Beta-sheet folding of fragment (16-36) of bovine pancreatic trypsin inhibitor as predicted by Monte Carlo simulated annealing.

A tertiary structure prediction is described using Monte Carlo simulated annealing for the peptide fragment corresponding to residues 16-36 of bovine pancreatic trypsin inhibitor (BPTI). The simulation starts with randomly chosen initial conformations and is performed without imposing experimental constraints using energy functions given for generic interatomic interactions. Out of 20 simulation trials, seven conformations show a sheet-like structure--two strands connected by a turn--although this sheet-like structure is not as rigid as that observed in native BPTI. It is also shown that these conformations are mostly looped and exhibit a native-like right-handed twist. Unlike the case with the C-peptide of RNase A, no conspicuous alpha-helical structure is found in any of the final conformations obtained in the simulation. However, the lowest-energy conformation does not resemble exactly the native structure. This indicates that the rigid beta-sheet conformation of native BPTI merely corresponds to a local minimum of the energy function if the fragment with residues 16-36 is isolated from the native protein. A statistical analysis of all 20 final conformations suggests that the tendency for the peptide segments to form extended beta-strands is strong for those with residues 18-24, and moderate for those with residues 30-35. The segment of residues 25-29 does not tend to form any definite structure. In native BPTI, the former segments are involved in the beta-sheet and the latter in the turn. A folding scenario is also speculated from this analysis.     

Structural basis of hierarchical multiple substates of a protein. I: Introduction

A computer experiment of protein dynamics is carried out, which consists of two steps: (1) A Monte Carlo simulation of thermal fluctuations in the native state of a globular protein, bovine pancreatic trypsin inhibitor; and (2) a simulation of the quick freezing of fluctuating conformations into energy minima by minimization of the energy of a number of conformations sampled in the Monte Carlo simulation. From the analysis of results of the computer experiment is obtained the following picture of protein dynamics: multiple energy minima exist in the native state, and they are distributed in clusters in the conformational space. The dynamics has a hierarchical structure which has at least two levels. In the first level, dynamics is restricted within one of the clusters of minima. In the second, transitions occur among the clusters. Local parts of a protein molecule, side chains and local main chain segments, can take multiple locally stable conformations in the native state. Many minima result from combinations of these multiple local conformations. The hierarchical structure in the dynamics comes from interactions among the local parts. Protein molecules have two types of flexibility, each associated with elastic and plastic deformations, respectively.     

Sampling realistic protein conformations using local structural bias

The prediction of protein structure from sequence remains a major unsolved problem in biology. The most successful protein structure prediction methods make use of a divide-and-conquer strategy to attack the problem: a conformational sampling method generates plausible candidate structures, which are subsequently accepted or rejected using an energy function. Conceptually, this often corresponds to separating local structural bias from the long-range interactions that stabilize the compact, native state. However, sampling protein conformations that are compatible with the local structural bias encoded in a given protein sequence is a long-standing open problem, especially in continuous space. We describe an elegant and mathematically rigorous method to do this, and show that it readily generates native-like protein conformations simply by enforcing compactness. Our results have far-reaching implications for protein structure prediction, determination, simulation, and design.     

Structural basis of hierarchical multiple substates of a protein. III: Side chain and main chain local conformations

An analysis is carried out of differences in the minimum energy conformations obtained in the previous paper by energy minimization starting from conformations sampled by a Monte Carlo simulation of conformational fluctuations in the native state of a globular protein, bovine pancreatic trypsin inhibitor. Main conformational differences in each pair of energy minima are found usually localized in several side chains and in a few local main chain segments. Such side chains and local main chain segments are found to take a few distinct local conformations in the minimum energy conformations. Energy minimum conformations can thus be described in terms of combinations of these multiple local conformations.     

Fragment-based local statistical potentials derived by combining an alphabet of protein local structures with secondary structures and solvent accessibilities

General and transferable statistical potentials to quantify the compatibility between local structures and local sequences of peptide fragments in proteins were derived. In the derivation, structure clusters of fragments are obtained by clustering five-residue fragments in native proteins based on their conformations represented by a local structure alphabet (de Brevern et al., Proteins 2000;41:271-287), secondary structure states, and solvent accessibilities. On the basis of the native sequences of the structurally clustered fragments, the probabilities of different amino acid sequences were estimated for each structure cluster. From the sequence probabilities, statistical energies as a function of sequence for a given structure were directly derived. The same sequence probabilities were employed in a database-matching approach to derive statistical energies as a function of local structure for a given sequence. Compared with prior models of local statistical potentials, we provided an integrated approach in which local conformations and local environments are treated jointly, structures are treated in units of fragments instead of individual residues so that coupling between the conformations of adjacent residues is included, and strong interdependences between the conformations of overlapping or neighboring fragment units are also considered. In tests including fragment threading, pseudosequence design, and local structure predictions, the potentials performed at least comparably and, in most cases, better than a number of existing models applicable to the same contexts indicating the advantages of such an integrated approach for deriving local potentials and suggesting applicability of the statistical potentials derived here in sequence designs and structure predictions.     

