of vital cellular processes and therapeutic application for remedy of a broad range of diseases. Experimental high-resolution 3D structure determination is the primary source of knowledge for protein-RNA complexes. However, due to technical limitations, the existing techniques for experimental structure determination couldn't match the demand from fast growing interest in academia and industry. This problem necessitates the alternative high-throughput computational method for protein-RNA complex structure prediction. Similar to the in silico methods used for protein-protein and protein-DNA interactions, a reliable prediction of protein-RNA complex structure requires a scoring function with commensurate discriminatory power. Derived from determined structures and purposed to predict the to-be-determined structures, the scoring function is not only a predictive tool but also a gauge of our knowledge of protein-RNA interaction. In this review, we present an overview of the status of existing scoring functions and the scientific principle behind their constructions as well as their strengths and limitations. Finally, we will discuss about future directions of the scoring function development for protein-RNA structure prediction.

Blind prediction of homo- and hetero-protein complexes: The CASP13-CAPRI experiment

We present the results for CAPRI Round 46, the third joint CASP-CAPRI protein assembly prediction challenge. The Round comprised a total of 20 targets including 14 homo-oligomers and 6 heterocomplexes. Eight of the homo-oligomer targets and one heterodimer comprised proteins that could be readily modeled using templates from the Protein Data Bank, often available for the full assembly. The remaining 11 targets comprised 5 homodimers, 3 heterodimers, and two higher-order assemblies. These were more difficult to model, as their prediction mainly involved "ab-initio" docking of subunit models derived from distantly related templates. A total of ~30 CAPRI groups, including 9 automatic servers, submitted on average ~2000 models per target. About 17 groups participated in the CAPRI scoring rounds, offered for most targets, submitting ~170 models per target. The prediction performance, measured by the fraction of models of acceptable quality or higher submitted across all predictors groups, was very good to excellent for the nine easy targets. Poorer performance was achieved by predictors for the 11 difficult targets, with medium and high quality models submitted for only 3 of these targets. A similar performance "gap" was displayed by scorer groups, highlighting yet again the unmet challenge of modeling the conformational changes of the protein components that occur upon binding or that must be accounted for in template-based modeling. Our analysis also indicates that residues in binding interfaces were less well predicted in this set of targets than in previous Rounds, providing useful insights for directions of future improvements.

Performance and enhancement of the LZerD protein assembly pipeline in CAPRI 38-46

We report the performance of the protein docking prediction pipeline of our group and the results for Critical Assessment of Prediction of Interactions (CAPRI) rounds 38-46. The pipeline integrates programs developed in our group as well as other existing scoring functions. The core of the pipeline is the LZerD protein-protein docking algorithm. If templates of the target complex are not found in PDB, the first step of our docking prediction pipeline is to run LZerD for a query protein pair. Meanwhile, in the case of human group prediction, we survey the literature to find information that can guide the modeling, such as protein-protein interface information. In addition to any literature information and binding residue prediction, generated docking decoys were selected by a rank aggregation of statistical scoring functions. The top 10 decoys were relaxed by a short molecular dynamics simulation before submission to remove atom clashes and improve side-chain conformations. In these CAPRI rounds, our group, particularly the LZerD server, showed robust performance. On the other hand, there are failed cases where some other groups were successful. To understand weaknesses of our pipeline, we analyzed sources of errors for failed targets. Since we noted that structure refinement is a step that needs improvement, we newly performed a comparative study of several refinement approaches. Finally, we show several examples that illustrate successful and unsuccessful cases by our group.

