Discrimination of near-native protein structures from misfolded models by empirical free energy functions

Free energy potentials, combining molecular mechanics with empirical solvation and entropic terms, are used to discriminate native and near-native protein conformations from slightly misfolded decoys. Since the functional forms of these potentials vary within the field, it is of interest to determine the contributions of individual free energy terms and their combinations to the discriminative power of the potential. This is achieved in terms of quantitative measures of discrimination that include the correlation coefficient between RMSD and free energy, and a new measure labeled the minimum discriminatory slope (MDS). In terms of these criteria, the internal energy is shown to be a good discriminator on its own, which implies that even well-constructed decoys are substantially more strained than the native protein structure. The discrimination improves if, in addition to the internal energy, the free energy expression includes the electrostatic energy, calculated by assuming non-ionized side chains, and an empirical solvation term, with the classical atomic solvation parameter model providing slightly better discrimination than a structure-based atomic contact potential. Finally, the inclusion of a term representing the side chain entropy change, and calculated by an established empirical scale, is so inaccurate that it makes the discrimination worse. It is shown that both the correlation coefficient and the MDS value (or its dimensionless form) are needed for an objective assessment of a potential, and that together they provide much more information on the origins of discrimination than simple inspection of the RMSD-free energy plots.     

Computational protein design is a challenge for implicit solvation models

Increasingly complex schemes for representing solvent effects in an implicit fashion are being used in computational analyses of biological macromolecules. These schemes speed up the calculations by orders of magnitude and are assumed to compromise little on essential features of the solvation phenomenon. In this work we examine this assumption. Five implicit solvation models, a surface area-based empirical model, two models that approximate the generalized Born treatment and a finite difference Poisson-Boltzmann method are challenged in situations differing from those where these models were calibrated. These situations are encountered in automatic protein design procedures, whose job is to select sequences, which stabilize a given protein 3D structure, from a large number of alternatives. To this end we evaluate the energetic cost of burying amino acids in thousands of environments with different solvent exposures belonging, respectively, to decoys built with random sequences and to native protein crystal structures. In addition we perform actual sequence design calculations. Except for the crudest surface area-based procedure, all the tested models tend to favor the burial of polar amino acids in the protein interior over nonpolar ones, a behavior that leads to poor performance in protein design calculations. We show, on the other hand, that three of the examined models are nonetheless capable of discriminating between the native fold and many nonnative alternatives, a test commonly used to validate force fields. It is concluded that protein design is a particularly challenging test for implicit solvation models because it requires accurate estimates of the solvation contribution of individual residues. This contrasts with native recognition, which depends less on solvation and more on other nonbonded contributions.     

Unrestrained stochastic dynamics simulations of the UUCG tetraloop using an implicit solvation model.

Three unrestrained stochastic dynamics simulations have been carried out on the RNA hairpin GGAC[UUCG] GUCC, using the AMBER94 force field (Cornell et al., 1995. J. Am. Chem. Soc. 117:5179-5197) in MacroModel 5.5 (Mohamadi et al., 1990. J. Comp. Chem. 11:440-467) and either the GB/SA continuum solvation model (Still et al., 1990. J. Am. Chem. Soc. 112:6127-6129) or a linear distance-dependent dielectric (1/R) treatment. The linear distance-dependent treatment results in severe distortion of the nucleic acid structure, restriction of all hydroxyl dihedrals, and collapse of the counterion atmosphere over the course of a 5-ns simulation. An additional vacuum simulation without counterions shows somewhat improved behavior. In contrast, the two GB/SA simulations (1.149 and 3.060 ns in length) give average structures within 1.2 A of the initial NMR structure and in excellent agreement with results of an earlier explicit solvent simulation (Miller and Kollman, 1997. J. Mol. Biol. 270:436-450). In a 3-ns GB/SA simulation starting with the incorrect UUCG tetraloop structure (Cheong et al., 1990. Nature. 346:680-682), this loop conformation converts to the correct loop geometry (Allain and Varani, 1995. J. Mol. Biol. 250:333-353), suggesting enhanced sampling relative to the previous explicit solvent simulation. Thermodynamic effects of 2'-deoxyribose substitutions of loop nucleotides were experimentally determined and are found to correlate with the fraction of time the ribose 2'-OH is hydrogen bonded and the distribution of the hydroxyl dihedral is observed in the GB/SA simulations. The GB/SA simulations thus appear to faithfully represent structural features of the RNA without the computational expense of explicit solvent.     

