Statistical potentials extracted from protein structures: how accurate are they?

Combining Complementarity and Binding Energetics in the Assessment of Protein Interactions: EnCPdock-A Practical Manual

The combined effect of shape and electrostatic complementarities (Sc, EC) at the interface of the interacting protein partners (PPI) serves as the physical basis for such associations and is a strong determinant of their binding energetics. EnCPdock (https://www.scinetmol.in/EnCPdock/) presents a comprehensive web platform for the direct conjoint comparative analyses of complementarity and binding energetics in PPIs. It elegantly interlinks the dual nature of local (Sc) and nonlocal complementarity (EC) in PPIs using the complementarity plot. It further derives an AI-based ΔGbinding with a prediction accuracy comparable to the state of the art. This book chapter presents a practical manual to conceptualize and implement EnCPdock with its various features and functionalities, collectively having the potential to serve as a valuable protein engineering tool in the design of novel protein interfaces.

Brewing COFFEE: A Sequence-Specific Coarse-Grained Energy Function for Simulations of DNA-Protein Complexes

DNA-protein interactions are pervasive in a number of biophysical processes ranging from transcription and gene expression to chromosome folding. To describe the structural and dynamic properties underlying these processes accurately, it is important to create transferable computational models. Toward this end, we introduce Coarse-grained Force Field for Energy Estimation, COFFEE, a robust framework for simulating DNA-protein complexes. To brew COFFEE, we integrated the energy function in the self-organized polymer model with side-chains for proteins and the three interaction site model for DNA in a modular fashion, without recalibrating any of the parameters in the original force-fields. A unique feature of COFFEE is that it describes sequence-specific DNA-protein interactions using a statistical potential (SP) derived from a data set of high-resolution crystal structures. The only parameter in COFFEE is the strength (λDNAPRO) of the DNA-protein contact potential. For an optimal choice of λDNAPRO, the crystallographic B-factors for DNA-protein complexes with varying sizes and topologies are quantitatively reproduced. Without any further readjustments to the force-field parameters, COFFEE predicts scattering profiles that are in quantitative agreement with small-angle X-ray scattering experiments, as well as chemical shifts that are consistent with NMR. We also show that COFFEE accurately describes the salt-induced unraveling of nucleosomes. Strikingly, our nucleosome simulations explain the destabilization effect of ARG to LYS mutations, which do not alter the balance of electrostatic interactions but affect chemical interactions in subtle ways. The range of applications attests to the transferability of COFFEE, and we anticipate that it would be a promising framework for simulating DNA-protein complexes at the molecular length-scale.

Brewing COFFEE: A sequence-specific coarse-grained energy function for simulations of DNA-protein complexes

DNA-protein interactions are pervasive in a number of biophysical processes ranging from transcription, gene expression, to chromosome folding. To describe the structural and dynamic properties underlying these processes accurately, it is important to create transferable computational models. Toward this end, we introduce Coarse grained force field for energy estimation, COFFEE, a robust framework for simulating DNA-protein complexes. To brew COFFEE, we integrated the energy function in the Self-Organized Polymer model with Side Chains for proteins and the Three Interaction Site model for DNA in a modular fashion, without re-calibrating any of the parameters in the original force-fields. A unique feature of COFFEE is that it describes sequence-specific DNA-protein interactions using a statistical potential (SP) derived from a dataset of high-resolution crystal structures. The only parameter in COFFEE is the strength (λ D N A P R O ) of the DNA-protein contact potential. For an optimal choice of λ D N A P R O , the crystallographic B-factors for DNA-protein complexes, with varying sizes and topologies, are quantitatively reproduced. Without any further readjustments to the force-field parameters, COFFEE predicts the scattering profiles that are in quantitative agreement with SAXS experiments as well as chemical shifts that are consistent with NMR. We also show that COFFEE accurately describes the salt-induced unraveling of nucleosomes. Strikingly, our nucleosome simulations explain the destabilization effect of ARG to LYS mutations, which does not alter the balance of electrostatic interactions, but affects chemical interactions in subtle ways. The range of applications attests to the transferability of COFFEE, and we anticipate that it would be a promising framework for simulating DNA-protein complexes at the molecular length-scale.

CADD, AI and ML in drug discovery: A comprehensive review

Computer-aided drug design (CADD) is an emerging field that has drawn a lot of interest because of its potential to expedite and lower the cost of the drug development process. Drug discovery research is expensive and time-consuming, and it frequently took 10-15 years for a drug to be commercially available. CADD has significantly impacted this area of research. Further, the combination of CADD with Artificial Intelligence (AI), Machine Learning (ML), and Deep Learning (DL) technologies to handle enormous amounts of biological data has reduced the time and cost associated with the drug development process. This review will discuss how CADD, AI, ML, and DL approaches help identify drug candidates and various other steps of the drug discovery process. It will also provide a detailed overview of the different in silico tools used and how these approaches interact.

