Use of a potential of mean force to analyze free energy contributions in protein folding.

A method for calculation of the free energy of residues as a function of residue burial is proposed. The method is based on the potential of mean force, with a reaction coordinate expressed by residue burial. Residue burials are calculated from high-resolution protein structures. The largest individual contributions to the free energy of a residue are found to be due to the hydrophobic interactions of the nonpolar atoms, interactions of the main chain polar atoms, and interactions of the charged groups of residues Arg and Lys. The contribution to the free energy of folding due to the uncharged side chain polar atoms is small. The contribution to the free energy of folding due to the main chain polar atoms is favorable for partially buried residues and less favorable or unfavorable for fully buried residues. Comparison of the accessible surface areas of proteins and model spheres shows that proteins deviate considerably from a spherical shape and that the deviations increase with the size of a protein. The implications of these results for protein folding are also discussed.     

Development of a four-body statistical pseudo-potential to discriminate native from non-native protein conformations

MOTIVATION: Most scoring functions used in protein fold recognition employ two-body (pseudo) potential energies. The use of higher-order terms may improve the performance of current algorithms. Methods: Proteins are represented by the side chain centroids of amino acids. Delaunay tessellation of this representation defines all sets of nearest neighbor quadruplets of amino acids. Four-body contact scoring function (log likelihoods of residue quadruplet compositions) is derived by the analysis of a diverse set of proteins with known structures. A test protein is characterized by the total score calculated as the sum of the individual log likelihoods of composing amino acid quadruplets. RESULTS: The scoring function distinguishes native from partially unfolded or deliberately misfolded structures. It also discriminates between pre- and post-transition state and native structures in the folding simulations trajectory of Chymotrypsin Inhibitor 2 (CI2).     

Discrimination of the native from misfolded protein models with an energy function including implicit solvation.

An essential requirement for theoretical protein structure prediction is an energy function that can discriminate the native from non-native protein conformations. To date most of the energy functions used for this purpose have been extracted from a statistical analysis of the protein structure database, without explicit reference to the physical interactions responsible for protein stability. The use of the statistical functions has been supported by the widespread belief that they are superior for such discrimination to physics-based energy functions. An effective energy function which combined the CHARMM vacuum potential with a Gaussian model for the solvation free energy is tested for its ability to discriminate the native structure of a protein from misfolded conformations; the results are compared with those obtained with the vacuum CHARMM potential. The test is performed on several sets of misfolded structures prepared by others, including sets of about 650 good decoys for six proteins, as well as on misfolded structures of chymotrypsin inhibitor 2. The vacuum CHARMM potential is successful in most cases when energy minimized conformations are considered, but fails when applied to structures relaxed by molecular dynamics. With the effective energy function the native state is always more stable than grossly misfolded conformations both in energy minimized and molecular dynamics-relaxed structures. The present results suggest that molecular mechanics (physics-based) energy functions, complemented by a simple model for the solvation free energy, should be tested for use in the inverse folding problem, and supports their use in studies of the effective energy surface of proteins in solution. Moreover, the study suggests that the belief in the superiority of statistical functions for these purposes may be ill founded.     

Application of statistical potentials to protein structure refinement from low resolution ab initio models

Recently ab initio protein structure prediction methods have advanced sufficiently so that they often assemble the correct low resolution structure of the protein. To enhance the speed of conformational search, many ab initio prediction programs adopt a reduced protein representation. However, for drug design purposes, better quality structures are probably needed. To achieve this refinement, it is natural to use a more detailed heavy atom representation. Here, as opposed to costly implicit or explicit solvent molecular dynamics simulations, knowledge-based heavy atom pair potentials were employed. By way of illustration, we tried to improve the quality of the predicted structures obtained from the ab initio prediction program TOUCHSTONE by three methods: local constraint refinement, reduced predicted tertiary contact refinement, and statistical pair potential guided molecular dynamics. Sixty-seven predicted structures from 30 small proteins (less than 150 residues in length) representing different structural classes (alpha, beta, alpha;/beta) were examined. In 33 cases, the root mean square deviation (RMSD) from native structures improved by more than 0.3 A; in 19 cases, the improvement was more than 0.5 A, and sometimes as large as 1 A. In only seven (four) cases did the refinement procedure increase the RMSD by more than 0.3 (0.5) A. For the remaining structures, the refinement procedures changed the structures by less than 0.3 A. While modest, the performance of the current refinement methods is better than the published refinement results obtained using standard molecular dynamics.     

