Wf Vangunsteren

ALGORITHMS FOR BROWNIAN DYNAMICS

A third order algorithm for brownian dynamics (BD) simulations is proposed, which is identical to the powerful molecular dynamics (MD) algorithm due to Verlet in the limit of infinitely small friction coefficient γ. In contrast to most BD algorithms used up till now, the integration time step Δt is not limited by the condition Δt ≪ γ-1. It is shown how constraints, such as bondlength or bond angle constraints, can be incorporated in the computational scheme. For the molecule considered here the proposed BD algorithm is about ten times more efficient than the second order ones that are generally used. The introduction of bondlength constraints saves about a factor of three in computing time, as in the MD case. The application of bond angle constraints is not recommended.

STOCHASTIC DYNAMICS FOR MOLECULES WITH CONSTRAINTS BROWNIAN DYNAMICS OF NORMAL-ALKANES

It is shown how constraints, such as bondlength or bond angle constraints, can be incorporated in the algorithms currently being used in brownian dynamics (BD) simulations of molecular liquids or solutions. The validity of the BD model, in which the stochastic and frictional force fields possess neither time correlations nor space correlations between different atoms of the molecule, is investigated by comparing the BD results with those of molecular dynamics (MD) simulations for liquid n-butane and n-decane. The BD model appears to yield a good approximation to the dynamics of a chain molecule in the liquid state. For butane, solvent packing effects play an important role in the condensed phase. For decane, the equilibrium conformation and dynamics are determined mainly by intramolecular interactions. When analysing the conformational transitions occurring in these molecules, one observes a correlation between consecutive transitions both of one dihedral angle and of two adjacent dihedral angles, due to ...

Calculation of relative free energy via indirect pathways

A general method is presented to reduce the simulation time required to compute the relative free energy between two states X and Y of a molecular system by computer simulation. Although the free energy difference DELTA-A(x-->y) is, in principle, independent of the pathway chosen to change X into Y, in practice its choice strongly affects the accuracy of the obtained DELTA-A value. The optimum path is the one for which the relaxation time of the system tau-system attains a minimum, allowing the system to remain as close as possible near equilibrium during a simulation. Downscaling the relevant parts of the potential energy function before the change from X to Y is made, and upscaling afterwards is a rather general way to shorten tau-system and thus save computing time. For a model system of butane like molecules the proposed procedure is more than 1 order of magnitude more efficient than the conventional technique of direct interconversion from state X to state Y.

MOLECULAR-DYNAMICS SIMULATION OF CRYSTALLINE BETA-CYCLODEXTRIN DODECAHYDRATE AT 293-K AND 120-K

Molecular dynamics (MD) simulations for crystalline β-cyclodextrin dodecahydrate (β-CD) at two different temperatures, 293 K and 120 K, have been performed using the GROMOS program package. The calculated structural properties are compared to those obtained from neutron diffraction studies of this system at the quoted temperatures. The simulation was carried out over a period of 20 ps on four unit cells containing 8 β-CD molecules and 96 water molecules, whereby all atoms were allowed to move.At room temperature, the experimental positions of the (non-hydrogen) glucose atoms are reproduced within 0.034 nm, a value which is smaller than the experimental (0.041 nm) or simulated (0.049 nm) overall root mean square (rms) positional fluctuation. The corresponding numbers for the low temperature study are 0.046 nm, 0.019 nm and 0.022 nm. At both temperatures the experimentally observed degree of anisotropy of the atomic motions is also found in the simulations.The comparison of a variety of structural properties leads to the conclusion that the molecular model and force field used are able to simulate the cyclodextrin system very well. Experimentally observed differences in properties as a function of number of glucose units in the CD molecule (α-CD, 6 versus β-CD, 7) and as a function of temperature are qualitatively reproduced by the simulations.

On the Occurrence of Three-Center Hydrogen Bonds in Cyclodextrins in Crystalline Form and in Aqueous Solution: Comparison of Neutron Diffraction and Molecular Dynamics Results

Three-center (bifurcated) hydrogen bonds may play a role by serving as an intermediate state between different dynamically changing hydrogen bonding patterns. Hydrogen bonding configurations can be studied experimentally by neutron diffraction and theoretically by computer simulation techniques. Here, both methods are used to analyse the occurrence of three-center hydrogen bonds in crystals of cyclodextrins. Almost all experimentally observed three-center hydrogen bonds in the crystal are reproduced in the molecular dynamics (MD) simulations, even as far as the detailed asymmetric geometry is concerned. On the basis of this result a MD simulation of cyclodextrin in aqueous solution is searched for the occurrence of three-center hydrogen bonds. Significant differences are found. In solution more different three-center hydrogen bonds per alpha-cyclodextrin molecule are observed than in the crystal but the population (existence as percent of the simulation period) of each three-center hydrogen bond is lower in solution than in crystal. These may indeed serve as intermediate states in the process of changing one hydrogen bonding pattern into another.

A COMPARISON OF THE STRUCTURE AND DYNAMICS OF AVIAN PANCREATIC-POLYPEPTIDE HORMONE IN SOLUTION AND IN THE CRYSTAL

A molecular dynamics simulation was carried out with avian pancreatic polypeptide hormone (aPP) as an isolated monomer explicitly including the solvent (MDS). The simulation and the resulting mean structure are compared with the results of a corresponding crystal simulation (MDC) with 4 aPP molecules plus interstitial water in a periodic boundary unit cell and with the X-ray structure (van Gunsteren, Haneef et al., manuscript in preparation). Comparison is based on the time span 5 to 15 ps and considering cartesian coordinates, dihedral angles, H-bond length, and accessible surface area. While in the MDC simulation equilibration is fast and complete, it does occur in MDS for most but not all parts of the molecule; the turn region starts moving away from the X-ray structure after 9 ps.Only minor differences result when dimerforming side chains, e.g. tyrosines 7 and 21, are exposed to solvent. The largest rms fluctuations are encountered in exposed polar side chains of Asp 11, Glu 15, Arg 19, and Arg 33, but also in the hydrophobic core residue Phe 20, the only phenylalanine residue present. The latter undergoes an abrupt reorientation suitable for verification by NMR spectroscopy, which is possibly related to the motion of the turn region. The main-chain dihedral angles of the α-helix are shifted from values generally found in crystal structures towards those of the ideal Pauling helix. There is concomitant H-bond elongation. The effects are most pronounced and consistent in the MDS simulation.

