Protein structure prediction aided by geometrical and probabilistic constraints

Database-assisted ab initio protein structure prediction methods have exhibited considerable promise in the recent past, with several implementations being successful in community-wide experiments (CASP). We have employed combinatorial optimization techniques toward solving the protein structure prediction problem. A Monte Carlo minimization algorithm has been employed on a constrained search space to identify minimum energy configurations. The search space is constrained by using radius of gyration cutoffs, the loop backbone dihedral probability distributions, and various secondary structure packing conformations. Simulations have been carried out on several sequences and 1000 conformations have been initially generated. Of these, 50 best candidates have then been selected as probable conformations. The search for the optimum has been simplified by incorporating various geometrical constraints on secondary structural elements using distance restraint potential functions. The advantages of the reported methodology are its simplicity, and modifiability to include other geometric and probabilistic restraints.     

Knowledge-based potential for the polypeptide backbone

A knowledge-based potential for the polypeptide backbone as a function of the dihedral angles is developed and tested. The potential includes correlations due to the conformations and compositions of adjacent residues. Its purpose is to serve as a major component of a coarse-grained protein potential by including the most relevant local interactions while averaging out nonbonded ones. A probability density estimation algorithm and a multi-resolution probability combination procedure are developed to produce smooth probability distributions and dihedral angle potentials. The potential is described by a set of two-dimensional dihedral angle surfaces involving the various combinations of amino acid triplets and duplets. Several tests are carried out to evaluate the quality of the potential. Monte Carlo simulations, using only the dihedral angle potential and a coarse-grained excluded volume potential, show that the resulting dihedral angle distributions and correlations are consistent with those extracted from protein structures. Additional simulations of unfolded proteins are carried out to measure the NMR residual dipolar coupling (RDC). Significant correlations are obtained between the simulations and the corresponding experiments consistent with other simulations in the literature. Finally, the dihedral angle entropies are calculated for the 20 amino acids. In particular, the entropy difference between alanine and glycine agrees with the ones computed from molecular dynamics simulations ( approximately 0.4 kcal/mol).     

From secondary structure to three-dimensional structure: Improved dihedral angle probability distribution function for use with energy searches for native structures of polypeptides and proteins

An improved scheme to help in the prediction of protein structure is presented. This procedure generates improved starting conformations of a protein suitable for energy minimization. Trivariate gaussian distribution functions for the π, ψ, and χ¹ dihedral angles have been derived, using conformational data from high resolution protein structures selected from the Protein Data Bank (PDB). These trivariate probability functions generate initial values for the π, ψ, and χ¹ dihedral angles which reflect the experimental values found in the PDB. These starting structures speed the search of the conformational space by focusing the search mainly in the regions of native proteins. The efficiency of the new trivariate probability distributions is demonstrated by comparing the results for the α-class polypeptide fragment, the mutant Antennapedia (C39 → S) homeodomain (2HOA), with those from two reference probability functions. The first reference probability function is a uniform or flat probability function and the second is a bivariate probability function for π and ψ. The trivariate gaussian probability functions are shown to search the conformational space more efficiently than the other two probability functions. The trivariate gaussian probability functions are also tested on the binding domain of Streptococcal protein G (2GB1), an α/β class protein. Since presently available energy functions are not accurate enough to identify the most native-like energy-minimized structures, three selection criteria were used to identify a native-like structure with a 1.90-Å rmsd from the NMR structure as the best structure for the Antennapedia fragment. Each individual selection criterion (ECEPP/3 energy, ECEPP/3 energy-plus-free energy of hydration, or a knowledge-based mean field method) was unable to identify a native-like structure, but simultaneous application of more than one selection criterion resulted in a successful identification of a native-like structure for the Antennapedia fragment. In addition to these tests, structure predictions are made for the Antennapedia polypeptide, using a Pattern Recognition-based Importance-Sampling Minimization (PRISM) procedure to predict the backbone conformational state of the mutant Antennapedia homeodomain. The ten most probable backbone conformational state predictions were used with the trivariate and bivariate gaussian dihedral angle probability distributions to generate starting structures (i.e., dihedral angles) suitable for energy minimization. The final energy-minimized structures show that neither the trivariate nor the bivariate gaussian probability distributions are able to overcome the inaccuracies in the backbone conformational state predictions to produce a native-like structure. Until highly accurate predictions of the backbone conformational states become available, application of these dihedral angle probability distributions must be limited to problems, such as homology modeling, in which only a limited portion of the backbone (e.g., surface loops) must be explored. © 1996 John Wiley & Sons, Inc.     