A Guide to In Silico Drug Design

The drug discovery process is a rocky path that is full of challenges, with the result that very few candidates progress from hit compound to a commercially available product, often due to factors, such as poor binding affinity, off-target effects, or physicochemical properties, such as solubility or stability. This process is further complicated by high research and development costs and time requirements. It is thus important to optimise every step of the process in order to maximise the chances of success. As a result of the recent advancements in computer power and technology, computer-aided drug design (CADD) has become an integral part of modern drug discovery to guide and accelerate the process. In this review, we present an overview of the important CADD methods and applications, such as in silico structure prediction, refinement, modelling and target validation, that are commonly used in this area.

Key interaction patterns in proteins revealed by cluster expansion of the partition function

The native conformation of structured proteins is stabilized by a complex network of interactions. We analyzed the elementary patterns that constitute such network and ranked them according to their importance in shaping protein sequence design. To achieve this goal, we employed a cluster expansion of the partition function in the space of sequences and evaluated numerically the statistical importance of each cluster. An important feature of this procedure is that it is applied to a dense finite system. We found that patterns that contribute most to the partition function are cycles with even numbers of nodes, while cliques are typically detrimental. Each cluster also gives a contribute to the sequence entropy, which is a measure of the evolutionary designability of a fold. We compared the entropies associated with different interaction patterns to their abundances in the native structures of real proteins.

Topological dynamics of an intrinsically disordered N‐terminal domain of the human androgen receptor

Human androgen receptor contains a large N‐terminal domain (AR‐NTD) that is highly dynamic and this poses a major challenge for experimental and computational analysis to decipher its conformation. Misfolding of the AR‐NTD is implicated in prostate cancer and Kennedy's disease, yet our knowledge of its structure is limited to primary sequence information of the chain and a few functionally important secondary structure motifs. Here, we employed an innovative combination of molecular dynamics simulations and circuit topology (CT) analysis to identify the tertiary structure of AR‐NTD. We found that the AR‐NTD adopts highly dynamic loopy conformations with two identifiable regions with distinct topological make‐up and dynamics. This consists of a N‐terminal region (NR, residues 1–224) and a C‐terminal region (CR, residues 225–538), which carries a dense core. Topological mapping of the dynamics reveals a traceable time‐scale dependent topological evolution. NR adopts different positioning with respect to the CR and forms a cleft that can partly enclose the hormone‐bound ligand‐binding domain (LBD) of the androgen receptor. Furthermore, our data suggest a model in which dynamic NR and CR compete for binding to the DNA‐binding domain of the receptor, thereby regulating the accessibility of its DNA‐binding site. Our approach allowed for the identification of a previously unknown regulatory binding site within the CR core, revealing the structural mechanisms of action of AR inhibitor EPI‐001, and paving the way for other drug discovery applications.

RNA-ligand molecular docking: advances and challenges

With rapid advances in computer algorithms and hardware, fast and accurate virtual screening has led to a drastic acceleration in selecting potent small molecules as drug candidates. Computational modeling of RNA-small molecule interactions has become an indispensable tool for RNA-targeted drug discovery. The current models for RNA-ligand binding have mainly focused on the docking-and-scoring method. Accurate docking and scoring should tackle four crucial problems: (1) conformational flexibility of ligand, (2) conformational flexibility of RNA, (3) efficient sampling of binding sites and binding poses, and (4) accurate scoring of different binding modes. Moreover, compared with the problem of protein-ligand docking, predicting ligand binding to RNA, a negatively charged polymer, is further complicated by additional effects such as metal ion effects. Thermodynamic models based on physics-based and knowledge-based scoring functions have shown highly encouraging success in predicting ligand binding poses and binding affinities. Recently, kinetic models for ligand binding have further suggested that including dissociation kinetics (residence time) in ligand docking would result in improved performance in estimating in vivo drug efficacy. More recently, the rise of deep-learning approaches has led to new tools for predicting RNA-small molecule binding. In this review, we present an overview of the recently developed computational methods for RNA-ligand docking and their advantages and disadvantages.

Statistical potentials from the Gaussian scaling behaviour of chain fragments buried within protein globules

Knowledge-based approaches use the statistics collected from protein data-bank structures to estimate effective interaction potentials between amino acid pairs. Empirical relations are typically employed that are based on the crucial choice of a reference state associated to the null interaction case. Despite their significant effectiveness, the physical interpretation of knowledge-based potentials has been repeatedly questioned, with no consensus on the choice of the reference state. Here we use the fact that the Flory theorem, originally derived for chains in a dense polymer melt, holds also for chain fragments within the core of globular proteins, if the average over buried fragments collected from different non-redundant native structures is considered. After verifying that the ensuing Gaussian statistics, a hallmark of effectively non-interacting polymer chains, holds for a wide range of fragment lengths, although with significant deviations at short spatial scales, we use it to define a ‘bona fide’ reference state. Notably, despite the latter does depend on fragment length, deviations from it do not. This allows to estimate an effective interaction potential which is not biased by the presence of correlations due to the connectivity of the protein chain. We show how different sequence-independent effective statistical potentials can be derived using this approach by coarse-graining the protein representation at varying levels. The possibility of defining sequence-dependent potentials is explored.