Empirical solvation models can be used to differentiate native from near-native conformations of bovine pancreatic trypsin inhibitor.

Several hydration models for peptides and proteins based on solvent accessible surface area have been proposed previously. We have evaluated some of these models as well as four new ones in the context of near-native conformations of a protein. In addition, we propose an empirical site-site distance-dependent correction that can be used in conjunction with any of these models. The set of near-native structures consisted of 39 conformations of bovine pancreatic trypsin inhibitor (BPTI) each of which was a local minimum of an empirical energy function (ECEPP) in the absence of solvent. Root-mean-square (rms) deviations from the crystallographically determined structure were in the following ranges: 1.06-1.94 A for all heavy atoms, 0.77-1.36 A for all backbone heavy atoms, 0.68-1.33 A for all alpha-carbon atoms, and 1.41-2.72 A for all side-chain heavy atoms. We have found that there is considerable variation among the solvent models when evaluated in terms of concordance between the solvation free energy and the rms deviations from the crystallographically determined conformation. The solvation model for which the best concordance (0.939) with the rms deviations of the C alpha atoms was found was derived from NMR coupling constants of peptides in water combined with an exponential site-site distance dependence of the potential of mean force. Our results indicate that solvation free energy parameters derived from nonpeptide free energies of hydration may not be transferrable to peptides. Parameters derived from peptide and protein data may be more applicable to conformational analysis of proteins. A general approach to derive parameters for free energy of hydration from ensemble-averaged properties of peptides in solution is described.     

Hydrophobic regions on protein surfaces. Derivation of the solvation energy from their area distribution in crystallographic protein structures.

For the first time, a direct approach for the derivation of an atomic solvation parameter from macromolecular structural data alone is presented. The specific free energy of solvation for hydrophobic surface regions of proteins is delineated from the area distribution of hydrophobic surface patches. The resulting value is 18 cal/(mol.A2), with a statistical uncertainty of +/-2 cal/mol.A2) at the 5% significance level. It compares favorably with the parameters for carbon obtained by other authors who use the the crystal geometry of succinic acid or energies of transfer from hydrophobic solvent to water for small organic compounds. Thus, the transferability of atomic solvation parameters for hydrophobic atoms to macromolecules has been directly demonstrated. A careful statistical analysis demonstrates that surface energy parameters derived from thermodynamic data of protein mutation experiments are clearly less confident.     

Identification of native protein folds amongst a large number of incorrect models. The calculation of low energy conformations from potentials of mean force

We present an approach that is able to detect native folds amongst a large number of non-native conformations. The method is based on the compilation of potentials of mean force of the interactions of the C beta atoms of all amino acid pairs from a database of known three-dimensional protein structures. These potentials are used to calculate the conformational energy of amino acid sequences in a number of different folds. For a substantial number of proteins we find that the conformational energy of the native state is lowest amongst the alternatives. Exceptions are proteins containing large prosthetic groups, Fe-S clusters or polypeptide chains that do not adopt globular folds. We discuss briefly potential applications in various fields of protein structural research.     

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.     

