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Conformation and aggregation of M13 coat protein studied by molecular dynamics.

Molecular dynamics (MD) simulations are performed on M13 coat protein, a small membrane protein for which both alpha- and beta-structures have been suggested. The simulations are started from initial conformations that are either monomers or dimers of alpha-helices or U-shaped beta-sheets. The lipid bilayer is represented by a hydrophobic potential. The results are analyzed in terms of stability, energy and secondary structure. The U-shaped beta-structure changes from a planar to a twisted form with larger twist for the monomer than the dimer. The beta-sheet is much more flexible than the alpha-helix as monitored by the root mean square (rms) fluctuations of the C alpha atoms. A comparison of the energies after 100 ps MD simulation shows that of the monomers, the alpha-helix has the lowest energy. The energy difference between alpha- and beta-structures decreases from 266 kJ/mol to 148 kJ/mol, when going from monomers to dimers. It is expected that this difference will decrease with higher aggregation numbers.

Amino Acid Sequence

Conformational transition of an alpha-helix studied by molecular dynamics.

Molecular dynamics simulations were performed on a 20-residue polyalanine helix and a spontaneous transition from a kinked to a straight conformation was observed. The kinetics of the transition was analyzed within the framework of the Kramers model for chemical reactions and within a random walk model. The Kramers model which is based on diffusion along a one-dimensional reaction pathway and the crossing of an energy barrier was found to be inadequate. Instead, a random walk model based on diffusion in the high-dimensional phase space of the system was found to be compatible with the data. The high dimensionality of the phase space permits the system to circumvent high energy barriers and diffuse rapidly at about constant energy, but decelerates the reaction since in the labyrinth of pathways the transition state is reached rarely.

Biophysical Phenomena

Molecular-dynamics investigation of molecular flexibility in ligand binding.

The molecular flexibility of an inhibitor in ligand-binding process has been investigated by the mass-weighted molecular-dynamics simulation, a computational method adopted from the standard molecular-dynamics simulation and one by which the conformational space of a biomolecular system over potential energy barriers can be sampled effectively. The bimolecular complex of the aspartyl proteinase from Rhizopus chinensis, rhizopuspepsin, and an octapeptide inhibitor was previously studied in a mass-weighted molecular-dynamics simulation; the study has been extended for investigating the molecular flexibility in ligand binding. A series of mass-weighted molecular-dynamics simulations was carried out in which libration of the inhibitor dihedral angles was parametrically controlled, and threshold values of dihedral angle libration amplitudes were observed from monitoring the sampling of the enzyme binding pocket by the inhibitor in the simulations. The computational results are consistent with the general notion of molecular-flexibility requirement for ligand binding; the freedom of dihedral rotations of side-chain groups was found to be particularly important for ligand binding. Thus the critical degree of molecular flexibility which would contribute to effective enzyme inhibition can be obtained precisely from the modified molecular-dynamics simulations; the procedure described herein represents a first step toward providing quantitative measures of such a molecular-flexibility index for inhibitor molecules that have been otherwise targeted for optimal protein-ligand interactions.

Amino Acid Sequence

Accessible conformations of melanin-concentrating hormone: a molecular dynamics approach.

Molecular dynamics simulations have been used to search for the accessible conformations of the melanin-concentrating hormone (MCH). The studies have been performed on native MCH and two of its peptide fragments, a cyclic MCH(5-14) fragment and a linear MCH(5-14) fragment. An analysis of the molecular dynamics trajectories of the three peptides indicates that two regions of the peptide have characteristic conformational properties that may be important for the biological activity. One is a region around Gly8, which is conformationally mobile, and the other is around Pro13, which shows unusual rigidity. The molecular dynamics simulation results are discussed in terms of backbone structural features like beta turns, side-chain interactions, and orientations of the disulfide bridge. The results of this analysis are used to suggest new analogues that will modify the conformational features of the peptide and further define the conformational requirements for activity. Finally, the results are related to nmr studies of the peptide and reveal agreements between the experimental nuclear Overhauser effect constraints and some of the accessible conformations obtained from the simulation.