Determination of an effective scoring function for RNA-RNA interactions with a physics-based double-iterative method

RNA–RNA interactions play fundamental roles in gene and cell regulation. Therefore, accurate prediction of RNA–RNA interactions is critical to determine their complex structures and understand the molecular mechanism of the interactions. Here, we have developed a physics-based double-iterative strategy to determine the effective potentials for RNA–RNA interactions based on a training set of 97 diverse RNA–RNA complexes. The double-iterative strategy circumvented the reference state problem in knowledge-based scoring functions by updating the potentials through iteration and also overcame the decoy-dependent limitation in previous iterative methods by constructing the decoys iteratively. The derived scoring function, which is referred to as DITScoreRR, was evaluated on an RNA–RNA docking benchmark of 60 test cases and compared with three other scoring functions. It was shown that for bound docking, our scoring function DITScoreRR obtained the excellent success rates of 90% and 98.3% in binding mode predictions when the top 1 and 10 predictions were considered, compared to 63.3% and 71.7% for van der Waals interactions, 45.0% and 65.0% for ITScorePP, and 11.7% and 26.7% for ZDOCK 2.1, respectively. For unbound docking, DITScoreRR achieved the good success rates of 53.3% and 71.7% in binding mode predictions when the top 1 and 10 predictions were considered, compared to 13.3% and 28.3% for van der Waals interactions, 11.7% and 26.7% for our ITScorePP, and 3.3% and 6.7% for ZDOCK 2.1, respectively. DITScoreRR also performed significantly better in ranking decoys and obtained significantly higher score-RMSD correlations than the other three scoring functions. DITScoreRR will be of great value for the prediction and design of RNA structures and RNA–RNA complexes.

What is the best reference state for building statistical potentials in RNA 3D structure evaluation?

Knowledge-based statistical potentials have been shown to be efficient in protein structure evaluation/prediction, and the core difference between various statistical potentials is attributed to the choice of reference states. However, for RNA 3D structure evaluation, a comprehensive examination on reference states is still lacking. In this work, we built six statistical potentials based on six reference states widely used in protein structure evaluation, including averaging, quasi-chemical approximation, atom-shuffled, finite-ideal-gas, spherical-noninteracting, and random-walk-chain reference states, and we examined the six reference states against three RNA test sets including six subsets. Our extensive examinations show that, overall, for identifying native structures and ranking decoy structures, the finite-ideal-gas and random-walk-chain reference states are slightly superior to others, while for identifying near-native structures, there is only a slight difference between these reference states. Our further analyses show that the performance of a statistical potential is apparently dependent on the quality of the training set. Furthermore, we found that the performance of a statistical potential is closely related to the origin of test sets, and for the three realistic test subsets, the six statistical potentials have overall unsatisfactory performance. This work presents a comprehensive examination on the existing reference states and statistical potentials for RNA 3D structure evaluation.

Alchemical Grid Dock (AlGDock) calculations in the D3R Grand Challenge 3 : Binding free energies between flexible ligands and rigid receptors

We participated in Subchallenges 1 and 2 of the Drug Design Data Resource (D3R) Grand Challenge 3. To prepare our submissions, we performed molecular docking with UCSF DOCK 6 and binding potential of mean force (BPMF) calculations-free energy calculations between flexible ligands and rigid receptors-using our open-source software package Alchemical Grid Dock (AlGDock). For each system, submissions were based on the minimum BPMF calculated for a selected set of crystal structures. In Subchallenge 1, our workflow performed poorly. Possible reasons for the poor performance include the neglect of cooperative ligands and limited sampling of ligand binding poses. In Subchallenge 2, our workflow led to some of most highly correlated submissions (Pearson R = 0.5) for vascular endothelial growth factor receptor 2. However, our results were poorly correlated for Janus Kinase 2 and Mitogen-activated protein kinase 14. Affinity prediction could potentially be improved by systematic selection of more diverse receptor configurations.

