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.     

A 175-psec molecular dynamics simulation of camphor-bound cytochrome P-450cam.

The structure and internal motions of cytochrome P-450cam, a monooxygenase heme enzyme with 414 amino acid residues, with camphor bound at the active site have been evaluated on the basis of a 175-psec molecular dynamics simulation carried out at 300 K. All hydrogen atoms were explicitly modeled, and 204 crystallographic waters were included in the simulation. Based on an analysis of the time course of the trajectory versus potential energy, root mean square deviation, radius of gyration, and hydrogen bonding, the simulation was judged to be stable and representative of the average experimental structure. The averaged structural properties of the enzyme were evaluated from the final 135 psec of the simulation. The average atomic displacement from the X-ray structure was 1.39 A for all heavy atoms and 1.17 A for just C-alpha atoms. The average root-mean-square (rms) fluctuations of all heavy atoms and backbone atoms were 0.42 and 0.37 A, respectively. The computed rms fluctuations were in reasonable agreement with the experimentally determined temperature factors. All 13 segments of alpha-helix and 5 segments of beta-sheet were well preserved with the exception of the N-terminal half of helix F which alternated between an alpha-helix and a 310-helix. In addition there were in general only small variations in the relative orientation of adjacent alpha-helices. The rms fluctuations of the backbone dihedral angles in the secondary structure elements were almost uniformly smaller, with the fluctuation in alpha-helices and beta-sheets, 31 and 10% less, respectively, than those in nonsecondary structure regions. The reported crystal structure contains kinks in both helices C and I. In the simulation, both of these regions showed high mobility and large deviations from their starting positions. Since the kink in the I helix is at the oxygen binding site, these motions may have mechanistic implications.     

The folding energy landscape of the dimerization domain of Escherichia coli Trp repressor: a joint experimental and theoretical investigation

Enhanced structural insights into the folding energy landscape of the N-terminal dimerization domain of Escherichia coli tryptophan repressor, [2-66]2 TR, were obtained from a combined experimental and theoretical analysis of its equilibrium folding reaction. Previous studies have shown that the three intertwined helices in [2-66]2 TR are sufficient to drive the formation of a stable dimer for the full-length protein, [2-107]2 TR. The monomeric and dimeric folding intermediates that appear during the folding reactions of [2-66]2 TR have counterparts in the folding mechanism of the full-length protein. The equilibrium unfolding energy surface on which the folding and dimerization reactions occur for [2-66]2 TR was examined with a combination of native-state hydrogen exchange analysis, pepsin digestion and matrix-assisted laser/desorption mass spectrometry performed at several concentrations of protein and denaturant. Peptides corresponding to all three helices in [2-66]2 TR show multi-layered protection patterns consistent with the relative stabilities of the dimeric and monomeric folding intermediates. The observation of protection exceeding that offered by the dimeric intermediate in segments from all three helices implies that a segment-swapping mechanism may be operative in the monomeric intermediate. Protection greater than that expected from the global stability for a single amide hydrogen in a peptide from the C-helix possibly and another from the A-helix may reflect non-random structure, possibly a precursor for segment swapping, in the urea-denatured state. Native topology-based model simulations that correspond to a funnel energy landscape capture both the monomeric and dimeric intermediates suggested by the HX MS data and provide a rationale for the progressive acquisition of secondary structure in their conformational ensembles.     

PackHelix: a tool for helix-sheet packing during protein structure prediction

The three‐dimensional structure of a protein is organized around the packing of its secondary structure elements. Predicting the topology and constructing the geometry of structural motifs involving α‐helices and/or β‐strands are therefore key steps for accurate prediction of protein structure. While many efforts have focused on how to pack helices and on how to sample exhaustively the topologies and geometries of multiple strands forming a β‐sheet in a protein, there has been little progress on generating native‐like packings of helices on sheets. We describe a method that can generate the packing of multiple helices on a given β‐sheet for αβα sandwich type protein folds. This method mines the results of a statistical analysis of the conformations of αβ₂ motifs in protein structures to provide input values for the geometric attributes of the packing of a helix on a sheet. It then proceeds with a geometric builder that generates multiple arrangements of the helices on the sheet of interest by sampling through these values and performing consistency checks that guarantee proper loop geometry between the helices and the strands, minimal number of collisions between the helices, and proper formation of a hydrophobic core. The method is implemented as a module of ProteinShop. Our results show that it produces structures that are within 4–6 Å RMSD of the native one, regardless of the number of helices that need to be packed, though this number may increase if the protein has several helices between two consecutive strands in the sequence that pack on the sheet formed by these two strands. Proteins 2011; Published 2011 Wiley‐Liss, Inc.     

