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.     

A Nonstatistical Approach to the Prediction of Regular Structures in Proteins by the Example of α Helices

A new approach to the analysis of regular structures in proteins that is based on the method of molecular mechanics is proposed. The method uses only the information about the amino acid sequence. The -helical conformation was simulated using the ICM program of molecular mechanics. Energy profiles of the sequences in the -helical conformation, spanning the entire polypeptide chain, were plotted for eight proteins from the Protein Data Bank. The regions of each profile that exhibit energy minima were found to correspond to the -helical regions of the real spatial structure of the protein. Twenty-four out of 25 helices were distinctly pronounced, which indicates a rather high accuracy of the prediction. The energy profiles also help reveal the short regions that correspond to 3/10-helices and the turns that include local -helical conformations. Unlike the known statistical methods of prediction, this method makes it possible to establish the physical principles of the formation of -helical conformations.     

Use of molecular mechanics for secondary structure prediction. Is it possible to reveal alpha-helix?

A new approach to predicting protein standard conformations is suggested. The idea consists in modeling by molecular mechanics tools a continuous alpha-helical conformation for the whole protein. The profile of energy along the model alpha-helix reveals minima corresponding to real alpha-helical segments in the native protein. The 3/10-helices and beta-turns including a local alpha-helical conformation may be detected as well. All alpha-helical segments in the test sample are delineated; mean residue by residue accuracy Q(3alpha) is 79%. This non-statistical approach can shed light on the physical grounds of alpha-helix formation.     

Noncontact dipole effects on channel permeation. II. Trp conformations and dipole potentials in gramicidin A

The four Trp dipoles in the gramicidin A (gA) channel modulate channel conductance, and their side chain conformations should therefore be important, but the energies of different conformations are unknown. A conformational search for the right-handed helix based on molecular mechanics in vacuo yielded 46 conformations within 20 kcal/mol of the lowest energy conformation. The two lowest energy conformations correspond to the solid-state and solution-state NMR conformations, suggesting that interactions within the peptide determine the conformation. For representative conformations, the electrostatic potential of the Trp side chains on the channel axis was computed. A novel application of the image-series method of. Biophys. J. 9:1160-1170) was introduced to simulate the polarization of bulk water by the Trp side chains. For the experimentally observed structures, the CHARm toph19 potential energy (PE) of a cation in the channel center is -1.65 kcal/mol without images. With images, the PE is -1.9 kcal/mol, demonstrating that the images further enhance the direct dipole effect. Nonstandard conformations yielded less favorable PEs by 0.4-1.1 kcal/mol.     

Loop modeling: Sampling, filtering, and scoring

We describe a fast and accurate protocol, LoopBuilder, for the prediction of loop conformations in proteins. The procedure includes extensive sampling of backbone conformations, side chain addition, the use of a statistical potential to select a subset of these conformations, and, finally, an energy minimization and ranking with an all-atom force field. We find that the Direct Tweak algorithm used in the previously developed LOOPY program is successful in generating an ensemble of conformations that on average are closer to the native conformation than those generated by other methods. An important feature of Direct Tweak is that it checks for interactions between the loop and the rest of the protein during the loop closure process. DFIRE is found to be a particularly effective statistical potential that can bias conformation space toward conformations that are close to the native structure. Its application as a filter prior to a full molecular mechanics energy minimization both improves prediction accuracy and offers a significant savings in computer time. Final scoring is based on the OPLS/SBG-NP force field implemented in the PLOP program. The approach is also shown to be quite successful in predicting loop conformations for cases where the native side chain conformations are assumed to be unknown, suggesting that it will prove effective in real homology modeling applications.     

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.     

Conformational analysis of d-tubocurarine: Implications for minimal dimensions of its binding site within ion channels

All the minimum-energy conformations of d-tubocurarine were calculated by the method of molecular mechanics. The energy was minimized from 413 closed forms of the 18-member ring. The set of minimum-energy conformations includes 10 forms with energies less than 6 kcal/mol from the most stable one. Among the four lowest minimum-energy conformations, two forms correspond to those known from X-ray studies, whereas two conformations were not detected experimentally earlier. The flexibility of d-tubocurarine was estimated by calculating six paths of interconversion between the four lowest minimum-energy conformations. Using a molecular graphics technique, it was found that the most extended minimum-energy conformation of d-tubocurarine may fit in an ion channel of a rectangular profile of 8.7 × 11.2 Å, while one tetrahydroisoquinoline head may fit a profile as small as 6.9 × 11.0 Å. A possible model of d-tubocurarine location within the ion channel of the neuronal nicotinic acetylcholine receptor is suggested.     

