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Jan Hermans
01/2012: pages 451 - 482; , ISBN: 9781118165850
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Jan Hermans
Proceedings of the National Academy of Sciences 02/2011; 108(8):3095-6. · 9.68 Impact Factor
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ABSTRACT: The recently developed self-consistent-charge density functional tight binding (SCCDFTB) method provides an accurate and inexpensive quantum mechanical solution to many molecular systems of interests. To examine the performance of the SCCDFTB method on (liquid) water, the most fundamental yet indispensable molecule in biological systems, we report here the simulation results of water in sizes ranging from molecular clusters to the liquid state. The latter simulation was achieved through the use of the linear scaling divide-and-conquer approach. The results of liquid water simulation indicate that the SCCDFTB method can describe the structural and energetics of liquid water in qualitative agreement with experiments, and the results for water clusters suggest potential future improvements of the SCCDFTB method.
The Journal of Physical Chemistry A 08/2007; 111(26):5685-91. · 2.95 Impact Factor
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ABSTRACT: The dynamic aspect of proteins is fundamental to understanding protein stability and function. One of the goals of NMR studies of side-chain dynamics in proteins is to relate spin relaxation rates to discrete conformational states and the timescales of interconversion between those states. Reported here is a physical analysis of side-chain dynamics that occur on a timescale commensurate with monitoring by 2H spin relaxation within methyl groups. Motivated by observations made from tens-of-nanoseconds long MD simulations on the small protein eglin c in explicit solvent, we propose a simple molecular mechanics-based model for the motions of side-chain methyl groups. By using a Boltzmann distribution within rotamers, and by considering the transitions between different rotamer states, the model semi-quantitatively correlates the population of rotamer states with 'model-free' order parameters typically fitted from NMR relaxation experiments. Two easy-to-use, analytical expressions are given for converting S2 (axis') values (order parameter for C-CH3 bond) into side-chain rotamer populations. These predict that S2 (axis') values below 0.8 result from population of more than one rotameric state. The relations are shown to predict rotameric sampling with reasonable accuracy on the ps-ns timescale for eglin c and are validated for longer timescales on ubiquitin, for which side-chain residual dipolar coupling (RDC) data have been collected.
Journal of Biomolecular NMR 07/2005; 32(2):151-62. · 3.61 Impact Factor
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ABSTRACT: In this paper, the variation of the values of dihedral angles in proteins is divided into two categories by analyzing distributions in a database of structures determined at a resolution of 1.8 A or better [Lovell et al. (2003), Proteins Struct. Funct. Genet. 50, 437-450]. The first analysis uses the torsion angle for the Calpha-Cbeta bond (chi1) of all Gln, Glu, Arg and Lys residues ('unbranched set'). Plateaued values at low B values imply a root-mean-square deviation (RMSD) of just 9 degrees for chi1 related to intrinsic structural differences between proteins. Extrapolation to high resolution gives a value of 11 degrees , while over the entire database the RMSD is 13.4 degrees . The assumption that the deviations arise from independent intrinsic and extrinsic sources gives approximately 10 degrees as the RMSD for chi1 of these unbranched side chains arising from all disorder and error over the entire set. It is also found that the decrease in chi1 deviation that is correlated with higher resolution structures is almost entirely a consequence of the higher percentage of low-B-value side chains in those structures and furthermore that the crystal temperature at which diffraction data are collected has a negligible effect on intrinsic deviation. Those intrinsic aspects of the distributions not related to statistical or other errors, data incompleteness or disorder correlate with energies of model compounds computed with high-level quantum mechanics. Mean side-chain torsion angles for specific rotamers correlate well with local energy minima of Ace-Leu-Nme, Ace-Ile-Nme and Ace-Met-Nme. Intrinsic RMSD values in examples with B < or = 20 A2 correlate inversely with calculated values for the relevant rotational energy barriers: from a low of 6.5 degrees for chi1 of some rotamers of Ile to a high of 14 degrees for some Met chi3 for fully tetrahedral angles and much higher for chi angles around bonds that are tetrahedral at one end and planar at the other (e.g. 30 degrees for chi2 of the gauche- rotamer of Phe). For the lower barrier Met chi3 rotations there are relatively more well validated cases near eclipsed values and calculated torques from the rest of the protein structure either confine or force the Cepsilon atom into the strained position. These results can be used to evaluate the variability and accuracy of chi angles in crystal structures and also to decide whether to restrain side-chain angles in refinement as a function of the resolution and atomic B values, depending on whether one aims for a realistic distribution of values or a spread that is statistically suitable to the probable data-set errors.
