Comparative conformational analysis of cholesterol and ergosterol by molecular mechanics

A comparative conformational analysis of cholesterol and ergosterol has been carried out using molecular mechanics methods. These studies are aimed at giving a better understanding of the molecular nature of the interaction of these sterols with polyene macrolide antibiotics. Structures of cholesterol and ergosterol determined by X-ray methods have been used as initial geometries of these molecules for force field calculations. The calculation of steric energy has also been made for conformations which do not appear in the crystal. The latter conformers have different conformations of the side chain as well as different conformations of rings A and D. The rotational barriers around bonds C17–C20 and C20–C22 have also been calculated. The results obtained on differences and similarities in the conformations of cholesterol and ergosterol allow us to postulate a mechanism for differential interaction with the antibiotics. The relatively rigid side chain of ergosterol (stretched molecule) in comparison with the flexible side chain of cholesterol (bent molecule), allows better intermolecular contact of the first sterol molecule with a polyene macrolide and in consequence facilitates complex formation involving Van der Waal's forces.     

Ramachandran maps for side chains in globular proteins

The Ramachandran plot for backbone ϕ,ψ-angles in a blocked monopeptide has played a central role in understanding protein structure. Curiously, a similar analysis for side chain χ-angles has been comparatively neglected. Instead, efforts have focused on compiling various types of side chain libraries extracted from proteins of known structure. Departing from this trend, the following analysis presents backbone-based maps of side chains in blocked monopeptides. As in the original ϕ,ψ-plot, these maps are derived solely from hard-sphere steric repulsion. Remarkably, the side chain biases exhibit marked similarities to corresponding biases seen in high-resolution protein structures. Consequently, some of the entropic cost for side chain localization in proteins is prepaid prior to the onset of folding events because conformational bias is built into the chain at the covalent level. Furthermore, side chain conformations are seen to experience fewer steric restrictions for backbone conformations in either the α or β basins, those map regions where repetitive ϕ,ψ-angles result in α-helices or strands of β-sheet, respectively. Here, these α and β basins are entropically favored for steric reasons alone; a blocked monopeptide is too short to accommodate the peptide hydrogen bonds that stabilize repetitive secondary structure. Thus, despite differing energetics, α/β-basins are favored for both monopeptides and repetitive secondary structure, underpinning an energetically unfrustrated compatibility between these two levels of protein structure.     

Reduced representation model of protein structure prediction: statistical potential and genetic algorithms.

A reduced representation model, which has been described in previous reports, was used to predict the folded structures of proteins from their primary sequences and random starting conformations. The molecular structure of each protein has been reduced to its backbone atoms (with ideal fixed bond lengths and valence angles) and each side chain approximated by a single virtual united-atom. The coordinate variables were the backbone dihedral angles phi and psi. A statistical potential function, which included local and nonlocal interactions and was computed from known protein structures, was used in the structure minimization. A novel approach, employing the concepts of genetic algorithms, has been developed to simultaneously optimize a population of conformations. With the information of primary sequence and the radius of gyration of the crystal structure only, and starting from randomly generated initial conformations, I have been able to fold melittin, a protein of 26 residues, with high computational convergence. The computed structures have a root mean square error of 1.66 A (distance matrix error = 0.99 A) on average to the crystal structure. Similar results for avian pancreatic polypeptide inhibitor, a protein of 36 residues, are obtained. Application of the method to apamin, an 18-residue polypeptide with two disulfide bonds, shows that it folds apamin to native-like conformations with the correct disulfide bonds formed.     

Spatial structure of apamin in solution]

The calculation of the complete spatial structure of the bee venom peptide neurotoxin apamin has been carried out by means of a method elaborated earlier. It is based on the joint utilization of the molecular mechanics algorithms and NMR spectroscopy data. It was established that the molecule backbone conformation in solution may be represented as the combination of the beta-turn III (residues 2-5) and alpha-helical segment (9-18) both separated by the non-standard bend IV (5-8). The most probable system of the intramolecular hydrogen bonds in the apamin polypeptide backbone was proposed. Certain amino acid residues have been shown to be characterized by the lack of strict determination of the conformations of their side chains which may be realized in a few states providing approximately equal stabilization of the same form of the main chain. The conformational parameters of the proposed apamin structural model are appropriate to the NMR spectroscopy data derived from the literature and used in the calculations and are not contradictory to other experimental information.     