Improved performance in CAPRI round 37 using LZerD docking and template-based modeling with combined scoring functions

We report our group's performance for protein-protein complex structure prediction and scoring in Round 37 of the Critical Assessment of PRediction of Interactions (CAPRI), an objective assessment of protein-protein complex modeling. We demonstrated noticeable improvement in both prediction and scoring compared to previous rounds of CAPRI, with our human predictor group near the top of the rankings and our server scorer group at the top. This is the first time in CAPRI that a server has been the top scorer group. To predict protein-protein complex structures, we used both multi-chain template-based modeling (TBM) and our protein-protein docking program, LZerD. LZerD represents protein surfaces using 3D Zernike descriptors (3DZD), which are based on a mathematical series expansion of a 3D function. Because 3DZD are a soft representation of the protein surface, LZerD is tolerant to small conformational changes, making it well suited to docking unbound and TBM structures. The key to our improved performance in CAPRI Round 37 was to combine multi-chain TBM and docking. As opposed to our previous strategy of performing docking for all target complexes, we used TBM when multi-chain templates were available and docking otherwise. We also describe the combination of multiple scoring functions used by our server scorer group, which achieved the top rank for the scorer phase.

Modeling the assembly order of multimeric heteroprotein complexes

Protein-protein interactions are the cornerstone of numerous biological processes. Although an increasing number of protein complex structures have been determined using experimental methods, relatively fewer studies have been performed to determine the assembly order of complexes. In addition to the insights into the molecular mechanisms of biological function provided by the structure of a complex, knowing the assembly order is important for understanding the process of complex formation. Assembly order is also practically useful for constructing subcomplexes as a step toward solving the entire complex experimentally, designing artificial protein complexes, and developing drugs that interrupt a critical step in the complex assembly. There are several experimental methods for determining the assembly order of complexes; however, these techniques are resource-intensive. Here, we present a computational method that predicts the assembly order of protein complexes by building the complex structure. The method, named Path-LzerD, uses a multimeric protein docking algorithm that assembles a protein complex structure from individual subunit structures and predicts assembly order by observing the simulated assembly process of the complex. Benchmarked on a dataset of complexes with experimental evidence of assembly order, Path-LZerD was successful in predicting the assembly pathway for the majority of the cases. Moreover, when compared with a simple approach that infers the assembly path from the buried surface area of subunits in the native complex, Path-LZerD has the strong advantage that it can be used for cases where the complex structure is not known. The path prediction accuracy decreased when starting from unbound monomers, particularly for larger complexes of five or more subunits, for which only a part of the assembly path was correctly identified. As the first method of its kind, Path-LZerD opens a new area of computational protein structure modeling and will be an indispensable approach for studying protein complexes.

The challenge of modeling protein assemblies: the CASP12-CAPRI experiment

We present the quality assessment of 5613 models submitted by predictor groups from both CAPRI and CASP for the total of 15 most tractable targets from the second joint CASP-CAPRI protein assembly prediction experiment. These targets comprised 12 homo-oligomers and 3 hetero-complexes. The bulk of the analysis focuses on 10 targets (of CAPRI Round 37), which included all 3 hetero-complexes, and whose protein chains or the full assembly could be readily modeled from structural templates in the PDB. On average, 28 CAPRI groups and 10 CASP groups (including automatic servers), submitted models for each of these 10 targets. Additionally, about 16 groups participated in the CAPRI scoring experiments. A range of acceptable to high quality models were obtained for 6 of the 10 Round 37 targets, for which templates were available for the full assembly. Poorer results were achieved for the remaining targets due to the lower quality of the templates available for the full complex or the individual protein chains, highlighting the unmet challenge of modeling the structural adjustments of the protein components that occur upon binding or which must be accounted for in template-based modeling. On the other hand, our analysis indicated that residues in binding interfaces were correctly predicted in a sizable fraction of otherwise poorly modeled assemblies and this with higher accuracy than published methods that do not use information on the binding partner. Lastly, the strengths and weaknesses of the assessment methods are evaluated and improvements suggested.

