Energy Function For Proteins Research Articles

Pareto Dominance Archive and Coordinated Selection Strategy-Based Many-Objective Optimizer for Protein Structure Prediction.

Protein structure prediction (PSP) is predicting the three-dimensional of protein from its amino acid sequence only based on the information hidden in the protein sequence. One of the efficient tools to describe this information is protein energy functions. Despite the advancements in biology and computer science, PSP is still a challenging problem due to its large protein conformation space and inaccurate energy functions. In this study, PSP is treated as a many-objective optimization problem and four conflicting energy functions are used as different objectives to be optimized. A novel Pareto-dominance-archive and Coordinated-selection-strategy-based Many-objective-optimizer (PCM) is proposed to perform the conformation search. In it, convergence and diversity-based selection metrics are used to enable PCM to find near-native proteins with well-distributed energy values, while a Pareto-dominance-based archive is proposed to save more potential conformations that can guide the search to more promising conformation areas. The experimental results on thirty-four benchmark proteins demonstrate the significant superiority of PCM in comparison with other single, multiple, and many-objective evolutionary algorithms. Additionally, the inherent characteristics of iterative search of PCM can also give more insights into the dynamic progress of protein folding besides the final predicted static tertiary structure. All these confirm that PCM is a fast, easy-to-use, and fruitful solution generation method for PSP.

Construction of a Deep Neural Network Energy Function for Protein Physics.

The traditional approach of computational biology consists of calculating molecule properties by using approximate classical potentials. Interactions between atoms are described by an energy function derived from physical principles or fitted to experimental data. Their functional form is usually limited to pairwise interactions between atoms and does not consider complex multibody effects. More recently, neural networks have emerged as an alternative way of describing the interactions between biomolecules. In this approach, the energy function does not have an explicit functional form and is learned bottom-up from simulations at the atomistic or quantum level. In this study, we attempt a top-down approach and use deep learning methods to obtain an energy function by exploiting the large amount of experimental data acquired with years in the field of structural biology. The energy function is represented by a probability density model learned from a large repertoire of building blocks representing local clusters of amino acids paired with their sequence signature. We demonstrated the feasibility of this approach by generating a neural network energy function and testing its validity on several applications such as discriminating decoys, assessing qualities of structural models, sampling structural conformations, and designing new protein sequences. We foresee that, in the future, our methodology could exploit the continuously increasing availability of experimental data and simulations and provide a new method for the parametrization of protein energy functions.

MO4: A Many-Objective Evolutionary Algorithm for Protein Structure Prediction

Protein structure prediction (PSP) problems are a major biocomputing challenge, owing to its scientific intrinsic that assists researchers to understand the relationship between amino acid sequences and protein structures, and to study the function of proteins. Although computational resources increased substantially over the last decade, a complete solution to PSP problems by computational methods has not yet been obtained. Using only one energy function is insufficient to characterize proteins because of their complexity. Diverse protein energy functions and evolutionary computation algorithms have been extensively studied to assist in the prediction of protein structures in different ways. Such algorithms are able to provide a better protein with less computational resources requirement than deep learning methods. For the first time, this study proposes a many-objective PSP (MaOPSP) problem with four types of objectives to alleviate the impact of imprecise energy functions for predicting protein structures. A many-objective evolutionary algorithm (MaOEA) is utilized to solve MaOPSP. The proposed method is compared with existing methods by examining 34 proteins. An analysis of the objectives demonstrates that our generated conformations are more reasonable than those generated by single/multiobjective optimization methods. Experimental results indicate that solving a PSP problem as an MaOPSP problem with four objectives yields better PSPs, in terms of both accuracy and efficiency. The source code of the proposed method can be found at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://toyamaailab.github.io/sourcedata.html</uri> .

Diverse Scientific Benchmarks for Implicit Membrane Energy Functions

Energy functions are fundamental to biomolecular modeling. Their success depends on robust physical formalisms, efficient optimization, and high-resolution data for training and validation. Over the past 20 years, progress in each area has advanced soluble protein energy functions. Yet, energy functions for membrane proteins lag behind due to sparse and low-quality data, leading to overfit tools. To overcome this challenge, we assembled a suite of 12 tests on independent data sets varying in size, diversity, and resolution. The tests probe an energy function's ability to capture membrane protein orientation, stability, sequence, and structure. Here, we present the tests and use the franklin2019 energy function to demonstrate them. We then identify areas for energy function improvement and discuss potential future integration with machine-learning-based optimization methods. The tests are available through the Rosetta Benchmark Server (https://benchmark.graylab.jhu.edu/) and GitHub (https://github.com/rfalford12/Implicit-Membrane-Energy-Function-Benchmark).