Statistical and conformational analysis of the electron density of protein side chains

Protein side chains make most of the specific contacts between proteins and other molecules, and their conformational properties have been studied for many years. These properties have been analyzed primarily in the form of rotamer libraries, which cluster the observed conformations into groups and provide frequencies and average dihedral angles for these groups. In recent years, these libraries have improved with higher resolution structures and using various criteria such as high thermal factors to eliminate side chains that may be misplaced within the crystallographic model coordinates. Many of these side chains have highly non-rotameric dihedral angles. The origin of side chains with high B-factors and/or with non-rotameric dihedral angles is of interest in the determination of protein structures and in assessing the prediction of side chain conformations. In this paper, using a statistical analysis of the electron density of a large set of proteins, it is shown that: (1) most non-rotameric side chains have low electron density compared to rotameric side chains; (2) up to 15% of chi1 non-rotameric side chains in PDB models can clearly be fit to density at a single rotameric conformation and in some cases multiple rotameric conformations; (3) a further 47% of non-rotameric side chains have highly dispersed electron density, indicating potentially interconverting rotameric conformations; (4) the entropy of these side chains is close to that of side chains annotated as having more than one chi(1) rotamer in the crystallographic model; (5) many rotameric side chains with high entropy clearly show multiple conformations that are not annotated in the crystallographic model. These results indicate that modeling of side chains alternating between rotamers in the electron density is important and needs further improvement, both in structure determination and in structure prediction.     

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.     

Improved energy bound accuracy enhances the efficiency of continuous protein design

Flexibility and dynamics are important for protein function and a protein's ability to accommodate amino acid substitutions. However, when computational protein design algorithms search over protein structures, the allowed flexibility is often reduced to a relatively small set of discrete side‐chain and backbone conformations. While simplifications in scoring functions and protein flexibility are currently necessary to computationally search the vast protein sequence and conformational space, a rigid representation of a protein causes the search to become brittle and miss low‐energy structures. Continuous rotamers more closely represent the allowed movement of a side chain within its torsional well and have been successfully incorporated into the protein design framework to design biomedically relevant protein systems. The use of continuous rotamers in protein design enables algorithms to search a larger conformational space than previously possible, but adds additional complexity to the design search. To design large, complex systems with continuous rotamers, new algorithms are needed to increase the efficiency of the search. We present two methods, PartCR and HOT, that greatly increase the speed and efficiency of protein design with continuous rotamers. These methods specifically target the large errors in energetic terms that are used to bound pairwise energies during the design search. By tightening the energy bounds, additional pruning of the conformation space can be achieved, and the number of conformations that must be enumerated to find the global minimum energy conformation is greatly reduced. Proteins 2015; 83:1151–1164. © 2015 Wiley Periodicals, Inc.     

Discrete restraint-based protein modeling and the Calpha-trace problem

We present a novel de novo method to generate protein models from sparse, discretized restraints on the conformation of the main chain and side chain atoms. We focus on Calpha-trace generation, the problem of constructing an accurate and complete model from approximate knowledge of the positions of the Calpha atoms and, in some cases, the side chain centroids. Spatial restraints on the Calpha atoms and side chain centroids are supplemented by constraints on main chain geometry, phi/xi angles, rotameric side chain conformations, and inter-atomic separations derived from analyses of known protein structures. A novel conformational search algorithm, combining features of tree-search and genetic algorithms, generates models consistent with these restraints by propensity-weighted dihedral angle sampling. Models with ideal geometry, good phi/xi angles, and no inter-atomic overlaps are produced with 0.8 A main chain and, with side chain centroid restraints, 1.0 A all-atom root-mean-square deviation (RMSD) from the crystal structure over a diverse set of target proteins. The mean model derived from 50 independently generated models is closer to the crystal structure than any individual model, with 0.5 A main chain RMSD under only Calpha restraints and 0.7 A all-atom RMSD under both Calpha and centroid restraints. The method is insensitive to randomly distributed errors of up to 4 A in the Calpha restraints. The conformational search algorithm is efficient, with computational cost increasing linearly with protein size. Issues relating to decoy set generation, experimental structure determination, efficiency of conformational sampling, and homology modeling are discussed.     