Structure‐conditioned amino‐acid couplings: how contact geometry affects pairwise sequence preferences

Relating a protein's sequence to its conformation is a central challenge for both structure prediction and sequence design. Statistical contact potentials, as well as their more descriptive versions that account for side‐chain orientation and other geometric descriptors, have served as simplistic but useful means of representing second‐order contributions in sequence–structure relationships. Here we ask what happens when a pairwise potential is conditioned on the fully defined geometry of interacting backbones fragments. We show that the resulting structure‐conditioned coupling energies more accurately reflect pair preferences as a function of structural contexts. These structure‐conditioned energies more reliably encode native sequence information and more highly correlate with experimentally determined coupling energies. Clustering a database of interaction motifs by structure results in ensembles of similar energies and clustering them by energy results in ensembles of similar structures. By comparing many pairs of interaction motifs and showing that structural similarity and energetic similarity go hand‐in‐hand, we provide a tangible link between modular sequence and structure elements. This link is applicable to structural modeling, and we show that scoring CASP models with structured‐conditioned energies results in substantially higher correlation with structural quality than scoring the same models with a contact potential. We conclude that structure‐conditioned coupling energies are a good way to model the impact of interaction geometry on second‐order sequence preferences.

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.

Docking and scoring for nucleic acid-ligand interactions: Principles and current status

Nucleic acid (NA)-ligand interactions have crucial roles in many cellular processes and, thus, are increasingly attracting therapeutic interest in drug discovery. Molecular docking is a valuable tool for studying molecular interactions. However, because NAs differ significantly from proteins in both their physical and chemical properties, traditional docking algorithms and scoring functions for protein-ligand interactions might not be applicable to NA-ligand docking. Therefore, various sampling strategies and scoring functions for NA-ligand interactions have been developed. Here, we review the basic principles and current status of docking algorithms and scoring functions for DNA/RNA-ligand interactions. We also discuss challenges and limitations of current docking and scoring approaches.

Topological principles of protein folding

What is the topology of a protein and what governs protein folding to a specific topology? This is a fundamental question in biology. The protein folding reaction is a critically important cellular process, which is failing in many prevalent diseases. Understanding protein folding is also key to the design of new proteins for applications. However, our ability to predict the folding of a protein chain is quite limited and much is still unknown about the topological principles of folding. Current predictors of folding kinetics, including the contact order and size, present a limited predictive power, suggesting that these models are fundamentally incomplete. Here, we use a newly developed mathematical framework to define and extract the topology of a native protein conformation beyond knot theory, and investigate the relationship between native topology and folding kinetics in experimentally characterized proteins. We show that not only the folding rate, but also the mechanistic insight into folding mechanisms can be inferred from topological parameters. We identify basic topological features that speed up or slow down the folding process. The approach enabled the decomposition of protein 3D conformation into topologically independent elementary folding units, called circuits. The number of circuits correlates significantly with the folding rate, offering not only an efficient kinetic predictor, but also a tool for a deeper understanding of theoretical folding models. This study contributes to recent work that reveals the critical relevance of topology to protein folding with a new, contact-based, mathematically rigorous perspective. We show that topology can predict folding kinetics when geometry-based predictors like contact order and size fail.

Minimalistic 3D chromatin models: Sparse interactions in single cells drive the chromatin fold and form many-body units

Computational three-dimensional chromatin modeling has helped uncover principles of genome organization. Here, we discuss methods for modeling three-dimensional chromatin structures, with focus on a minimalistic polymer model which inverts population Hi-C into single-cell conformations. Utilizing only basic physical properties, this model reveals that a few specific Hi-C interactions can fold chromatin into conformations consistent with single-cell imaging, Dip-C, and FISH measurements. Aggregated single-cell chromatin conformations also reproduce Hi-C frequencies. This approach allows quantification of structural heterogeneity and discovery of many-body interaction units and has revealed additional insights, including (1) topologically associating domains as a byproduct of folding driven by specific interactions, (2) cell subpopulations with different structural scaffolds are developmental stage dependent, and (3) the functional landscape of many-body units within enhancer-rich regions. We also discuss these findings in relation to the genome structure-function relationship.

Use of molecular docking computational tools in drug discovery

Molecular docking has become an important component of the drug discovery process. Since first being developed in the 1980s, advancements in the power of computer hardware and the increasing number of and ease of access to small molecule and protein structures have contributed to the development of improved methods, making docking more popular in both industrial and academic settings. Over the years, the modalities by which docking is used to assist the different tasks of drug discovery have changed. Although initially developed and used as a standalone method, docking is now mostly employed in combination with other computational approaches within integrated workflows. Despite its invaluable contribution to the drug discovery process, molecular docking is still far from perfect. In this chapter we will provide an introduction to molecular docking and to the different docking procedures with a focus on several considerations and protocols, including protonation states, active site waters and consensus, that can greatly improve the docking results.

Kirkwood-Buff-Derived Force Field for Peptides and Proteins: Philosophy and Development of KBFF20

A new classical nonpolarizable force field, KBFF20, for the simulation of peptides and proteins is presented. The force field relies heavily on the use of Kirkwood-Buff theory to provide a comparison of simulated and experimental Kirkwood-Buff integrals for solutes containing the functional groups common in proteins, thus ensuring intermolecular interactions that provide a good balance between the peptide-peptide, peptide-solvent, and solvent-solvent distributions observed in solution mixtures. In this way, it differs significantly from other biomolecular force fields. Further development and testing of the intermolecular potentials are presented here. Subsequently, rotational potentials for the ϕ/ψ and χ dihedral degrees of freedom are obtained by analysis of the Protein Data Bank, followed by small modifications to provide a reasonable balance between simulated and observed α and β percentages for small peptides. This, the first of two articles, describes in detail the philosophy and development behind KBFF20.