Big Data from Sparse Data: Diverse Scientific Benchmarks Reveal Optimization Imperatives for Implicit Membrane Energy Functions

In computational protein structure prediction and design, energy functions discriminate non-native from near-native biomolecule conformations. These functions approximate the balance of enthalpic and entropic contributions to protein stability through mathematical models derived from thermodynamic and structural data. Over the past decade, an influx of high-resolution data paired with machine learning techniques has significantly improved the accuracy of soluble protein energy functions. However, membrane protein energy functions remain low-resolution because the experimental data are sparse, leading to overfitting. To overcome this challenge, we assembled a suite of 12 computational benchmark tests against experimental targets. The tests probe various membrane protein energy function capabilities ranging from reproducing protein stabilities and orientations to accurately predicting the three-dimensional structures of monomeric proteins and protein complexes. To evaluate current performance, we ran the benchmark on Franklin19, the current state-of-the-art implicit membrane protein energy function in Rosetta. The benchmark revealed areas for improvement including treatment of electrostatic interactions, representation of the interfacial head-group region, and accounting for entropic effects on protein orientation. Ultimately, these benchmarks will enable big-data-style optimization of membrane energy functions, leading to improved membrane protein design capabilities.

Adoption of an improved PSO to explore a compound multi-objective energy function in protein structure prediction

The protein structure prediction (PSP) problem, i.e., predicting the three-dimensional structure of a protein from its sequence, remains challenging in computational biology. The inaccuracy of existing protein energy functions and the huge conformation search space make the problem difficult to solve. In this study, the PSP problem is modeled as a multi-objective optimization problem. A physics-based energy function and a knowledge-based energy function are combined to construct the three-objective energy function. An improved multi-objective particle swarm optimization coupled with two archives is employed to execute the conformation space search. In addition, a mechanism based on Pareto non-dominated sorting is designed to properly address the slightly worse solutions. Finally, the experimental results demonstrate the effectiveness of the proposed approach. A new perspective for solving the PSP problem by means of multi-objective optimization is given in this paper.

From Extraction of Local Structures of Protein Energy Landscapes to Improved Decoy Selection in Template-Free Protein Structure Prediction.

Due to the essential role that the three-dimensional conformation of a protein plays in regulating interactions with molecular partners, wet and dry laboratories seek biologically-active conformations of a protein to decode its function. Computational approaches are gaining prominence due to the labor and cost demands of wet laboratory investigations. Template-free methods can now compute thousands of conformations known as decoys, but selecting native conformations from the generated decoys remains challenging. Repeatedly, research has shown that the protein energy functions whose minima are sought in the generation of decoys are unreliable indicators of nativeness. The prevalent approach ignores energy altogether and clusters decoys by conformational similarity. Complementary recent efforts design protein-specific scoring functions or train machine learning models on labeled decoys. In this paper, we show that an informative consideration of energy can be carried out under the energy landscape view. Specifically, we leverage local structures known as basins in the energy landscape probed by a template-free method. We propose and compare various strategies of basin-based decoy selection that we demonstrate are superior to clustering-based strategies. The presented results point to further directions of research for improving decoy selection, including the ability to properly consider the multiplicity of native conformations of proteins.

Incorporation of Solvent Effect into Multi-Objective Evolutionary Algorithm for Improved Protein Structure Prediction.

The problem of predicting the three-dimensional (3-D) structure of a protein from its one-dimensional sequence has been called the "holy grail of molecular biology", and it has become an important part of structural genomics projects. Despite the rapid developments in computer technology and computational intelligence, it remains challenging and fascinating. In this paper, to solve it we propose a multi-objective evolutionary algorithm. We decompose the protein energy function Chemistry at HARvard Macromolecular Mechanics force fields into bond and non-bond energies as the first and second objectives. Considering the effect of solvent, we innovatively adopt a solvent-accessible surface area as the third objective. We use 66 benchmark proteins to verify the proposed method and obtain better or competitive results in comparison with the existing methods. The results suggest the necessity to incorporate the effect of solvent into a multi-objective evolutionary algorithm to improve protein structure prediction in terms of accuracy and efficiency.