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.     

Conformational dynamics of cytochrome c: correlation to hydrogen exchange.

We study the dynamical fluctuations of horse heart cytochrome c by molecular dynamics (MD) simulations in aqueous solution, at four temperatures: 300 K, 360 K, 430 K, and 550 K. Each simulation covers a production time of at least 1.5 nanoseconds (ns). The conformational dynamics of the system is analyzed in terms of collective motions that involve the whole protein, and local motions that involve the formation and breaking of intramolecular hydrogen bonds. The character of the MD trajectories can be described within the framework of rugged energy landscape dynamics. The MD trajectories sample multiple conformational minima, with basins in protein conformational space being sampled for a few hundred picoseconds. The trajectories of the system in configurational space can be described in terms of diffusion of a particle in real space with a waiting time distribution due to partial trapping in shallow minima. As a consequence of the hierarchical nature of the dynamics, the mean square displacement autocorrelation function, <|x(t) - x(0)|2>, exhibits a power law dependence on time, with an exponent of around 0.5 for times shorter than 100 ps, and an exponent of 1.75 for longer times. This power law behavior indicates that the system exhibits suppressed diffusion (sub-diffusion) in sampling of configurational space at time scales shorter than 100 ps, and enhanced (super-diffusion) at longer time scales. The multi-basin feature of the trajectories is present at all temperatures simulated. Structural changes associated with inter-basin displacements correspond to collective motions of the Omega loops and coiled regions and relative motions of the alpha-helices as rigid bodies. Similar motions may be involved in experimentally observed amide hydrogen exchange. However, some groups showing large correlated motions do not expose the amino hydrogens to the solvent. We show that large fluctuations are not necessarily correlated to hydrogen exchange. For example, regions of the proteins forming alpha helices and turns show significant fluctuations, but as rigid bodies, and the hydrogen bonds involved in the formation of these structures do not break in proportion to these fluctuations. Proteins 1999;36:175-191. Published 1999 Wiley-Liss, Inc.     

Characterization of "native" apomyoglobin by molecular dynamics simulation.

We have used molecular dynamics simulation methods to study the structure and fluctuations of "native" apomyoglobin in aqueous solution for a period of greater than 0.5 nanosecond. This work was motivated by the recent attempts of Hughson et al. to characterize the structure and motion of both this molecule and the less compact, acid stabilized I stage, using methods of pulsed H/2H exchange. The study of these systems provides new insights into protein folding intermediates and our simulation has yielded a detailed model for structure and fluctuations in apomyoglobin which complements the experimental studies. We find that local (short-time) fluctuations agree well with fluctuations observed for the holoprotein in aqueous solution, as well as results from the crystallographic B-factors. In addition, the structural features we observe for native apomyoglobin are very similar to the holoprotein, in basic agreement with the findings of Hughson et al. By examining larger-scale motions, developing only over timescales in excess of a 100 picoseconds, we are able to identify conformationally "labile" and "non-labile" regions within native apomyoglobin. These regions correspond extremely well to those identified in the nuclear magnetic resonance experiments as unstable and stable "folding subdomains" in the I state of apomyoglobin. Overall we find that helices A, B, E, G and H show the least amount of motion and helices C, D and F move substantially over the timescales examined. The major motions, and the primary difference between the holo and apo structures as we have observed them, are due to the shifting motion of helices C, D and F into the vacant heme cavity. We also find that motions at the interface of helical segments can be large, with one important exception being the chain segment connecting helices G and H. This segment of chain interacts with the conformationally "non-labile" helix A to form a relatively rigid subdomain composed of helices A, G and H. We believe that these findings provide direct support for the suggestion of Hughson et al. that helices A, G and H constitute a compact subdomain that remains in a native-like conformation as the protein begins to unfold in environments of decreasing pH.     