AK-Score: Accurate Protein-Ligand Binding Affinity Prediction Using an Ensemble of 3D-Convolutional Neural Networks

Accurate prediction of the binding affinity of a protein-ligand complex is essential for efficient and successful rational drug design. Therefore, many binding affinity prediction methods have been developed. In recent years, since deep learning technology has become powerful, it is also implemented to predict affinity. In this work, a new neural network model that predicts the binding affinity of a protein-ligand complex structure is developed. Our model predicts the binding affinity of a complex using the ensemble of multiple independently trained networks that consist of multiple channels of 3-D convolutional neural network layers. Our model was trained using the 3772 protein-ligand complexes from the refined set of the PDBbind-2016 database and tested using the core set of 285 complexes. The benchmark results show that the Pearson correlation coefficient between the predicted binding affinities by our model and the experimental data is 0.827, which is higher than the state-of-the-art binding affinity prediction scoring functions. Additionally, our method ranks the relative binding affinities of possible multiple binders of a protein quite accurately, comparable to the other scoring functions. Last, we measured which structural information is critical for predicting binding affinity and found that the complementarity between the protein and ligand is most important.

An information gain-based approach for evaluating protein structure models

For three decades now, knowledge-based scoring functions that operate through the "potential of mean force" (PMF) approach have continuously proven useful for studying protein structures. Although these statistical potentials are not to be confused with their physics-based counterparts of the same name-i.e. PMFs obtained by molecular dynamics simulations-their particular success in assessing the native-like character of protein structure predictions has lead authors to consider the computed scores as approximations of the free energy. However, this physical justification is a matter of controversy since the beginning. Alternative interpretations based on Bayes' theorem have been proposed, but the misleading formalism that invokes the inverse Boltzmann law remains recurrent in the literature. In this article, we present a conceptually new method for ranking protein structure models by quality, which is (i) independent of any physics-based explanation and (ii) relevant to statistics and to a general definition of information gain. The theoretical development described in this study provides new insights into how statistical PMFs work, in comparison with our approach. To prove the concept, we have built interatomic distance-dependent scoring functions, based on the former and new equations, and compared their performance on an independent benchmark of 60,000 protein structures. The results demonstrate that our new formalism outperforms statistical PMFs in evaluating the quality of protein structural decoys. Therefore, this original type of score offers a possibility to improve the success of statistical PMFs in the various fields of structural biology where they are applied. The open-source code is available for download at https://gitlab.rpbs.univ-paris-diderot.fr/src/ig-score.

AlphaFold at CASP13

SUMMARY

Computational prediction of protein structure from sequence is broadly viewed as a foundational problem of biochemistry and one of the most difficult challenges in bioinformatics. Once every two years the Critical Assessment of protein Structure Prediction (CASP) experiments are held to assess the state of the art in the field in a blind fashion, by presenting predictor groups with protein sequences whose structures have been solved but have not yet been made publicly available. The first CASP was organized in 1994, and the latest, CASP13, took place last December, when for the first time the industrial laboratory DeepMind entered the competition. DeepMind's entry, AlphaFold, placed first in the Free Modeling (FM) category, which assesses methods on their ability to predict novel protein folds (the Zhang group placed first in the Template-Based Modeling (TBM) category, which assess methods on predicting proteins whose folds are related to ones already in the Protein Data Bank.) DeepMind's success generated significant public interest. Their approach builds on two ideas developed in the academic community during the preceding decade: (i) the use of co-evolutionary analysis to map residue co-variation in protein sequence to physical contact in protein structure, and (ii) the application of deep neural networks to robustly identify patterns in protein sequence and co-evolutionary couplings and convert them into contact maps. In this Letter, we contextualize the significance of DeepMind's entry within the broader history of CASP, relate AlphaFold's methodological advances to prior work, and speculate on the future of this important problem.

Molecular Docking: Challenges, Advances and its Use in Drug Discovery Perspective

Molecular docking is a process through which small molecules are docked into the macromolecular structures for scoring its complementary values at the binding sites. It is a vibrant research area with dynamic utility in structure-based drug-designing, lead optimization, biochemical pathway and for drug designing being the most attractive tools. Two pillars for a successful docking experiment are correct pose and affinity prediction. Each program has its own advantages and drawbacks with respect to their docking accuracy, ranking accuracy and time consumption so a general conclusion cannot be drawn. Moreover, users don't always consider sufficient diversity in their test sets which results in certain programs to outperform others. In this review, the prime focus has been laid on the challenges of docking and troubleshooters in existing programs, underlying algorithmic background of docking, preferences regarding the use of docking programs for best results illustrated with examples, comparison of performance for existing tools and algorithms, state of art in docking, recent trends of diseases and current drug industries, evidence from clinical trials and post-marketing surveillance are discussed. These aspects of the molecular drug designing paradigm are quite controversial and challenging and this review would be an asset to the bioinformatics and drug designing communities.