AB-Bind: Antibody binding mutational database for computational affinity predictions.

Antibodies (Abs) are a crucial component of the immune system and are often used as diagnostic and therapeutic agents. The need for high-affinity and high-specificity antibodies in research and medicine is driving the development of computational tools for accelerating antibody design and discovery. We report a diverse set of antibody binding data with accompanying structures that can be used to evaluate methods for modeling antibody interactions. Our Antibody-Bind (AB-Bind) database includes 1101 mutants with experimentally determined changes in binding free energies (ΔΔG) across 32 complexes. Using the AB-Bind data set, we evaluated the performance of protein scoring potentials in their ability to predict changes in binding free energies upon mutagenesis. Numerical correlations between computed and observed ΔΔG values were low (r = 0.16-0.45), but the potentials exhibited predictive power for classifying variants as improved vs weakened binders. Performance was evaluated using the area under the curve (AUC) for receiver operator characteristic (ROC) curves; the highest AUC values for 527 mutants with |ΔΔG| > 1.0 kcal/mol were 0.81, 0.87, and 0.88 using STATIUM, FoldX, and Discovery Studio scoring potentials, respectively. Some methods could also enrich for variants with improved binding affinity; FoldX and Discovery Studio were able to correctly rank 42% and 30%, respectively, of the 80 most improved binders (those with ΔΔG < -1.0 kcal/mol) in the top 5% of the database. This modest predictive performance has value but demonstrates the continuing need to develop and improve protein energy functions for affinity prediction.

DNA Damage Processing by Human 8-Oxoguanine-DNA Glycosylase Mutants with the Occluded Active Site

8-Oxoguanine-DNA glycosylase (OGG1) removes premutagenic lesion 8-oxoguanine (8-oxo-G) from DNA and then nicks the nascent abasic (apurinic/apyrimidinic) site by β-elimination. Although the structure of OGG1 bound to damaged DNA is known, the dynamic aspects of 8-oxo-G recognition are not well understood. To comprehend the mechanisms of substrate recognition and processing, we have constructed OGG1 mutants with the active site occluded by replacement of Cys-253, which forms a wall of the base-binding pocket, with bulky leucine or isoleucine. The conformational dynamics of OGG1 mutants were characterized by single-turnover kinetics and stopped-flow kinetics with fluorescent detection. Additionally, the conformational mobility of wild type and the mutant OGG1 substrate complex was assessed using molecular dynamics simulations. Although pocket occlusion distorted the active site and greatly decreased the catalytic activity of OGG1, it did not fully prevent processing of 8-oxo-G and apurinic/apyrimidinic sites. Both mutants were notably stimulated in the presence of free 8-bromoguanine, indicating that this base can bind to the distorted OGG1 and facilitate β-elimination. The results agree with the concept of enzyme plasticity, suggesting that the active site of OGG1 is flexible enough to compensate partially for distortions caused by mutation.

Expanded Explorations into the Optimization of an Energy Function for Protein Design

Nature possesses a secret formula for the energy as a function of the structure of a protein. In protein design, approximations are made to both the structural representation of the molecule and to the form of the energy equation, such that the existence of a general energy function for proteins is by no means guaranteed. Here, we present new insights toward the application of machine learning to the problem of finding a general energy function for protein design. Machine learning requires the definition of an objective function, which carries with it the implied definition of success in protein design. We explored four functions, consisting of two functional forms, each with two criteria for success. Optimization was carried out by a Monte Carlo search through the space of all variable parameters. Cross-validation of the optimized energy function against a test set gave significantly different results depending on the choice of objective function, pointing to relative correctness of the built-in assumptions. Novel energy cross terms correct for the observed nonadditivity of energy terms and an imbalance in the distribution of predicted amino acids. This paper expands on the work presented at the 2012 ACM-BCB.