De novo protein structure prediction by dynamic fragment assembly and conformational space annealing

Ab initio protein structure prediction is a challenging problem that requires both an accurate energetic representation of a protein structure and an efficient conformational sampling method for successful protein modeling. In this article, we present an ab initio structure prediction method which combines a recently suggested novel way of fragment assembly, dynamic fragment assembly (DFA) and conformational space annealing (CSA) algorithm. In DFA, model structures are scored by continuous functions constructed based on short- and long-range structural restraint information from a fragment library. Here, DFA is represented by the full-atom model by CHARMM with the addition of the empirical potential of DFIRE. The relative contributions between various energy terms are optimized using linear programming. The conformational sampling was carried out with CSA algorithm, which can find low energy conformations more efficiently than simulated annealing used in the existing DFA study. The newly introduced DFA energy function and CSA sampling algorithm are implemented into CHARMM. Test results on 30 small single-domain proteins and 13 template-free modeling targets of the 8th Critical Assessment of protein Structure Prediction show that the current method provides comparable and complementary prediction results to existing top methods.     

Structural basis of hierarchical multiple substates of a protein. V: Nonlocal deformations

Distances between centers of gravity of individual residues are compared among the minimum energy conformations derived from the record of the Monte Carlo simulation of conformational fluctuations in the native state of a globular protein, bovine pancreatic trypsin inhibitor. It is found that local deformations originating from the multiplicity of local conformations cause deformations of the whole structure of the molecule in various ways, which can be classified into two types. Type 1: When a local deformation occurs in a region consisting of a few residues near the surface of the molecule, the whole shape of the molecule responds by deforming elastically. The magnitude of this deformation is in the range of thermal fluctuations calculated by the harmonic approximation around a single minimum. Type 2: We have observed one case belonging to the second type in which local deformations occur cooperatively in an extended region. This region goes across the whole molecule and divide the remaining parts into two. Atom packing changes in and around the extended region of local deformations. For this reason deformation in this region is plastic. Relative location and orientation between the divided two parts change very much. Deformation of the whole shape in this case, associated with the plastic deformation in an extended region, demonstrates that protein molecules have a flexibility beyond the harmonic limit.     

Denatured proteins and early folding intermediates simulated in a reduced conformational space

Conformations of globular proteins in the denatured state were studied using a high-resolution lattice model of proteins and Monte Carlo dynamics. The model assumes a united-atom and high-coordination lattice representation of the polypeptide conformational space. The force field of the model mimics the short-range protein-like conformational stiffness, hydrophobic interactions of the side chains and the main-chain hydrogen bonds. Two types of approximations for the short-range interactions were compared: simple statistical potentials and knowledge-based protein-specific potentials derived from the sequence-structure compatibility of short fragments of protein chains. Model proteins in the denatured state are relatively compact, although the majority of the sampled conformations are globally different from the native fold. At the same time short protein fragments are mostly native-like. Thus, the denatured state of the model proteins has several features of the molten globule state observed experimentally. Statistical potentials induce native-like conformational propensities in the denatured state, especially for the fragments located in the core of folded proteins. Knowledge-based protein-specific potentials increase only slightly the level of similarity to the native conformations, in spite of their qualitatively higher specificity in the native structures. For a few cases, where fairly accurate experimental data exist, the simulation results are in semiquantitative agreement with the physical picture revealed by the experiments. This shows that the model studied in this work could be used efficiently in computational studies of protein dynamics in the denatured state, and consequently for studies of protein folding pathways, i.e. not only for the modeling of folded structures, as it was shown in previous studies. The results of the present studies also provide a new insight into the explanation of the Levinthal's paradox.     

