Showing papers by "Wilfred F. van Gunsteren published in 2006"

Biomolecular modeling: Goals, problems, perspectives.

Abstract: Computation based on molecular models is playing an increasingly important role in biology, biological chemistry, and biophysics. Since only a very limited number of properties of biomolecular systems is actually accessible to measurement by experimental means, computer simulation can complement experiment by providing not only averages, but also distributions and time series of any definable quantity, for example, conformational distributions or interactions between parts of systems. Present day biomolecular modeling is limited in its application by four main problems: 1) the force-field problem, 2) the search (sampling) problem, 3) the ensemble (sampling) problem, and 4) the experimental problem. These four problems are discussed and illustrated by practical examples. Perspectives are also outlined for pushing forward the limitations of biomolecular modeling.

Multigraining: an algorithm for simultaneous fine-grained and coarse-grained simulation of molecular systems.

Abstract: A method to combine fine-grained and coarse-grained simulations is presented. The coarse-grained particles are described as virtual particles defined by the underlying fine-grained particles are described as virtual particles defined by the underlying fine-grained particles. The contribution of the two grain levels to the interaction between particles is specified by a grain-level parameter lambda. Setting lambda = 0 results in a completely fine-grained simulation, whereas lambda = 1 yields a simulation governed by the coarse-grained potential energy surface with small contributions to keep the fine-grained covalently bound particles together. Simulations at different lambda values may be coupled using the replica-exchange molecular dynamics method to achieve enhanced sampling at the fine-grained level.

Molecular dynamics simulations of liquid methanol and methanol-water mixtures with polarizable models.

Abstract: A polarizable model for simulation of liquid methanol, compatible with the COS/G2 water model, has been developed using the Charge-on-Spring (COS) technique. The model consists of three point charges, with one polarizable center on the oxygen atom. The Lennard-Jones parameters on the oxygen atom together with the molecular polarizability were varied to reproduce the experimental heat of vaporization and density of liquid methanol at ambient conditions. We examined the energies of various methanol dimers in the gas phase and compared them with values obtained from ab initio calculations. The model was then used to study the thermodynamic, dynamic, structural, and dielectric properties of liquid methanol as well as of a methanol-water mixture. A microscopic picture of the structure of pure liquid methanol and of the methanol-water mixture is provided. Good agreement was found between the results from our model simulations and available experimental and ab initio calculation data. In particular, the experimental dielectric permittivity of 32 could be reproduced, which had been shown to be difficult when using nonpolarizable models.

Comparing atomistic simulation data with the NMR experiment: how much can NOEs actually tell us?

Abstract: Simulated molecular dynamics trajectories of proteins and nucleic acids are often compared with nuclear magnetic resonance (NMR) data for the purposes of assessing the quality of the force field used or, equally important, trying to interpret ambiguous experimental data. In particular, nuclear Overhauser enhancement (NOE) intensities or atom-atom distances derived from them are frequently calculated from the simulated ensembles because the distance restraints derived from NOEs are the key ingredient in NMR-based protein structure determination. In this study, we ask how diverse and nonnative-like an ensemble of structures can be and still match the experimental NOE distance upper bounds well. We present two examples in which simulated ensembles of highly nonnative polypeptide structures (an unfolded state ensemble of the villin headpiece and a high-temperature denatured ensemble of lysozyme) are shown to match fairly well the experimental NOE distance upper bounds from which the corresponding native structures were derived. For example, the unfolded ensemble of villin headpiece, which is on average 0.90 +/- 0.13 nm root-mean-square deviation away from the native NMR structure, deviates from the experimental restraints by only 0.027 nm on average. However, this artificially good agreement is largely a consequence of 1) the highly nonlinear effects of r(-6) (or r(-3)) averaging and 2) focusing only on the experimentally observed set of NOE bounds. Namely, in addition to the experimentally observed NOEs, both simulated ensembles (especially the villin ensemble) also predict a large number of NOEs, which are not seen in the experiment. If these are taken into account, the agreement between simulation and experiment gets markedly worse, as it should, given the nonnative nature of the underlying simulated ensembles. In light of the examples given, we conclude that comparing experimental NOE distance restraints with large simulated ensembles provides just by itself only limited information about the quality of simulation.

Configurational entropies of lipids in pure and mixed bilayers from atomic-level and coarse-grained molecular dynamics simulations.