Analysis and evaluation of channel models: simulations of alamethicin

Alamethicin is an antimicrobial peptide that forms stable channels with well-defined conductance levels. We have used extended molecular dynamics simulations of alamethicin bundles consisting of 4, 5, 6, 7, and 8 helices in a palmitoyl-oleolyl-phosphatidylcholine bilayer to evaluate and analyze channel models and to link the models to the experimentally measured conductance levels. Our results suggest that four helices do not form a stable water-filled channel and might not even form a stable intermediate. The lowest measurable conductance level is likely to correspond to the pentamer. At higher aggregation numbers the bundles become less symmetrical. Water properties inside the different-sized bundles are similar. The hexamer is the most stable model with a stability comparable with simulations based on crystal structures. The simulation was extended from 4 to 20 ns or several times the mean passage time of an ion. Essential dynamics analyses were used to test the hypothesis that correlated motions of the helical bundles account for high-frequency noise observed in open channel measurements. In a 20-ns simulation of a hexameric alamethicin bundle, the main motions are those of individual helices, not of the bundle as a whole. A detailed comparison of simulations using different methods to treat long-range electrostatic interactions (a twin range cutoff, Particle Mesh Ewald, and a twin range cutoff combined with a reaction field correction) shows that water orientation inside the alamethicin channels is sensitive to the algorithms used. In all cases, water ordering due to the protein structure is strong, although the exact profile changes somewhat. Adding an extra 4-nm layer of water only changes the water ordering slightly in the case of particle mesh Ewald, suggesting that periodicity artifacts for this system are not serious.     

Picosecond timescale rigid-helix and side-chain motions in deoxymyoglobin

The contribution of rigidbody motions to the atomic trajectories in a 100 ps molecular dynamics simulation of deoxymyoglobin is examined. Two typesof rigid-body motions are considered: one in which the helices are rigid units and one in which the side-chains are rigid units. Using a quaternionbased algorithm, fits of the rigid reference structures are made to each time frame of the simulation to derive trajectories of the rigid-body motions. The fitted trajectories are analysed in terms of atomic position fluctuations, mean-square displacements as a function of time, velocity autocorrelation functions and densities of states. The results are compared with the corresponding quantities calculated from the full trajectory. The relative contribution of the rigid helix motions to the helix atom dynamics depends on which quantity is examined and on which subset of atoms is chosen: rigid-helix motions contribute 86% of the rms helix backbone atomic position fluctuations, but 30% of the helix,: atom (backbone and side-chain) mean square displacements and only 1.1% of total kinetic energy. Only very low-frequency motions contribute to the rigid-helix dynamics; the rigid-body analysis allows characteristic rigid-helix vibrations to be identified and described. Treating the side-chains as rigid bodies is foundto be an excellent approximation to both their diffusive and vibrationalmean-square displacements: 96% of side-chain atom mean-square displacements originate from rigid side-Chain motions. However, the errors in theside-chain atomic positional fits are not always small. An analysis is madeof factors contributing to the positional error for different types of side-chain. © Wiley-Liss, Inc.     

Molecular-dynamics simulation of phenylalanine transfer RNA. II. Amplitudes, anisotropies, and anharmonicities of atomic motions

The atomic motions from a molecular-dynamics simulation of yeast tRNA^Phe are analyzed and compared with those observed in protein simulations. In general, the tRNA motions are of larger amplitude, they are more anisotropic, and they arise from potentials of mean force that are more anharmonic than in the protein case. In both cases, the amplitudes are largest for atoms on the surface of the molecules. On the other hand, the most anisotropic and anharmonic atomic motions are generally found in the interior of the tRNA, while they are found on the surface of the protein. These differences are discussed in terms of the differences in structure between nucleic acids and proteins.     