Building epidemiological models from R0: an implicit treatment of transmission in networks

Simple deterministic models are still at the core of theoretical epidemiology despite the increasing evidence for the importance of contact networks underlying transmission at the individual level. These mean-field or 'compartmental' models based on homogeneous mixing have made, and continue to make, important contributions to the epidemiology and the ecology of infectious diseases but fail to reproduce many of the features observed for disease spread in contact networks. In this work, we show that it is possible to incorporate the important effects of network structure on disease spread with a mean-field model derived from individual level considerations. We propose that the fundamental number known as the basic reproductive number of the disease, R0, which is typically derived as a threshold quantity, be used instead as a central parameter to construct the model from. We show that reliable estimates of individual level parameters can replace a detailed knowledge of network structure, which in general may be difficult to obtain. We illustrate the proposed model with small world networks and the classical example of susceptible-infected-recovered (SIR) epidemics.     

Lysyl-tRNA synthetase from yeast. Discrimination of amino acids by native and phosphorylated species.

Discrimination factors (D) which are characteristic for discrimination between lysine and 19 naturally occurring non-cognate amino acids have been determined from kcat and Km values for native and phosphorylated lysyl-tRNA synthetases from yeast. Generally, both species of this class II aminoacyl-tRNA synthetase are considerably less specific than the class I synthetases specific for isoleucine, valine, tyrosine, and arginine. D values of the native enzyme are in the range 90-1700, D values of the phosphorylated species in the range 40-770. The phosphorylated enzyme acts faster and less accurately. In aminoacylation of tRNALys-C-C-A(2'NH2) discrimination factors D1 vary over 30-980 for the native and over 8-300 for the phosphorylated enzyme. From AMP formation stoichiometry and D1 values pretransfer proof-reading factors (II1) of 1.1-56 were calculated for for the native enzyme, factors of 1.0-44 for the phosphorylated species. Post-transfer proof-reading factors (II2) were calculated from D values and AMP formation stoichiometry in acylation of tRNALys-C-C-A. Pretransfer proof-reading is the main correction step, posttransfer proof-reading is less effective or negligible (II2 approximately 1-8). Initial discrimination factors (I), which are due to differences in Gibbs free energies of binding between lysine and noncognate substrates (delta delta GI), were calculated from discrimination and proof-reading factors. In contrast to class I synthetases, for lysyl-tRNA synthetase only one initial discrimination step can be assumed and amino acid recognition is reduced to a three-step process instead of the four-step recognition observed for the class I synthetases. Plots of delta delta GI values against accessible surface areas of amino acids show clearly that phosphorylation of the enzyme changes the structures of the amino acid binding sites. This is illustrated by a hypothetical 'stopper model' of these sites.     

Discrimination power of knowledge-based potential dictated by the dominant energies in native protein structures

Amino Acids - Extracting a well-designed energy function is important for protein structure evaluation. Knowledge-based potential functions are one type of the energy functions which can be...     

Chain length dependence of apomyoglobin folding: structural evolution from misfolded sheets to native helices

Very little is known about how protein structure evolves during the polypeptide chain elongation that accompanies cotranslational protein folding. This in vitro model study is aimed at probing how conformational space evolves for purified N-terminal polypeptides of increasing length. These peptides are derived from the sequence of an all-alpha-helical single domain protein, Sperm whale apomyoglobin (apoMb). Even at short chain lengths, ordered structure is found. The nature of this structure is strongly chain length dependent. At relatively short lengths, a predominantly non-native beta-sheet conformation is present, and self-associated amyloid-like species are generated. As chain length increases, alpha-helix progressively takes over, and it replaces the beta-strand. The observed trends correlate with the specific fraction of solvent-accessible nonpolar surface area present at different chain lengths. The C-terminal portion of the chain plays an important role by promoting a large and cooperative overall increase in helical content and by consolidating the monomeric association state of the full-length protein. Thus, a native-like energy landscape develops late during apoMb chain elongation. This effect may provide an important driving force for chain expulsion from the ribosome and promote nearly-posttranslational folding of single domain proteins in the cell. Nature has been able to overcome the above intrinsic misfolding trends by modulating the composition of the intracellular environment. An imbalance or improper functioning by the above modulating factors during translation may play a role in misfolding-driven intracellular disorders.     