Validation of NMR side-chain conformations by packing calculations

The precision and accuracy of protein structures determined by nuclear magnetic resonance (NMR) spectroscopy depend on the completeness of input experimental data set. Typically, rather than a single structure, an ensemble of up to 20 equally representative conformers is generated and routinely deposited in the Protein Database. There are substantially more experimentally derived restraints available to define the main-chain coordinates than those of the side chains. Consequently, the side-chain conformations among the conformers are more variable and less well defined than those of the backbone. Even when a side chain is determined with high precision and is found to adopt very similar orientations among all the conformers in the ensemble, it is possible that its orientation might still be incorrect. Thus, it would be helpful if there were a method to assess independently the side-chain orientations determined by NMR. Recently, homology modeling by side-chain packing algorithms has been shown to be successful in predicting the side-chain conformations of the buried residues for a protein when the main-chain coordinates and sequence information are given. Since the main-chain coordinates determined by NMR are consistently more reliable than those of the side-chains, we have applied the side-chain packing algorithms to predict side-chain conformations that are compatible with the NMR-derived backbone. Using four test cases where the NMR solution structures and the X-ray crystal structure of the same protein are available, we demonstrate that the side-chain packing method can provide independent validation for the side-chain conformations of NMR structures. Comparison of the side-chain conformations derived by side-chain packing prediction and by NMR spectroscopy demonstrates that when there is agreement between the NMR model and the predicted model, on average 78% of the time the X-ray structure also concurs. While the side-chain packing method can confirm the reliable residue conformations in NMR models, more importantly, it can also identify the questionable residue conformations with an accuracy of 60%. This validation method can serve to increase the confidence level for potential users of structural models determined by NMR.     

Physical-chemical determinants of turn conformations in globular proteins

Globular proteins are assemblies of alpha-helices and beta-strands, interconnected by reverse turns and longer loops. Most short turns can be classified readily into a limited repertoire of discrete backbone conformations, but the physical-chemical determinants of these distinct conformational basins remain an open question. We investigated this question by exhaustive analysis of all backbone conformations accessible to short chain segments bracketed by either an alpha-helix or a beta-strand (i.e., alpha-segment-alpha, beta-segment-beta, alpha-segment-beta, and beta-segment-alpha) in a nine-state model. We find that each of these four secondary structure environments imposes its own unique steric and hydrogen-bonding constraints on the intervening segment, resulting in a limited repertoire of conformations. In greater detail, an exhaustive set of conformations was generated for short backbone segments having reverse-turn chain topology and bracketed between elements of secondary structure. This set was filtered, and only clash-free, hydrogen-bond-satisfied conformers having reverse-turn topology were retained. The filtered set includes authentic turn conformations, observed in proteins of known structure, but little else. In particular, over 99% of the alternative conformations failed to satisfy at least one criterion and were excluded from the filtered set. Furthermore, almost all of the remaining alternative conformations have close tolerances that would be too tight to accommodate side chains longer than a single beta-carbon. These results provide a molecular explanation for the observation that reverse turns between elements of regular secondary can be classified into a small number of discrete conformations.     

Sparse networks of directly coupled,polymorphic, and functional side chains in allosteric proteins