Abstract: Single-chain and single-fragment configurational entropies of lipid tails in hydrated lipid bilayers are evaluated from molecular dynamics simulations using the quasi-harmonic approximation. The entropy distribution along individual acyl tails is obtained and compared to that of corresponding hydrocarbon chains in the liquid phase. We consider pure dipalmitoylphosphatidylcholine and mixed dioleoylphosphatidylcholine/dioleoylphosphatidylethanolamine bilayers. The systems are modeled at different levels of spatial resolution: In an atomic-level (AL) model all (heavy) atoms are explicitly simulated; in a coarse-grained (CG) model particles (beads) representing groups of covalently bound atoms are used, which map approximately four non-hydrogen atoms to one interaction site. Single-chain and single-fragment entropies and correlations between the motions of (single) acyl chains are compared. A good correspondence is found between the flexibility of the AL and CG models. The loss in configurational entropy due to the reduction in the number of degrees of freedom upon coarse-graining of the model is estimated. The CG model shows about 4 times faster convergence of the chain entropies than the more detailed AL model. Corrections to the quasi-harmonic entropy estimates were found to be small for the CG model. For the AL model, the correction due to mode anharmonicities is small, but the correction due to pairwise (supralinear) mode correlations is sizable.

A molecular dynamics study of the bee venom melittin in aqueous solution, in methanol, and inserted in a phospholipid bilayer.

Abstract: The structural properties of melittin, a small amphipathic peptide found in the bee venom, are investigated in three different environments by molecular dynamics simulation. Long simulations have been performed for monomeric melittin solvated in water, in methanol, and shorter ones for melittin inserted in a dimyristoylphosphatidylcholine bilayer. The resulting trajectories were analysed in terms of structural properties of the peptide and compared to the available NMR data. While in water and methanol solution melittin is observed to partly unfold, the peptide retains its structure when embedded in a lipid bilayer. The latter simulation shows good agreement with the experimentally derived 3J-coupling constants. Generally, it appears that higher the stability of the helical conformation of melittin, lower is the dielectric permittivity of the environment. In addition, peptide-lipid interactions were investigated showing that the C-terminus of the peptide provides an anchor to the lipid bilayer by forming hydrogen bonds with the lipid head groups.

Protein under pressure: molecular dynamics simulation of the arc repressor.

Abstract: Experimental nuclear magnetic resonance results for the Arc Repressor have shown that this dimeric protein dissociates into a molten globule at high pressure. This structural change is accompanied by a modification of the hydrogen-bonding pattern of the intermolecular beta-sheet: it changes its character from intermolecular to intramolecular with respect to the two monomers. Molecular dynamics simulations of the Arc Repressor, as a monomer and a dimer, at elevated pressure have been performed with the aim to study this hypothesis and to identify the major structural and dynamical changes of the protein under such conditions. The monomer appears less stable than the dimer. However, the complete dissociation has not been seen because of the long timescale needed to observe this phenomenon. In fact, the protein structure altered very little when increasing the pressure. It became slightly compressed and the dynamics of the side-chains and the unfolding process slowed down. Increasing both, temperature and pressure, a tendency of conversion of intermolecular into intramolecular hydrogen bonds in the beta-sheet region has been detected, supporting the mentioned hypothesis. Also, the onset of denaturation of the separated chains was observed.

Catalytic mechanism of cyclophilin as observed in molecular dynamics simulations: Pathway prediction and reconciliation of X-ray crystallographic and NMR solution data

Abstract: Cyclophilins are proteins that catalyze X-proline cis–trans interconversion, where X represents any amino acid. Its mechanism of action has been investigated over the past years but still generates discussion, especially because until recently structures of the ligand in the cis and trans conformations for the same system were lacking. X-ray crystallographic structures for the complex cyclophilin A and HIV-1 capsid mutants with ligands in the cis and trans conformations suggest a mechanism where the N-terminal portion of the ligand rotates during the cis–trans isomerization. However, a few years before, a C-terminal rotating ligand was proposed to explain NMR solution data. In the present study we use molecular dynamics (MD) simulations to generate a trans structure starting from the cis structure. From simulations starting from the cis and trans structures obtained through the rotational pathways, the seeming contradiction between the two sets of experimental data could be resolved. The simulated N-terminal rotated trans structure shows good agreement with the equivalent crystal structure and, moreover, is consistent with the NMR data. These results illustrate the use of MD simulation at atomic resolution to model structural transitions and to interpret experimental data.

Sampling of rare events using hidden restraints.