Extended solvent-contact model for protein solvation: Test cases for dipeptides

Solvation effects are critically important in the structural stabilization and functional optimization of proteins. Here, we propose a new solvation free energy function for proteins, and test its applicability in predicting the solvation free energies of dipeptides. The present solvation model involves the improvement of the previous solvent-contact model assuming that the molecular solvation free energy could be given by the sum over the individual atomic contributions. In addition to the existing solvent-contact term, the modified solvation free energy function includes the self-solvation term that reflects the effects of intramolecular interactions in the solute molecule on solute–solvent interactions. Four kinds of atomic parameters should be determined in this solvation model: atomic fragmental volume, maximum atomic occupancy, atomic solvation, and atomic self-solvation parameters. All of these parameters for 16 atom types are optimized with a standard genetic algorithm in such a way to minimize the difference between the solvation free energies of dipeptides obtained from high-level quantum chemical calculations and those predicted by the solvation free energy function. The solvation free energies of dipeptides estimated from the new solvation model are in good agreement with the quantum chemical results. Therefore, the optimized solvation free energy function is expected to be useful for examining the structural and energetic features of proteins in aqueous solution.

Learning Protein Folding Energy Functions.

A critical open problem in ab initio protein folding is protein energy function design, which pertains to defining the energy of protein conformations in a way that makes folding most efficient and reliable. In this paper, we address this issue as a weight optimization problem and utilize a machine learning approach, learning-to-rank, to solve this problem. We investigate the ranking-via-classification approach, especially the RankingSVM method and compare it with the state-of-the-art approach to the problem using the MINUIT optimization package. To maintain the physicality of the results, we impose non-negativity constraints on the weights. For this we develop two efficient non-negative support vector machine (NNSVM) methods, derived from L2-norm SVM and L1-norm SVMs, respectively. We demonstrate an energy function which maintains the correct ordering with respect to structure dissimilarity to the native state more often, is more efficient and reliable for learning on large protein sets, and is qualitatively superior to the current state-of-the-art energy function.

Electrostatics in Proteins and Protein–Ligand Complexes

Accurate computational methods for predicting electrostatic energies are of major importance for our understanding of protein energetics in general for computer-aided drug design as well as for the design of novel biocatalysts and protein therapeutics. Electrostatic energies are of particular importance in such applications as virtual screening, drug design and protein-protein docking due to the high charge density of protein ligands and small-molecule drugs, and the frequent protonation state changes observed when drugs bind to their protein targets. Therefore, the development of a reliable and fast algorithm for the evaluation of electrostatic free energies, as an important contributor to the overall protein energy function, has been the focus for many scientists over the past three decades. In this review we describe the current state-of-the-art in modeling electrostatic effects in proteins and protein-ligand complexes. We focus mainly on the merits and drawbacks of the continuum methodology, and speculate on future directions in refining algorithms for calculating electrostatic energies in proteins using experimental data.

GP challenge: evolving energy function for protein structure prediction

One of the key elements in protein structure prediction is the ability to distinguish between good and bad candidate structures. This distinction is made by estimation of the structure energy. The energy function used in the best state-of-the-art automatic predictors competing in the most recent CASP (Critical Assessment of Techniques for Protein Structure Prediction) experiment is defined as a weighted sum of a set of energy terms designed by experts. We hypothesised that combining these terms more freely will improve the prediction quality. To test this hypothesis, we designed a genetic programming algorithm to evolve the protein energy function. We compared the predictive power of the best evolved function and a linear combination of energy terms featuring weights optimised by the Nelder---Mead algorithm. The GP based optimisation outperformed the optimised linear function. We have made the data used in our experiments publicly available in order to encourage others to further investigate this challenging problem by using GP and other methods, and to attempt to improve on the results presented here.

Reduced Cβ statistical potentials can outperform all‐atom potentials in decoy identification

We developed a series of statistical potentials to recognize the native protein from decoys, particularly when using only a reduced representation in which each side chain is treated as a single C(beta) atom. Beginning with a highly successful all-atom statistical potential, the Discrete Optimized Protein Energy function (DOPE), we considered the implications of including additional information in the all-atom statistical potential and subsequently reducing to the C(beta) representation. One of the potentials includes interaction energies conditional on backbone geometries. A second potential separates sequence local from sequence nonlocal interactions and introduces a novel reference state for the sequence local interactions. The resultant potentials perform better than the original DOPE statistical potential in decoy identification. Moreover, even upon passing to a reduced C(beta) representation, these statistical potentials outscore the original (all-atom) DOPE potential in identifying native states for sets of decoys. Interestingly, the backbone-dependent statistical potential is shown to retain nearly all of the information content of the all-atom representation in the C(beta) representation. In addition, these new statistical potentials are combined with existing potentials to model hydrogen bonding, torsion energies, and solvation energies to produce even better performing potentials. The ability of the C(beta) statistical potentials to accurately represent protein interactions bodes well for computational efficiency in protein folding calculations using reduced backbone representations, while the extensions to DOPE illustrate general principles for improving knowledge-based potentials.

