Exact distances and internal dynamics of perdeuterated ubiquitin from NOE buildups.

It is proposed to convert nuclear Overhauser effects (NOEs) into relatively precise distances for detailed structural studies of proteins. To this purpose, it is demonstrated that the measurement of NOE buildups between amide protons in perdeuterated human ubiquitin using a designed (15)N-resolved HMQC-NOESY experiment enables the determination of (1)H(N)-(1)H(N) distances up to 5 A with high accuracy and precision. These NOE-derived distances have an experimental random error of approximately 0.07 A, which is smaller than the pairwise rmsd (root-mean-square deviation) of 0.24 A obtained with corresponding distances extracted from either an NMR or an X-ray structure (pdb codes: 1D3Z and 1UBQ), and also smaller than the pairwise rmsd between distances from X-ray and NMR structures (0.15 A). Because the NOE contains both structural and dynamical information, a comparison between the 3D structures and NOE-derived distances may also give insights into through-space dynamics. It appears that the extraction of motional information from NOEs by comparison to the X-ray structure or the NMR structure is challenging because the motion may be masked by the quality of the structures. Nonetheless, a detailed analysis thereof suggests motions between beta-strands and large complex motions in the alpha-helix of ubiquitin. The NOE-derived motions are, however, of smaller amplitude and possibly of a different character than those present in a 20 ns molecular dynamic simulation of ubiquitin in water using the GROMOS force field. Furthermore, a recently published set of structures representing the conformational distribution over time scales up to milliseconds (pdb: 2K39) does not satisfy the NOEs better than the single X-ray structure. Hence, the measurement of possibly thousands of exact NOEs throughout the protein may serve as an excellent probe toward a correct representation of both structure and dynamics of proteins.

On using a too large integration time step in molecular dynamics simulations of coarse-grained molecular models.

The use of a coarse-grained (CG) model that is widely used in molecular dynamics simulations of biomolecular systems is investigated with respect to the dependence of a variety of quantities upon the size of the used integration time step and cutoff radius. The results suggest that when using a non-bonded interaction-cutoff radius of 1.4 nm a time step of maximally 10 fs should be used, in order not to produce energy sinks or wells. Using a too-large time step, e.g. 50 fs with a cutoff of 1.2 nm, as is done in the coarse-grained model of Marrink et al. (J. Phys. Chem. B, 2004, 108, 250 and 2007, 111, 7812), induces errors due to the linear approximation of the integrators that are commonly used to integrate the equations of motion. As a spin-off of the investigation of the mentioned CG models, we found that the parameters of the CG water model place it at physiological temperatures well into the solid phase of the phase diagram.

Comparison of thermodynamic properties of coarse-grained and atomic-level simulation models.

Thermodynamic data are often used to calibrate or test amomic-level (AL) force fields for molecular dynamics (MD) simulations. In contrast, the majority of coarse-grained (CG) force fields do not rely extensively on thermodynamic quantities. Recently, a CG force field for lipids, hydrocarbons, ions, and water, in which approximately four non-hydrogen atoms are mapped onto one interaction site, has been proposed and applied to study various aspects of lipid systems. To date, no extensive investigation of its capability to describe salvation thermodynamics has been undertaken. In the present study, a detailed picture of vaporization, solvation, and phase-partitioning thermodynamics for liquid hydrocarbons and water was obtained at CG and AL resolutions, in order to compare the two types or models and evaluate their ability to describe thermodynamic properties in the temperature range between 263 and 343 K. Both CG and AL models capture the experimental dependence of the thermodynamic properties on the temperature, albeit a systematically weaker dependence is found for the CG model. Moreover, deviations are found for solvation thermodynamics and for the corresponding enthalpy-entropy compensation for the CG model. Particularly water/oil repulsion seems to be overestimated. However, the results suggest that the thermodynamic properties considered should be reproducible by a CG model provided it is reparametrized on the basis of these liquid-phase properties.

A comparison of methods to compute the potential of mean force.