Genetic algorithms for protein conformation sampling and optimization in a discrete backbone dihedral angle space

We have investigated protein conformation sampling and optimization based on the genetic algorithm and discrete main chain dihedral state model. An efficient approach combining the genetic algorithm with local minimization and with a niche technique based on the sharing function is proposed. Using two different types of potential energy functions, a Go-type potential function and a knowledge-based pairwise potential energy function, and a test set containing small proteins of varying sizes and secondary structure compositions, we demonstrated the importance of local minimization and population diversity in protein conformation optimization with genetic algorithms. Some general properties of the sampled conformations such as their native-likeness and the influences of including side-chains are discussed.     

Standard-geometry chains fitted to X-ray derived structures: Validation of the rigid-geometry approximation. II. Systematic searches for short loops in proteins: Applications to bovine pancreatic ribonuclease A and human lysozyme

A rigid-geometry approach to protein conformational searches has been used to calculate stable structures for localized regions of the molecules bovine pancreatic ribonuclease A and human lysozyme. The search method is essentially an application of the local deformation algorithm of Gō and Scheraga [Macromolecules, 3 , 178–187 (1970)]. A series of local chain deformations is produced in the polypeptide chain. The deformations are screened to eliminate structures having serious atomic overlaps or energetically unreasonable backbone dihedral angles. The remaining structures are refined by energy minimization and the rms deviations of the energy-minimized structures, relative to the native structures, are calculated. The correlation between low rms deviation and low energy is reasonably good, indicating that this method should be useful in generating a small number of candidate structures for further energy refinement. Further applications to proteins with an unknown structure, such as homology-based modeling applications, should now be amenable to this type of procedure.     

Reference energy extremal optimization: a stochastic search algorithm applied to computational protein design

We adapt a combinatorial optimization algorithm, extremal optimization (EO), for the search problem in computational protein design. This algorithm takes advantage of the knowledge of local energy information and systematically improves on the residues that have high local energies. Power-law probability distributions are used to select the backbone sites to be improved on and the rotamer choices to be changed to. We compare this method with simulated annealing (SA) and motivate and present an improved method, which we call reference energy extremal optimization (REEO). REEO uses reference energies to convert a problem with a structured local-energy profile to one with more random profile, and extremal optimization proves to be extremely efficient for the latter problem. We show in detail the large improvement we have achieved using REEO as compared to simulated annealing and discuss a number of other heuristics we have attempted to date.     

氟比洛芬构象异构体的理论计算

用Hypercbem软件中构象搜寻模块,对氟比洛芬进行构象搜索,寻找分子低能构象．用B3LYP／6-31G（d）法优化计算22个低能构象,PCM溶剂模型用于水相计算,获得低能构象的优化几何结构、分子总能量和标准吉布斯自由能．结果表明,在气相和水相时,Z-型构象异构体稳定性最高．     

High–quality protein backbone reconstruction from alpha carbons using Gaussian mixture models

Coarse‐grained protein structure models offer increased efficiency in structural modeling, but these must be coupled with fast and accurate methods to revert to a full‐atom structure. Here, we present a novel algorithm to reconstruct mainchain models from C traces. This has been parameterized by fitting Gaussian mixture models (GMMs) to short backbone fragments centered on idealized peptide bonds. The method we have developed is statistically significantly more accurate than several competing methods, both in terms of RMSD values and dihedral angle differences. The method produced Ramachandran dihedral angle distributions that are closer to that observed in real proteins and better Phaser molecular replacement log‐likelihood gains. Amino acid residue sidechain reconstruction accuracy using SCWRL4 was found to be statistically significantly correlated to backbone reconstruction accuracy. Finally, the PD2 method was found to produce significantly lower energy full‐atom models using Rosetta which has implications for multiscale protein modeling using coarse‐grained models. A webserver and C++ source code is freely available for noncommercial use from: http://www.sbg.bio.ic.ac.uk/phyre2/PD2_ca2main/ . © 2013 Wiley Periodicals, Inc.     