iStable 2.0: Predicting protein thermal stability changes by integrating various characteristic modules

Protein mutations can lead to structural changes that affect protein function and result in disease occurrence. In protein engineering, drug design or and optimization industries, mutations are often used to improve protein stability or to change protein properties while maintaining stability. To provide possible candidates for novel protein design, several computational tools for predicting protein stability changes have been developed. Although many prediction tools are available, each tool employs different algorithms and features. This can produce conflicting prediction results that make it difficult for users to decide upon the correct protein design. Therefore, this study proposes an integrated prediction tool, iStable 2.0, which integrates 11 sequence-based and structure-based prediction tools by machine learning and adds protein sequence information as features. Three coding modules are designed for the system, an Online Server Module, a Stand-alone Module and a Sequence Coding Module, to improve the prediction performance of the previous version of the system. The final integrated structure-based classification model has a higher Matthews correlation coefficient than that of the single prediction tool (0.708 vs 0.547, respectively), and the Pearson correlation coefficient of the regression model likewise improves from 0.669 to 0.714. The sequence-based model not only successfully integrates off-the-shelf predictors but also improves the Matthews correlation coefficient of the best single prediction tool by at least 0.161, which is better than the individual structure-based prediction tools. In addition, both the Sequence Coding Module and the Stand-alone Module maintain performance with only a 5% decrease of the Matthews correlation coefficient when the integrated online tools are unavailable. iStable 2.0 is available at http://ncblab.nchu.edu.tw/iStable2.

Scale-consistent approach to the derivation of coarse-grained force fields for simulating structure, dynamics, and thermodynamics of biopolymers

In this chapter the scale-consistent approach to the derivation of coarse-grained force fields developed in our laboratory is presented, in which the effective energy function originates from the potential of mean force of the system under consideration and embeds atomistically detailed interactions in the resulting energy terms through use of Kubo's cluster-cumulant expansion, appropriate selection of the major degrees of freedom to be averaged out in the derivation of analytical approximations to the energy terms, and appropriate expression of the interaction energies at the all-atom level in these degrees of freedom. Our approach enables the developers to find correct functional forms of the effective coarse-grained energy terms, without having to import them from all-atom force fields or deriving them on a heuristic basis. In particular, the energy terms derived in such a way exhibit correct dependence on coarse-grained geometry, in particular on site orientation. Moreover, analytical formulas for the multibody (correlation) terms, which appear to be crucial for coarse-grained modeling of many of the regular structures such as, e.g., protein α-helices and β-sheets, can be derived in a systematic way. Implementation of the developed theory to the UNIfied COarse-gRaiNed (UNICORN) model of biological macromolecules, which consists of the UNRES (for proteins), NARES-2P (for nucleic acids), and SUGRES-1P (for polysaccharides) components, and is being developed in our laboratory is described. Successful applications of UNICORN to the prediction of protein structure, simulating the folding and stability of proteins and nucleic acids, and solving biological problems are discussed.

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.

Computational chemistry methods to investigate the effects caused by DNA variants linked with disease

Computational chemistry offers variety of tools to study properties of biological macromolecules. These tools vary in terms of levels of details from quantum mechanical treatment to numerous macroscopic approaches. Here, we provide a review of computational chemistry algorithms and tools for modeling the effects of genetic variations and their association with diseases. Particular emphasis is given on modeling the effects of missense mutations on stability, conformational dynamics, binding, hydrogen bond network, salt bridges, and pH-dependent properties of the corresponding macromolecules. It is outlined that the disease may be caused by alteration of one or several of above-mentioned biophysical characteristics, and a successful prediction of pathogenicity requires detailed analysis of how the alterations affect the function of involved macromolecules. The review provides a short list of most commonly used algorithms to predict the molecular effects of mutations as well.

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.

Reoptimized UNRES Potential for Protein Model Quality Assessment

Ranking protein structure models is an elusive problem in bioinformatics. These models are evaluated on both the degree of similarity to the native structure and the folding pathway. Here, we simulated the use of the coarse-grained UNited RESidue (UNRES) force field as a tool to choose the best protein structure models for a given protein sequence among a pool of candidate models, using server data from the CASP11 experiment. Because the original UNRES was optimized for Molecular Dynamics simulations, we reoptimized UNRES using a deep feed-forward neural network, and we show that introducing additional descriptive features can produce better results. Overall, we found that the reoptimized UNRES performs better in selecting the best structures and tracking protein unwinding from its native state. We also found a relatively poor correlation between UNRES values and the model’s Template Modeling Score (TMS). This is remedied by reoptimization. We discuss some cases where our reoptimization procedure is useful.

