Structure and internal mobility of proteins: a molecular dynamics study of hen egg white lysozyme

The structure and internal motions of the protein hen egg white lysozyme are studied by analysis of simulation and experimental data. A molecular dynamics simulation and an energy minimization of the protein in vacuum have been made and the results compared with high-resolution structures and temperature factors of hen egg white lysozyme in two different crystal forms and of the homologous protein human lysozyme. The structures obtained from molecular dynamics and energy minimization have root-mean-square deviations for backbone atoms of 2.3 Å and 1.1–1.3 Å, respectively, relative to the crystal structures; the different crystal structures have root-mean-square deviations of 0.73–0.81 Å for the backbone atoms. In comparing the backbone dihedral angles, the difference between the dynamics and the crystal structure on which it is based is the same as that between any two crystal structures. The internal fluctuations of atomic positions calculated from the molecular dynamics trajectory agree well with the temperature factors from the three structures. Simulation and crystal results both show that there are large motions for residues involved in exposed turns of the backbone chain, relatively smaller motions for residues involved in the middle of helices or β-sheet structures, and relatively small motions of residues near disulfide bridges. Also, both the simulation and crystal data show that side-chain atoms have larger fluctuations than main-chain atoms. Moreover, the regions that have large deviations among the x-ray crystal structures, which indicates flexibility, are found to have large fluctuations in the simulation.     

Docking of calcium ions in proteins with flexible side chains and deformable backbones

A method of docking Ca²⁺ ions in proteins with flexible side chains and deformable backbones is proposed. The energy was calculated with the AMBER force field, implicit solvent, and solvent exposure-dependent and distance-dependent dielectric function. Starting structures were generated with Ca²⁺ coordinates and side-chain torsions sampled in 1000 Å³ cubes centered at the experimental Ca²⁺ positions. The energy was Monte Carlo-minimized. The method was tested on fourteen Ca²⁺-binding sites. For twelve Ca²⁺-binding sites the root mean square (RMS) deviation of the apparent global minimum from the experimental structure was below 1.3 and 1.7 Å for Ca²⁺ ions and side-chain heavy atoms, respectively. Energies of multiple local minima correlate with the RMS deviations from the X-ray structures. Two Ca²⁺-binding sites at the surface of proteinase K were not predicted, because of underestimation of Ca²⁺ hydration energy by the implicit-solvent method.     

Refinement of protein structures in explicit solvent

We present a CPU efficient protocol for refinement of protein structures in a thin layer of explicit solvent and energy parameters with completely revised dihedral angle terms. Our approach is suitable for protein structures determined by theoretical (e.g., homology modeling or threading) or experimental methods (e.g., NMR). In contrast to other recently proposed refinement protocols, we put a strong emphasis on consistency with widely accepted covalent parameters and computational efficiency. We illustrate the method for NMR structure calculations of three proteins: interleukin-4, ubiquitin, and crambin. We show a comparison of their structure ensembles before and after refinement in water with and without a force field energy term for the dihedral angles; crambin was also refined in DMSO. Our results demonstrate the significant improvement of structure quality by a short refinement in a thin layer of solvent. Further, they show that a dihedral angle energy term in the force field is beneficial for structure calculation and refinement. We discuss the optimal weight for the energy constant for the backbone angle omega and include an extensive discussion of meaning and relevance of the calculated validation criteria, in particular root mean square Z scores for covalent parameters such as bond lengths.     

Packing of α-helices: Geometrical constraints and contact areas

The helical packing in sperm whale myoglobin has been examined. Using cylindrical co-ordinates based on each helix axis in turn, the overlap of the side-chain atoms of a helix with the surrounding atoms from other parts of the structure was 2.3 Å, but the distribution was not at all uniform and severe overlap occurred in at least one location for each helix. Simple axial translations or rotations of any helix in the native structure are not permitted motions. Translation perpendicular to the helix axis in at least one direction is not restricted by interlocking side-chains.The approach of two helices along the contact normal connecting their axes produces solvent exclusion effects at a distance of about 6 Å from the final position. The solvent-excluded area found in such interaction sites is equivalent to a large hydrophobic contribution to the free energy of association. The six principal sites correspond by themselves to 40% of the total area change in going from the extended sausage model to the native structure. The mean atom-packing densities for these sites and the standard deviations of these values are similar and are equal to that found for the protein as a whole.Helices of close-packed spheres form useful approximations to actual peptide helices. The helix of index number four corresponds closely to an α-helix. The required sphere size corresponds in volume to residues such as leucine or methionine. The predicted packing scheme for such helices corresponds to the three general classes of interactions actually seen.Making use of the geometry implied by the close-packed sphere helix, an algorithm is proposed for picking potentially strong helix-helix interaction sites in peptide chains of known sequence. When combined with preliminary secondary structure predictions, it is suggested that this algorithm might usefully restrict the search for these specific types of contact in the docking portion of a general folding program.     

