A method for determining the positions of polar hydrogens added to a protein structure that maximizes protein hydrogen bonding.

An automated method for the optimal placement of polar hydrogens in a protein structure is described. This method treats the polar, side chain hydrogens of lysine, serine, threonine, and tyrosine and the amino terminus of a protein. The program, called NETWORK, divides the potential hydrogen-bonding pairs of a protein into groups of interacting donors and acceptors. A search is conducted on each of the local groups to find an arrangement which forms the most hydrogen bonds. If two or more arrangements have the same number of hydrogen bonds, the arrangement with the shortest set of hydrogen bonds is selected. The polar hydrogens of the histidyl side chain are specifically treated, and the ionization state of this residue is allowed to change, if this change results in additional hydrogen bonds for the local group. The program will accept Protein Data Bank as well as Biosym-format coordinate files. Input and output routines can be easily modified to accept other coordinate file formats. The predictions from this method are compared to known hydrogen positions for bovine pancreatic trypsin inhibitor, insulin, RNase-A, and trypsin for which the neutron diffraction structures have been determined. The usefulness of this program is further demonstrated by a comparison of molecular dynamics simulations for the enzyme cytochrome P-450cam with and without using NETWORK.     

Polar hydrogen positions in proteins: Empirical energy placement and neutron diffraction comparison

A method for the prediction of hydrogen positions in proteins is presented. The method is based on the knowledge of the heavy atom positions obtained, for instance, from X-ray crystallography. It employs an energy minimization limited to the environment of the hydrogen atoms bound to a common heavy atom or to a single water molecule. The method is not restricted to proteins and can be applied without modification to nonpolar hydrogens and to nucleic acids. The method has been applied to the neutron diffraction structures of trypsin ribonuclease A, and bovine pancreatic trypsin inhibitor. A comparison of the constructed and the observed hydrogen positions shows few deviations except in situations in which several energetically similar conformations are possible. Analysis of the potential energy of rotation of Lys amino and Ser, Thr, Tyr hydroxyl groups reveals that the conformations of lowest intrinsic torsion energies are statistically favored in both the crystal and the constructed structures.     

Evaluation of the conformational free energies of loops in proteins

In this paper we discuss the problem of including solvation free energies in evaluating the relative stabilities of loops in proteins. A conformational search based on a gas-phase potential function is used to generate a large number of trial conformations. As has been found previously, the energy minimization step in this process tends to pack charged and polar side chains against the protein surface, resulting in conformations which are unstable in the aqueous phase. Various solvation models can easily identify such structures. In order to provide a more severe test of solvation models, gas phase conformations were generated in which side chains were kept extended so as to maximize their interaction with the solvent. The free energies of these conformations were compared to that calculated for the crystal structure in three loops of the protein E. coli RNase H, with lengths of 7, 8, and 9 residues. Free energies were evaluated with a finite difference Poisson-Boltzmann (FDPB) calculation for electrostatics and a surface area-based term for nonpolar contributions. These were added to a gas-phase potential function. A free energy function based on atomic solvation parameters was also tested. Both functions were quite successful in selecting, based on a free energy criterion, conformations quite close to the crystal structure for two of the three loops. For one loop, which is involved in crystal contacts, conformations that are quite different from the crystal structure were also selected. A method to avoid precision problems associated with using the FDPB method to evaluate conformational free energies in proteins is described. © 1994 John Wiley & Sons, Inc.     

Empirical solvation models in the context of conformational energy searches: application to bovine pancreatic trypsin inhibitor.

Continuum solvation models that estimate free energies of solvation as a function of solvent accessible surface area are computationally simple enough to be useful for predicting protein conformation. The behavior of three such solvation models has been examined by applying them to the minimization of the conformational energy of bovine pancreatic trypsin inhibitor. The models differ only with regard to how the constants of proportionality between free energy and surface area were derived. Each model was derived by fitting to experimentally measured equilibrium solution properties. For two models, the solution property was free energy of hydration. For the third, the property was NMR coupling constants. The purpose of this study is to determine the effect of applying these solvation models to the nonequilibrium conformations of a protein arising in the course of global searches for conformational energy minima. Two approaches were used: (1) local energy minimization of an ensemble of conformations similar to the equilibrium conformation and (2) global search trajectories using Monte Carlo plus minimization starting from a single conformation similar to the equilibrium conformation. For the two models derived from free energy measurements, it was found that both the global searches and local minimizations yielded conformations more similar to the X-ray crystallographic structures than did searches or local minimizations carried out in the absence of a solvation component of the conformational energy. The model derived from NMR coupling constants behaved similarly to the other models in the context of a global search trajectory. For one of the models derived from measured free energies of hydration, it was found that minimization of an ensemble of near-equilibrium conformations yielded a new ensemble in which the conformation most similar to the X-ray determined structure PTI4 had the lowest total free energy. Despite the simplicity of the continuum solvation models, the final conformation generated in the trajectories for each of the models exhibited some of the characteristics that have been reported for conformations obtained from molecular dynamics simulations in the presence of a bath of explicit water molecules. They have smaller root mean square (rms) deviations from the experimentally determined conformation, fewer incorrect hydrogen bonds, and slightly larger radii of gyration than do conformations derived from search trajectories carried out in the absence of solvent.     