Recent studies have highlighted the role of coupled side‐chain fluctuations alone in the allosteric behavior of proteins. Moreover, examination of X‐ray crystallography data has recently revealed new information about the prevalence of alternate side‐chain conformations (conformational polymorphism), and attempts have been made to uncover the hidden alternate conformations from X‐ray data. Hence, new computational approaches are required that consider the polymorphic nature of the side chains, and incorporate the effects of this phenomenon in the study of information transmission and functional interactions of residues in a molecule. These studies can provide a more accurate understanding of the allosteric behavior. In this article, we first present a novel approach to generate an ensemble of conformations and an efficient computational method to extract direct couplings of side chains in allosteric proteins, and provide sparse network representations of the couplings. We take the side‐chain conformational polymorphism into account, and show that by studying the intrinsic dynamics of an inactive structure, we are able to construct a network of functionally crucial residues. Second, we show that the proposed method is capable of providing a magnified view of the coupled and conformationally polymorphic residues. This model reveals couplings between the alternate conformations of a coupled residue pair. To the best of our knowledge, this is the first computational method for extracting networks of side chains' alternate conformations. Such networks help in providing a detailed image of side‐chain dynamics in functionally important and conformationally polymorphic sites, such as binding and/or allosteric sites. Proteins 2015; 83:497–516. © 2014 Wiley Periodicals, Inc.     

Conformational study of angiotensin II

Conformational free energy calculations using an empirical potential ECEPP/3 (Empirical Conformational Energy Program for Peptides, Version 3) were carried out on angiotensin II (AII) of sequence Asp-Arg-Val-Tyr-Ile-His-Pro-Phe to find the stable conformations of the free state in the unhydrated and the hydrated states. A conformational analysis of the unhydrated state was carried out using the buildup procedure. The free energy calculation using the hydration shell model was also carried out to obtain the stable conformation of the hydrated state. The calculated stable conformations of AII in both states have a partially right-handed α-helical structure stabilized by short- and medium-range interactions. The similarity between the lowest free energy conformations of the unhydrated and hydrated states suggests that the hydration might not be important to stabilize the overall conformation of AII in a free state. The absence of any intramolecular interaction of the Tyr side chain suggests the possible interaction of this residue with the receptor. In this study, we found that the low free energy conformations contain both the parallel-plate and the perpendicular-plate geometries of the His and Phe rings, suggesting the coexistence of both conformations. © 1996 John Wiley & Sons, Inc.     

The Free Energy Barrier for Arginine Gating Charge Translation Is Altered by Mutations in the Voltage Sensor Domain

The gating of voltage-gated ion channels is controlled by the arginine-rich S4 helix of the voltage-sensor domain moving in response to an external potential. Recent studies have suggested that S4 moves in three to four steps to open the conducting pore, thus visiting several intermediate conformations during gating. However, the exact conformational changes are not known in detail. For instance, it has been suggested that there is a local rotation in the helix corresponding to short segments of a 3-helix moving along S4 during opening and closing. Here, we have explored the energetics of the transition between the fully open state (based on the X-ray structure) and the first intermediate state towards channel closing (C), modeled from experimental constraints. We show that conformations within 3 Å of the X-ray structure are obtained in simulations starting from the C model, and directly observe the previously suggested sliding 3-helix region in S4. Through systematic free energy calculations, we show that the C state is a stable intermediate conformation and determine free energy profiles for moving between the states without constraints. Mutations indicate several residues in a narrow hydrophobic band in the voltage sensor contribute to the barrier between the open and C states, with F233 in the S2 helix having the largest influence. Substitution for smaller amino acids reduces the transition cost, while introduction of a larger ring increases it, largely confirming experimental activation shift results. There is a systematic correlation between the local aromatic ring rotation, the arginine barrier crossing, and the corresponding relative free energy. In particular, it appears to be more advantageous for the F233 side chain to rotate towards the extracellular side when arginines cross the hydrophobic region.     

Semi empirical calculations of cyclo-(L-threonyl-L-histidyl) conformations.

The conformations of cyclo-(L-Thr-L-His) have been calculated by semi-empirical method without taking account on the solvent. The Thr side chain is folded above the DKP ring with $\text{χ}{}^{\mathrm{I}}{}_1\text{= 60°}$; this conformation seems to be due to a specific interaction of the hydroxylated side chain with the DKP ring. The His side chain can be folded in order to interact with the Thr side chain. In the open forms, the His side chain interacts with the peptide backbone. The most stable conformations are the folded forms in which the unprotonated imidazole ring is in the N^ε-H^ε tautomeric form.     