Modeling disordered protein interactions from biophysical principles

Disordered protein-protein interactions (PPIs), those involving a folded protein and an intrinsically disordered protein (IDP), are prevalent in the cell, including important signaling and regulatory pathways. IDPs do not adopt a single dominant structure in isolation but often become ordered upon binding. To aid understanding of the molecular mechanisms of disordered PPIs, it is crucial to obtain the tertiary structure of the PPIs. However, experimental methods have difficulty in solving disordered PPIs and existing protein-protein and protein-peptide docking methods are not able to model them. Here we present a novel computational method, IDP-LZerD, which models the conformation of a disordered PPI by considering the biophysical binding mechanism of an IDP to a structured protein, whereby a local segment of the IDP initiates the interaction and subsequently the remaining IDP regions explore and coalesce around the initial binding site. On a dataset of 22 disordered PPIs with IDPs up to 69 amino acids, successful predictions were made for 21 bound and 18 unbound receptors. The successful modeling provides additional support for biophysical principles. Moreover, the new technique significantly expands the capability of protein structure modeling and provides crucial insights into the molecular mechanisms of disordered PPIs.

A substantial fraction of the proteins encoded in genomes are intrinsically disordered proteins (IDPs), which lack a single stable structure in the native state. IDPs serve many functions including mediating protein-protein interactions (PPIs). Such disordered PPIs are prevalent in important regulatory pathways, including many interactions of the tumor suppressor protein p53. To elucidate the molecular mechanisms of disordered PPIs, obtaining tertiary structure information is essential; however, they are difficult to study with experimental techniques and existing computational protein-protein and protein-peptide modeling methods are unable to model disordered PPIs. Here we present a novel computational method for modeling the structure of disordered PPIs, which is the first of this sort. The method, IDP-LZerD, is designed to follow a known biophysical picture of the mechanism of how IDPs interact with structured proteins. IDP-LZerD successfully modeled the majority of disordered PPIs tested. This technique opens up new possibilities for structural studies of IDPs and their interactions.

Human and server docking prediction for CAPRI round 30-35 using LZerD with combined scoring functions

We report the performance of protein-protein docking predictions by our group for recent rounds of the Critical Assessment of Prediction of Interactions (CAPRI), a community-wide assessment of state-of-the-art docking methods. Our prediction procedure uses a protein-protein docking program named LZerD developed in our group. LZerD represents a protein surface with 3D Zernike descriptors (3DZD), which are based on a mathematical series expansion of a 3D function. The appropriate soft representation of protein surface with 3DZD makes the method more tolerant to conformational change of proteins upon docking, which adds an advantage for unbound docking. Docking was guided by interface residue prediction performed with BindML and cons-PPISP as well as literature information when available. The generated docking models were ranked by a combination of scoring functions, including PRESCO, which evaluates the native-likeness of residues' spatial environments in structure models. First, we discuss the overall performance of our group in the CAPRI prediction rounds and investigate the reasons for unsuccessful cases. Then, we examine the performance of several knowledge-based scoring functions and their combinations for ranking docking models. It was found that the quality of a pool of docking models generated by LZerD, that is whether or not the pool includes near-native models, can be predicted by the correlation of multiple scores. Although the current analysis used docking models generated by LZerD, findings on scoring functions are expected to be universally applicable to other docking methods. Proteins 2017; 85:513-527. © 2016 Wiley Periodicals, Inc.

Distance-Guided Forward and Backward Chain-Growth Monte Carlo Method for Conformational Sampling and Structural Prediction of Antibody CDR-H3 Loops

Antibodies recognize antigens through the complementary determining regions (CDR) formed by six-loop hypervariable regions crucial for the diversity of antigen specificities. Among the six CDR loops, the H3 loop is the most challenging to predict because of its much higher variation in sequence length and identity, resulting in much larger and complex structural space, compared to the other five loops. We developed a novel method based on a chain-growth sequential Monte Carlo method, called distance-guided sequential chain-growth Monte Carlo for H3 loops (DiSGro-H3). The new method samples protein chains in both forward and backward directions. It can efficiently generate low energy, near-native H3 loop structures using the conformation types predicted from the sequences of H3 loops. DiSGro-H3 performs significantly better than another ab initio method, RosettaAntibody, in both sampling and prediction, while taking less computational time. It performs comparably to template-based methods. As an ab initio method, DiSGro-H3 offers satisfactory accuracy while being able to predict any H3 loops without templates.