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.     

Amide proton exchange rates of oxidized and reduced Saccharomyces cerevisiae iso-1-cytochrome c.

Proton NMR spectroscopy was used to determine the rate constant, kobs, for exchange of labile protons in both oxidized (Fe(III)) and reduced (Fe(II)) iso-1-cytochrome c. We find that slowly exchanging backbone amide protons tend to lack solvent-accessible surface area, possess backbone hydrogen bonds, and are present in regions of regular secondary structure as well as in omega-loops. Furthermore, there is no correlation between kobs and the distance from a backbone amide nitrogen to the nearest solvent-accessible atom. These observations are consistent with the local unfolding model. Comparisons of the free energy change for denaturation, delta Gd, at 298 K to the free energy change for local unfolding, delta Gop, at 298 K for the oxidized protein suggest that certain conformations possessing higher free energy than the denatured state are detected at equilibrium. Reduction of the protein results in a general increase in delta Gop. Comparisons of delta Gd to delta Gop for the reduced protein show that the most open states of the reduced protein possess more structure than its chemically denatured form. This persistent structure in high-energy conformations of the reduced form appears to involve the axially coordinated heme.     

Selecting near-native conformations in homology modeling: the role of molecular mechanics and solvation terms

A free energy function, combining molecular mechanics energy with empirical solvation and entropic terms, is used for ranking near-native conformations that occur in the conformational search steps of homology modeling, i.e., side-chain search and loop closure calculations. Correlations between the free energy and RMS deviation from the X-ray structure are established. It is shown that generally both molecular mechanics and solvation/entropic terms should be included in the potential. The identification of near-native backbone conformations is accomplished primarily by the molecular mechanics term that becomes the dominant contribution to the free energy if the backbone is even slightly strained, as frequently occurs in loop closure calculations. Both terms become equally important if a sufficiently accurate backbone conformation is found. Finally, the selection of the best side-chain positions for a fixed backbone is almost completely governed by the solvation term. The discriminatory power of the combined potential is demonstrated by evaluating the free energies of protein models submitted to the first meeting on Critical Assessment of techniques for protein Structure Prediction (CASP1), and comparing them to the free energies of the native conformations.     

An algorithm for determining the conformation of polypeptide segments in proteins by systematic search

The feasibility of determining the conformation of segments of a polypeptide chain up to six residues in length in globular proteins by means of a systematic search through the possible conformations has been investigated. Trial conformations are generated by using representative sets of phi, psi, and chi angles that have been derived from an examination of the distributions of these angles in refined protein structures. A set of filters based on simple rules that protein structures obey is used to reduce the number of conformations to a manageable total. The most important filters are the maintenance of chain integrity and the avoidance of too-short van der Waals contacts with the rest of the protein and with other portions of the segment under construction. The procedure is intended to be used with approximate models so that allowance is made throughout for errors in the rest of the structure. All possible main chains are first constructed and then all possible side-chain conformations are built onto each of these. The electrostatic energy, including a solvent screening term, and the exposed hydrophobic area are evaluated for each accepted conformation. The method has been tested on two segments of chain in the trypsin like enzyme from Streptomyces griseus. It is found that there is a wide spread of energies among the accepted conformations, and the lowest energy ones have satisfactorily small root mean square deviations from the X-ray structure.     