Conformational mapping of the N-terminal segment of surfactant protein B in lipid using 13C-enhanced Fourier transform infrared spectroscopy.

Synthetic peptides based on the N-terminal domain of human surfactant protein B (SP-B1-25; 25 amino acid residues; NH2-FPIPLPYCWLCRALIKRIQAMIPKG) retain important lung activities of the full-length, 79-residue protein. Here, we used physical techniques to examine the secondary conformation of SP-B1-25 in aqueous, lipid and structure-promoting environments. Circular dichroism and conventional, 12C-Fourier transform infrared (FTIR) spectroscopy each indicated a predominate alpha-helical conformation for SP-B1-25 in phosphate-buffered saline, liposomes of 1-palmitoyl-2-oleoyl phosphatidylglycerol and the structure-promoting solvent hexafluoroisopropanol; FTIR spectra also showed significant beta- and random conformations for peptide in these three environments. In further experiments designed to map secondary structure to specific residues, isotope-enhanced FTIR spectroscopy was performed with 1-palmitoyl-2-oleoyl phosphatidylglycerol liposomes and a suite of SP-B1-25 peptides labeled with 13C-carbonyl groups at either single or multiple sites. Combining these 13C-enhanced FTIR results with energy minimizations and molecular simulations indicated the following model for SP-B1-25 in 1-palmitoyl-2-oleoyl phosphatidylglycerol: beta-sheet (residues 1-6), alpha-helix (residues 8-22) and random (residues 23-25) conformations. Analogous structural motifs are observed in the corresponding homologous N-terminal regions of several proteins that also share the 'saposin-like' (i.e. 5-helix bundle) folding pattern of full-length, human SP-B. In future studies, 13C-enhanced FTIR spectroscopy and energy minimizations may be of general use in defining backbone conformations at amino acid resolution, particularly for peptides or proteins in membrane environments.     

Molecular modeling of an antigenic complex between a viral peptide and a class I major histocompatibility glycoprotein.

Computer simulation of the conformations of short antigenic peptides (5-10 residues) either free or bound to their receptor, the major histocompatibility complex (MHC)-encoded glycoprotein H-2 Ld, was employed to explain experimentally determined differences in the antigenic activities within a set of related peptides. Starting for each sequence from the most probable conformations disclosed by a pattern-recognition technique, several energy-minimized structures were subjected to molecular dynamics simulations (MD) either in vacuo or solvated by water molecules. Notably, antigenic potencies were found to correlate to the peptides propensity to form and maintain an overall alpha-helical conformation through regular i,i + 4 hydrogen bonds. Accordingly, less active or inactive peptides showed a strong tendency to form i,i + 3 hydrogen bonds at their N-terminal end. Experimental data documented that the C-terminal residue is critical for interaction of the peptide with H-2 Ld. This finding could be satisfactorily explained by a 3-D Q.S.A.R. analysis postulating interactions between ligand and receptor by hydrophobic forces. A 3-D model is proposed for the complex between a high-affinity nonapeptide and the H-2 Ld receptor. First, the H-2 Ld molecule was built from X-ray coordinates of two homologous proteins: HLA-A2 and HLA-Aw68, energy-minimized and studied by MD simulations. With HLA-A2 as template, the only realistic simulation was achieved for a solvated model with minor deviations of the MD mean structure from the X-ray conformation. Water simulation of the H-2 Ld protein in complex with the antigenic nonapeptide was then achieved with the template-derived optimal parameters. The bound peptide retains mainly its alpha-helical conformation and binds to hydrophobic residues of H-2 Ld that correspond to highly polymorphic positions of MHC proteins. The orientation of the nonapeptide in the binding cleft is in accordance with the experimentally determined distribution of its MHC receptor-binding residues (agretope residues). Thus, computer simulation was successfully employed to explain functional data and predicts alpha-helical conformation for the bound peptide.     