Most processes occurring in a system are determined by the relative free energy between two or more states because the free energy is a measure of the probability of finding the system in a given state. When the two states of interest are connected by a pathway, usually called reaction coordinate, along which the free-energy profile is determined, this profile or potential of mean force (PMF) will also yield the relative free energy of the two states. Twelve different methods to compute a PMF are reviewed and compared, with regard to their precision, for a system consisting of a pair of methane molecules in aqueous solution. We analyze all combinations of the type of sampling (unbiased, umbrella-biased or constraint-biased), how to compute free energies (from density of states or force averaging) and the type of coordinate system (internal or Cartesian) used for the PMF degree of freedom. The method of choice is constraint-bias simulation combined with force averaging for either an internal or a Cartesian PMF degree of freedom.

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

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.

Simulation of an all-beta 3-icosapeptide containing the 20 proteinogenic side chains: effect of temperature, pH, counterions, solvent, and force field on helix stability.

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.

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

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.

Biomolecular modeling: Goals, problems, perspectives.

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.

Enthalpy-entropy compensation in the effects of urea on hydrophobic interactions.

By comparison of neopentane pair potentials of mean force (PMFs) in room temperature water and 6.9 molar aqueous urea, it was recently shown that urea molecules affect the PMF minima in an unexpected way (Lee, M.-E.; van der Vegt, N. F. A. J. Am. Chem. Soc. 2006, 128, 4948). While the first PMF minimum in urea solution has an identical shape and depth to those of the corresponding minimum in water, the second minimum in urea solution is broader, deeper, and shifted out to a slightly larger distance. Here, we present a study of the enthalpic and entropic contributions to these PMFs. Its significance for understanding the driving forces responsible for thermodynamically favorable neopentane contact and solvent-separated distances in urea solution is discussed. We propose that the solute-solvent entropy and solute-solvent enthalpy changes should be analyzed for obtaining an unambiguous molecular-scale picture. In urea solution, enthalpy-entropy compensation effects associated with structural solvent reorganization processes are large, causing changes of the system's enthalpy and entropy with hydrophobic pair separation to be very different from the solute-solvent enthalpy and entropy changes. The entropies are discussed in terms of the molecular-scale solvent reorganization processes.

The GROMOS software for biomolecular simulation: GROMOS05.

We present the latest version of the Groningen Molecular Simulation program package, GROMOS05. It has been developed for the dynamical modelling of (bio)molecules using the methods of molecular dynamics, stochastic dynamics, and energy minimization. An overview of GROMOS05 is given, highlighting features not present in the last major release, GROMOS96. The organization of the program package is outlined and the included analysis package GROMOS++ is described. Finally, some applications illustrating the various available functionalities are presented.

Interpreting NMR data for beta-peptides using molecular dynamics simulations.

NMR is one of the most used techniques to resolve structure of proteins and peptides in solution. However, inconsistencies may occur due to the fact that a polypeptide may adopt more than one conformation. Since the NOE distance bounds and (3)J-values used in such structure determination represent a nonlinear average over the total ensemble of conformers, imposition of NOE or (3)J-value restraints to obtain one unique conformation is not an appropriate procedure in such cases. Here, we show that unrestrained MD simulation of a solute in solution using a high-quality force field yields a conformational ensemble that is largely compatible with the experimental NMR data on the solute. Four 100 ns MD simulations of two forms of a nine-residue beta-peptide in methanol at two temperatures produced conformational ensembles that were used to interpret the NMR data on this molecule and resolve inconsistencies between the experimental NOEs. The protected and unprotected forms of the beta-peptide adopt predominantly a 12/10-helix in agreement with the qualitative interpretation of the NMR data. However, a particular NOE was not compatible with this helix indicating the presence of other conformations. The simulations showed that 3(14)()-helical structures were present in the ensemble of the unprotected form and that their presence correlates with the fulfillment of the particular NOE. Additionally, all inter-hydrogen distances were calculated to compare NOEs predicted by the simulations to the ones observed experimentally. The MD conformational ensembles allowed for a detailed and consistent interpretation of the experimental data and showed the small but specific conformational differences between the protected and unprotected forms of the peptide.