Calculation of protein conformation by the build-up procedure. Application to bovine pancreatic trypsin inhibitor using limited simulated nuclear magnetic resonance data

Low-energy conformations of a set of tetrapeptides derived from the small protein bovine pancreatic trypsin inhibitor (BPTI) were generated by a build-up procedure from the low-energy conformations of single amino acid residues. At each stage, various-size fragments were built up from all combinations of smaller ones, the total energies were then minimized, and the low-energy conformations were retained for the next stage. The energies of the tetrapeptides were re-ordered by including the effects of hydration. No information other than the amino acid sequence was used to obtain the low-energy conformations of the hydrated tetrapeptides. The latter were then supplemented with a limited set of simulated NMR distance information, derived from the X-ray structure of BPTI, to provide a basis for building the rest of the whole protein molecule by the same procedure. A total of 189 upper bounds, plus 12 pairs of upper and lower bounds pertaining to the location of the three disulfide bonds in this molecule, were used. Four sets of conformations of the entire molecule were generated by utilizing different combinations of smaller fragments. It was possible to obtain low-energy conformations with small rms deviations, 1.1 to 1.4 A for the alpha-carbons, from the structure derived by X-ray diffraction. The average deviations of the backbone dihedral angles were also low, viz. 23 degrees to 26 degrees.     

Necessary conditions for avoiding incorrect polypeptide folds in conformational search by energy minimization

Low energy conformations have been generated for melittin, pancreatic polypeptide, and ribonuclease S-peptide, both in the vicinity of x-ray structures by energy refinement and by an unconstrained search over the entire conformational space. Since the structural polymorphism of these medium-sized peptides in crystal and solution is moderate, comparing the calculated conformations to x-ray and nmr data provides information on local and global behavior of potential functions. Local analysis includes standardization calculations, which show that models with standard geometry can approximate good resolution x-ray data with less than 0.5 Å rms deviation (RMSD). However, the atomic coordinates are shifted up to 2 Å RMSD by local energy minimization, and thus 2 Å is generally the smallest RMSD value one can target in a conformational search using the same energy evaluation models. The unconstrained search was performed by a buildup-type method based on dynamic programming. To accelerate the generation of structures in the conformational search, we used the ECEPP potential, defined in terms of standard polypeptide geometry. A number of low energy conformations were further refined by relaxing the assumption of standard bond lengths and bond angles through the use of the CHARMM potential, and the hydrophobic folding energies of Eisenberg and McLachlan were calculated. Each conformation is described in terms of the RMSD from the native, hydrogen-bonding structure, solvent-acessible surface area, and the ratio of surfaces corresponding to nonpolar and polar residues. The unconstrained search finds conformations that are different from the native, sometimes substantially, and in addition, have lower conformational energies than the native. The origin of deviations is different for each of the three peptides, but in all examples the refined x-ray structures have lower energies than the calculated incorrect folds when (1) the assumption of standard bond lengths and bond angles is relaxed; (2) a small and constant effective dielectric permittivity (ε < 10) is used; and (3) the hydrophobic folding energy is incorporated into the potential. © 1993 John Wiley & Sons, Inc.     

Comparisons of LET distributions for protons with energies between 50 and 200 MeV determined using a spherical tissue-equivalent proportional counter (TEPC) and a position-sensitive silicon spectrometer (RRMD-III)

Experiments have been performed to measure the response of a spherical tissue-equivalent proportional counter (TEPC) and a silicon-based LET spectrometer (RRMD-III) to protons with energies ranging from 50-200 MeV. This represents a large portion of the energy distribution for trapped protons encountered by astronauts in low-Earth orbit. The beam energies were obtained using plastic polycarbonate degraders with a monoenergetic beam that was extracted from a proton synchrotron. The LET spectrometer provided excellent agreement with the expected LET distribution emerging from the energy degraders. The TEPC cannot measure the LET distribution directly. However, the frequency mean value of lineal energy, y(-)(f), provided a good approximation to LET. This is in contrast to previous results for high-energy heavy ions where y(-)(f) underestimated LET, whereas the dose-averaged lineal energy, y(-)(D), provided a good approximation to LET.     

Influence of hydration on the conformational stability and formation of bends in terminally blocked dipeptides

The conformations of 23 terminally blocked dipeptide sequences were examined by conformational energy calculations that included the effects of the aqueous solvent. Starting structures were derived from combinations of minimum-energy conformations of hydrated single residues. Their conformational energies were then minimized using the ECEPP potential (Empirical Conformational Energy Program for Peptides) with hydration included. Short-range interactions dominate in stabilizing the conformations of the hydrated dipeptides. Differences between conformational stabilities of hydrated and unhydrated dipeptides in many cases are due to the competition of solute–water and intramolecular hydrogen bonds. In other cases, perturbation of the hydration shell of the solute by close approach of solute atoms alters conformational preferences. Probabilities of formation of bends were calculated and compared to the corresponding quantities for unhydrated dipeptides and to those calculated from x-ray structures. For bends in dipeptides containing two nonpolar amino acids, computations omitting hydration yield better results. However, better agreement with experimental (x-ray) bend probabilities for dipeptides containing glycine or polar amino acids is obtained only in some sequences when hydration is included. The results are rationalized by the observation that, in proteins, bends containing nonpolar sequences occur on the inside, shielded from the solvent. Bends containing glycine or polar amino acids occur frequently on the surface of the protein, but they are not completely hydrated.     