Analysis of protein main-chain solvation as a function of secondary structure

We have analysed the hydration of main-chain carbonyl and amide groups in 24 high-resolution well-refined protein structures as a function of the secondary structure in which these polar groups occur. We find that main-chain atoms in beta-sheets are as hydrated as those in alpha-helices, with most interactions involving "free" amide and carbonyl groups that do not participate in secondary structure hydrogen bonds. The distributions of water molecules around these non-bonded carbonyl groups reflect specific steric interactions due to the local secondary structure. Approximately 20% and 4%, respectively of bonded carbonyl and amide groups interact with solvent. These include interactions with carbonyl groups on the exposed faces of alpha-helices that have been correlated previously with bending of the helix. Water molecules interacting with alpha-helices occur mainly at the amino and carbonyl termini of the helices, in which case the solvent sites maintain the hydrogen bonding by bridging between residues i and i-3 or i-4 at the amino terminus and between i and i+3 or i+4 at the carbonyl terminus. We also see a number of solvent-mediated Ncap and Ccap interactions. The water molecules interacting with beta-sheets occur mainly at the edges, in which case they extend the sheet structure, or at the ends of strands, in which case they extend the beta-ladder. In summary, the solvent networks appear to extend the hydrogen-bonding structure of the secondary structures. In beta-turns, which usually occur at the surface of a protein, exposed amide and carbonyl groups are often hydrated, especially close to glycine residues. Occasionally water molecules form a bridge between residues i and i+3 in the turn and this may provide extra stabilization.     

Hydrostatic pressure rescues native protein from aggregates.

Misfolding and misassembly of proteins are major problems in the biotechnology industry, in biochemical research, and in human disease. Here we describe a novel approach for reversing aggregation and increasing refolding by application of hydrostatic pressure. Using P22 tailspike protein as a model system, intermediates along the aggregation pathway were identified and quantitated by size-exclusion high-performance liquid chromatography (HPLC). Tailspike aggregates were subjected to hydrostatic pressures of 2.4 kbar (35,000 psi). This treatment dissociated the tailspike aggregates and resulted in increased formation of native trimers once pressure was released. Tailspike trimers refolded at these pressures were fully active for formation of infectious viral particles. This technique can facilitate conversion of aggregates to native proteins without addition of chaotropic agents, changes in buffer, or large-scale dilution of reagents required for traditional refolding methods. Our results also indicate that one or more intermediates at the junction between the folding and aggregation pathways is pressure sensitive. This finding supports the hypothesis that specific determinants of recognition exist for protein aggregation, and that these determinants are similar to those involved in folding to the native state. An increased understanding of this specificity should lead to improved refolding methods.     

Export of a cysteine-free misfolded secretory protein from the endoplasmic reticulum for degradation requires interaction with protein disulfide isomerase

Protein disulfide isomerase (PDI) interacts with secretory proteins, irrespective of their thiol content, late during translocation into the ER; thus, PDI may be part of the quality control machinery in the ER. We used yeast pdi1 mutants with deletions in the putative peptide binding region of the molecule to investigate its role in the recognition of misfolded secretory proteins in the ER and their export to the cytosol for degradation. Our pdi1 deletion mutants are deficient in the export of a misfolded cysteine-free secretory protein across the ER membrane to the cytosol for degradation, but ER-to-Golgi complex transport of properly folded secretory proteins is only marginally affected. We demonstrate by chemical cross-linking that PDI specifically interacts with the misfolded secretory protein and that mutant forms of PDI have a lower affinity for this protein. In the ER of the pdi1 mutants, a higher proportion of the misfolded secretory protein remains associated with BiP, and in export-deficient sec61 mutants, the misfolded secretory protein remain bounds to PDI. We conclude that the chaperone PDI is part of the quality control machinery in the ER that recognizes terminally misfolded secretory proteins and targets them to the export channel in the ER membrane.     