蛋白质分子与配体结合过程构象变化的研究

蛋白质分子与配体的作用模式主要有直接的环区结合及铰链式结合两种方式。针对这两种不同的作用方式,我们提出采用不同的策略进行结合过程的构象研究。对于直接的环区结合模式,通过建立环区主链构象库,来实现蛋白质环区与配体的准柔性对接,并以链霉抗生物素蛋白体系为例对构象库建立的可行性进行了验证计算。对铰链结合方式,采用分步对接的方法进行计算,并具体应用于HIV蛋白酶与其小分子配体的结合过程。计算结果表明,这两种处理方法分别能较好地模拟不同类型的蛋白质与配体结合的的构象变化。     

The relationship between peptide plane rotation (PPR) and similar conformations

Currently, several energy functions and conformational search methods have been developed that are based on the observed distribution of phi and psi angles in protein structures. The definition of phi and psi angles is directly related to the orientation of the peptide plane (CA CO NH CA). Starting from one conformation and rotating a single peptide plane, the angles psi for one residue and phi for the consecutive residue that are linked by the peptide plane, display a continuous range of values within one global conformation. When peptide plane rotation is analyzed in several different conformations generated from a restricted conformation database, a large number of these conformations are related. Based on these observations, a new simplified all-atom representation for protein folding simulations is presented where only one torsion angle variable is required for each residue. The underlying theme of this article is that conformational search methods using phi and psi torsion space, search through many redundant conformations. These conformations are related by anticorrelated torsion changes of peptide plane rotations. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 947–955, 1999     

Impact of Stable Protein-protein Interaction on Protein Conformational Space

Backbone dihedral angle based clustering approach was applied to investigate the effect of protein complexation on backbone conformational space and the effect on protein dynamics. Three representative enzyme-inhibitor complexes and their comprised proteins were used as models for small-and moderate-sized globular proteins to compare available backbone conformational space before and after complexation. Microsecond time scale molecular dynamic simulations were generated to ensure sufficient statistics. The result suggests that stable protein-protein interactions lead to redistribution of protein backbone mobility and restriction of the protein backbone conformational space, especially for short time scale motions. Surprisingly, these effects are found to be uncorrelated with protein-protein interaction surface. Consistent with many experimental and computational observations, our results indicate that both induced-fit and conformational selection models play roles in stable protein complexation process, with the dominant role being different for different protein complexes.     

Efficient evaluation of sampling quality of molecular dynamics simulations by clustering of dihedral torsion angles and Sammon mapping

A direct conformational clustering and mapping approach for peptide conformations based on backbone dihedral angles has been developed and applied to compare conformational sampling of Met-enkephalin using two molecular dynamics (MD) methods. Efficient clustering in dihedrals has been achieved by evaluating all combinations resulting from independent clustering of each dihedral angle distribution, thus resolving all conformational substates. In contrast, Cartesian clustering was unable to accurately distinguish between all substates. Projection of clusters on dihedral principal component (PCA) subspaces did not result in efficient separation of highly populated clusters. However, representation in a nonlinear metric by Sammon mapping was able to separate well the 48 highest populated clusters in just two dimensions. In addition, this approach also allowed us to visualize the transition frequencies between clusters efficiently. Significantly, higher transition frequencies between more distinct conformational substates were found for a recently developed biasing-potential replica exchange MD simulation method allowing faster sampling of possible substates compared to conventional MD simulations. Although the number of theoretically possible clusters grows exponentially with peptide length, in practice, the number of clusters is only limited by the sampling size (typically much smaller), and therefore the method is well suited also for large systems. The approach could be useful to rapidly and accurately evaluate conformational sampling during MD simulations, to compare different sampling strategies and eventually to detect kinetic bottlenecks in folding pathways.     