A Membrane Burial Potential with H-Bonds and Applications to Curved Membranes and Fast Simulations

We use the statistics of a large and curated training set of transmembrane helical proteins to develop a knowledge-based potential that accounts for the dependence on both the depth of burial of the protein in the membrane and the degree of side-chain exposure. Additionally, the statistical potential includes depth-dependent energies for unsatisfied backbone hydrogen bond donors and acceptors, which are found to be relatively small, ∼2 RT. Our potential accurately places known proteins within the bilayer. The potential is applied to the mechanosensing MscL channel in membranes of varying thickness and curvature, as well as to the prediction of protein structure. The potential is incorporated into our new Upside molecular dynamics algorithm. Notably, we account for the exchange of protein-lipid interactions for protein-protein interactions as helices contact each other, thereby avoiding overestimating the energetics of helix association within the membrane. Simulations of most multimeric complexes find that isolated monomers and the oligomers retain the same orientation in the membrane, suggesting that the assembly of prepositioned monomers presents a viable mechanism of oligomerization.

Generation of Pairwise Potentials Using Multidimensional Data Mining

The rapid development of molecular structural databases provides the chemistry community access to an enormous array of experimental data that can be used to build and validate computational models. Using radial distribution functions collected from experimentally available X-ray and NMR structures, a number of so-called statistical potentials have been developed over the years using the structural data mining strategy. These potentials have been developed within the context of the two-particle Kirkwood equation by extending its original use for isotropic monatomic systems to anisotropic biomolecular systems. However, the accuracy and the unclear physical meaning of statistical potentials have long formed the central arguments against such methods. In this work, we present a new approach to generate molecular energy functions using structural data mining. Instead of employing the Kirkwood equation and introducing the "reference state" approximation, we model the multidimensional probability distributions of the molecular system using graphical models and generate the target pairwise Boltzmann probabilities using the Bayesian field theory. Different from the current statistical potentials that mimic the "knowledge-based" PMF based on the 2-particle Kirkwood equation, the graphical-model-based structure-derived potential developed in this study focuses on the generation of lower-dimensional Boltzmann distributions of atoms through reduction of dimensionality. We have named this new scoring function GARF, and in this work we focus on the mathematical derivation of our novel approach followed by validation studies on its ability to predict protein-ligand interactions.

Contact Potential for Structure Prediction of Proteins and Protein Complexes from Potts Model

The energy function is the key component of protein modeling methodology. This work presents a semianalytical approach to the development of contact potentials for protein structure modeling. Residue-residue and atom-atom contact energies were derived by maximizing the probability of observing native sequences in a nonredundant set of protein structures. The optimization task was formulated as an inverse statistical mechanics problem applied to the Potts model. Its solution by pseudolikelihood maximization provides consistent estimates of coupling constants at atomic and residue levels. The best performance was achieved when interacting atoms were grouped according to their physicochemical properties. For individual protein structures, the performance of the contact potentials in distinguishing near-native structures from the decoys is similar to the top-performing scoring functions. The potentials also yielded significant improvement in the protein docking success rates. The potentials recapitulated experimentally determined protein stability changes upon point mutations and protein-protein binding affinities. The approach offers a different perspective on knowledge-based potentials and may serve as the basis for their further development.

MyPMFs: a simple tool for creating statistical potentials to assess protein structural models

Evaluating the model quality of protein structures that evolve in environments with particular physicochemical properties requires scoring functions that are adapted to their specific residue compositions and/or structural characteristics. Thus, computational methods developed for structures from the cytosol cannot work properly on membrane or secreted proteins. Here, we present MyPMFs, an easy-to-use tool that allows users to train statistical potentials of mean force (PMFs) on the protein structures of their choice, with all parameters being adjustable. We demonstrate its use by creating an accurate statistical potential for transmembrane protein domains. We also show its usefulness to study the influence of the physical environment on residue interactions within protein structures. Our open-source software is freely available for download at https://github.com/bibip-impmc/mypmfs.

IsRNA: An Iterative Simulated Reference State Approach to Modeling Correlated Interactions in RNA Folding

Coarse-grained RNA folding models promise great potential for RNA structure prediction. A key component in a coarse-grained folding model is the force field. One of the challenges in the coarse-grained force field calculation is how to treat the correlation between the different degrees of freedoms. Here, we describe a new approach (IsRNA) to extract the correlated energy functions from the known structures. Through iterative molecular dynamics simulations, we build the correlation effects into the reference states, from which we extract the energy functions. The validity of IsRNA is supported by the close agreement between the simulated Boltzmann-like probability distributions for all the structure parameters and those observed from the experimentally determined structures. The correlated energy functions derived here may provide a new tool for RNA 3D structure prediction.

Finding the needle in the haystack: towards solving the protein-folding problem computationally

Prediction of protein tertiary structures from amino acid sequence and understanding the mechanisms of how proteins fold, collectively known as "the protein folding problem," has been a grand challenge in molecular biology for over half a century. Theories have been developed that provide us with an unprecedented understanding of protein folding mechanisms. However, computational simulation of protein folding is still difficult, and prediction of protein tertiary structure from amino acid sequence is an unsolved problem. Progress toward a satisfying solution has been slow due to challenges in sampling the vast conformational space and deriving sufficiently accurate energy functions. Nevertheless, several techniques and algorithms have been adopted to overcome these challenges, and the last two decades have seen exciting advances in enhanced sampling algorithms, computational power and tertiary structure prediction methodologies. This review aims at summarizing these computational techniques, specifically conformational sampling algorithms and energy approximations that have been frequently used to study protein-folding mechanisms or to de novo predict protein tertiary structures. We hope that this review can serve as an overview on how the protein-folding problem can be studied computationally and, in cases where experimental approaches are prohibitive, help the researcher choose the most relevant computational approach for the problem at hand. We conclude with a summary of current challenges faced and an outlook on potential future directions.