Abstract: A method to enhance sampling of rare events is presented. It makes use of distance or dihedral-angle restraints to overcome an energy barrier separating two metastable states or to stabilize a transition state between the two metastable states. In order not to perturb these metastable end states themselves, a prefactor is introduced into the restraining energy function, which smoothly increases the weight of this function from zero to one at the transition state or on top of the separating energy barrier and then decreases the weight again to zero at the final state. The method is combined with multi-configurational thermodynamic integration and applied to two biomolecular systems, which were difficult to treat using standard thermodynamic integration. As first example the free energy difference of a cyclic α-aminoxy-hexapeptide−ion complex upon changing the ion from Cl- to Na+ was calculated. A large conformational rearrangement of the peptide was necessary to accommodate this change. Stabilizing the tra...

Force Field Evaluation for Biomolecular Simulation: Free Enthalpies of Solvation of Polar and Apolar Compounds in Various Solvents

Abstract: Recently, the GROMOS biomolecular force field parameter set 53A6—which has been parametrized to reproduce experimentally determined free enthalpies of hydration and solvation in cyclohexane of amino acid side-chain analogs—was presented. To investigate the transferability of the new parameter set, we calculated free enthalpies of solvation of a range of polar and apolar compounds in different solvents (methanol, dimethyl sulfoxide (DMSO), acetonitrile, and acetone) from molecular dynamics simulations using the GROMOS 53A6 force field. For methanol and DMSO, parameters were used that are available in the 53A6 parameter set. For acetonitrile, a recently developed model was taken and for acetone, two models available in literature were used. We found that trends in and values for the solvation free enthalpies are in satisfactory agreement with experiment, except for the solvation in acetone for which deviations from experiment can be explained in terms of the properties of the models used.

Biomolekulare Modellierung: Ziele, Probleme, Perspektiven

Abstract: Computerverfahren auf der Grundlage von Molekulmodellen gewinnen in Biologie, biologischer Chemie und Biophysik zunehmend an Bedeutung. Da nur wenige Eigenschaften biomolekularer Systeme durch Messungen zuganglich sind, konnen Computersimulationen experimentelle Daten erganzen, indem sie nicht nur Durchschnittswerte, sondern auch Verteilungen und Zeitreihen jeder bestimmbaren Grose liefern, z. B. Konformationsverteilungen oder Wechselwirkungen zwischen Teilen eines Systems. Die Anwendung moderner biomolekularer Modellierungsverfahren wird zurzeit durch vier grundlegende Probleme eingeschrankt: 1) das Kraftfeldproblem, 2) das Suchproblem, 3) das Ensembleproblem und 4) das Experimentalproblem. Diese vier Probleme werden anhand praktischer Beispiele erlautert, auserdem werden Losungsperspektiven aufgezeigt.

Numerical Simulation of the Effect of Solvent Viscosity on the Motions of a β‐Peptide Heptamer

Abstract: This report examines the effect of a decrease in solvent viscosity on the simulated folding behaviour of a beta-peptide heptamer in methanol. Simulations of the molecular dynamics of the heptamer H-beta3-HVal-beta3-HAla-beta3-HLeu-(S,S)-beta3-HAla(alphaMe)-beta3-HVal-beta3-HAla-beta3-HLeu-OH in methanol, with an explicit representation of the methanol molecules, were performed for 80 ns at various solvent viscosities. The simulations indicate that at a solvent viscosity of one third of that of methanol, only the dynamic aspects of the folding process are altered, and that the rate of folding is increased. At a viscosity of one tenth of that of methanol, insufficient statistics are obtained within the 80 ns period. We suggest that 80 ns is an insufficient time to reach conformational equilibrium at very low viscosity because the dependence of the folding rate of a beta-peptide on solvent viscosity has two regimes; a result that was observed in another computational study for alpha-peptides.

Orientation and conformational preference of leucine-enkephalin at the surface of a hydrated dimyristoylphosphatidylcholine bilayer: NMR and MD simulation.