Sampling multiple scoring functions can improve protein loop structure prediction accuracy

Accurately predicting loop structures is important for understanding functions of many proteins. In order to obtain loop models with high accuracy, efficiently sampling the loop conformation space to discover reasonable structures is a critical step. In loop conformation sampling, coarse-grain energy (scoring) functions coupling with reduced protein representations are often used to reduce the number of degrees of freedom as well as sampling computational time. However, due to implicitly considering many factors by reduced representations, the coarse-grain scoring functions may have potential insensitivity and inaccuracy, which can mislead the sampling process and consequently ignore important loop conformations. In this paper, we present a new computational sampling approach to obtain reasonable loop backbone models, so-called the Pareto optimal sampling (POS) method. The rationale of the POS method is to sample the function space of multiple, carefully selected scoring functions to discover an ensemble of diversified structures yielding Pareto optimality to all sampled conformations. The POS method can efficiently tolerate insensitivity and inaccuracy in individual scoring functions and thereby lead to significant accuracy improvement in loop structure prediction. We apply the POS method to a set of 4-12-residue loop targets using a function space composed of backbone-only Rosetta and distance-scale finite ideal-gas reference (DFIRE) and a triplet backbone dihedral potential developed in our lab. Our computational results show that in 501 out of 502 targets, the model sets generated by POS contain structure models are within subangstrom resolution. Moreover, the top-ranked models have a root mean square deviation (rmsd) less than 1 A in 96.8, 84.1, and 72.2% of the short (4-6 residues), medium (7-9 residues), and long (10-12 residues) targets, respectively, when the all-atom models are generated by local optimization from the backbone models and are ranked by our recently developed Pareto optimal consensus (POC) method. Similar sampling effectiveness can also be found in a set of 13-residue loop targets.     

Flexible protein‐protein docking based on Best‐First search algorithm

We developed a new high resolution protein‐protein docking method based on Best‐First search algorithm that loosely imitates protein‐protein associations. The method operates in two stages: first, we perform a rigid search on the unbound proteins. Second, we search alternately on rigid and flexible degrees of freedom starting from multiple configurations from the rigid search. Both stages use heuristics added to the energy function, which causes the proteins to rapidly approach each other and remain adjacent, while optimizing on the energy. The method deals with backbone flexibility explicitly by searching over ensembles of conformations generated before docking. We ran the rigid docking stage on 66 complexes and grouped the results into four classes according to evaluation criteria used in Critical Assessment of Predicted Interactions (CAPRI; “high,” “medium,” “acceptable,” and “incorrect”). Our method found medium binding conformations for 26% of the complexes and acceptable for additional 44% among the top 10 configurations. Considering all the configurations, we found medium binding conformations for 55% of the complexes and acceptable for additional 39% of the complexes. Introducing side‐chains flexibility in the second stage improves the best found binding conformation but harms the ranking. However, introducing side‐chains and backbone flexibility improve both the best found binding conformation and the best found conformation in the top 10. Our approach is a basis for incorporating multiple flexible motions into protein‐protein docking and is of interest even with the current use of a simple energy function. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Predicting 15N amide chemical shifts in proteins. I. An additive model for the backbone contribution

Because proteins adopt unique structures, chemically identical nuclei in proteins exhibit different chemical shifts. Amide ¹⁵N chemical shifts have been shown to vary over 20 ppm. The cause of these chemical shift inequivalencies is the different intra‐ and intermolecular interactions that individual nuclei experience at different locations in the protein structure. These chemical shift inequivalencies can be described as structural shifts, the difference between the actual chemical shift and the random coil chemical shift. As a first step toward the prediction of these amide ¹⁵N structural shifts, calculations have been carried out on acetyl‐glycine‐methyl amide to examine how a neighboring peptide group influences the amide ¹⁵N structural shifts. The ϕ,ψ dihedral angle space is completely surveyed, while all other geometrical variables are held fixed, to isolate the effect of the backbone conformation. Similar calculations for a limited number of conformations of acetyl‐glycine‐glycine‐methyl amide were carried out, where the effects of the two terminal peptide groups on the central amide ¹⁵N structural shift are examined. It is shown that the effect of the two adjacent groups can be accurately modeled by combining their individual effects additively. This provides a quite simple method to predict the backbone influence on amide ¹⁵N structural shifts in proteins. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 366–372, 2001     

Determination of the major solution conformation of tyrocidine A,using molecular mechanics energy minimization and NMR-derived distance and torsion angle constraints