iATTRACT: Simultaneous global and local interface optimization for protein–protein docking refinement

Protein‐protein interactions are abundant in the cell but to date structural data for a large number of complexes is lacking. Computational docking methods can complement experiments by providing structural models of complexes based on structures of the individual partners. A major caveat for docking success is accounting for protein flexibility. Especially, interface residues undergo significant conformational changes upon binding. This limits the performance of docking methods that keep partner structures rigid or allow limited flexibility. A new docking refinement approach, iATTRACT, has been developed which combines simultaneous full interface flexibility and rigid body optimizations during docking energy minimization. It employs an atomistic molecular mechanics force field for intermolecular interface interactions and a structure‐based force field for intramolecular contributions. The approach was systematically evaluated on a large protein‐protein docking benchmark, starting from an enriched decoy set of rigidly docked protein–protein complexes deviating by up to 15 Å from the native structure at the interface. Large improvements in sampling and slight but significant improvements in scoring/discrimination of near native docking solutions were observed. Complexes with initial deviations at the interface of up to 5.5 Å were refined to significantly better agreement with the native structure. Improvements in the fraction of native contacts were especially favorable, yielding increases of up to 70%. Proteins 2015; 83:248–258. © 2014 Wiley Periodicals, Inc.     

A Practical Implicit Membrane Potential for NMR Structure Calculations of Membrane Proteins

The highly anisotropic environment of the lipid bilayer membrane imposes significant constraints on the structures and functions of membrane proteins. However, NMR structure calculations typically use a simple repulsive potential that neglects the effects of solvation and electrostatics, because explicit atomic representation of the solvent and lipid molecules is computationally expensive and impractical for routine NMR-restrained calculations that start from completely extended polypeptide templates. Here, we describe the extension of a previously described implicit solvation potential, eefxPot, to include a membrane model for NMR-restrained calculations of membrane protein structures in XPLOR-NIH. The key components of eefxPot are an energy term for solvation free energy that works together with other nonbonded energy functions, a dedicated force field for conformational and nonbonded protein interaction parameters, and a membrane function that modulates the solvation free energy and dielectric screening as a function of the atomic distance from the membrane center, relative to the membrane thickness. Initial results obtained for membrane proteins with structures determined experimentally in lipid bilayer membranes show that eefxPot affords significant improvements in structural quality, accuracy, and precision. Calculations with eefxPot are straightforward to implement and can be used to both fold and refine structures, as well as to run unrestrained molecular-dynamics simulations. The potential is entirely compatible with the full range of experimental restraints measured by various techniques. Overall, it provides a useful and practical way to calculate membrane protein structures in a physically realistic environment.     

Molecular dynamics of sickle and normal hemoglobins

Molecular dynamics (MD) simulations have been carried out for 62.5 ps on crystal structures of deoxy sickle cell hemoglobin (HbS) and normal deoxy hemoglobin (HbA) using the CHARMM MD algorithm, with a time step of 0.001 ps. In the trajectory analysis of the 12.5–62.5 (50 ps) simulation, oscillations of the radius of gyration and solvent-accessible surface area were calculated. HbS exhibited a general contraction during the simulation, while HbA exhibited a nearly constant size. The average deviations of simulated structures from the starting structures were found to be 1.8 Å for HbA and 2.3 Å for HbS. The average rms amplitudes of atomic motions (atomic flexibility) were about 0.7 Å for HbA and about 1.0 Å for HbS. The amplitudes of backbone motion correlate well with temperature factors derived from x-ray crystallography. A comparison of flexibility between the α- and β-chains in both HbA and HbS indicates that the β-chains generally exhibited greater flexibility than the α-chains, and that the HbS β-chains exhibit greater flexibility in the N-terminal and D- and F-helix regions than do those of HbA. The average amplitude of backbone torsional oscillations was about 9°, a value comparable with that of other simulations, with enhanced torsional oscillation occurring primarily at the ends of helices or in loop regions between helices. Comparison of atomic flexibility and torsional oscillation results suggests that the increased β-chain flexibility results from relatively concerted motions of secondary structure elements. The increased flexibility may play an important role in HbS polymerization. Time course analysis of conformational energy of association, hydrogen bonding and hydrophobic bonding (as calculated from solvent accessibility) shows that all three of these factors contribute to the stability of subunit association for both hemoglobins. © 1993 John Wiley & Sons, Inc.     