The conformation of dolichol

An understanding of the natural conformation of dolichol is important for the elucidation of the mechanism of protein glycosylation and dolichol's other as yet undisclosed biological functions. Since the molecular mechanics method has been shown to be well suited for the prediction of alcohol and alkene conformations, we have employed it to study the conformations of apparent least energy of dolichol-19 and smaller polymers of isoprene, namely, squalene, trans,trans-farnesol, and cis,cis-farnesol. Additionally, the small-angle X-ray scattering (SAXS) method was employed to determine the validity of the apparent least energy conformer of dolichol-19 derived by the molecular mechanics method. The results indicate that the solution conformation of dolichol-19 is comprised of a central coiled region flanked by two arms. The central coiled region has two and a half turns of dimensions 9.84 x 16.55 x 51.66 A3. The arms of dimensions 3.99 x 5.89 x 17.47 A3 and 4.49 x 9.23 x 11.14 A3 are approximately diametrically opposed. Measurement of the intrinsic viscosity of dolichol in both isopentyl alcohol and oleyl alcohol showed that the natural conformation of dolichol is capable of increasing solution fluidity (i.e., lowering solution viscosity). Thus, while examination of the conformation of dolichol in a membrane-mimetic solvent by SAXS is not possible, the quantitative measure of the effect of dolichol on solution viscosity (and thus solution fluidity) is possible. The results are consistent with dolichol acting as a membrane-fluidizing agent and provide the first quantitative measure of the effect of dolichol on solution fluidity of a membrane-mimetic solvent.     

Role of hydrophobicity and solvent-mediated charge-charge interactions in stabilizing alpha-helices.

A theoretical study to identify the conformational preferences of lysine-based oligopeptides has been carried out. The solvation free energy and free energy of ionization of the oligopeptides have been calculated by using a fast multigrid boundary element method that considers the coupling between the conformation of the molecule and the ionization equilibria explicitly, at a given pH value. It has been found experimentally that isolated alanine and lysine residues have somewhat small intrinsic helix-forming tendencies; however, results from these simulations indicate that conformations containing right-handed alpha-helical turns are energetically favorable at low values of pH for lysine-based oligopeptides. Also, unusual patterns of interactions among lysine side chains with large hydrophobic contacts and close proximity (5-6 A) between charged NH3+ groups are observed. Similar arrangements of charged groups have been seen for lysine and arginine residues in experimentally determined structures of proteins available from the Protein Data Bank. The lowest-free-energy conformation of the sequence Ac-(LYS)6-NMe from these simulations showed large pKalpha shifts for some of the NH3+ groups of the lysine residues. Such large effects are not observed in the lowest-energy conformations of oligopeptide sequences with two, three, or four lysine residues. Calculations on the sequence Ac-LYS-(ALA)4-LYS-NMe also reveal low-energy alpha-helical conformations with interactions of one of the LYS side chains with the helix backbone in an arrangement quite similar to the one described recently by (Proc. Natl. Acad. Sci. U.S.A. 93:4025-4029). The results of this study provide a sound basis with which to discuss the nature of the interactions, such as hydrophobicity, charge-charge interaction, and solvent polarization effects, that stabilize right-handed alpha-helical conformations.     

A Free-Energy Approach for All-Atom Protein Simulation

All-atom free-energy methods offer a promising alternative to kinetic molecular mechanics simulations of protein folding and association. Here we report an accurate, transferable all-atom biophysical force field (PFF02) that stabilizes the native conformation of a wide range of proteins as the global optimum of the free-energy landscape. For 32 proteins of the ROSETTA decoy set and six proteins that we have previously folded with PFF01, we find near-native conformations with an average backbone RMSD of 2.14 Å to the native conformation and an average Z-score of −3.46 to the corresponding decoy set. We used nonequilibrium sampling techniques starting from completely extended conformations to exhaustively sample the energy surface of three nonhomologous hairpin-peptides, a three-stranded β-sheet, the all-helical 40 amino-acid HIV accessory protein, and a zinc-finger ββα motif, and find near-native conformations for the minimal energy for each protein. Using a massively parallel evolutionary algorithm, we also obtain a near-native low-energy conformation for the 54 amino-acid engrailed homeodomain. Our force field thus stabilized near-native conformations for a total of 20 proteins of all structure classes with an average RMSD of only 3.06 Å to their respective experimental conformations.     