Asymmetry in structural response of inner and outer transmembrane segments of CorA protein by a coarse-grain model

Structure of CorA protein and its inner (i.corA) and outer (o.corA) transmembrane (TM) components are investigated as a function of temperature by a coarse-grained Monte Carlo simulation. Thermal response of i.corA is found to differ considerably from that of the outer component, o.corA. Analysis of the radius of gyration reveals that the inner TM component undergoes a continuous transition from a globular conformation to a random coil structure on raising the temperature. In contrast, the outer transmembrane component exhibits an abrupt (nearly discontinuous) thermal response in a narrow range of temperature. Scaling of the structure factor shows a globular structure of i.corA at a low temperature with an effective dimension D ∼ 3 and a random coil at a high temperature with D ∼ 2. The residue distribution in o.corA is slightly sparser than that of i.corA in a narrow thermos-responsive regime. The difference in thermos-response characteristics of these components (i.corA and o.corA) may reflect their unique transmembrane functions.

Predicting 3D Structure, Flexibility, and Stability of RNA Hairpins in Monovalent and Divalent Ion Solutions

A full understanding of RNA-mediated biology would require the knowledge of three-dimensional (3D) structures, structural flexibility, and stability of RNAs. To predict RNA 3D structures and stability, we have previously proposed a three-bead coarse-grained predictive model with implicit salt/solvent potentials. In this study, we further develop the model by improving the implicit-salt electrostatic potential and including a sequence-dependent coaxial stacking potential to enable the model to simulate RNA 3D structure folding in divalent/monovalent ion solutions. The model presented here can predict 3D structures of RNA hairpins with bulges/internal loops (<77 nucleotides) from their sequences at the corresponding experimental ion conditions with an overall improved accuracy compared to the experimental data; the model also makes reliable predictions for the flexibility of RNA hairpins with bulge loops of different lengths at several divalent/monovalent ion conditions. In addition, the model successfully predicts the stability of RNA hairpins with various loops/stems in divalent/monovalent ion solutions.

Fully Blind Docking at the Atomic Level for Protein-Peptide Complex Structure Prediction

Protein-peptide interactions play an important role in many cellular processes. In silico prediction of protein-peptide complex structure is highly desirable for mechanistic investigation of these processes and for therapeutic design. However, predicting all-atom structures of protein-peptide complexes without any knowledge about the peptide binding site and the bound peptide conformation remains a big challenge. Here, we present a docking-based method for predicting protein-peptide complex structures, referred to as MDockPeP, which starts with the peptide sequence and globally docks the all-atom, flexible peptide onto the protein structure. MDockPeP was tested on the peptiDB benchmarking database using both bound and unbound protein structures. The results show that MDockPeP successfully generated near-native peptide binding modes in 95.0% of the bound docking cases and in 92.2% of the unbound docking cases. The performance is significantly better than other existing docking methods. MDockPeP is computationally efficient and suitable for large-scale applications.

An Atomistic Statistically Effective Energy Function for Computational Protein Design