Folding of Globular Proteins by Energy Minimization and Monte Carlo Simulations with Hydrophobic Surface Area Potentials

We describe an efficient method to calculate analytically the solvent accessible surface areas and their gradients in proteins for empirical force field calculations on serial and parallel computers. In an application to the small three helix bundle protein Er-10, energy minimizations and Monte Carlo simulations were performed with the empirical ECEPP/2 force field, which was extended by a protein solvent interaction term. We show that the NMR structure is stable when refined with the force field including the protein solvent interaction term, but large structural deviations are observed in energy minimization in vacuo. When we started from random structures with preformed helices and maintained the helical segments by dihedral angle constraints, the final structures with the lowest energies resembled the native form. The root-mean-square deviations for the backbone atoms of the three helices compared to the experimentally determined structure was 3 Å to 4 Å.     

Molecular dynamics of individual alpha-helices of bacteriorhodopsin in dimyristol phosphatidylocholine. I. Structure and dynamics.

Understanding the role of the lipid bilayer in membrane protein structure and dynamics is needed for tertiary structure determination methods. However, the molecular details are not well understood. Molecular dynamics computer calculations can provide insight into these molecular details of protein:lipid interactions. This paper reports on 10 simulations of individual alpha-helices in explicit lipid bilayers. The 10 helices were selected from the bacteriorhodopsin structure as representative alpha-helical membrane folding components. The bilayer is constructed of dimyristoyl phosphatidylcholine molecules. The only major difference between simulations is the primary sequence of the alpha-helix. The results show dramatic differences in motional behavior between alpha-helices. For example, helix A has much smaller root-mean-squared deviations than does helix D. This can be understood in terms of the presence of aromatic residues at the interface for helix A that are not present in helix D. Additional motions are possible for the helices that contain proline side chains relative to other amino acids. The results thus provide insight into the types of motion and the average structures possible for helices within the bilayer setting and demonstrate the strength of molecular simulations in providing molecular details that are not directly visualized in experiments.     

Essential dynamics of helices provide a functional classification of EF-hand proteins

Low energy modes have been calculated for the largest possible number of available representatives (>150) of EF-hand domains belonging to different members of the calcium-binding EF-hand protein superfamily. These proteins are the major actors in signal transduction. The latter, in turn, relies on the dynamical properties of the systems, in particular on the relative movements of the four helices characterizing each EF-hand domain upon calcium binding. The peculiar structural and dynamical features of this protein superfamily are systematically investigated by a novel approach, where the lowest energy (essential) modes are described in the space of the six interhelical angles among the four helices constituting the EF-hand domain. The modes, obtained through a general and transferable coarse-graining scheme, identify the easy directions of helical motions. It is found that, for most proteins, the two lowest energy modes are sufficient to capture most of the helices' fluctuation dynamics. Strikingly, the comparison of such modes for all possible pairs of EF-hand domain representatives reveals that only few easy directions are preferred within this large protein superfamily. This enables us to introduce a novel dynamics-based classification of EF-hand domains that complements existing structure-based characterizations from an unexplored biological perspective.     

Molecular dynamics simulation of the M2 helices within the nicotinic acetylcholine receptor transmembrane domain: structure and collective motions

Multiple nanosecond duration molecular dynamics simulations were performed on the transmembrane region of the Torpedo nicotinic acetylcholine receptor embedded within a bilayer mimetic octane slab. The M2 helices and M2-M3 loop regions were free to move, whereas the outer (M1, M3, M4) helix bundle was backbone restrained. The M2 helices largely retain their hydrogen-bonding pattern throughout the simulation, with some distortions in the helical end and loop regions. All of the M2 helices exhibit bending motions, with the hinge point in the vicinity of the central hydrophobic gate region (corresponding to residues alphaL251 and alphaV255). The bending motions of the M2 helices lead to a degree of dynamic narrowing of the pore in the region of the proposed hydrophobic gate. Calculations of Born energy profiles for various structures along the simulation trajectory suggest that the conformations of the M2 bundle sampled correspond to a closed conformation of the channel. Principal components analyses of each of the M2 helices, and of the five-helix M2 bundle, reveal concerted motions that may be relevant to channel function. Normal mode analyses using the anisotropic network model reveal collective motions similar to those identified by principal components analyses.     