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

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

Constructing side chains on near-native main chains for ab initio protein structure prediction

Is there value in constructing side chains while searching protein conformational space during an ab initio simulation? If so, what is the most computationally efficient method for constructing these side chains? To answer these questions, four published approaches were used to construct side chain conformations on a range of near-native main chains generated by ab initio protein structure prediction methods. The accuracy of these approaches was compared with a naive approach that selects the most frequently observed rotamer for a given amino acid to construct side chains. An all-atom conditional probability discriminatory function is useful at selecting conformations with overall low all-atom root mean square deviation (r.m.s.d.) and the discrimination improves on sets that are closer to the native conformation. In addition, the naive approach performs as well as more sophisticated methods in terms of the percentage of chi(1) angles built accurately and the all-atom r. m.s.d., between the native and near-native conformations. The results suggest that the naive method would be extremely useful for fast and efficient side chain construction on vast numbers of conformations for ab initio prediction of protein structure.     

CAP: conformation angles package-displaying the conformation angles of side chains in proteins

SUMMARY: A graphics package has been developed to display all side chain conformation angles of the user selected residue in a given protein structure. The proposed package is incorporated with all the protein structures (solved using X-ray diffraction and NMR spectroscopy) available in the Protein Data Bank. The package displays the multiple conformations adopted by a single amino acid residue whose structure is solved and refined at very high resolution. In addition, it shows the percentage distribution of the side chain conformation angles in different rotameric states. AVAILABILITY: http://144.16.71.146/cap/     

New type of helix and 2(7) ribbon structure formation in poly DeltaLeu peptides: construction of a single-handed template

alpha,beta-Dehydroamino acid residues due to the presence of Calpha = Cbeta double bond influences the main chain and the side chain conformations. These residues have interesting chemical features including the increased resistance to enzymatic degradation. The chain length dependent conformational behavior of poly alpha,beta-dehydroleucine (DeltaLeu) peptides in both the pure forms Z and E and their various combinations like alternate ZE/EZ etc. have been investigated by using quantum mechanical method PCILO (perturbative configuration interaction of localized orbitals). The conformational states in alternate Z and E forms, with Phi, Psi values of -10 degrees , 105 degrees /1 degrees , -88 degrees for Z form and 35 degrees , 22 degrees /-34 degrees , -27 degrees for the E form are found to be the most stable and degenerate than the states in pure Z and E forms and the EZ form etc. The repeated Phi, Psi values give rise to altogether new types of left and right handed helices, and their stability increases with increasing chain length. These structures are stabilized by intramolecular hydrogen bonding, carbonyl-carbonyl interactions and hydrophobic interactions between the side chains of DeltaZLeu and DeltaELeu residues. The 2(7) ribbon structure (seven-membered hydrogen-bonded ring involving two consecutive amino acid residues) is found to be most stable and degenerate in the pentapeptide Ac-DeltaELeu5-NHMe, due to the formation of maximum hydrogen bonds. A right-handed template from achiral DeltaLeu peptides has been achieved by incorporating L-Leu at the C-terminal or D-Leu at the N-terminal.     

RASP: rapid modeling of protein side chain conformations

MOTIVATION: Modeling of side chain conformations constitutes an indispensable effort in protein structure modeling, protein-protein docking and protein design. Thanks to an intensive attention to this field, many of the existing programs can achieve reasonably good and comparable prediction accuracy. Moreover, in our previous work on CIS-RR, we argued that the prediction with few atomic clashes can complement the current existing methods for subsequent analysis and refinement of protein structures. However, these recent efforts to enhance the quality of predicted side chains have been accompanied by a significant increase of computational cost. RESULTS: In this study, by mainly focusing on improving the speed of side chain conformation prediction, we present a RApid Side-chain Predictor, called RASP. To achieve a much faster speed with a comparable accuracy to the best existing methods, we not only employ the clash elimination strategy of CIS-RR, but also carefully optimize energy terms and integrate different search algorithms. In comprehensive benchmark testings, RASP is over one order of magnitude faster (~ 40 times over CIS-RR) than the recently developed methods, while achieving comparable or even better accuracy.