Shortcomings in the definition of effective free-energy surfaces of proteins are recognized to be a major contributory factor responsible for the low success rates of existing automated methods for computational protein design (CPD). The formulation of an atomistic statistically effective energy function (SEEF) suitable for a wide range of CPD applications and its derivation from structural data extracted from protein domains and protein-ligand complexes are described here. The proposed energy function comprises nonlocal atom-based and local residue-based SEEFs, which are coupled using a novel atom connectivity number factor to scale short-range, pairwise, nonbonded atomic interaction energies and a surface-area-dependent cavity energy term. This energy function was used to derive additional SEEFs describing the unfolded-state ensemble of any given residue sequence based on computed average energies for partially or fully solvent-exposed fragments in regions of irregular structure in native proteins. Relative thermal stabilities of 97 T4 bacteriophage lysozyme mutants were predicted from calculated energy differences for folded and unfolded states with an average unsigned error (AUE) of 0.84 kcal mol(-1) when compared to experiment. To demonstrate the utility of the energy function for CPD, further validation was carried out in tests of its capacity to recover cognate protein sequences and to discriminate native and near-native protein folds, loop conformers, and small-molecule ligand binding poses from non-native benchmark decoys. Experimental ligand binding free energies for a diverse set of 80 protein complexes could be predicted with an AUE of 2.4 kcal mol(-1) using an additional energy term to account for the loss in ligand configurational entropy upon binding. The atomistic SEEF is expected to improve the accuracy of residue-based coarse-grained SEEFs currently used in CPD and to extend the range of applications of extant atom-based protein statistical potentials.

HybridDock: A Hybrid Protein-Ligand Docking Protocol Integrating Protein- and Ligand-Based Approaches

Structure-based molecular docking and ligand-based similarity search are two commonly used computational methods in computer-aided drug design. Structure-based docking tries to utilize the structural information on a drug target like protein, and ligand-based screening takes advantage of the information on known ligands for a target. Given their different advantages, it would be desirable to use both protein- and ligand-based approaches in drug discovery when information for both the protein and known ligands is available. Here, we have presented a general hybrid docking protocol, referred to as HybridDock, to utilize both the protein structures and known ligands by combining the molecular docking program MDock and the ligand-based similarity search method SHAFTS, and evaluated our hybrid docking protocol on the CSAR 2013 and 2014 exercises. The results showed that overall our hybrid docking protocol significantly improved the performance in both binding affinity and binding mode predictions, compared to the sole MDock program. The efficacy of the hybrid docking protocol was further confirmed using the combination of DOCK and SHAFTS, suggesting an alternative docking approach for modern drug design/discovery.

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 1:53 A° , with a lowest energy RMSD of 2:99 A° , and an average ensembleRMSD of 5:23 A° . 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 10 cpu minutes for 12-residue loops, compared to ca 180 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 (10-17 residues).

A knowledge-based scoring function for protein-RNA interactions derived from a statistical mechanics-based iterative method

Protein-RNA interactions play important roles in many biological processes. Given the high cost and technique difficulties in experimental methods, computationally predicting the binding complexes from individual protein and RNA structures is pressingly needed, in which a reliable scoring function is one of the critical components. Here, we have developed a knowledge-based scoring function, referred to as ITScore-PR, for protein-RNA binding mode prediction by using a statistical mechanics-based iterative method. The pairwise distance-dependent atomic interaction potentials of ITScore-PR were derived from experimentally determined protein–RNA complex structures. For validation, we have compared ITScore-PR with 10 other scoring methods on four diverse test sets. For bound docking, ITScore-PR achieved a success rate of up to 86% if the top prediction was considered and up to 94% if the top 10 predictions were considered, respectively. For truly unbound docking, the respective success rates of ITScore-PR were up to 24 and 46%. ITScore-PR can be used stand-alone or easily implemented in other docking programs for protein–RNA recognition.

ITScorePro: an efficient scoring program for evaluating the energy scores of protein structures for structure prediction

One important component in protein structure prediction is to evaluate the free energy of a given conformation. Given the enormous number of possible conformations for a sequence, it is extremely challenging to quickly and accurately score the energies of these conformations and predict a reasonable structure within a practical computational time. Here, we describe an efficient program for energy evaluation, referred to as ITScorePro (Copyright © 2012). The energy scoring function in the ITScorePro program is based on the distance-dependent, pairwise atomic potentials for protein structure prediction that we recently derived by using statistical mechanics principles (Huang and Zou, Proteins 79:2648-2661, 2011). ITScorePro is a stand-alone program and can also be easily implemented in other software suites for protein structure prediction.