최적설계 기법을 이용한 단백질 3차원 구조 예측

Many researchers are developing computational prediction methods for protein tertiary structures to get much more information of protein. These methods are very attractive on the aspects of breaking technologies of computer hardware and simulation software. One of the computational methods for the prediction is a fragment assembly method which shows good ab initio predictions at several cases. There are many barriers, however, in conventional fragment assembly methods. Argues on protein energy functions and global optimization to predict the structures are in progress for example. In this study, a new prediction method for protein structures is proposed. The proposed method mainly consists of two parts. The first one is a fragment assembly which uses very shot fragments of representative proteins and produces a prototype of a given sequence query of amino acids. The second one is a global optimization which folds the prototype and makes the only protein structure. The goodness of the proposed method is shown through numerical experiments.

What is a Desirable Statistical Energy Function for Proteins and How Can It Be Obtained?

Can one obtain a physical energy function for proteins from statistical analysis of protein structures? A direct answer to this question is likely "no." Aless demanding question is whether one can produce a statistical energy function that has the desirable features of a physical-based energy function. Such a desirable energy function would be founded on a physical basis with few or no adjustable parameters, reproduce the known physical characters of amino acid residues, be mostly database independent and transferable, and, more importantly, reasonably accurate in various applications. In this review, we show how such a desirable energy function can be obtained via introducing a simple physical-based reference state called DFIRE (Distance-scaled, Finite, Ideal-gas REference state).

A Hierarchical Multiscale Approach to Protein Structure Prediction: Production of Low‐Resolution Packing Arrangements of Helices and Refinement of the Best Models with a United‐Residue Force Field

A hierarchical, two‐stage approach to ab initio protein structure prediction is presented and applied to four α‐helical proteins. In the first stage, a bank of low‐resolution models is generated using a highly simplified protein representation and energy function, coupled with a Conformation‐Family Monte Carlo (CFMC) search for the energy minimum. For helical proteins, this procedure (referred to as REPACK) produces a set of plausible packed arrangements of the helices, given their positions in the amino acid sequence. Secondary structure prediction methods such as JPRED can be used to provide the secondary structure assignment. In the second stage, these packing arrangements are used as starting points for a new search method (Local Search), based on the Monte Carlo‐with‐Minimization (MCM) algorithm and a united‐residue (UNRES) energy function. The focus of the Local Search is mainly on improving loop conformations and side‐chain positions, with minor modifications to the overall packing of the helices. ...

A Knowledge-Based Energy Function for Protein−Ligand, Protein−Protein, and Protein−DNA Complexes

We developed a knowledge-based statistical energy function for protein-ligand, protein-protein, and protein-DNA complexes by using 19 atom types and a distance-scale finite ideal-gas reference (DFIRE) state. The correlation coefficients between experimentally measured protein-ligand binding affinities and those predicted by the DFIRE energy function are around 0.63 for one training set and two testing sets. The energy function also makes highly accurate predictions of binding affinities of protein-protein and protein-DNA complexes. Correlation coefficients between theoretical and experimental results are 0.73 for 82 protein-protein (peptide) complexes and 0.83 for 45 protein-DNA complexes, despite the fact that the structures of protein-protein (peptide) and protein-DNA complexes were not used in training the energy function. The results of the DFIRE energy function on protein-ligand complexes are compared to the published results of 12 other scoring functions generated from either physical-based, knowledge-based, or empirical methods. They include AutoDock, X-Score, DrugScore, four scoring functions in Cerius 2 (LigScore, PLP, PMF, and LUDI), four scoring functions in SYBYL (F-Score, G-Score, D-Score, and ChemScore), and BLEEP. While the DFIRE energy function is only moderately successful in ranking native or near native conformations, it yields the strongest correlation between theoretical and experimental binding affinities of the testing sets and between rmsd values and energy scores of docking decoys in a benchmark of 100 protein-ligand complexes. The parameters and the program of the all-atom DFIRE energy function are freely available for academic users at http://theory.med.buffalo.edu.