Folding proteins with a simple energy function and extensive conformational searching.

We describe a computer algorithm for predicting the three-dimensional structures of proteins using only their amino acid sequences. The method differs from others in two ways: (1) it uses very few energy parameters, representing hydrophobic and polar interactions, and (2) it uses a new "constraint-based exhaustive" searching method, which appears to be among the fastest and most complete search methods yet available for realistic protein models. It finds a relatively small number of low-energy conformations, among which are native-like conformations, for crambin (1CRN), avian pancreatic polypeptide (1PPT), melittin (2MLT), and apamin. Thus, the lowest-energy states of very simple energy functions may predict the native structures of globular proteins.     

Stopped-flow NMR measurement of hydrogen exchange rates in reduced horse cytochrome c under strongly destabilizing conditions

A procedure to measure exchange rates of fast exchanging protein amide hydrogens by time-resolved NMR spectroscopy following in situ initiation of the reaction by diluting a native protein solution into an exchanging deuterated buffer is described. The method has been used to measure exchange rates of a small set of amide hydrogens of reduced cytochrome c, maintained in a strictly anaerobic atmosphere, in the presence of an otherwise inaccessible range of guanidinium deuterochloride concentrations. The results for the measured protons indicate that hydrogen exchange in the unfolding transition region of cytochrome c reach the EX2 limit, but emphasize the difficulty in interpretation of the exchange mechanism in protein hydrogen exchange studies. Comparison of free energies of structure opening for the measured hydrogens with the global unfolding free energy monitored by far-UV CD measurements has indicated the presence of at least one partially unfolded equilibrium species of reduced cytochrome c. The results provide the first report of measurement of free energy of opening of structure to exchange in the 0–2-kcal/mol range. Proteins 32:241–247, 1998. © 1998 Wiley-Liss, Inc.     

Calculations of electrostatic energies in proteins. The energetics of ionized groups in bovine pancreatic trypsin inhibitor

The importance of including different energy contributions in calculations of electrostatic energies in proteins is examined by calculating the intrinsic pKa values of the acidic groups of bovine pancreatic trypsin inhibitor. It appears that such calculations provide a powerful and revealing test; the relevant solvation energies of the ionized acids are of the order of -70 kcal/mol (1 cal = 4.184 J), and microscopic calculations that do not attempt to simulate the complete protein dielectric effect (including the surrounding solvent) can underestimate the solvation energy by as much as 50 kcal/mol. Reproducing correctly, by the same set of parameters, the solvation energies of ionized acids in different sites of a protein cannot be accomplished by including only part of the key energy contributions. The problems associated with macroscopic calculations are also considered and illustrated by the specific case of bovine pancreatic trypsin inhibitor. A promising approach is shown to be provided by a refinement of the previously developed Protein Dipoles Langevin Dipoles model. This model seems to represent consistently the microscopic dielectric of the protein and the surrounding water molecules. The model overcomes the problems associated with the macroscopic models (by treating explicitly the solvent molecules) and avoids the convergence problems associated with all-atom solvent models (by treating the average solvent polarization rather than averaging the actual polarization energy). This paper describes in detail the actual implementation of the model and examines its performance in evaluating intrinsic pKa values. Preliminary microscopic considerations of charge-charge interactions are presented.     

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.     

Folding subdomains of thioredoxin characterized by native-state hydrogen exchange

Native-state hydrogen exchange (HX) studies, used in conjunction with NMR spectroscopy, have been carried out on Escherichia coli thioredoxin (Trx) for characterizing two folding subdomains of the protein. The backbone amide protons of only the slowest-exchanging 24 amino acid residues, of a total of 108 amino acid residues, could be followed at pH 7. The free energy of the opening event that results in an amide hydrogen exchanging with solvent (DeltaG(op)) was determined at each of the 24 amide hydrogen sites. The values of DeltaG(op) for the amide hydrogens belonging to residues in the helices alpha(1), alpha(2), and alpha(4) are consistent with them exchanging with the solvent only when the fully unfolded state is sampled transiently under native conditions. The denaturant-dependences of the values of DeltaG(op) provide very little evidence that the protein samples partially unfolded forms, lower in energy than the unfolded state. The amide hydrogens belonging to the residues in the beta strands, which form the core of the protein, appear to have higher values of DeltaG(op) than amide hydrogens belonging to residues in the helices, suggesting that they might be more stable to exchange. This apparently higher stability to HX of the beta strands might be either because they exchange out their amide hydrogens in a high energy intermediate preceding the globally unfolded state, or, more likely, because they form residual structure in the globally unfolded state. In either case, the central beta strands-beta(3,) beta(2), and beta(4)-would appear to form a cooperatively folding subunit of the protein. The native-state HX methodology has made it possible to characterize the free energy landscape that Trx can sample under equilibrium native conditions.     