The histidine-phosphocarrier protein of Streptomyces coelicolor folds by a partially folded species at low pH.

The folding of a 93-residue protein, the histidine-phosphocarrier protein of Streptomyces coelicolor, HPr, has been studied using several biophysical techniques, namely fluorescence, 8-anilinonaphthalene-1-sulfate binding, circular dichroism, Fourier transform infrared spectroscopy, gel filtration chromatography and differential scanning calorimetry. The chemical-denaturation behaviour of HPr, followed by fluorescence, CD and gel filtration, at pH 7.5 and 25 degrees C, is described as a two-state process, which does not involve the accumulation of thermodynamically stable intermediates. Its conformational stability under those conditions is deltaG = 4.0 +/- 0.2 kcal x mol-1 (1 kcal = 4.18 kJ), which makes the HPr from S. coelicolor the most unstable member of the HPr family described so far. The stability of the protein does not change significantly from pH 7-9, as concluded from the differential scanning calorimetry and thermal CD experiments. Conformational studies at low pH (pH 2.5-4) suggest that, in the absence of cosmotropic agents, HPr does not unfold completely; rather, it accumulates partially folded species. The transition from those species to other states with native-like secondary and tertiary structure, occurs with a pKa = 3.3 +/- 0.3, as measured by the averaged measurements obtained by CD and fluorescence. However, this transition does not agree either with: (a) that measured by burial of hydrophobic patches (8-anilinonaphthalene-1-sulfate binding experiments); or (b) that measured by acquisition of native-like compactness (gel-filtration studies). It seems that acquisition of native-like features occurs in a wide pH range and it cannot be ascribed to a unique side-chain titration. These series of intermediates have not been reported previously in any member of the HPr family.     

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.     

Origins of protein denatured state compactness and hydrophobic clustering in aqueous urea: inferences from nonpolar potentials of mean force

Free energies of pairwise hydrophobic association are simulated in aqueous solutions of urea at concentrations ranging from 0-8 M. Consistent with the expectation that hydrophobic interactions are weakened by urea, the association of relatively large nonpolar solutes is destabilized by urea. However, the association of two small methane-sized nonpolar solutes in water has the opposite tendency of being slightly strengthened by the addition of urea. Such size effects and the dependence of urea-induced stability changes on the configuration of nonpolar solutes are not predicted by solvent accessible surface area approaches based on energetic parameters derived from bulk-phase solubilities of model compounds. Thus, to understand hydrophobic interactions in proteins, it is not sufficient to rely solely on transfer experiment data that effectively characterize a single nonpolar solute in an aqueous environment but not the solvent-mediated interactions among two or more nonpolar solutes. We find that the m-values for the rate of change of two-methane association free energy with respect to urea concentration is a dramatically nonmonotonic function of the spatial separation between the two methanes, with a distance-dependent profile similar to the corresponding two-methane heat capacity of association in pure water. Our results rationalize the persistence of residual hydrophobic contacts in some proteins at high urea concentrations and explain why the heat capacity signature (DeltaC(P)) of a compact denatured state can be similar to DeltaC(P) values calculated by assuming an open random-coil-like unfolded state.     