Conformational response to solvent interaction and temperature of a protein (Histone h3.1) by a multi-grained monte carlo simulation

Interaction with the solvent plays a critical role in modulating the structure and dynamics of a protein. Because of the heterogeneity of the interaction strength, it is difficult to identify multi-scale structural response. Using a coarse-grained Monte Carlo approach, we study the structure and dynamics of a protein (H3.1) in effective solvent media. The structural response is examined as a function of the solvent-residue interaction strength (based on hydropathy index) in a range of temperatures (spanning low to high) involving a knowledge-based (Miyazawa-Jernigan(MJ)) residue-residue interaction. The protein relaxes rapidly from an initial random configuration into a quasi-static structure at low temperatures while it continues to diffuse at high temperatures with fluctuating conformation. The radius of gyration (R_g) of the protein responds non-monotonically to solvent interaction, i.e., on increasing the residue-solvent interaction strength (f_s), the increase in R_g (f_s≤f_sc) is followed by decay (f_s≥f_sc) with a maximum at a characteristic value (f_sc) of the interaction. Raising the temperature leads to wider spread of the distribution of the radius of gyration with higher magnitude of f_sc. The effect of solvent on the multi-scale (λ: residue to R_g) structures of the protein is examined by analyzing the structure factor (S(q),|q| = 2π/λ is the wave vector of wavelength, λ) in detail. Random-coil to globular transition with temperature of unsolvated protein (H3.1) is dramatically altered by the solvent at low temperature while a systematic change in structure and scale is observed on increasing the temperature. The interaction energy profile of the residues is not sufficient to predict its mobility in the solvent. Fine-grain representation of protein with two-node and three-node residue enhances the structural resolution; results of the fine-grained simulations are consistent with the finding described above of the coarse-grained description with one-node residue.

A hierarchical coarse-grained (all-atom-to-all-residue) computer simulation approach: self-assembly of peptides

A hierarchical computational approach (all-atom residue to all-residue peptide) is introduced to study self-organizing structures of peptides as a function of temperature. A simulated residue-residue interaction involving all-atom description, analogous to knowledge-based analysis (with different input), is used as an input to a phenomenological coarse-grained interaction for large scales computer simulations. A set of short peptides P1 (¹H ²S ³S ⁴Y ⁵W ⁶Y ⁷A ⁸F ⁹N ¹⁰N ¹¹K ¹²T) is considered as an example to illustrate the utility. We find that peptides assemble rather fast into globular aggregates at low temperatures and disperse as random-coil at high temperatures. The specificity of the mass distribution of the self-assembly depends on the temperature and spatial lengths which are identified from the scaling of the structure factor. Analysis of energy and mobility profiles, gyration radius of peptide, and radial distribution function of the assembly provide insight into the multi-scale (intra- and inter-chain) characteristics. Thermal response of the global assembly with the simulated residue-residue interaction is consistent with that of the knowledge-based analysis despite expected quantitative differences.

Scoring and lessons learned with the CSAR benchmark using an improved iterative knowledge-based scoring function

Based on a statistical mechanics-based iterative method, we have extracted a set of distance-dependent, all-atom pairwise potentials for protein-ligand interactions from the crystal structures of 1300 protein-ligand complexes. The iterative method circumvents the long-standing reference state problem in knowledge-based scoring functions. The resulted scoring function, referred to as ITScore 2.0, has been tested with the CSAR (Community Structure-Activity Resource, 2009 release) benchmark of 345 diverse protein-ligand complexes. ITScore 2.0 achieved a Pearson correlation of R(2) = 0.54 in binding affinity prediction. A comparative analysis has been done on the scoring performances of ITScore 2.0, the van der Waals (VDW) scoring function, the VDW with heavy atoms only, and the force field (FF) scoring function of DOCK which consists of a VDW term and an electrostatic term. The results reveal several important factors that affect the scoring performances, which could be helpful for the improvement of scoring functions.