Enhanced sampling near the native conformation using statistical potentials for local side-chain and backbone interactions

In the preceding article in this issue of Proteins, an empirical energy function consisting of 4 statistical potentials that quantify local side-chain-backbone and side-chain-side-chain interactions has been demonstrated to successfully identify the native conformations of short sequence fragments and the native structure within large sets of high-quality decoys. Because this energy function consists entirely of interactions between residues separated by fewer than 5 positions, it can be used at the earliest stage of ab initio structure prediction to enhance the efficiency of conformational search. In this article, protein fragments are generated de novo by recombining very short segments of protein structures (2, 4, or 6 residues), either selected at random or optimized with respect this local energy function. When local energy is optimized in selected fragments, more efficient sampling of conformational space near the native conformation is consistently observed for 450 randomly selected single turn fragments, with turn lengths varying from 3 to 12 residues and all 4 combinations of flanking secondary structure. These results further demonstrate the energetic significance of local interactions in protein conformations. When used in combination with longer range energy functions, application of these potentials should lead to more accurate prediction of protein structure.     

A computational method for the design of nested proteins by loop‐directed domain insertion

The computational design of novel nested proteins—in which the primary structure of one protein domain (insert) is flanked by the primary structure segments of another (parent)—would enable the generation of multifunctional proteins. Here we present a new algorithm, called Loop‐Directed Domain Insertion (LooDo), implemented within the Rosetta software suite, for the purpose of designing nested protein domain combinations connected by flexible linker regions. Conformational space for the insert domain is sampled using large libraries of linker fragments for linker‐to‐parent domain superimposition followed by insert‐to‐linker superimposition. The relative positioning of the two domains (treated as rigid bodies) is sampled efficiently by a grid‐based, mutual placement compatibility search. The conformations of the loop residues, and the identities of loop as well as interface residues, are simultaneously optimized using a generalized kinematic loop closure algorithm and Rosetta EnzymeDesign, respectively, to minimize interface energy. The algorithm was found to consistently sample near‐native conformations and interface sequences for a benchmark set of structurally similar but functionally divergent domain‐inserted enzymes from the α/β hydrolase superfamily, and discriminates well between native and nonnative conformations and sequences, although loop conformations tended to deviate from the native conformations. Furthermore, in cross‐domain placement tests, native insert‐parent domain combinations were ranked as the best‐scoring structures compared to nonnative domain combinations. This algorithm should be broadly applicable to the design of multi‐domain protein complexes with any combination of inserted or tandem domain connections.     

The role of weakly polar and H-bonding interactions in the stabilization of the conformers of FGG, WGG, and YGG: an aqueous phase computational study

The energetics of intramolecular interactions on the conformational potential energy surface of the terminally protected N-Ac-Phe-Gly-Gly-NHMe (FGG), N-Ac-Trp-Gly-Gly-NHMe (WGG), and N-Ac-Tyr-Gly-Gly-NHMe (YGG) tripeptides was investigated. To identify the representative conformations, simulated annealing molecular dynamics (MD) and density functional theory (DFT) methods were used. The interaction energies were calculated at the BHandHLYP/aug-cc-pVTZ level of theory. In the global minima, 10%, 31%, and 10% of the stabilization energy come from weakly polar interactions, respectively, in FGG, WGG, and YGG. In the prominent cases 46%, 62%, and 46% of the stabilization energy is from the weakly polar interactions, respectively, in FGG, WGG, and YGG. On average, weakly polar interactions account for 15%, 34%, and 9% of the stabilization energies of the FGG, WGG, and YGG conformers, respectively. Thus, weakly polar interactions can make an important energetic contribution to protein structure and function. (c) 2008 Wiley Periodicals, Inc. Biopolymers 89: 1002-1011, 2008.This article was originally published online as an accepted preprint. The "Published Online" date corresponds to the preprint version. You can request a copy of the preprint by emailing the Biopolymers editorial office at biopolymers@wiley.com.