Amino Acid Sequence

Cooperative ligand reorientations in cytochrome c3: a molecular dynamics simulation.

Molecular dynamics simulations of a tetraheme cytochrome c3 were performed to investigate dynamic aspects of the motion of the axial heme iron ligands. It was found that persistent transitions between alternate axial imidazole orientations of the histidine incorporated in the CXXCH heme binding sequence occurred via correlated motions. The correlated motions involved virtually all of the atoms comprising the polypeptide backbone of the heme binding sequence as well as the histidine imidazole side-chain.

Amino Acid Sequence

Conformational space of alpha 1-4 glycosidic linkage: a molecular dynamics study.

Molecular Dynamics simulations have been carried out for 100 ps on crystal structure of beta-cyclodextrin in vacuo and with explicit inclusion of solvent at constant pressure and constant temperature using the GROMOS MD algorithm, with a time step of 0.005 ps. The conformational space of the glycosidic linkage was studied by calculating two virtual dihedrals connecting the successive glucose units for the 2000 structures saved during the two simulations. Three preferred regions for alpha 1-4 glycosidic linkage were found in both the simulations. The use of these virtual dihedral angles in representing the glycosidic linkage is also brought out from these studies.

Algorithms

The conformational behaviour of complexes of alpha-cyclodextrin with p-chlorophenol and p-hydroxybenzoic acid in water as studied by molecular dynamics simulations.

Molecular dynamics simulations were performed to obtain information about the conformational behaviour and stabilization of alpha-cyclodextrin (alpha CD) complexes in water. Simulations of p-chlorophenol and p-hydroxybenzoic acid in alpha CD showed that the complex is a very flexible system. The guest compound rotates inside the cavity and partly moves in and out. alpha CD continuously adapts its conformation to the orientation of the guest compound (or vice versa): the hexagon of the glycosidic oxygen atoms is stretched parallel to the plane of the aromatic ring of the guest compound during 80% of the simulation. This suggests that Van der Waals interactions play an important role in the stabilization of the complex. Each intramolecular hydrogen bond between neighbouring glucose units is formed during 30-80% of the simulation. Hydrogen bonds between alpha CD and the guest compound, on the other hand, are rarely formed. Thus, intermolecular hydrogen bonding seems to play a minor role in the stabilization of alpha CD complexes.

Chlorophenols

Cholesterol in model membranes. A molecular dynamics simulation.

Molecular dynamics simulations of a model membrane with inserted cholesterol molecules have been performed to study the perturbing influence of cholesterol. In the fluid phase of a lipid bilayer at 13 mol% concentration of cholesterol, local ordering of the hydrocarbon chains is induced. This perturbation decays with the distance from the cholesterol, and the effect extends 1.25 nm. It can be monitored in several ways, e.g., by an order parameter corresponding to deuterium nuclear magnetic resonance quadrupolar splittings, by the fraction of gauche bonds, or by the local bilayer thickness. At constant surface density, the local ordering is accompanied by disordering of the bulk phase, and, consequently, the net ordering effect is small. After compressing the system laterally in accordance with experimentally known surface areas, the bulk order parameters agree with those of a pure system, and the average order parameters are in accordance with experimental data. The necessity for this lateral compression is supported by calculated lateral pressures. At lower cholesterol concentration (3%), no direct perturbing effect is observed. A smaller lateral pressure than in a pure system indicates that the system with cholesterol is expected to have a smaller surface area, which would result in an increase of the order parameters, thus accounting for the experimental observations. The lack of spatial variation is, however, puzzling and may indicate a cooperative ordering effect.

Cholesterol

Binding of substrate CO2 to the active site of human carbonic anhydrase II: a molecular dynamics study.