Guiding conformation space search with an all-atom energy potential

The most significant impediment for protein structure prediction is the inadequacy of conformation space search. Conformation space is too large and the energy landscape too rugged for existing search methods to consistently find near-optimal minima. To alleviate this problem, we present model-based search, a novel conformation space search method. Model-based search uses highly accurate information obtained during search to build an approximate, partial model of the energy landscape. Model-based search aggregates information in the model as it progresses, and in turn uses this information to guide exploration toward regions most likely to contain a near-optimal minimum. We validate our method by predicting the structure of 32 proteins, ranging in length from 49 to 213 amino acids. Our results demonstrate that model-based search is more effective at finding low-energy conformations in high-dimensional conformation spaces than existing search methods. The reduction in energy translates into structure predictions of increased accuracy.     

Application of the multiensemble sampling to the equilibrium folding of proteins

MOTIVATION: Conventional Monte Carlo and molecular dynamics simulations of proteins in the canonical ensemble are of little use, because they tend to get trapped in states of energy local minima at low temperatures. One way to surmount this difficulty is to use a non-Boltzmann sampling method in which conformations are sampled upon a general weighting function instead of the conventional Boltzmann weighting function. The multiensemble sampling (MES) method is a non-Boltzmann sampling method that was originally developed to estimate free energy differences between systems with different potential energies and/or at different thermodynamic states. The method has not yet been applied to studies of complex molecular systems such as proteins. RESULTS: MES Monte Carlo simulations of small proteins have been carried out using a united-residue force field. The proteins at several temperatures from the unfolded to the folded states were simulated in a single MC run at a time and their equilibrium thermodynamic properties were calculated correctly. The distributions of sampled conformations clearly indicate that, when going through states of energy local minima, the MES simulation did not get trapped in them but escaped from them so quickly that all the relevant parts of conformation space could be sampled properly. A two-step folding process consisting of a collapse transition followed by a folding transition is observed. This study demonstrates that the use of MES alleviates the multiple-minima problem greatly. AVAILABILITY: Available on request from the authors.     

The electrostatically driven Monte Carlo method: application to conformational analysis of decaglycine

The Electrostatically Driven Monte Carlo (EDMC) method was applied in a study of a decamer of glycine whose conformational behavior is described by the Empirical Conformational Energy Program for Peptides (ECEPP/2) potential energy model. When free neutral end groups were used, it was found that conformations that were not alpha-helical had significantly lower potential energies than fully alpha-helical ones. However, when the N- and C-termini were blocked by acetyl and methyl amide groups, respectively, the number of unsatisfied hydrogen-bond donors and acceptors at the helix termini was diminished from 8 to 6; in this case, the possibility of forming two additional alpha-helical hydrogen bonds was an important enough factor in making the alpha-helical conformation the one with the lowest energy. The EDMC method was used as a global energy optimizer since it does not often become trapped in high-energy local minima.     

Protein side chain conformation predictions with an MMGBSA energy function

The prediction of protein side chain conformations from backbone coordinates is an important task in structural biology, with applications in structure prediction and protein design. It is a difficult problem due to its combinatorial nature. We study the performance of an “MMGBSA” energy function, implemented in our protein design program Proteus, which combines molecular mechanics terms, a Generalized Born and Surface Area (GBSA) solvent model, with approximations that make the model pairwise additive. Proteus is not a competitor to specialized side chain prediction programs due to its cost, but it allows protein design applications, where side chain prediction is an important step and MMGBSA an effective energy model. We predict the side chain conformations for 18 proteins. The side chains are first predicted individually, with the rest of the protein in its crystallographic conformation. Next, all side chains are predicted together. The contributions of individual energy terms are evaluated and various parameterizations are compared. We find that the GB and SA terms, with an appropriate choice of the dielectric constant and surface energy coefficients, are beneficial for single side chain predictions. For the prediction of all side chains, however, errors due to the pairwise additive approximation overcome the improvement brought by these terms. We also show the crucial contribution of side chain minimization to alleviate the rigid rotamer approximation. Even without GB and SA terms, we obtain accuracies comparable to SCWRL4, a specialized side chain prediction program. In particular, we obtain a better RMSD than SCWRL4 for core residues (at a higher cost), despite our simpler rotamer library. Proteins 2016; 84:803–819. © 2016 Wiley Periodicals, Inc.     