The simulated dynamics of the insulin monomer and their relationship to the molecule's structure

Insulin crystallizes in different forms, some of which show different conformations for the different molecules in the asymmetric unit. This observation leads to the question as to which conformation the molecule will adopt in solution. Molecular dynamics computer simulations of rhombohedral 2 Zn pig insulin have been carried out for both monomers (1 and 2) independently in order to study their behaviour in the absence of quaternary structure and crystal packing forces.These preliminary 120 ps simulations suggest that both monomers converge in solution to very similar conformations which differ from the X-ray structures of both monomer 1 and 2 (Chinese nomenclature), but are closer to the former, as has previously been suggested by an analysis of the crystal packing (Chothia et al. 1983) and by energy minimization (Wodak et al. 1984). The secondary structure of the molecules is basically preserved, as expected. A detailed description of the conformational changes is given.

DYNAMICAL STRUCTURE OF CARBOXYPEPTIDASE-A

Structural fluctuations of the apoenzyme form of carboxypeptidase A (EC 3.4.12.2) have been evaluated on the basis of molecular dynamics. The Konnert-Hendrickson refined coordinates of 2437 non-hydrogen atoms of the 307 amino acid residues derived from the X-ray structure of the holoenzyme served as the molecular model together with 548 calculated polar hydrogen atoms and 25 buried solvent molecules. Molecular dynamics simulations were carried out at 277 K, and the averaged structural properties of the protein were evaluated for the terminal 20 picosecond portion of a 48 picosecond trajectory. The average atomic displacement from the initial X-ray structure was 2.49 A for all atoms and 1.79 A for C alpha atoms. The average root-mean-square (r.m.s.) fluctuation of all atoms was 0.67 A as compared to 0.54 A evaluated from the X-ray-defined temperature factors. Corresponding r.m.s. fluctuations for backbone atoms were 0.56 A by molecular dynamics and 0.49 A by X-ray. On the basis of these molecular dynamics studies of the isolated molecule, it is shown that amino acid residues corresponding to intermolecular contact sites of the crystalline enzyme are associated with high amplitude motion. All eight segments of alpha-helix and eight regions of beta-strand were well preserved except for unwinding of the five C-terminal residues of the alpha-helix 112-122 that form part of an intermolecular contact in the crystal. Four regions of beta-strand and one alpha-helix with residues adjacent to or in the active site constitute a core of constant secondary structure and are shown not to change in relative orientation to each other during the course of the trajectory. The absence of the zinc ion does not markedly influence the stereochemical relationships of active site residues in the dynamically averaged protein. The extent of motional fluctuations of each of the subsites of substrate recognition in the active site has been evaluated. Active site residues responsible for specificity of substrate binding or splitting of the scissile bond exhibit low simulated motion. In contrast, residues in more distal sites of substrate recognition exhibit markedly greater motional fluctuations. This differential extent of dynamical motion is related to structural requirements of substrate hydrolysis.

On the fluctuation-dissipation theorem for interacting brownian particles

The correct form of the fluctuation-dissipation theorem for interacting brownian particles contains a term due to the interparticle force, which has usually been ignored in brownian dynamics (BD) simulations. In order to estimate its size, a BD simulation of n-butane has been performed. The term appears to be virtually zero. Besides, the process of energy transfer through the molecule has been studied. It displays two time scales. Energy relaxation involving the bond length and bond angle degrees of freedom takes less than 1 ps, whereas the energy is only completely redistributed after about 100 ps, which is due to the weak coupling of the atoms through the dihedral degree of freedom.

A MOLECULAR-DYNAMICS COMPUTER-SIMULATION STUDY OF THE TEMPERATURE-DEPENDENCE OF HYDRATION OF 1,4-DIOXANE AND 1,3-DIOXANE

Abstract This paper describes a study of the hydration of 1,3-dioxane and 1,4-dioxane at two different temperatures using different molecular dynamics (MD) computer simulation techniques. Three major conclusions have been drawn. Firstly, the simulations of 1,4-dioxane—water and 1,3-dioxane—water at constant pressure lead essentially to the same conclusions as earlir MD studies at constant volume. Secondly, the numerical values of dynamic properties depend critically on the density of the system. Simulations at constant pressure provide densities which are dependent on the periodicity requirement imposed on the system by the periodic boundary conditions. The smaller the periodic box, the stronger this effect is. Thirdly, in 1,4-dioxane—water an increase in temperature results in an enhanced mobility of water molecules in the solvation shell, whereas in the case of 1,3-dioxane—water these water molecules become more strongly bound by the solute. This effect is entirely due to a reduction of the mobility of water molecules in the 1,3-dioxane oxygen hydration subshells. The contrasting behavior is explained in terms of a situation where solvent—solvent interactions dominate solute—solvent interactions in 1,4-dioxane—water at both temperatures and in 1,3-dioxane—water at the lower temperature, while the opposite situation holds for 1,3-dioxane—water at the higher temperature.