A protein folding potential that places the native states of a large number of proteins near a local minimum

Background

We present a simple method to train a potential function for the protein folding problem which, even though trained using a small number of proteins, is able to place a significantly large number of native conformations near a local minimum. The training relies on generating decoys by energy minimization of the native conformations using the current potential and using a physically meaningful objective function (derivative of energy with respect to torsion angles at the native conformation) during the quadratic programming to place the native conformation near a local minimum.

Results

We also compare the performance of three different types of energy functions and find that while the pairwise energy function is trainable, a solvation energy function by itself is untrainable if decoys are generated by minimizing the current potential starting at the native conformation. The best results are obtained when a pairwise interaction energy function is used with solvation energy function.

Conclusions

We are able to train a potential function using six proteins which places a total of 42 native conformations within ~4 Å rmsd and 71 native conformations within ~6 Å rmsd of a local minimum out of a total of 91 proteins. Furthermore, the threading test using the same 91 proteins ranks 89 native conformations to be first and the other two as second.     

Assembly of polypeptide and protein backbone conformations from low energy ensembles of short fragments: development of strategies and construction of models for myoglobin, lysozyme, and thymosin beta 4.

Recently we developed methods for the construction of knowledge-based mean fields from a data base of known protein structures. As shown previously, this approach can be used to calculate ensembles of probable conformations for short fragments of polypeptide chains. Here we develop procedures for the assembly of short fragments to complete three-dimensional models of polypeptide chains. The amino acid sequence of a given protein is decomposed into all possible overlapping fragments of a given length, and an ensemble of probable conformations is calculated for each fragment. The fragments are assembled to a complete model by choosing appropriate conformations from the individual ensembles and by averaging over equivalent angles. Finally a consistent model is obtained by rebuilding the conformation from the average angles. From the average angles the local variability of the structure can be calculated, which is a useful criterion for the reliability of the model. The procedure is applied to the calculation of the local backbone conformations of myoglobin and lysozyme whose structures have been solved by X-ray analysis and thymosin beta 4, a polypeptide of 43 amino acid residues whose structure was recently investigated by NMR spectroscopy. We demonstrate that substantial fractions of the calculated local backbone conformations are similar to the experimentally determined structures.     

Distinguishing native conformations of proteins from decoys with an effective free energy estimator based on the OPLS all-atom force field and the Surface Generalized Born solvent model

Protein decoy data sets provide a benchmark for testing scoring functions designed for fold recognition and protein homology modeling problems. It is commonly believed that statistical potentials based on reduced atomic models are better able to discriminate native-like from misfolded decoys than scoring functions based on more detailed molecular mechanics models. Recent benchmark tests on small data sets, however, suggest otherwise. In this work, we report the results of extensive decoy detection tests using an effective free energy function based on the OPLS all-atom (OPLS-AA) force field and the Surface Generalized Born (SGB) model for the solvent electrostatic effects. The OPLS-AA/SGB effective free energy is used as a scoring function to detect native protein folds among a total of 48,832 decoys for 32 different proteins from Park and Levitt's 4-state-reduced, Levitt's local-minima, Baker's ROSETTA all-atom, and Skolnick's decoy sets. Solvent electrostatic effects are included through the Surface Generalized Born (SGB) model. All structures are locally minimized without restraints. From an analysis of the individual energy components of the OPLS-AA/SGB energy function for the native and the best-ranked decoy, it is determined that a balance of the terms of the potential is responsible for the minimized energies that most successfully distinguish the native from the misfolded conformations. Different combinations of individual energy terms provide less discrimination than the total energy. The results are consistent with observations that all-atom molecular potentials coupled with intermediate level solvent dielectric models are competitive with knowledge-based potentials for decoy detection and protein modeling problems such as fold recognition and homology modeling.     

Classification of large array surface myoelectric potentials from subjects with and without low back pain.

