Knowledge-based Energy Function Research Articles

Prediction of protein thermostability with a direction‐ and distance‐dependent knowledge‐based potential

The increasing use of enzymes in industrial processes and the importance of understanding protein folding and stability have led to several attempts to predict and quantify the effect of every possible amino acid exchange (mutation) on the thermostability of proteins. In this article we describe a knowledge-based discrimination function that acts as a fast and reliable guide in protein engineering and optimization. The function used consists of two parts, a pairwise energy function based on a distance- and direction-dependent atomic description of the amino acid environment, and a torsion angle energy function. In a first step a training set of 11 proteins including 646 mutant proteins with experimentally determined thermostability was used to optimize the knowledge-based energy functions. The resulting potential function was then tested using a test mutant database consisting of 918 various point mutations introduced in 27 proteins. The best correlation coefficient obtained for the experimental data and the predicted thermostability for the training set is r = 0.81 (561 data points). A total of 76% of the mutations could be predicted correctly as being either stabilizing or destabilizing. The results for the test set are r = 0.74 (747 data points) and 72%, respectively. The global correlation over the combined data (1308 mutants) obtained is 0.78.

Threading with environment-specific score by artificial neural networks

Protein threading programs align a probe amino acid sequence onto a library of representative folds of known protein structure to identify a structural homology. A scoring function is usually formulated in terms of the threading energy to evaluate the protein sequence-structure fitness. In this paper, a model named threading with environment-specific score (TES) is proposed to build a new threading score function with the use of artificial neural networks. Given a protein structure with a residue level environment description, the compatibility of residue in sequence with its structural environment is presented. A threading score is constructed by log-odds scores of predicted probabilities from the trained model to determine which residue best fits its environment. Two decoy sets are used to test the proposed TES method on discrimination of native and decoy protein three-dimensional structure. The results showed that the performance of the proposed method is comparable to those of knowledge-based potential energy function.

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.

Monte Carlo simulations of the peptide recognition at the consensus binding site of the constant fragment of human immunoglobulin G: The energy landscape analysis of a hot spot at the intermolecular interface

Monte Carlo simulations of molecular recognition at the consensus binding site of the constant fragment (Fc) of human immunoglobulin G (Ig) protein have been performed to analyze structural and thermodynamic aspects of binding for the 13-residue cyclic peptide DCAWHLGELVWCT. The energy landscape analysis of a hot spot at the intermolecular interface using alanine scanning and equilibrium-simulated tempering dynamics with the simplified, knowledge-based energy function has enabled the role of the protein hot spot residues in providing the thermodynamic stability of the native structure to be determined. We have found that hydrophobic interactions between the peptide and the Met-252, Ile-253, His-433, and His-435 protein residues are critical to guarantee the thermodynamic stability of the crystallographic binding mode of the complex. Binding free energy calculations, using a molecular mechanics force field and a solvation energy model, combined with alanine scanning have been conducted to determine the energetic contribution of the protein hot spot residues in binding affinity. The conserved Asn-434, Ser-254, and Tyr-436 protein residues contribute significantly to the binding affinity of the peptide-protein complex, serving as an energetic hot spot at the intermolecular interface. The results suggest that evolutionary conserved hot spot protein residues at the intermolecular interface may be partitioned in fulfilling thermodynamic stability of the native binding mode and contributing to the binding affinity of the complex.

Hierarchy of simulation models in predicting structure and energetics of the Src SH2 domain binding to tyrosyl phosphopeptides.

Structure and energetics of the Src Src Homology 2 (SH2) domain binding with the recognition phosphopeptide pYEEI and its mutants are studied by a hierarchical computational approach. The proposed structure prediction strategy includes equilibrium sampling of the peptide conformational space by simulated tempering dynamics with the simplified, knowledge-based energy function, followed by structural clustering of the resulting conformations and binding free energy evaluation of a single representative from each cluster, a cluster center. This protocol is robust in rapid screening of low-energy conformations and recovers the crystal structure of the pYEEI peptide. Thermodynamics of the peptide-SH2 domain binding is analyzed by computing the average energy contributions over conformations from the clusters, structurally similar to the predicted peptide bound structure. Using this approach, the binding thermodynamics for a panel of studied peptides is predicted in a better agreement with the experiment than previously suggested models. However, the overall correlation between computed and experimental binding affinity remains rather modest. The results of this study show that small differences in binding free energies between the Ala and Gly mutants of the pYEEI peptide are considerably more difficult to predict than the structure of the bound peptides, indicating that accurate computational prediction of binding affinities still remains a major methodological and technical challenge.