Acta Crystallographica Section D Biological Crystallography 02/2005; 61(Pt 1):88-98. · 12.62 Impact Factor
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Jan Hermans
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ABSTRACT: This chapter reviews formulation and parametrization of molecular mechanics force fields with special attention to technical and inherent problems. Most striking among the shortcomings is the inadequacy of the simple point charge description as a means to describe energy and forces of interactions between polar molecules and between polar groups in macromolecules, including hydrogen bonds. The current state of efforts to improve the description of polar interactions is discussed.
Advances in protein chemistry 02/2005; 72:105-19. · 3.20 Impact Factor
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ABSTRACT: We analyze packing imperfections in globular proteins as reflected in deviations of torsion angles from the equilibrium values for the isolated side chains. The distribution of conformations of methionine and lysine residues in a database of high-resolution structures is compared with energies of model compounds calculated with high-level quantum-mechanics. The distribution of the C-C and C-S torsion angles (chi(3)) correlates well with the Boltzmann factor of the torsion energy, exp(-betaE) of the model compounds C(2)H(5)-C(2)H(5) and C(2)H(5)-S-CH(3). An exponential relation was again found between the relative occurrence of g+, g- and t conformations for C(alpha)-C(beta) bonds in long side chains and the energy differences of rotamers of alpha-amino n-butyric acid, when dependence on backbone conformation was taken into account. The distribution of all 27 rotamers of methionine was correlated with the energy differences between the model's rotamers, corrected for clashes with nearby residues, the correlation being good for a set with backbone in the beta-conformation, but less clear for backbone alpha-conformation. In all correlations, the value of the coefficient beta corresponds to a temperature of circa 300 K. These results can be interpreted with a model that considers the structure of a folded protein as resulting from packing imperfectly complementary parts, with a requirement of an overall low energy. Compromises are required to optimize the fit of nonbonded contacts with surrounding groups, and side chains assume conformations away from the energy minimum. An exponential distribution is a most probable distribution, and this can be established easily under conditions other than thermal equilibrium.
Protein Science 01/2004; 12(12):2719-31. · 2.80 Impact Factor
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ABSTRACT: To gain physical insights into how proteins respond to changes in pH, the picosecond to nanosecond time scale dynamics of the small serine protease inhibitor eglin c have been studied by NMR spin relaxation experiments and MD simulations under two pH solution conditions, pH 7 and 3. Like many proteins, eglin c is destabilized by a lowering of the pH, although it retains enough stability to maintain its native conformation at pH 3. Backbone (15)N relaxation results show comparable global tumbling times (tau(m)) and model-free order parameters (S(2)) under the two pH conditions, indicating that the molecule maintains its overall molecular shape and structure at low pH, although the backbone rigidity is slightly increased (<DeltaS(pH3-pH7)(2)>/<S(2)> = 0.6%). In contrast, the side-chain methyl dynamics, as measured from (2)H relaxation experiments, show a substantial increase in rigidity at lower pH (<DeltaS(axis,pH3-pH7)(2)>/<S(axis)(2)> = 14.8%). Molecular dynamics simulations performed at these pH states produce results consistent with NMR measurements, showing that the two methods are in qualitative agreement. Although a full accounting of the physical basis for the concurrent conformational rigidification and destabilization at low pH requires further investigation, the high level of detail in the MD simulations provides a potential molecular mechanism: the breaking of the hydrogen bond between the side chains of Asp46 and Arg53, and changes in electrostatic interactions, appear to allow the binding loop to move closer to the core part of the protein, resulting in a more compact structure at low pH. This more compact structure may be responsible for the increased level of restriction of molecular motion. As these findings show, the stability of a molecular structure is distinct from its conformational rigidity, and the two can even change in opposite directions, against naïve expectation.
Biochemistry 12/2003; 42(47):13856-68. · 3.42 Impact Factor
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ABSTRACT: We compare the conformational distributions of Ace-Ala-Nme and Ace-Gly-Nme sampled in long simulations with several molecular mechanics (MM) force fields and with a fast combined quantum mechanics/molecular mechanics (QM/MM) force field, in which the solute's intramolecular energy and forces are calculated with the self-consistent charge density functional tight binding method (SCCDFTB), and the solvent is represented by either one of the well-known SPC and TIP3P models. All MM force fields give two main states for Ace-Ala-Nme, beta and alpha separated by free energy barriers, but the ratio in which these are sampled varies by a factor of 30, from a high in favor of beta of 6 to a low of 1/5. The frequency of transitions between states is particularly low with the amber and charmm force fields, for which the distributions are noticeably narrower, and the energy barriers between states higher. The lower of the two barriers lies between alpha and beta at values of psi near 0 for all MM simulations except for charmm22. The results of the QM/MM simulations vary less with the choice of MM force field; the ratio beta/alpha varies between 1.5 and 2.2, the easy pass lies at psi near 0, and transitions between states are more frequent than for amber and charmm, but less frequent than for cedar. For Ace-Gly-Nme, all force fields locate a diffuse stable region around phi = pi and psi = pi, whereas the amber force field gives two additional densely sampled states near phi = +/-100 degrees and psi = 0, which are also found with the QM/MM force field. For both solutes, the distribution from the QM/MM simulation shows greater similarity with the distribution in high-resolution protein structures than is the case for any of the MM simulations.