Prediction of protein disorder based on IUPred

Many proteins contain intrinsically disordered regions (IDRs), functional polypeptide segments that in isolation adopt a highly flexible conformational ensemble instead of a single, well-defined structure. Disorder prediction methods, which can discriminate ordered and disordered regions from the amino acid sequence, have contributed significantly to our current understanding of the distinct properties of intrinsically disordered proteins by enabling the characterization of individual examples as well as large-scale analyses of these protein regions. One popular method, IUPred provides a robust prediction of protein disorder based on an energy estimation approach that captures the fundamental difference between the biophysical properties of ordered and disordered regions. This paper reviews the energy estimation method underlying IUPred and the basic properties of the web server. Through an example, it also illustrates how the prediction output can be interpreted in a more complex case by taking into account the heterogeneous nature of IDRs. Various applications that benefited from IUPred to provide improved disorder predictions, complementing domain annotations and aiding the identification of functional short linear motifs are also described here. IUPred is freely available for noncommercial users through the web server (http://iupred.enzim.hu and http://iupred.elte.hu) . The program can also be downloaded and installed locally for large-scale analyses.

SPA-LN: a scoring function of ligand-nucleic acid interactions via optimizing both specificity and affinity

Nucleic acids have been widely recognized as potential targets in drug discovery and aptamer selection. Quantifying the interactions between small molecules and nucleic acids is critical to discover lead compounds and design novel aptamers. Scoring function is normally employed to quantify the interactions in structure-based virtual screening. However, the predictive power of nucleic acid–ligand scoring functions is still a challenge compared to other types of biomolecular recognition. With the rapid growth of experimentally determined nucleic acid–ligand complex structures, in this work, we develop a knowledge-based scoring function of nucleic acid–ligand interactions, namely SPA-LN. SPA-LN is optimized by maximizing both the affinity and specificity of native complex structures. The development strategy is different from those of previous nucleic acid–ligand scoring functions which focus on the affinity only in the optimization. The native conformation is stabilized while non-native conformations are destabilized by our optimization, making the funnel-like binding energy landscape more biased toward the native state. The performance of SPA-LN validates the development strategy and provides a relatively more accurate way to score the nucleic acid–ligand interactions.

Computational tools help improve protein stability but with a solubility tradeoff

Accurately predicting changes in protein stability upon amino acid substitution is a much sought after goal. Destabilizing mutations are often implicated in disease, whereas stabilizing mutations are of great value for industrial and therapeutic biotechnology. Increasing protein stability is an especially challenging task, with random substitution yielding stabilizing mutations in only ∼2% of cases. To overcome this bottleneck, computational tools that aim to predict the effect of mutations have been developed; however, achieving accuracy and consistency remains challenging. Here, we combined 11 freely available tools into a meta-predictor (meieringlab.uwaterloo.ca/stabilitypredict/). Validation against ∼600 experimental mutations indicated that our meta-predictor has improved performance over any of the individual tools. The meta-predictor was then used to recommend 10 mutations in a previously designed protein of moderate thermodynamic stability, ThreeFoil. Experimental characterization showed that four mutations increased protein stability and could be amplified through ThreeFoil's structural symmetry to yield several multiple mutants with >2-kcal/mol stabilization. By avoiding residues within functional ties, we could maintain ThreeFoil's glycan-binding capacity. Despite successfully achieving substantial stabilization, however, almost all mutations decreased protein solubility, the most common cause of protein design failure. Examination of the 600-mutation data set revealed that stabilizing mutations on the protein surface tend to increase hydrophobicity and that the individual tools favor this approach to gain stability. Thus, whereas currently available tools can increase protein stability and combining them into a meta-predictor yields enhanced reliability, improvements to the potentials/force fields underlying these tools are needed to avoid gaining protein stability at the cost of solubility.

Sequence statistics of tertiary structural motifs reflect protein stability

The Protein Data Bank (PDB) has been a key resource for learning general rules of sequence-structure relationships in proteins. Quantitative insights have been gained by defining geometric descriptors of structure (e.g., distances, dihedral angles, solvent exposure, etc.) and observing their distributions and sequence preferences. Here we argue that as the PDB continues to grow, it may become unnecessary to reduce structure into a set of elementary descriptors. Instead, it could be possible to deduce quantitative sequence-structure relationships in the context of precisely-defined complex structural motifs by mining the PDB for closely matching backbone geometries. To validate this idea, we turned to the the task of predicting changes in protein stability upon amino-acid substitution—a difficult problem of broad significance. We defined non-contiguous tertiary motifs (TERMs) around a protein site of interest and extracted sequence preferences from ensembles of closely-matching substructures in the PDB to predict mutational stability changes at the site, ΔΔG_m. We demonstrate that these ensemble statistics predict ΔΔG_m on par with state-of-the-art statistical and machine-learning methods on large thermodynamic datasets, and outperform these, along with a leading structure-based modeling approach, when tested in the context of unbiased diverse mutations. Further, we show that the performance of the TERM-based method is directly related to the amount of available relevant structural data, automatically improving with the growing PDB. This enables a means of estimating prediction accuracy. Our results clearly demonstrate that: 1) statistics of non-contiguous structural motifs in the PDB encode fundamental sequence-structure relationships related to protein thermodynamic stability, and 2) the PDB is now large enough that such statistics are already useful in practice, with their accuracy expected to continue increasing as the database grows. These observations suggest new ways of using structural data towards addressing problems of computational structural biology.