Abstract: The morphogenic opiate pentapeptide leucine-enkephalin (lenk) in a hydrated dimyristoylphosphatidylcholine (DMPC) bilayer is studied using NMR spectroscopy and molecular dynamics simulation. Contrary to the frequent assumption that the peptide attains a single fixed conformation in the presence of membranes, we find that the lenk molecule is flexible, switching between specific bent conformations. The constraints to the orientation of the aromatic rings that are identified by the NMR experiment are found by the MD simulation to be related to the depth of the peptide in the bilayer. The motion of the N−H vectors of the peptide bonds with respect to the magnetic field direction as observed by MD largely explain the magnitude of the observed residual dipolar coupling (RDC), which are much reduced over the static 15N−1H coupling. The measured RDCs are nevertheless significantly larger than the predicted ones, possibly due the absence of long-time motions in the simulations. The conformational behavior of lenk...

Molecular dynamics study of the stabilities of consensus designed ankyrin repeat proteins

Abstract: Two designed ankyrin repeat (AR) proteins (E3_5 and E3_19) are high homologous (with about 87% sequence identity) and their crys- tal structures have a Ca atom-positional root-mean- square difference of about 0.14 nm. However, it was found that E3_5 is considerably more stable than E3_19 in guanidinium hydrochloride and thermal denaturation experiments. With the goal of provid- ing insights into the various factors contributing to the stabilities of the designed AR proteins and sug- gesting possible mutations to enhance their stabil- ities, homology modeling and molecular dynamics (MD) simulations with explicit solvent have been performed. Because the crystal structure of E3_19 was solved later than that of E3_5, a homology model of E3_19 based on the crystal structure of E3_5 was also used in the simulations. E3_5 shows a very stable trajectory in both crystal and solution simulations. In contrast, the C-terminal repeat of E3_19 unfolds in the simulations starting from ei- ther the modeled structure or the crystal structure, although it has a sequence identical to that of E3_5. A continuum electrostatic model was used to esti- mate the effect of single mutations on protein sta- bility and to study the interaction between the internal ARs and the C-terminal capping AR. Muta- tions involving charged residues were found to have large effects on stability. Due to the differ- ence in charge distribution in the internal ARs of E3_19 and E3_5, their interaction with the C-termi- nal capping AR is less favorable in E3_19. The sim- ulation trajectories suggest that the stability of the designed AR proteins can be increased by optimiz- ing the electrostatic interactions within and be- tween the different repeats. Proteins 2006;65:285- 295. V C 2006 Wiley-Liss, Inc.

Terminal‐group effects on the folding behavior of selected beta‐peptides

Abstract: It has been suggested that the stability of a beta-peptide helical fold is affected by the interplay between the electrical charge of terminal groups and the dipole due to the helical conformation, the so-called charge-dipole stabilization; the numerical simulations presented herein test that suggestion. The motions of two beta-peptide oligomers, each of which has been shown by NMR spectroscopy to fold into a different helical conformation, have been simulated. The simulated motions bear out empirical observations as to the effect of chemical protection of terminal groups on the stability of beta-peptide helical folds and they support the hypothesis of charge-dipole stabilization.

Computational study of ground-state chiral induction in small peptides: comparison of the relative stability of selected amino acid dimers and oligomers in homochiral and heterochiral combinations.

Abstract: The relative stabilities of homochiral and heterochiral forms of selected dipeptides, AA, AS, AC, AV, AF, AD, AK, tripeptides, AAA, AVA, and an acetylpentapeptide, AcGLSFA, have been calculated using thermodynamic integration protocols and the GROMOS 53A6 force field. Integration pathways have been designed that produce minimal disturbance to the system, including the use of soft atoms, low-energy intermediates, and chiral inversion of the smaller amino acid in the peptide. Comparison of the results obtained by thermodynamic integration between the diastereomeric forms (in explicit water, at 300 K) and from exhaustive global minimum-energy searches for the individual dipeptides (implicit water, e = 78, 0 K) suggests that entropic contributions to the relative stability of the chiral forms are important. This conclusion is supported by the results of explicit calculation of the effect of temperature on the relative stability of alanylvalylalanine diastereomers. The Gibbs free energy calculations predict that at ambient temperature and pressure homochiral dipeptides with small side chains or polar groups in the vicinity of the peptide backbone, AA, AS, and AD, are more stable than their heterochiral counterparts by fractions of a kJ/mol. For bigger side chains, AC, AV, AF, and AK, the heterochiral diastereomers appear to be more stable. Predicted relative stabilities are in line with observations reported in the literature for AE and YY. Excellent agreement is found for the calculated and experimentally determined relative stabilities of the diastereomers of the dipeptide AA and of all-L, AcGLSFA and its diastereomer containing D-serine in the central position. Addition of counterions to the solvent box has no significant effects on charged and neutral forms. From the present findings it would appear unlikely that the intrinsic stability difference between homo- and heterochiral dipeptides has been a driving force in a primordial selection process leading to the incorporation of amino acids with a single enantiomeric configuration in natural proteins. © 2006 Wiley Periodicals, Inc.