The double-helical molecular structure of crystalline b-amylose

The crystal structure of the B-polymorph of amylose appears to be based on double-stranded helices. The individual strands are in a right-handed six-fold helical conformation repeating in 20.8 Å and are wound parallel around each other. The steric disposition of O-6 is gt. The double helices pack in a hexagonal unit-cell (a  b  18.50 Å, c (fiber repeat)  10.40 Å, γ  120°), with two helices (12 d-glucose residues) per cell. The helices are packed antiparallel and leave an open channel within a hexagonal array that is filled with water molecules. The reliability of the structure analysis is indicated by R  0.22. The structure of B-amylose is consistent with the diffraction diagrams of B-starches and accounts for the physical properties of such starches.     

Free energies of protein decoys provide insight into determinants of protein stability

We have calculated the stability of decoy structures of several proteins (from the CASP3 models and the Park and Levitt decoy set) relative to the native structures. The calculations were performed with the force field-consistent ES/IS method, in which an implicit solvent (IS) model is used to calculate the average solvation free energy for snapshots from explicit simulations (ESs). The conformational free energy is obtained by adding the internal energy of the solute from the ESs and an entropic term estimated from the covariance positional fluctuation matrix. The set of atomic Born radii and the cavity-surface free energy coefficient used in the implicit model has been optimized to be consistent with the all-atom force field used in the ESs (cedar/gromos with simple point charge (SPC) water model). The decoys are found to have a consistently higher free energy than that of the native structure; the gap between the native structure and the best decoy varies between 10 and 15 kcal/mole, on the order of the free energy difference that typically separates the native state of a protein from the unfolded state. The correlation between the free energy and the extent to which the decoy structures differ from the native (as root mean square deviation) is very weak; hence, the free energy is not an accurate measure for ranking the structurally most native-like structures from among a set of models. Analysis of the energy components shows that stability is attained as a result of three major driving forces: (1) minimum size of the protein-water surface interface; (2) minimum total electrostatic energy, which includes solvent polarization; and (3) minimum protein packing energy. The detailed fit required to optimize the last term may underlie difficulties encountered in recovering the native fold from an approximate decoy or model structure.     

Locating interaction sites on proteins: the crystal structure of thermolysin soaked in 2% to 100% isopropanol

Multiple-solvent crystal structure determination (MSCS) allows the position and orientation of bound solvent fragments to be identified by determining the structure of protein crystals soaked in organic solvents. We have extended this technique by the determination of high-resolution crystal structures of thermolysin (TLN), generated from crystals soaked in 2% to 100% isopropanol. The procedure causes only minor changes to the conformation of the protein, and an increasing number of isopropanol interaction sites could be identified as the solvent concentration is increased. Isopropanol occupies all four of the main subsites in the active site, although this was only observed at very high concentrations of isopropanol for three of the four subsites. Analysis of the isopropanol positions shows little correlation with interaction energy computed using a molecular mechanics force field, but the experimentally determined positions of isopropanol are consistent with the structures of known protein-ligand complexes of TLN.     

An all-atom force field for tertiary structure prediction of helical proteins

We have developed an all-atom free-energy force field (PFF01) for protein tertiary structure prediction. PFF01 is based on physical interactions and was parameterized using experimental structures of a family of proteins believed to span a wide variety of possible folds. It contains empirical, although sequence-independent terms for hydrogen bonding. Its solvent-accessible surface area solvent model was first fit to transfer energies of small peptides. The parameters of the solvent model were then further optimized to stabilize the native structure of a single protein, the autonomously folding villin headpiece, against competing low-energy decoys. Here we validate the force field for five nonhomologous helical proteins with 20-60 amino acids. For each protein, decoys with 2-3 A backbone root mean-square deviation and correct experimental Cbeta-Cbeta distance constraints emerge as those with the lowest energy.     