Molecular dynamics has been used to study binding of substrate CO2 to the active site of human carbonic anhydrase II. Three potential CO2 binding sites have been located. The first is at the active-site hydrophobic pocket (the catalytically productive site), where CO2 is approximately 3.5 A from the zinc ion and interacts with His-94, His-119, Val-121, Val-143, Leu-198, Thr-199, the zinc ion, and the zinc-bound hydroxide ion. The second CO2 binding site is approximately 6 A from the zinc ion, where CO2 interacts with His-64, His-94, Leu-198, Thr-200, Pro-201, Pro-202, and some active-site water molecules. The third CO2 binding site is approximately 10 A from the zinc ion, is largely solvated by water molecules, and interacts with His-64, Asn-67, and Gln-92. At these three CO2 binding sites, the CO2 molecule is highly localized (the average Zn-CO2 distance fluctuation is approximately 1 A) and favors the linear binding orientation toward the zinc ion. This linear binding orientation of CO2 and its electrostatic interaction with the zinc ion direct diffusion of CO2 toward the zinc ion and facilitate the nucleophilic attack from O of the zinc-bound OH- to C of CO2 in the productive hydrophobic binding site. Finally, the two CO2 binding sites outside the hydrophobic binding pocket, which may represent two intermediate states along the CO2 binding pathway, could play important roles as a CO2 relay.

Amino Acid Sequence

Real-time interactive frequency filtering of molecular dynamics trajectories.

Molecular dynamics simulations of atomic motion in protein and nucleic acid molecules must be done on a femtosecond time-scale. Much of this rapid motion is unimportant for the slower changes that are most relevant to biological function (conformational changes, substrate binding, protein folding). The high-frequency motion makes simulations computationally expensive. More importantly, the high frequencies obscure visualization of the relevant dynamics processes. Sessions, Dauber-Osguthorpe and Osguthorpe presented a method for removing high-frequency motions from atomic co-ordinates of trajectories generated by simulation. While that study used fast Fourier methods and emphasized the use of filtering for analysis of trajectories, this communication describes a new method that makes it much easier to use frequency filtering in programs that display trajectories as a sequence of moving images. Tests of the method on systems extending from pure water to proteins and nucleic acid molecules in vacuo and in solution have demonstrated its general utility. Impressed with the power and simplicity of the new method, we wish to present it in sufficient detail to allow others to implement it themselves.

Fourier Analysis

Conformation and fluctuations of free stefin B: a molecular dynamics study.

Molecular dynamics study was performed on the cysteine proteinase inhibitor stefin B. Structure of inhibitor from the complex with papain was used as a starting point. Amino terminal "trunk" of the inhibitor which lies extended along the cleft of the enzyme in the complex, folded onto the body of inhibitor during MD simulation, thereby reducing the total and particularly hydrophobic surface exposed to the solvent. This effect counterbalances hydrophobic contribution of the "trunk" and explains why its deletion in stefin B and related inhibitors doesn't reduce the dissociation constant. The rest of stefin B conformation is conserved together with main chain hydrogen bonds. Fluctuations of C alpha atoms resembles crystallographic B factors with exception of residues in contact with enzyme.

Chemical Phenomena

Molecular dynamics studies of a DNA-binding protein: 2. An evaluation of implicit and explicit solvent models for the molecular dynamics simulation of the Escherichia coli trp repressor.