An algorithm was developed and tested for differentiating between the spatial distribution of large arrays of surface electromyographic (LASE) data from subjects with and without low back pain (LBP). The surface EMG data from 62 channels were collected from the low back of 161 healthy and 44 acute (less than 6-weeks) LBP subjects in three minimum stress postural positions including standing, 20 degrees of trunk flexion (at hip joint) and standing with arms extended forward holding a 1.36kg (3lb) weight in each hand. These data were statistically analyzed and the spatial distribution of the root mean square (RMS) values was used in a multivariate quadratic discriminant model to reclassify the healthy and acute LBP subjects. The most predictive results were obtained from the 'flexion' group of experiments and correctly reclassified 95.5% (42/44) of the acute LBP subjects and 99.4% (160/161) of the healthy subjects. The success rate of this reclassification based on surface distribution of myoelectric potentials was found to be better than the reported patient classifications based on a smaller set of electrode pairs using fewer subjects [Peach JP, McGill SM, Classification of low back pain with use of spectral electromyogram parameters. Spine 23(10):1998;1117-23; Roy SH, De Luca CJ, Emley M, Oddsson LI, Buijs RJ, Levins JA, Newcombe DS, Jabre JF. Classification of back muscle impairment based on the surface electromyographic signal. J Rehabil Res Dev 34(4):1997;405-14 [review]]. The results indicated the potential of the model for clinical patient classification.     

Calculation of conformational ensembles from potentials of mean force. An approach to the knowledge-based prediction of local structures in globular proteins

We present a prototype of a new approach to the folding problem of polypeptide chains. This approach is based on the analysis of known protein structures. It derives the energy potentials for the atomic interactions of all amino acid residue pairs as a function of the distance between the involved atoms. These potentials are then used to calculate the energies of all conformations that exist in the data base with respect to a given sequence. Then, by using only the most stable conformations, clusters of the most probable conformations for the given sequence are obtained. To discuss the results properly we introduce a new classification of segments based on their conformational stability. Special care is taken to allow for sparse data sets. The use of the method is demonstrated in the discussion of the identical oligopeptide sequences found in different conformations in unrelated proteins. VNTFV, for example, adopts a beta-strand in ribonuclease but it is found in an alpha-helical conformation in erythrocruorin. In the case of VNTFV the ensemble obtained consists of a single cluster of beta-strand conformations, indicating that this may be the preferred conformation for the pentapeptide. When the flanking residues are included in the calculation the hepapeptide P-VNTFV-H (ribonuclease) again yields an ensemble of beta-strands. However, in the ensemble of D-VNTFV-A (erythrocruorin) the major cluster is of alpha-helical type. In the present study we concentrate on the local aspects of protein conformations. However, the theory presented is quite general and not restricted to oligopeptides. We indicate extensions of the approach to the calculation of global conformations of proteins as well as conceivable applications to a number of molecular systems.     

Comparison of the low energy conformations of an oncogenic and a non-oncogenic p21 protein, neither of which binds GTP or GDP