The Crystal Structure of Glutamine-binding Protein fromEscherichia coli

The crystal structure of the glutamine-binding protein (GlnBP) fromEscherichia coliin a ligand-free “open” conformational state has been determined by isomorphous replacement methods and refined to anR-value of 21.4% at 2.3 Å resolution. There are two molecules in the asymmetric unit, related by pseudo 4-fold screw symmetry. The refined model consists of 3587 non-hydrogen atoms from 440 residues (two monomers), and 159 water molecules. The structure has root-mean-square deviations of 0.013 Å from “deal” bond lengths and 1.5° from “ideal” bond angles.The GlnBP molecule has overall dimensions of approximately 60 Å × 40 Å × 35 Å and is made up of two domains (termed large and small), which exhibit a similar supersecondary structure, linked by two antiparallel β-strands. The small domain contains three α-helices and four parallel and one antiparallel β-strands. The large domain is similar to the small domain but contains two additional α-helices and three more short antiparallel β-strands. A comparison of the secondary structural motifs of GlnBP with those of other periplasmic binding proteins is discussed.A model of the “closed form” GlnBP-Gln complex has been proposed based on the crystal structures of the histidine-binding protein-His complex and “open form” GlnBP. This model has been successfully used as a search model in the crystal structure determination of the “closed form” GlnBP-Gln complex by molecular replacement methods. The model agrees remarkably well with the crystal structure of the Gln-GlnBP complex with root-mean-square deviation of 1.29 Å. Our study shows that, at least in our case, it is possible to predict one conformational state of a periplasmic binding protein from another conformational state of the protein. The glutamine-binding pockets of the model and the crystal structure are compared and the modeling technique is described.     

Free energy determinants of tertiary structure and the evaluation of protein models

We develop a protocol for estimating the free energy difference between different conformations of the same polypeptide chain. The conformational free energy evaluation combines the CHARMM force field with a continuum treatment of the solvent. In almost all cases studied, experimentally determined structures are predicted to be more stable than misfolded "decoys." This is due in part to the fact that the Coulomb energy of the native protein is consistently lower than that of the decoys. The solvation free energy generally favors the decoys, although the total electrostatic free energy (sum of Coulomb and solvation terms) favors the native structure. The behavior of the solvation free energy is somewhat counterintuitive and, surprisingly, is not correlated with differences in the burial of polar area between native structures and decoys. Rather. the effect is due to a more favorable charge distribution in the native protein, which, as is discussed, will tend to decrease its interaction with the solvent. Our results thus suggest, in keeping with a number of recent studies, that electrostatic interactions may play an important role in determining the native topology of a folded protein. On this basis, a simplified scoring function is derived that combines a Coulomb term with a hydrophobic contact term. This function performs as well as the more complete free energy evaluation in distinguishing the native structure from misfolded decoys. Its computational efficiency suggests that it can be used in protein structure prediction applications, and that it provides a physically well-defined alternative to statistically derived scoring functions.     

Solution structure of the DNA binding domain of AraC protein

We report the solution structure of the DNA binding domain of the Escherichia coli regulatory protein AraC determined in the absence of DNA. The 20 lowest energy structures, determined on the basis of 1507 unambiguous nuclear Overhauser restraints and 180 angle restraints, are well resolved with a pair wise backbone root mean square deviation of 0.7 Å. The protein, free of DNA, is well folded in solution and contains seven helices arranged in two semi‐independent sub domains, each containing one helix‐turn‐helix DNA binding motif, joined by a 19 residue central helix. This solution structure is discussed in the context of extensive biochemical and physiological data on AraC and with respect to the DNA‐bound structures of the MarA and Rob homologs. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

Ab initio folding of extended α‐helix: A theoretical study about the role of electrostatic polarization in the folding of helical structures

In this work, we report the ab initio folding of three different extended helical peptides namely 2khk, N36, and C34 through conventional molecular dynamics simulation at room temperature using implicit solvation model. Employing adaptive hydrogen bond specific charge (AHBC) scheme to account for the polarization effect of hydrogen bonds established during the simulation, the effective folding of the three extended helices were observed with best backbone RMSDs in comparison to the experimental structures over the helical region determined to be 1.30 Å for 2khk, 0.73 Å for N36 and 0.72 Å for C34. In this study, 2khk will be used as a benchmark case serving as a means to compare the ability of polarized (AHBC) and nonpolarized force field in the folding of an extended helix. Analyses conducted revealed the ability of the AHBC scheme in effectively folding the extended helix by promoting helix growth through the stabilization of backbone hydrogen bonds upon formation during the folding process. Similar observations were also noted when AHBC scheme was employed during the folding of C34 and N36. However, under Amber03 force field, helical structures formed during the folding of 2khk was not accompanied by stabilization thus highlighting the importance of electrostatic polarization in the folding of helical structures. Proteins 2013. © 2013 Wiley Periodicals, Inc.     