Although aqueous simulations with periodic boundary conditions more accurately describe protein dynamics than in vacuo simulations, these are computationally intensive for most proteins. Trp repressor dynamic simulations with a small water shell surrounding the starting model yield protein trajectories that are markedly improved over gas phase, yet computationally efficient. Explicit water in molecular dynamics simulations maintains surface exposure of protein hydrophilic atoms and burial of hydrophobic atoms by opposing the otherwise asymmetric protein-protein forces. This properly orients protein surface side chains, reduces protein fluctuations, and lowers the overall root mean square deviation from the crystal structure. For simulations with crystallographic waters only, a linear or sigmoidal distance-dependent dielectric yields a much better trajectory than does a constant dielectric model. As more water is added to the starting model, the differences between using distance-dependent and constant dielectric models becomes smaller, although the linear distance-dependent dielectric yields an average structure closer to the crystal structure than does a constant dielectric model. Multiplicative constants greater than one, for the linear distance-dependent dielectric simulations, produced trajectories that are progressively worse in describing trp repressor dynamics. Simulations of bovine pancreatic trypsin were used to ensure that the trp repressor results were not protein dependent and to explore the effect of the nonbonded cutoff on the distance-dependent and constant dielectric simulation models. The nonbonded cutoff markedly affected the constant but not distance-dependent dielectric bovine pancreatic trypsin inhibitor simulations. As with trp repressor, the distance-dependent dielectric model with a shell of water surrounding the protein produced a trajectory in better agreement with the crystal structure than a constant dielectric model, and the physical properties of the trajectory average structure, both with and without a nonbonded cutoff, were comparable.

Amino Acid Sequence

Conformational sampling using high-temperature molecular dynamics.

High-temperature molecular dynamics as a method for conformational search was explored on the antigen combining site of McPC 603, a phosphorylcholine binding immunoglobulin. Simulations at temperatures of 500, 800, and 1500 K were run for 111.5, 101.7, and 76.3 ps, respectively. The effectiveness of the search was assessed using a variety of methods. For the shorter hypervariable loops, molecular dynamics explored an appreciable fraction of the conformational space as evidenced by a comparison to a simple theoretical model of the size of the conformational space. However, for the longer loops and the antigen combining site as a whole, the simulation times were too short for a complete search. The simulations at 500 and 800 K both generated conformations that minimized to energies 200 kcal/mole lower than the crystal structure. However, the 1500 K simulation produced higher energy structures, even after minimization; in addition, this highest temperature run had many cis-trans peptide isomerizations. This suggests that 1500 K is too high a temperature for unconstrained conformational sampling. Comparison of the results of high temperature molecular dynamics with a direct conformational search method, [R. E. Bruccoleri & M. Karplus (1987) Biopolymers 26, 137-168]. showed that the two methods did not overlap much in conformational space. Simple geometric measures of the conformational space indicated that the direct method covered more space than molecular dynamics at the lower temperature, but not at 1500 K. The results suggest that high-temperature molecular dynamics can aid in conformational searches.

Amino Acid Sequence

Solution structure of neuronal bungarotoxin determined by two-dimensional NMR spectroscopy: calculation of tertiary structure using systematic homologous model building, dynamical simulated annealing, and restrained molecular dynamics.

Neuronal bungarotoxin has previously been shown, using two-dimensional 1H NMR spectroscopy, to have a triple-stranded antiparallel beta-sheet structure which dimerizes in solution [Oswald, R.E., Sutcliffe, M.J., Bamberger, M., Loring, R.H., Braswell, E., & Dobson, C.M. (1991) Biochemistry 30, 4901-4909]. In this paper, structural calculations are described which use the 582 experimentally measured NOE restraints in conjunction with 27 phi-angle restraints from J-value measurements. The positions of the N-terminal region and C-terminal region were poorly defined in the calculated structures with respect to the remainder of the structure. The region of the structure containing the triple-stranded beta-sheet was, however, well defined and similar to that found in the structure of homologous alpha-bungarotoxin (45% amino acid identity). The experimental restraints did not result in a well-defined dimer interface region because of the small number of NOEs which could be identified in this region. An approach was therefore adopted which produced model structures based to varying degrees on the alpha-bungarotoxin structure. Fourteen different structures were generated in this manner and subsequently used as starting points for refinement using dynamical simulated annealing followed by restrained molecular dynamics. This approach, which combines NMR data and homologous model building, has enabled a family of structures to be proposed for the dimeric molecule. In particular, Phe49 has been identified as possibly playing an important role in dimer formation, this residue in one chain interacting with the corresponding residue in the adjacent chain.