Oncogenic p21 protein, encoded by theras-oncogene, that causes malignant transformation of normal cells and many human tumors, is almost identical in sequence to its normal protooncogene-encoded counterpart protein, except for the substitution of arbitrary amino acids for the normally occurring amino acids at critical positions such as Gly 12 and Gin 61. Since p21 is normally activated by the binding of GTP in place of GDP, it has been postulated that oncogenic forms must retain bound GTP for prolonged time periods. However, two multiply substituted p21 proteins have been cloned, neither of which binds GDP or GTP. One of these mutant proteins with Val for Gly 10, Arg for Gly 12, and Thr for Ala 59 causes cell transformation, while the other, similar protein with Gly 10, Arg 12, Val for Gly 13 and Thr 59 does not transform cells. To define the critical conformational changes that occur in the p21 protein that cause it to become oncogenic, we have calculated the low energy conformations of the two multiply substituted mutant p21 proteins using a new adaptation of the electrostatically driven Monte Carlo (EDMC) technique, based on the program ECEPP. We have used this method to explore the conformational space available to both proteins and to compute the average structures for both using statistical mechanical averaging. Comparison of the average structures allows us to detect the major differences in conformation between the two proteins. Starting structures for each protein were calculated using the recently deposited x-ray crystal coordinates for the p21 protein, that was energy-refined using ECEPP, and then perturbed using the EDMC method to compute its average structure. The specific amino acid substitutions for both proteins were then generated into the lowest energy structure generated by this procedure, subjected to energy minimization and then to full EDMC perturbations. We find that both mutant proteins exhibit major differences in conformation in specific regions, viz., residues 35–47, 55–78, 81–93, 96–110, 115–126, and 123–134, compared with the EDMC-refined x-ray structure of the wild-type protein. These regions have been found to be the most flexible in the p21 protein bound to GDP from prior molecular dynamics calculations (Dykeset al., 1993). Comparison of the EDMC-average structure of the transforming mutant with that of the nontransforming mutant reveals major structural differences at residues 10–16, 32–40, and 60–68. These structural differences appear to be the ones that are critical in activation of the p21 protein. Analysis of the correlated motions of the different regions of the two mutant proteins reveals that changes in the conformation of regions in the carboxyl half of the protein are caused by changes in conformation around residues 10–16 and are transmitted by means of residues around Gln 61. The latter region therefore constitutes a molecular switch unit, in agreement with conclusions from prior work.On leave from the Department of Chemistry, University of Gdask, ul. Sobieskiego 18, 80-952 Gdask, Poland.     

Effects of protein binding on a lipid bilayer containing local anesthetic articaine, and the potential of mean force calculation: a molecular dynamics simulation approach

Articaine, as a local anesthetic drug has been simulated in neutral and charged forms, and its interaction with the dimyristoylphosphatidylcholine (DMPC) lipid bilayer membrane is investigated by molecular dynamics simulation using GROMACS software. In order to obtain the optimum location of the drug molecules, as they penetrate into the membrane, umbrella sampling is applied and the free energy is calculated. The effect of protein binding to DMPC membrane on the process of drug diffusion through the membrane is considered. Five simulation systems are designed and by applying the potential of mean force, the molecular dynamics simulation on the system is performed. In light of the obtained results, the electrostatic potential, variation of lipid bilayer’s order parameter and the diffusion coefficient of drug are discussed.

Saturation of transgene protein synthesis from mRNA in cells producing a large number of transgene mRNA

Experimental results have suggested that transgene expression can be saturated when large amounts of plasmid vectors are delivered into cells. To investigate this saturation kinetic behavior, cells were transfected with monitoring and competing plasmids using cationic liposomes. Even although an identical amount of a monitoring plasmid expressing firefly luciferase (FL) was used for transfection, transgene expression from the plasmid was greatly affected by the level of transgene expression from competing plasmids expressing renilla luciferase (RL). Similar results were obtained by exchanging the monitoring and competing plasmids. The competing plasmid‐dependent reduction in transgene expression from the monitoring plasmid was also observed in mouse liver after hydrodynamic injection of plasmids. On the other hand, the mRNA and protein expression level of glyceraldehyde‐3‐phosphate dehydrogenase (GAPDH), an endogenous gene, in the liver hardly changed even when transgene expression process is saturated. The expression of FL from a monitoring plasmid was significantly restored by siRNA‐mediated degradation of RL mRNA that was expressed from a competing plasmid. These results suggest that the efficiency of protein synthesis from plasmid vectors is reduced when a large amount of mRNA is transcribed with no significant changes in endogenous gene expression. Biotechnol. Bioeng. 2011;108: 2380–2389. © 2011 Wiley Periodicals, Inc.     

A 30-residue fragment of the carp granulin-1 protein folds into a stack of two beta-hairpins similar to that found in the native protein.