A new protein folding algorithm based on hydrophobic compactness: Rigid Unconnected Secondary Structure Iterative Assembly (RUSSIA). II: Applications

The RUSSIA procedure (Rigid Unconnected Secondary Structure Iterative Assembly) produces structural models of cores of small- and medium-sized proteins. Loops are omitted from this treatment and regular secondary structures are reduced to points, the centers of their hydrophobic faces. This methodology relies on the maximum compactness of the hydrophobic residues, as described in detail in Part I. Starting data are the sequence and the predicted limits and natures of regular secondary structures (alpha or beta). Helices are treated as rigid cylinders, whereas beta-strands are collectively taken into account within beta-sheets modeled by helicoid surfaces. Strands are allowed to shift along their mean axis to allow some flexibility and the alpha-helices can be placed on either side of beta-sheets. Numerous initial conformations are produced by discrete rotations of the helices and sheets around the direction going from the center of their hydrophobic face to the global center of the protein. Selection of proposed models is based upon a criterion lying on the minimization of distances separating hydrophobic residues belonging to different regular secondary structures. The procedure is rapid and appears to be robust relative to the quality of starting data (nature and length of regular secondary structures). This dependence of the quality of the model on secondary structure prediction and in particular the beta-sheet topology, is one of the limits of the present algorithm. We present here some results for a set of 12 proteins (alpha, beta and alpha/beta classes) of lengths 40-166 amino acids. The r.m.s. deviations for core models with respect to the native proteins are in the range 1.4-3.7 A.     

A model for the coupling of alpha-helix and tertiary contact formation

Peptides corresponding to excised alpha-helical segments of natural proteins can spontaneously form helices in solution. However, peptide helices are usually substantially less stable in solution than in the structural context of a folded protein, because of the additional interactions possible between helices in a protein. Such interactions can be thought of as coupling helix formation and tertiary contact formation. The relative energetic contributions of the two processes to the total energy of the folded state of a protein is a matter of current debate. To investigate this balance, an extended helix-coil model (XHC) that incorporates both effects has been constructed. The model treats helix formation with the Lifson-Roig formalism, which describes helix initiation and propagation through cooperative local interactions. The model postulates an additional parameter representing participation of a site in a tertiary contact. In the model, greater helix stability can be achieved through combinations of these short-range and long-range interactions. For instance, stronger tertiary contacts can compensate for helices with little intrinsic stability. By varying the strength of the nonlocal interactions, the model can exhibit behavior consistent with a variety of qualitative models describing the relative importance of secondary and tertiary structure. Moreover, the model is explicit in that it can be used to fit experimental data to individual peptide sequences, providing a means to quantify the two contributions on a common energetic basis.     

Conformation of alpha zeins in solid state by Fourier transform IR

The major maize storage proteins (alpha zeins) are deposited as an insoluble mass in the protein bodies of the endosperm. Because they are insoluble in water, most structural studies are performed in alcohol solutions. To solve the question raised by several authors about denaturation of the alpha zein structure by alcohol, we analyze the secondary structure of alpha zeins prepared with and without solubilization in alcohol (corn gluten meal and protein bodies with high concentrations of alpha zeins and traces of beta zeins). The secondary structures of alpha zeins are analyzed in the solid state by Fourier transform IR spectroscopy (FTIR) in KBr pellets and solid-state 13C-NMR spectroscopy. The proportion of secondary structures obtained by FTIR of alpha zeins prepared with and without solubilization in alcohol yield almost identical proportions of alpha helices and beta sheets. The proportion of alpha helices (43%) agrees with that measured by circular dichroism in an alcohol solution. However, the proportion of beta sheets (28%) is higher than the one measured by the same technique. Gluten and protein body samples with high beta zein content showed higher beta sheet and lower alpha helix proportions than that obtained for alpha zein preparations. The solid-state 13C-NMR spectra show the carbonyl peak for the alpha zeins at delta 176 and for the sample rich in beta zeins at delta 172, which demonstrates the presence of a high content of alpha helices and beta sheets, respectively. These results indicate that alcohol solubilization does not affect the conformation of alpha zeins, validating the secondary structure measurements in solution.