Extracting knowledge-based energy functions from protein structures by error rate minimization: Comparison of methods using lattice model

We describe a general framework for extracting knowledge-based energy function from a set of native protein structures. In this scheme, the energy function is optimal when there is least chance that a random structure has a lower energy than the corresponding native structure. We first show that subject to certain approximations, most current database-derived energy functions fall within this framework, including mean-field potentials, Z-score optimization, and constraint satisfaction methods. We then propose a simple method for energy function parametrization derived from our analysis. We go on to compare our method to other methods using a simple lattice model in the context of three different energy function scenarios. We show that our method, which is based on the most stringent criteria, performs best in all cases. The power and limitations of each method for deriving knowledge-based energy function is examined.

A novel exhaustive search algorithm for predicting the conformation of polypeptide segments in proteins

We present a fast ab initio method for the prediction of local conformations in proteins. The program, PETRA, selects polypeptide fragments from a computer-generated database (APD) encoding all possible peptide fragments up to twelve amino acids long. Each fragment is defined by a representative set of eight straight phi/psi pairs, obtained iteratively from a trial set by calculating how fragments generated from them represent the protein databank (PDB). Ninety-six percent (96%) of length five fragments in crystal structures, with a resolution better than 1.5 A and less than 25% identity, have a conformer in the database with less than 1 A root-mean-square deviation (rmsd). In order to select segments from APD, PETRA uses a set of simple rule-based filters, thus reducing the number of potential conformations to a manageable total. This reduced set is scored and sorted using rmsd fit to the anchor regions and a knowledge-based energy function dependent on the sequence to be modelled. The best scoring fragments can then be optimized by minimization of contact potentials and rmsd fit to the core model. The quality of the prediction made by PETRA is evaluated by calculating both the differences in rmsd and backbone torsion angles between the final model and the native fragment. The average rmsd ranges from 1.4 A for three residue loops to 3.9 A for eight residue loops.

A novel exhaustive search algorithm for predicting the conformation of polypeptide segments in proteins

We present a fast ab initio method for the prediction of local conformations in proteins. The program, PETRA, selects polypeptide fragments from a computer-generated database (APD) encoding all possible peptide fragments up to twelve amino acids long. Each fragment is defined by a representative set of eight ϕ/ψ pairs, obtained iteratively from a trial set by calculating how fragments generated from them represent the protein databank (PDB). Ninety-six percent (96%) of length five fragments in crystal structures, with a resolution better than 1.5 Å and less than 25% identity, have a conformer in the database with less than 1 Å root-mean-square deviation (rmsd). In order to select segments from APD, PETRA uses a set of simple rule-based filters, thus reducing the number of potential conformations to a manageable total. This reduced set is scored and sorted using rmsd fit to the anchor regions and a knowledge-based energy function dependent on the sequence to be modelled. The best scoring fragments can then be optimized by minimization of contact potentials and rmsd fit to the core model. The quality of the prediction made by PETRA is evaluated by calculating both the differences in rmsd and backbone torsion angles between the final model and the native fragment. The average rmsd ranges from 1.4 Å for three residue loops to 3.9 Å for eight residue loops. Proteins 2000;40:135–144. © 2000 Wiley-Liss, Inc.

Ab initio construction of protein tertiary structures using a hierarchical approach

We present a hierarchical method to predict protein tertiary structure models from sequence. We start with complete enumeration of conformations using a simple tetrahedral lattice model. We then build conformations with increasing detail, and at each step select a subset of conformations using empirical energy functions with increasing complexity. After enumeration on lattice, we select a subset of low energy conformations using a statistical residue-residue contact energy function, and generate all-atom models using predicted secondary structure. A combined knowledge-based atomic level energy function is then used to select subsets of the all-atom models. The final predictions are generated using a consensus distance geometry procedure. We test the feasibility of the procedure on a set of 12 small proteins covering a wide range of protein topologies. A rigorous double-blind test of our method was made under the auspices of the CASP3 experiment, where we did ab initio structure predictions for 12 proteins using this approach. The performance of our methodology at CASP3 is reasonably good and completely consistent with our initial tests.