Upon air oxidation, a peptide corresponding to the 30-residue N-terminal subdomain of carp granulin-1 spontaneously formed the disulfide pairing observed in the native protein. Structural characterization using NMR showed the presence of a defined secondary structure within this peptide. The chemical shifts for most of the alphaCH protons of the peptide and the protein are very similar, and the observed NOE contacts of the peptide strongly resemble those in the protein. A structure calculation of the peptide using NOE distance constraints indicates that the peptide fragment adopts the same conformation as formed within the native protein. The 30-residue N-terminal peptide of carp granulin-1 is the first example of an independently folded stack of two beta-hairpins reinforced by two interhairpin disulfide bonds. Two key areas of the structure show a clustering of hydrophobic residues that may account for its exceptional conformational stability.     

Identification and functional clustering of genes regulating muscle protein degradation from amongst the known C. elegans muscle mutants

Loss of muscle mass via protein degradation is an important clinical problem but we know little of how muscle protein degradation is regulated genetically. To gain insight our labs developed C. elegans into a model for understanding the regulation of muscle protein degradation. Past studies uncovered novel functional roles for genes affecting muscle and/or involved in signalling in other cells or tissues. Here we examine most of the genes previously identified as the sites of mutations affecting muscle for novel roles in regulating degradation. We evaluate genomic (RNAi knockdown) approaches and combine them with our established genetic (mutant) and pharmacologic (drugs) approaches to examine these 159 genes. We find that RNAi usually recapitulates both organismal and sub-cellular mutant phenotypes but RNAi, unlike mutants, can frequently be used acutely to study gene function solely in differentiated muscle. In the majority of cases where RNAi does not produce organismal level phenotypes, sub-cellular defects can be detected; disrupted proteostasis is most commonly observed. We identify 48 genes in which mutation or RNAi knockdown causes excessive protein degradation; myofibrillar and/or mitochondrial morphologies are also disrupted in 19 of these 48 cases. These 48 genes appear to act via at least three sub-networks to control bulk degradation of protein in muscle cytosol. Attachment to the extracellular matrix regulates degradation via unidentified proteases and affects myofibrillar and mitochondrial morphology. Growth factor imbalance and calcium overload promote lysosome based degradation whereas calcium deficit promotes proteasome based degradation, in both cases myofibrillar and mitochondrial morphologies are largely unaffected. Our results provide a framework for effectively using RNAi to identify and functionally cluster novel regulators of degradation. This clustering allows prioritization of candidate genes/pathways for future mechanistic studies.     

Assessment of a large number of empirical plant species niche models by elicitation of knowledge from two national experts

Quantitative models play an increasing role in exploring the impact of global change on biodiversity. To win credibility and trust, they need validating. We show how expert knowledge can be used to assess a large number of empirical species niche models constructed for the British vascular plant and bryophyte flora. Key outcomes were (a) scored assessments of each modeled species and niche axis combination, (b) guidance on models needing further development, (c) exploration of the trade‐off between presenting more complex model summaries, which could lead to more thorough validation, versus the longer time these take to evaluate, (d) quantification of the internal consistency of expert opinion based on comparison of assessment scores made on a random subset of models evaluated by both experts. Overall, the experts assessed 39% of species and niche axis combinations to be “poor” and 61% to show a degree of reliability split between “moderate” (30%), “good” (25%), and “excellent” (6%). The two experts agreed in only 43% of cases, reaching greater consensus about poorer models and disagreeing most about models rated as better by either expert. This low agreement rate suggests that a greater number of experts is required to produce reliable assessments and to more fully understand the reasons underlying lack of consensus. While area under curve (AUC) statistics showed generally very good ability of the models to predict random hold‐out samples of the data, there was no correspondence between these and the scores given by the experts and no apparent correlation between AUC and species prevalence. Crowd‐sourcing further assessments by allowing web‐based access to model fits is an obvious next step. To this end, we developed an online application for inspecting and evaluating the fit of each niche surface to its training data.