Guiding probabilistic search of the protein conformational space with structural profiles

The roughness of the protein energy surface poses a significant challenge to search algorithms that seek to obtain a structural characterization of the native state. Recent research seeks to bias search toward near-native conformations through one-dimensional structural profiles of the protein native state. Here we investigate the effectiveness of such profiles in a structure prediction setting for proteins of various sizes and folds. We pursue two directions. We first investigate the contribution of structural profiles in comparison to or in conjunction with physics-based energy functions in providing an effective energy bias. We conduct this investigation in the context of Metropolis Monte Carlo with fragment-based assembly. Second, we explore the effectiveness of structural profiles in providing projection coordinates through which to organize the conformational space. We do so in the context of a robotics-inspired search framework proposed in our lab that employs projections of the conformational space to guide search. Our findings indicate that structural profiles are most effective in obtaining physically realistic near-native conformations when employed in conjunction with physics-based energy functions. Our findings also show that these profiles are very effective when employed instead as projection coordinates to guide probabilistic search toward undersampled regions of the conformational space.     

Influence of solvent molecules on the stereochemical code of glycyl residues in proteins

The Ramachandran steric map and energy diagrams of the glycyl residue are symmetric. A plot of (phi,psi) angles of glycyl residues in 250 nonhomologous and high-resolution protein structures is also largely symmetric. However, there is a clear aberration in the symmetry. Although there is a cluster of points corresponding to the right-handed alpha-helical region, the "equivalent" cluster is clearly shifted to in and around the (phi,psi) values of (90 degrees, 0 degrees ) instead of being centered at the left-handed alpha-helical region of (60 degrees, 40 degrees ). This lack of symmetry exists even in the (phi,psi) distribution of residues from non-alpha-helical regions in proteins. Here we provide an explanation for this observation. An analysis of glycyl conformations in small peptide structures and in "coil" proteins, which are largely devoid of helical and sheet regions, shows that glycyl residues prefer to adopt conformations around (+/-90 degrees, 0 degrees ) instead of right- and left-handed alpha-helical regions. By using theoretical calculations, such conformations are shown to have highest solvent accessibility in a system of two-linked peptide units with glycyl residue at the central C(alpha) atom. This finding is consistent with the observations from 250 nonhomologous protein structures where glycyl residues with conformations close to (+/-90 degrees, 0 degrees ) are seen to have high solvent accessibility. Analysis of a subset of nonhomologous structures with very high resolution (1.5 A or better) shows that water molecules are indeed present at distances suitable for hydrogen bond interaction with glycyl residues possessing conformations close to (+/-90 degrees, 0 degrees ). It is suggested that water molecules play a key role in determining and stabilizing these conformations of glycyl residues and explain the aberration in the symmetry of glycyl conformations in proteins.     

What befalls the proteins and water in a living cell when the cell dies?

The solvency of solutes of varying molecular size in the intracellular water of freshly-killed Ehrlich carcinoma cells fits the same theoretical curve that describes the solvency of similar solutes in a 36% solution of native bovine hemoglobin--a protein found only in red blood cells and making up 97.3% of the red cell's total intracellular proteins. The merging of the two sets of data confirms the prediction of the AI Hypothesis that key intracellular protein(s) in dying cells undergo(es) a transition from: (1) one in which the polypeptide NHCO groups assume a fully-extended conformation with relatively strong power of polarizing and orienting the bulk-phase water in multilayers; to (2) one in which most of the polypeptide NHCO groups are engaged in alpha-helical and other "introvert" conformations (see below for definition) with much weaker power in polarizing-orienting multilayers of bulk-phase water. This concordance of the two sets of data also shows that what we now call native hemoglobin--supposedly denoting hemoglobin found in its natural state in living red blood cells--, in fact, more closely resembles the water-polarizing, and -orienting intracellular proteins in dead cells. Although in the dead Ehrlich carcinoma cells as well as in the 36% solution of native hemoglobin, much of the protein's polypeptide NHCO groups are engaged in alpha-helical and other "introvert" conformation (Perutz 1969; Weissbluth 1974), both systems produce a weak but nonetheless pervasive and "long-range" water polarization and orientation. It is suggested that in both the dead Ehrlich carcinoma ascites cells and in the 36% native bovine hemoglobin solution, enough polypeptide NHCO groups assume the fully-extended conformation to produce the weak but far-reaching multilayer water polarization and orientation observed.