Molecular mechanics energy calculations coupled with nuclear magnetic resonance-determined distance and torsion angle constraints have been used to determine the three-dimensional structure of tyrocidine A, a cyclic decapeptide which exists largely as a single conformation in solution. Two open-chain polyalanine models were used to represent separate halves of the peptide backbone and a combinatorial method of searching conformation space used to generate candidate structures consistent with experimental distance constraints. These structures were energy-minimized using the AMBER molecular mechanics forcefield and the resulting conformations classified by factor analysis of their Cartesian coordinates. Representative low-energy conformers of the two halves of the backbone were fused together and two candidate conformations of the completed backbone refined by further minimization using both distance and torsional constraints. Side chains were then added as their experimentally preferred rotamers and the whole molecule minimized without constraints to give the final model structure. This shows type II' and III ß turns at residues 4–5 and 9–10, respectively, coupled by twisted antiparallel strands which show hydrogen bonds between all four pairs of opposing peptide groups. The backbone conformation of residues 2–6 closely resembles that found in the crystal structure of gramicidin S.     

Sequence-structure relationships in DNA oligomers: a computational approach

A collective-variable model for DNA structure is used to predict the conformation of a set of 30 octamer, decamer, and dodecamer oligomers for which high-resolution crystal structures are available. The model combines an all-atom base pair representation with an empirical backbone, emphasizing the role of base stacking in fixing sequence-dependent structure. We are able to reproduce trends in roll and twist to within 5 degrees across a large database of both A- and B-DNA oligomers. A genetic algorithm approach is used to search for global minimum structures and this is augmented by a grid search to identify local minimums. We find that the number of local minimums is highly sequence dependent, with certain sequences having a set of minimums that span the entire range between canonical A- and B-DNA conformations. Although the global minimum does not always agree with the crystal structure, for 24 of the 30 oligomers, we find low-energy local minimums that match the experimental step parameters. Discrepancies throw some light on the role of crystal packing in determining the solid-state conformation of double-helical DNA.     

Enhanced sampling method in molecular simulations using genetic algorithm for biomolecular systems

We propose a molecular simulation method using genetic algorithm (GA) for biomolecular systems to obtain ensemble averages efficiently. In this method, we incorporate the genetic crossover, which is one of the operations of GA, to any simulation method such as conventional molecular dynamics (MD), Monte Carlo, and other simulation methods. The genetic crossover proposes candidate conformations by exchanging parts of conformations of a target molecule between a pair of conformations during the simulation. If the candidate conformations are accepted, the simulation resumes from the accepted ones. While conventional simulations are based on local update of conformations, the genetic crossover introduces global update of conformations. As an example of the present approach, we incorporated genetic crossover to MD simulations. We tested the validity of the method by calculating ensemble averages and the sampling efficiency by using two kinds of peptides, ALA3 and (AAQAA)₃. The results show that for ALA3 system, the distribution probabilities of backbone dihedral angles are in good agreement with those of the conventional MD and replica-exchange MD simulations. In the case of (AAQAA)₃ system, our method showed lower structural correlation of α-helix structures than the other two methods and more flexibility in the backbone ψ angles than the conventional MD simulation. These results suggest that our method gives more efficient conformational sampling than conventional simulation methods based on local update of conformations. © 2018 Wiley Periodicals, Inc.     

Heuristic-based tabu search algorithm for folding two-dimensional AB off-lattice model proteins

The protein structure prediction problem is a classical NP hard problem in bioinformatics. The lack of an effective global optimization method is the key obstacle in solving this problem. As one of the global optimization algorithms, tabu search (TS) algorithm has been successfully applied in many optimization problems. We define the new neighborhood conformation, tabu object and acceptance criteria of current conformation based on the original TS algorithm and put forward an improved TS algorithm. By integrating the heuristic initialization mechanism, the heuristic conformation updating mechanism, and the gradient method into the improved TS algorithm, a heuristic-based tabu search (HTS) algorithm is presented for predicting the two-dimensional (2D) protein folding structure in AB off-lattice model which consists of hydrophobic (A) and hydrophilic (B) monomers. The tabu search minimization leads to the basins of local minima, near which a local search mechanism is then proposed to further search for lower-energy conformations. To test the performance of the proposed algorithm, experiments are performed on four Fibonacci sequences and two real protein sequences. The experimental results show that the proposed algorithm has found the lowest-energy conformations so far for three shorter Fibonacci sequences and renewed the results for the longest one, as well as two real protein sequences, demonstrating that the HTS algorithm is quite promising in finding the ground states for AB off-lattice model proteins.