A new approach to prediction of short-range conformational propensities in proteins

MOTIVATION: Knowledge-based potentials are valuable tools for protein structure modeling and evaluation of the quality of the structure prediction obtained by a variety of methods. Potentials of such type could be significantly enhanced by a proper exploitation of the evolutionary information encoded in related protein sequences. The new potentials could be valuable components of threading algorithms, ab-initio protein structure prediction, comparative modeling and structure modeling based on fragmentary experimental data. RESULTS: A new potential for scoring local protein geometry is designed and evaluated. The approach is based on the similarity of short protein fragments measured by an alignment of their sequence profiles. Sequence specificity of the resulting energy function has been compared with the specificity of simpler potentials using gapless threading and the ability to predict specific geometry of protein fragments. Significant improvement in threading sensitivity and in the ability to generate sequence-specific protein-like conformations has been achieved.     

Analysis of forces that determine helix formation in alpha-proteins

A model for prediction of alpha-helical regions in amino acid sequences has been tested on the mainly-alpha protein structure class. The modeling represents the construction of a continuous hypothetical alpha-helical conformation for the whole protein chain, and was performed using molecular mechanics tools. The positive prediction of alpha-helical and non-alpha-helical pentapeptide fragments of the proteins is 79%. The model considers only local interactions in the polypeptide chain without the influence of the tertiary structure. It was shown that the local interaction defines the alpha-helical conformation for 85% of the native alpha-helical regions. The relative energy contributions to the energy of the model were analyzed with the finding that the van der Waals component determines the formation of alpha-helices. Hydrogen bonds remain at constant energy independently whether alpha-helix or non-alpha-helix occurs in the native protein, and do not determine the location of helical regions. In contrast to existing methods, this approach additionally permits the prediction of conformations of side chains. The model suggests the correct values for ~60% of all chi-angles of alpha-helical residues.     

Optimized distance‐dependent atom‐pair‐based potential DOOP for protein structure prediction

The DOcking decoy‐based Optimized Potential (DOOP) energy function for protein structure prediction is based on empirical distance‐dependent atom‐pair interactions. To optimize the atom‐pair interactions, native protein structures are decomposed into polypeptide chain segments that correspond to structural motives involving complete secondary structure elements. They constitute near native ligand–receptor systems (or just pairs). Thus, a total of 8609 ligand–receptor systems were prepared from 954 selected proteins. For each of these hypothetical ligand–receptor systems, 1000 evenly sampled docking decoys with 0–10 Å interface root‐mean‐square‐deviation (iRMSD) were generated with a method used before for protein–protein docking. A neural network‐based optimization method was applied to derive the optimized energy parameters using these decoys so that the energy function mimics the funnel‐like energy landscape for the interaction between these hypothetical ligand–receptor systems. Thus, our method hierarchically models the overall funnel‐like energy landscape of native protein structures. The resulting energy function was tested on several commonly used decoy sets for native protein structure recognition and compared with other statistical potentials. In combination with a torsion potential term which describes the local conformational preference, the atom‐pair‐based potential outperforms other reported statistical energy functions in correct ranking of native protein structures for a variety of decoy sets. This is especially the case for the most challenging ROSETTA decoy set, although it does not take into account side chain orientation‐dependence explicitly. The DOOP energy function for protein structure prediction, the underlying database of protein structures with hypothetical ligand–receptor systems and their decoys are freely available at http://agknapp.chemie.fu‐berlin.de/doop/ . Proteins 2015; 83:881–890. © 2015 Wiley Periodicals, Inc.     

Evaluating conformational changes in protein structures binding RNA

Many protein-RNA recognition events are known to exhibit conformational changes from qualitative observations of individual complexes. However, a quantitative estimation of conformational changes is required if protein-RNA docking and template-based methods for RNA binding site prediction are to be developed. This study presents the first quantitative evaluation of conformational changes that occur when proteins bind RNA. The analysis of twelve RNA-binding proteins in the bound and unbound states using error-scaled difference distance matrices is presented. The binding site residues are mapped to each structure, and the conformational changes that affect these residues are evaluated. Of the twelve proteins four exhibit greater movements in nonbinding site residues, and a further four show the greatest movements in binding site residues. The remaining four proteins display no significant conformational change. When interface residues are found to be in conformationally variable regions of the protein they are typically seen to move less than 2 A between the bound and unbound conformations. The current data indicate that conformational changes in the binding site residues of RNA binding proteins may not be as significant as previously suggested, but a larger data set is required before wider conclusions may be drawn. The implications of the observed conformational changes for protein function prediction are discussed.     