High-Dimensional Mutant and Modular Thermodynamic Cycles, Molecular Switching, and Free Energy Transduction

Understanding how distinct parts of proteins produce coordinated behavior has driven and continues to drive advances in protein science and enzymology. However, despite consensus about the conceptual basis for allostery, the idiosyncratic nature of allosteric mechanisms resists general approaches. Computational methods can identify conformational transition states from structural changes, revealing common switching mechanisms that impose multistate behavior. Thermodynamic cycles use factorial perturbations to measure coupling energies between side chains in molecular switches that mediate shear during domain motion. Such cycles have now been complemented by modular cycles that measure energetic coupling between separable domains. For one model system, energetic coupling between domains has been shown to be quantitatively equivalent to that between dynamic side chains. Linkages between domain motion, switching residues, and catalysis make nucleoside triphosphate hydrolysis conditional on domain movement, confirming an essential yet neglected aspect of free energy transduction and suggesting the potential generality of these studies.

Scoring Functions of Protein-Ligand Interactions

Scoring function of protein-ligand interactions is used to recognize the “native” binding pose of a ligand on the protein and to predict the binding affinity, so that the active small molecules can be discriminated from the non-active ones. Scoring function is widely used in computationally molecular docking and structure-based drug discovery. The development and improvement of scoring functions have broad implications in pharmaceutical industry and academic research. During the past three decades, much progress have been made in methodology and accuracy for scoring functions, and many successful cases have be witnessed in virtual database screening. In this chapter, the authors introduced the basic types of scoring functions and their derivations, the commonly-used evaluation methods and benchmarks, as well as the underlying challenges and current solutions. Finally, the authors discussed the promising directions to improve and develop scoring functions for future molecular docking-based drug discovery.

Pairwise contact energy statistical potentials can help to find probability of point mutations

To adopt a particular fold, a protein requires several interactions between its amino acid residues. The energetic contribution of these residue-residue interactions can be approximated by extracting statistical potentials from known high resolution structures. Several methods based on statistical potentials extracted from unrelated proteins are found to make a better prediction of probability of point mutations. We postulate that the statistical potentials extracted from known structures of similar folds with varying sequence identity can be a powerful tool to examine probability of point mutation. By keeping this in mind, we have derived pairwise residue and atomic contact energy potentials for the different functional families that adopt the (α/β)₈ TIM-Barrel fold. We carried out computational point mutations at various conserved residue positions in yeast Triose phosphate isomerase enzyme for which experimental results are already reported. We have also performed molecular dynamics simulations on a subset of point mutants to make a comparative study. The difference in pairwise residue and atomic contact energy of wildtype and various point mutations reveals probability of mutations at a particular position. Interestingly, we found that our computational prediction agrees with the experimental studies of Silverman et al. (Proc Natl Acad Sci 2001;98:3092-3097) and perform better prediction than i_Mutant and Cologne University Protein Stability Analysis Tool. The present work thus suggests deriving pairwise contact energy potentials and molecular dynamics simulations of functionally important folds could help us to predict probability of point mutations which may ultimately reduce the time and cost of mutation experiments. Proteins 2016; 85:54-64. © 2016 Wiley Periodicals, Inc.

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.

KECSA-Movable Type Implicit Solvation Model (KMTISM)

Computation of the solvation free energy for chemical and biological processes has long been of significant interest. The key challenges to effective solvation modeling center on the choice of potential function and configurational sampling. Herein, an energy sampling approach termed the “Movable Type” (MT) method, and a statistical energy function for solvation modeling, “Knowledge-based and Empirical Combined Scoring Algorithm” (KECSA) are developed and utilized to create an implicit solvation model: KECSA-Movable Type Implicit Solvation Model (KMTISM) suitable for the study of chemical and biological systems. KMTISM is an implicit solvation model, but the MT method performs energy sampling at the atom pairwise level. For a specific molecular system, the MT method collects energies from prebuilt databases for the requisite atom pairs at all relevant distance ranges, which by its very construction encodes all possible molecular configurations simultaneously. Unlike traditional statistical energy functions, KECSA converts structural statistical information into categorized atom pairwise interaction energies as a function of the radial distance instead of a mean force energy function. Within the implicit solvent model approximation, aqueous solvation free energies are then obtained from the NVT ensemble partition function generated by the MT method. Validation is performed against several subsets selected from the Minnesota Solvation Database v2012. Results are compared with several solvation free energy calculation methods, including a one-to-one comparison against two commonly used classical implicit solvation models: MM-GBSA and MM-PBSA. Comparison against a quantum mechanics based polarizable continuum model is also discussed (Cramer and Truhlar’s Solvation Model 12).