Conformational sampling with implicit solvent models: application to the PHF6 peptide in tau protein

Implicit solvent models approximate the effects of solvent through a potential of mean force and therefore make solvated simulations computationally efficient. Yet despite their computational efficiency, the inherent approximations made by implicit solvent models can sometimes lead to inaccurate results. To test the accuracy of a number of popular implicit solvent models, we determined whether implicit solvent simulations can reproduce the set of potential energy minima obtained from explicit solvent simulations. For these studies, we focus on a six-residue amino-acid sequence, referred to as the paired helical filament 6 (PHF6), which may play an important role in the formation of intracellular aggregates in patients with Alzheimer's disease. Several implicit solvent models form the basis of this work--two based on the generalized Born formalism, and one based on a Gaussian solvent-exclusion model. All three implicit solvent models generate minima that are in good agreement with minima obtained from simulations with explicit solvent. Moreover, free-energy profiles generated with each implicit solvent model agree with free-energy profiles obtained with explicit solvent. For the Gaussian solvent-exclusion model, we demonstrate that a straightforward ranking of the relative stability of each minimum suggests that the most stable structure is extended, a result in excellent agreement with the free-energy profiles. Overall, our data demonstrate that for some peptides like PHF6, implicit solvent can accurately reproduce the set of local energy minimum arising from quenched dynamics simulations with explicit solvent. More importantly, all solvent models predict that PHF6 forms extended beta-structures in solution, a finding consistent with the notion that PHF6 initiates neurofibrillary tangle formation in patients with Alzheimer's disease.     

Inclusion of solvation free energy with molecular mechanics energy: alanyl dipeptide as a test case.

A combined force field of molecular mechanics and solvation free energy is tested by carrying out energy minimization and molecular dynamics on several conformations of the alanyl dipeptide. Our results are qualitatively consistent with previous experimental and computational studies, in that the addition of solvation energy stabilizes the C5 conformation of the alanyl dipeptide relative to the C7.     

Formation of native insulin from the scrambled molecule by protein disulphide-isomerase.

The formation of native insulin either from scrambled insulin or from the separated A chain and B chain S-sulphonates by protein disulphide-isomerase was demonstrated with yields of 20-30% as measured by h.p.l.c. analysis, receptor binding and stimulation of lipogenesis. The h.p.l.c. profile of the reaction products shows that, among all the possible isomers containing both chains, the native hormone is by far the predominating product and consequently the most stable under certain conditions.     

Extracting protein alignment models from the sequence database.

Biologists often gain structural and functional insights into a protein sequence by constructing a multiple alignment model of the family. Here a program called Probe fully automates this process of model construction starting from a single sequence. Central to this program is a powerful new method to locate and align only those, often subtly, conserved patterns essential to the family as a whole. When applied to randomly chosen proteins, Probe found on average about four times as many relationships as a pairwise search and yielded many new discoveries. These include: an obscure subfamily of globins in the roundworm Caenorhabditis elegans ; two new superfamilies of metallohydrolases; a lipoyl/biotin swinging arm domain in bacterial membrane fusion proteins; and a DH domain in the yeast Bud3 and Fus2 proteins. By identifying distant relationships and merging families into superfamilies in this way, this analysis further confirms the notion that proteins evolved from relatively few ancient sequences. Moreover, this method automatically generates models of these ancient conserved regions for rapid and sensitive screening of sequences.     

Outer membrane protein folding from an energy landscape perspective

The cell envelope is essential for the survival of Gram-negative bacteria. This specialised membrane is densely packed with outer membrane proteins (OMPs), which perform a variety of functions. How OMPs fold into this crowded environment remains an open question. Here, we review current knowledge about OMP folding mechanisms in vitro and discuss how the need to fold to a stable native state has shaped their folding energy landscapes. We also highlight the role of chaperones and the β-barrel assembly machinery (BAM) in assisting OMP folding in vivo and discuss proposed mechanisms by which this fascinating machinery may catalyse OMP folding.