Molecular dynamics simulations of Hydrogenobacter thermophilus cytochrome c552: comparisons of the wild-type protein, a b-type variant, and the apo state.

Abstract: Molecular dynamic simulations have been performed for wild-type Hydrogenobacter thermophilus cytochrome c552, a b-type variant of the protein, and the apo state with the heme prosthetic group removed. In the b-type variant, Cys 10 and Cys 13 were mutated to alanine residues, and so the heme group was no longer covalently bound to the protein. Two 8-ns simulations have been performed for each system at 298 and 360 K. The simulations of the wild-type protein at 298 K show a very close agreement with experimental NMR data. A fluxional process involving the side chain of Met 59, which coordinates to the heme iron, is observed in accord with proposals from NMR studies. Overall, the structure and dynamical behavior of the protein during the simulations of the b-type variant is closely similar to that of the wild-type protein. However, side chains in the heme-binding site show larger fluctuations in the b-type variant simulation at 360 K. In addition, structural changes are seen for a number of residues close to the heme group, particularly Gly 22 and Ser 51. The simulations of the apo state show significant conformational changes for residues 50–59. These residues form a loop region, which packs over the heme group in the wild-type protein and hydrogen bonds to the heme propionate groups. In the absence of heme, in the apo state simulations, these residues form short but persistent regions of β-sheet secondary structure. These could provide nucleation sites for the conversion to amyloid fibrils. Proteins 2006. © 2006 Wiley-Liss, Inc.

Pathway dependence of the efficiency of calculating free energy and entropy of solute–solute association in water

Abstract: In this study we investigate two alternative pathways to compute the free energy and the entropy of small molecule association (Δ F assoc and Δ S assoc ) in water The first route (direct pathway) uses thermodynamic integration as function of the distance R between the solutes The mean force and the mean covariance of the force with the energy in solution are calculated from molecular dynamics simulation followed by integration of these quantities with respect to the reaction coordinate R The alternative approach examined (solvation pathway) would first remove the solutes from the solution using thermodynamic integration as function of a solvation coupling parameter λ , change the solute–solute distance in vacuo and then solvate back the solute pair at the new separation distance The system studied was a pair of CH 4 molecules in water We investigate the influence of the CH 4 –water interaction strength on the obtained Δ F assoc and Δ S assoc values by changing van der Waals and Coulomb interaction and evaluated the accuracy and efficiency for the two pathways We find that the direct route seems more suitable for the calculation of free energies of hydrophobic solutes while the solvation pathway performs better when calculating entropy changes for solutes that have a stronger interaction with the solvent

Simulation of an all‐β3‐icosapeptide containing the 20 proteinogenic side chains: Effect of temperature, pH, counterions, solvent, and force field on helix stability

Abstract: Simulations of various beta-peptides have in the last years clarified several issues concerning peptide folding equilibria and interpretation of experimental data, especially from NMR and CD spectroscopy. These simulations involved different temperatures, pH-values, ionic strengths, solvents, and force-field parameters, but a variation of these factors for one beta-peptide has not yet been done. To investigate the influence of varying these factors, we analyze the helix stability of an all-beta3-icosapeptide bearing all 20 proteinogenic amino acid side chains, which is experimentally observed to fold into a 3(14)-helix in methanol but not in water. Structural aspects, such as hydrogen-bonded rings and salt bridges, are discussed and a comparison with NMR primary (NOE distance bounds and 3J-values) and secondary (NMR derived model structures) data is made. We further investigate the reasons for the 3(14)-helix stability/instability in methanol/water. Of all factors studied, the presence of counterions seems to be the one inducing most significant effects in the simulations.

Numerical Simulation of the Pressure Denaturation of a Helical β‐Peptide Heptamer Solvated in Methanol

Abstract: The effect of elevated pressure on the conformational behavior of a β-peptide heptamer (1) in MeOH solution was considered. The response of the peptide to elevated pressure was probed by means of molecular dynamics (MD) simulations, and described in atomic terms. The most-striking features of the response are that the region of the ‘unfolded’ state of the peptide accessible at elevated pressure is narrow, and that thermal and pressure denaturation produce similar ‘unfolded’ states in the case of 1.