Amino Acid Sequence

Solution conformations of the B-loop fragments of human transforming growth factor alpha and epidermal growth factor by 1H nuclear magnetic resonance and restrained molecular dynamics.

A restrained molecular dynamics simulation approach that explicitly includes the effect of the surrounding solvent molecules is applied to the NMR determination of the conformations of the B-loop fragments of human transforming growth factor alpha and epidermal growth factor. Backbone interproton distance restraints are obtained by using two-dimensional rotating frame nuclear Overhauser effect spectroscopy (ROESY). The simulations are carried out both in "vacuum" and in "water." The results are discussed in terms of the energetics, agreement with the NMR distances, and the flexibility of the peptides.

Computer Simulation

Molecular dynamics simulations in biology.

Molecular dynamics--the science of simulating the motions of a system of particles--applied to biological macromolecules gives the fluctuations in the relative positions of the atoms in a protein or in DNA as a function of time. Knowledge of these motions provides insights into biological phenomena such as the role of flexibility in ligand binding and the rapid solvation of the electron transfer state in photosynthesis. Molecular dynamics is also being used to determine protein structures from NMR, to refine protein X-ray crystal structures faster from poorer starting models, and to calculate the free energy changes resulting from mutations in proteins.

Chemical Phenomena

Anti-insulin antibody structure and conformation. II. Molecular dynamics with explicit solvent.

Molecular dynamics at 300 K was used as a conformation searching tool to analyze a knowledge-based structure prediction of an anti-insulin antibody. Solvation effects were modeled by packing water molecules around the antigen binding loops. Some loops underwent backbone and side-chain conformational changes during the 95-ps equilibration, and most of these new, lower potential energy conformations were stable during the subsequent 200-ps simulation. Alterations to the model include changes in the intraloop, main-chain hydrogen bonding network of loop H3, and adjustments of Tyr and Lys side chains of H3 induced by hydrogen bonding to water molecules. The structures observed during molecular dynamics support the conclusion of the previous paper that hydrogen bonding will play the dominant role in antibody-insulin recognition. Determination of the structure of the antibody by x-ray crystallography is currently being pursued to provide an experimental test of these results. The simulation appears to improve the model, but longer simulations at higher temperatures should be performed.

Binding Sites

Proton nuclear magnetic resonance studies on the molecular dynamics of plasmenylcholine/cholesterol and phosphatidylcholine/cholesterol bilayers.

Physiologically relevant molecular species of plasmenylcholine and phosphatidylcholine were synthesized and their molecular dynamics and interactions with cholesterol were compared by determination of salient proton spin-lattice relaxation times and apparent activation energies for 1H-NMR observable motion. The molecular dynamics of PA PhosCho (1-hexadecanoyl-2-eicosatetra-5',8',11',14'-enoyl-sn-glycero-3-pho sphocholine) in multiple regions of the bilayer. Furthermore, the fluidity gradient of PA PhosCho was larger than that of PA PlasCho as ascertained by 1H spin-lattice relaxation time measurements. Introduction of cholesterol into each bilayer resulted in disparate effects on the dynamics of each subclass including: (1) increased motional freedom in the polar head group of PA PlasCho without substantial alterations in the dynamics of the polar head group of PA PhosCho; and (2) increased immobilization of the membrane interior in PA PlasCho in comparison to PA PhosCho. Analysis of Arrhenius plots of T1 relaxation times demonstrated that the apparent activation energies for vinyl and bisallylic methylene proton NMR observable motion in PA PhosCho were greater than that in PA PlasCho. Thus, comparisons of spin-lattice relaxation times and apparent activation energies demonstrate that vesicles comprised of PA PlasCho and PA PhosCho possess differential molecular dynamics and distinct interactions with cholesterol. Collectively, these results underscore the significance of the conjoint presence of the vinyl ether linkage and arachidonic acid as an important determinant of membrane dynamics in specialized mammalian membranes.

Cholesterol