Local sequence information in cellular retinoic acid-binding protein I: specific residue roles in beta-turns

We have recently shown that two of the beta-turns (III and IV) in the ten-stranded, beta-clam protein, cellular retinoic acid-binding protein I (CRABP I), are favored in short peptide fragments, arguing that they are encoded by local interactions (K. S. Rotondi and L. M. Gierasch, Biochemistry, 2003, Vol. 42, pp. 7976-7985). In this paper we examine these turns in greater detail to dissect the specific local interactions responsible for their observed native conformational biases. Conformations of peptides corresponding to the turn III and IV fragments were examined under conditions designed to selectively disrupt stabilizing interactions, using pH variation, chaotrope addition, or mutagenesis to probe specific side-chain influences. We find that steric constraints imposed by excluded volume effects between near neighbor residues (i,i+2), favorable polar (i,i+2) interactions, and steric permissiveness of glycines are the principal factors accounting for the observed native bias in these turns. Longer-range stabilizing interactions across the beta-turns do not appear to play a significant role in turn stability in these short peptides, in contrast to their importance in hairpins. Additionally, our data add to a growing number of examples of the 3:5 type I turn with a beta-bulge as a class of turns with high propensity to form locally defined structure. Current work is directed at the interplay between the local sequence information in the turns and more long-range influences in the mechanism of folding of this predominantly beta-sheet protein.     

Free energy determinants of tertiary structure and the evaluation of protein models

We develop a protocol for estimating the free energy difference between different conformations of the same polypeptide chain. The conformational free energy evaluation combines the CHARMM force field with a continuum treatment of the solvent. In almost all cases studied, experimentally determined structures are predicted to be more stable than misfolded "decoys." This is due in part to the fact that the Coulomb energy of the native protein is consistently lower than that of the decoys. The solvation free energy generally favors the decoys, although the total electrostatic free energy (sum of Coulomb and solvation terms) favors the native structure. The behavior of the solvation free energy is somewhat counterintuitive and, surprisingly, is not correlated with differences in the burial of polar area between native structures and decoys. Rather. the effect is due to a more favorable charge distribution in the native protein, which, as is discussed, will tend to decrease its interaction with the solvent. Our results thus suggest, in keeping with a number of recent studies, that electrostatic interactions may play an important role in determining the native topology of a folded protein. On this basis, a simplified scoring function is derived that combines a Coulomb term with a hydrophobic contact term. This function performs as well as the more complete free energy evaluation in distinguishing the native structure from misfolded decoys. Its computational efficiency suggests that it can be used in protein structure prediction applications, and that it provides a physically well-defined alternative to statistically derived scoring functions.     

The multiple-minima problem in the conformational analysis of polypeptides. III. An Electrostatically Driven Monte Carlo Method: Tests on enkephalin

The three-dimensional conformation of Met-enkephalin, corresponding to the lowest minimum of the empirical potential energy function ECEPP/2 (empirical conformational energy program for peptides), has been determined using a new algorithm, viz. the Electrostatically Driven Monte Carlo Method. This methodology assumes that a polypeptide or protein molecule is driven toward the native structure by the combined action of electrostatic interactions and stochastic conformational changes associated with thermal movements. These features are included in the algorithm that produces a Monte Carlo search in the conformational hyperspace of the polypeptide, using electrostatic predictions and a random sampling technique to locate low-energy conformations. In addition, we have incorporated an alternative mechanism that allows the structure to escape from some conformational regions representing metastable local energy minima and even from regions of the conformational space with great stability. In 33 test calculations on Met-enkephalin, starting from arbitrary or completely random conformations, the structure corresponding to the global energy minimum was found inall the cases analyzed, with a relatively small search of the conformational space. Some of these starting conformations wereright orleft-handed -helices, characterized by good electrostatic interactions involving their backbone peptide dipoles; nevertheless, the procedure was able to convert such locally stable structures to the global-minimum conformation.On leave from the National University of San Luis, Faculty of Sciences and Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Instituto de Matemática Aplicada, San Luis, Ejército de los Andes 950, 5700 San Luis, Argentina.     