Using a Hydrophobic Contact Potential to Evaluate Native and Near-native Folds Generated by Molecular Dynamics Simulations

There are several knowledge-based energy functions that can distinguish the native fold from a pool of grossly misfolded decoys for a given sequence of amino acids. These decoys, which are typically generated by mounting, or “threading”, the sequence onto the backbones of unrelated protein structures, tend to be non-compact and quite different from the native structure: the root-mean-squared (RMS) deviations from the native are commonly in the range of 15 to 20 Å. Effective energy functions should also demonstrate a similar recognition capability when presented with compact decoys that depart only slightly in conformation from the correct structure (i.e. those with RMS deviations of ∼5 Å or less). Recently, we developed a simple yet powerful method for native fold recognition based on the tendency for native folds to form hydrophobic cores. Our energy measure, which we call the hydrophobic fitness score, is challenged to recognize the native fold from 2000 near-native structures generated for each of five small monomeric proteins. First, 1000 conformations for each protein were generated by molecular dynamics simulation at room temperature. The average RMS deviation of this set of 5000 was 1.5 Å. A total of 323 decoys had energies lower than native; however, none of these had RMS deviations greater than 2 Å. Another 1000 structures were generated for each at high temperature, in which a greater range of conformational space was explored (4.3 Å average RMS deviation). Out of this set, only seven decoys were misrecognized. The hydrophobic fitness energy of a conformation is strongly dependent upon the RMS deviation. On average our potential yields energy values which are lowest for the population of structures generated at room temperature, intermediate for those produced at high temperature and highest for those constructed by threading methods. In general, the lowest energy decoy conformations have backbones very close to native structure. The possible utility of our method for screening backbone candidates for the purpose of modelling by side-chain packing optimization is discussed.     

Using a SMALP platform to determine a sub-nm single particle cryo-EM membrane protein structure

The field of membrane protein structural biology has been revolutionized over the last few years with a number of high profile structures being solved using cryo-EM including Piezo, Ryanodine receptor, TRPV1 and the Glutamate receptor. Further developments in the EM field hold the promise of even greater progress in terms of greater resolution, which for membrane proteins is still typically within the 4–7 Å range. One advantage of a cryo-EM approach is the ability to study membrane proteins in more “native” like environments for example proteoliposomes, amphipols and nanodiscs. Recently, styrene maleic acid co-polymers (SMA) have been used to extract membrane proteins surrounded by native lipids (SMALPs) maintaining a more natural environment. We report here the structure of the Escherichia coli multidrug efflux transporter AcrB in a SMALP scaffold to sub-nm resolution, with the resulting map being consistent with high resolution crystal structures and other EM derived maps. However, both the C-terminal helix (TM12) and TM7 are poorly defined in the map. These helices are at the exterior of the helical bundle and form the greater interaction with the native lipids and SMA polymer and may represent a more dynamic region of the protein. This work shows the promise of using an SMA approach for single particle cryo-EM studies to provide sub-nm structures.     

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.     

A family of double helices of alternating poly(gamma-benzyl-D-L-glutamate), a stereochemical model for gramicidin A.

Poly(γ-benzyl-d-l-glutamate) with strict alternation of l and d residues is found to exist, in addition to the α_DL and π_DL^4.4 helical structures already described (Heitz et al., 1975a), in four more helical structures. Models based on double helices made of antiparallel strands are proposed for all four structures, based on infrared, X-ray and electron diffraction data. These double helices are, like the single-stranded π_DL helices, specific to polypeptides with a strict stereosequence of alternating l and d residues. The diameter of the helical core of three of these helices appears to depend on the dimensions of the solvent molecules. Conformational angles (located in the β regions) and atomic co-ordinates determined by conformational energy analysis are given for the four structures. Experimental conditions used to obtain these helices, and to induce transconformations between the various helical structures of PBd-lG are described. The present investigations on PBd-lG help to make more precise the structure and geometry of models proposed (Veatch et al., 1974) for the antibiotic gramicidin A.