Structural and functional properties of designed globins

De novo design of artificial proteins is an essential approach to elucidate the principles of protein architecture and to understand specific functions of natural proteins and also to yield novel molecules for medical and industrial aims. We have designed artificial sequences of 153 amino acids to fit the main-chain framework of the sperm whale myoglobin structure based on the knowledge-based energy functions to evaluate the compatibility between protein tertiary structures and amino acid sequences. The synthesized artificial globins bind a single heme per protein molecule as designed, which show well-defined electrochemical and spectroscopic features characteristic of proteins with a low-spin heme. Redox and ligand binding reactions of the artificial heme proteins were investigated and these heme-related functions were found to vary with their structural uniqueness. Relationships between the structural and functional properties are discussed.

Using a Hydrophobic Contact Potential to Evaluate Native and Near-native Folds Generated by Molecular Dynamics Simulations

There are several knowledge-based energy functions that can distinguish the native fold from a pool of grossly misfolded decoys for a given sequence of amino acids. These decoys, which are typically generated by mounting, or “threading”, the sequence onto the backbones of unrelated protein structures, tend to be non-compact and quite different from the native structure: the root-mean-squared (RMS) deviations from the native are commonly in the range of 15 to 20 Å. Effective energy functions should also demonstrate a similar recognition capability when presented with compact decoys that depart only slightly in conformation from the correct structure (i.e. those with RMS deviations of ∼5 Å or less). Recently, we developed a simple yet powerful method for native fold recognition based on the tendency for native folds to form hydrophobic cores. Our energy measure, which we call the hydrophobic fitness score, is challenged to recognize the native fold from 2000 near-native structures generated for each of five small monomeric proteins. First, 1000 conformations for each protein were generated by molecular dynamics simulation at room temperature. The average RMS deviation of this set of 5000 was 1.5 Å. A total of 323 decoys had energies lower than native; however, none of these had RMS deviations greater than 2 Å. Another 1000 structures were generated for each at high temperature, in which a greater range of conformational space was explored (4.3 Å average RMS deviation). Out of this set, only seven decoys were misrecognized. The hydrophobic fitness energy of a conformation is strongly dependent upon the RMS deviation. On average our potential yields energy values which are lowest for the population of structures generated at room temperature, intermediate for those produced at high temperature and highest for those constructed by threading methods. In general, the lowest energy decoy conformations have backbones very close to native structure. The possible utility of our method for screening backbone candidates for the purpose of modelling by side-chain packing optimization is discussed.

Local moves: An efficient algorithm for simulation of protein folding

We have enhanced genetic algorithms and Monte Carlo methods for simulation of protein folding by introducing "local moves" in dihedral space. A local move consists of changes in backbone dihedral angles in a sequential window while the positions of all atoms outside the window remain unchanged. We find three advantages of local moves: (1) For some energy functions, protein conformations of lower energy are found; (2) these low energy conformations are found in fewer steps; and (3) the simulations are less sensitive to the details of the annealing protocol. To distinguish the effectiveness of local move algorithm from the complexity of the energy function, we have used several different energy functions. These energy functions include the Profile score (Bowie et al., Science 253:164-170, 1991), the knowledge-based energy function used by Bowie and Eisenberg 1994 (Proc. Natl. Acad. Sci. U.S.A. 91:4434-4440, 1994), two energy terms developed as suggested by Sippl and coworkers (Hendlich et al., J. Mol. Biol. 216:167-180, 1990), and AMBER (Weiner and Kollman, J. Comp. Chem. 2:287-303, 1981). Besides these energy functions we have used three energy functions that include knowledge of the native structures: the RMSD from the native structure, the distance matrix error, and an energy term based on the distance between different residue types called DBIN. In some of these simulations the main advantage of local moves is the reduced dependence on the details of the annealing schedule. In other simulations, local moves are superior to other algorithms as structures with lower energy are found.