A novel approach to decoy set generation: designing a physical energy function having local minima with native structure characteristics

We suggest a new approach to the generation of candidate structures (decoys) for ab initio prediction of protein structures. Our method is based on random sampling of conformation space and subsequent local energy minimization. At the core of this approach lies the design of a novel type of energy function. This energy function has local minima with native structure characteristics and wide basins of attraction. The current work presents our motivation for deriving such an energy function and also tests the derived energy function.Our approach is novel in that it takes advantage of the inherently rough energy landscape of proteins, which is generally considered a major obstacle for protein structure prediction. When local minima have wide basins of attraction, the protein's conformation space can be greatly reduced by the convergence of large regions of the space into single points, namely the local minima corresponding to these funnels. We have implemented this concept by an iterative process. The potential is first used to generate decoy sets and then we study these sets of decoys to guide further development of the potential. A key feature of our potential is the use of cooperative multi-body interactions that mimic the role of the entropic and solvent contributions to the free energy.The validity and value of our approach is demonstrated by applying it to 14 diverse, small proteins. We show that, for these proteins, the size of conformation space is considerably reduced by the new energy function. In fact, the reduction is so substantial as to allow efficient conformational sampling. As a result we are able to find a significant number of near-native conformations in random searches performed with limited computational resources.     

Local and nonlocal interactions in globular proteins and mechanisms of alcohol denaturation.

How important are helical propensities in determining the conformations of globular proteins? Using the two-dimensional lattice model and two monomer types, H (hydrophobic) and P (polar), we explore both nonlocal interactions, through an HH contact energy, as developed in earlier work, and local interactions, through a helix energy, σ. By computer enumeration, the partition functions for short chains are obtained without approximation for the full range of both types of energy. When nonlocal interactions dominate, some sequences undergo coil-globule collapse to a unique native structure. When local interactions dominate, all sequences undergo helix–coil transitions. For two different conformational properties, the closest correspondence between the lattice model and proteins in the Protein Data Bank is obtained if the model local interactions are made small compared to the HH contact interaction, suggesting that helical propensities may be only weak determinants of globular protein structures in water. For some HP sequences, varying σ/ leads to additional sharp transitions (sometimes several) and to “conformational switching” between unique conformations. This behavior resembles the transitions of globular proteins in water to helical states in alcohols. In particular, comparison with experiments shows that whereas urea as a denaturant is best modeled as weakening both local and nonlocal interactions, trifluoroethanol is best modeled as mainly weakening HH interactions and slightly enhancing local helical interactions.     

Local propensities and statistical potentials of backbone dihedral angles in proteins

The following three issues concerning the backbone dihedral angles of protein structures are presented. (1) How do the dihedral angles of the 20 amino acids depend on the identity and conformation of their nearest residues? (2) To what extent are the native dihedral angles determined by local (dihedral) potentials? (3) How to build a knowledge-based potential for a residue's dihedral angles, considering the identity and conformation of its nearest residues? We find that the dihedral angle distribution for a residue can significantly depend on the identity and conformation of its adjacent residues. These correlations are in sharp contrast to the Flory isolated-pair hypothesis. Statistical potentials are built for all combinations of residue triplets and depend on the dihedral angles between consecutive residues. First, a low-resolution potential is obtained, which only differentiates between the main populated basins in the dihedral angle density plots. Minimization of the dihedral potential for 125 test proteins reveals that most native alpha-helical residues (89%) and a large fraction of native beta-sheet residues (47%) adopt conformations close to their native one. For native loop residues, the percentage is 48%. It is also found that this fraction is higher for residues away from the ends of alpha or beta secondary structure elements. In addition, a higher resolution potential is built as a function of dihedral angles by a smoothing procedure and continuous functions interpolations. Monte Carlo energy minimization with this potential results in a lower fraction for native beta-sheet residues. Nevertheless, because of the higher flexibility and entropy of beta structures, they could be preferred under the influence of non-local interactions. In general, most alpha-helices and many beta-sheets are strongly determined by the local potential, while the conformations in loops and near the end of beta-sheets are more influenced by non-local interactions.     

Exploring the conformational space of protein side chains using dead-end elimination and the A* algorithm

We describe an algorithm which enables us to search the conformational space of the side chains of a protein to identify the global minimum energy combination of side chain conformations as well as all other conformations within a specified energy cutoff of the global energy minimum. The program is used to explore the side chain conformational energy surface of a number of proteins, to investigate how this surface varies with the energy model used to describe the interactions within the system and the rotamer library. Enumeration of the rotamer combinations enables us to directly evaluate the partition function, and thus calculate the side chain contribution to the conformational entropy of the folded protein. An investigation of these conformations and the relationships between them shows that most of the conformations near to the global energy minimum arise from changes in side chain conformations that are essentially independent; very few result from a concerted change in conformation of two or more residues. Some of the limitations of the approach are discussed. Proteins 33:227–239, 1998. © 1998 Wiley-Liss, Inc.