Proteins Structure Function and Bioinformatics 03/2003; 50(3):451-63. · 3.39 Impact Factor
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Methods in Enzymology 02/2003; 374:412-61. · 2.04 Impact Factor
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Protein Science 05/2002; 11(4):994. · 2.80 Impact Factor
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ABSTRACT: Qmd-plot is a utility to obtain rapid information about past or on-going simulations, or real-time data collections, in the form of graphs of recorded variables (x, y, ...), as x-y plots or as a function of simulated or real time. Time series records in the data file must be named. Variable names and their locations in the data file are initially unknown to the program, but are identified in a first scan, in which header records are located on the basis of a predefined key (that can be changed interactively). The names of the time series are then presented in an interactive menu, from which the user can repeatedly specify a graph to be viewed. Qmd-plot has been developed in the context of molecular dynamics simulations. We give examples of time series and x-y plots made from output of the sigma program. Qmd-plot code is a Java application; source and class files can be obtained free from the authors.
Journal of Computational Chemistry 02/2002; 23(1):184-8. · 4.58 Impact Factor
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ABSTRACT: The calculation of the electrostatic potential inside a polar liquid in an infinitely large system simulated with periodic boundary conditions allows several alternative choices for carrying out the summation over all particles. For a summation of contributions from charge centers limited to the contents of a sphere surrounding the point where the potential is calculated, the cutoff can be based on the location of individual charge centers (so-called q-based summation) or on the location of molecular centers (M-based summation); these two methods have been found to provide consistently different values of the potential. On the other hand, for a summation based on the Ewald method, the choice of the latter's boundary conditions (“vacuum” versus “tinfoil”) affects the value of the calculated potential. A recent discussion (see, Aqvist et al. J. Phys. Chem. 1998, B 102, 3837−3840, and references therein) did not lead to a conclusion as to which is the right choice. Here, we provide a new analysis of M- and q-based cutoff methods and show the following. (i) The M-based method is the correct method to calculate the Coulombic average potential exerted by a polar molecular liquid in the center of a Lennard-Jones (LJ) solute. (ii) Each solute−solvent force field is characterized by a unique M-center for which the potential is zero in the high-temperature limit. This unique M-center is the center of the solvent−solute hard-core interaction for which the solvent molecule's orientational phase space is uncoupled from its positional phase space in the rotational high-temperature limit. (iii) The best value of the average Coulomb potential of water solvent inside a “methane” LJ solute in SPC water at T = 300 K and P = 1 bar is negative, of the order of −7 to − 8 kcal/(mol·e); this includes a uniform potential of the order of +2 to +3 kcal/(mol·e) produced by the polarized surface of the outer liquid−vapor interface of a macroscopic droplet. (iv) The q-based method of calculation of the potential violates the self-consistency of statistical sampling of the configurations of charged sites of the solvent molecules. (v) The effective M- or q-based potentials calculated with Ewald “vacuum” potential are equal to the respective Coulombic potentials. (vi) Use of “tinfoil” boundary conditions for the Ewald potential overestimates the interaction of the central cell with its surroundings and enhances periodicity, and is therefore less appropriate for simulations of liquid systems.
10/1999;
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ABSTRACT: This paper reviews a recently developed method for calculating the total conformational free energy of a solute macromolecule in water solvent. The method consists of a relatively short simulation by molecular dynamics with explicit solvent molecules (ES) to produce a set of microstates of the macroscopic conformation. Conformational internal solute energy and entropy are obtained from the simulation, the latter in the quasi-harmonic approximation by analysis of the covariance matrix. The implicit solvent (IS) surface energy–dielectric continuum model is used to calculate the average solvation free energy as the sum of the free energies of creating the solute-size hydrophobic cavity, of the van der Waals solute–solvent interactions and of the polarization of water solvent by the solute's charges. We have earlier applied this method to calculate the conformational free energy of native and intentionally misfolded globular conformations of proteins (the EMBL set of deliberately misfolded proteins), and have obtained good discrimination in favor of the native conformations in all instances. These results are summarized and further analyzed to show that, on average, three major component terms of the free energy all contribute in favor of discrimination. We discuss possible improvements of the ES/IS method. It is shown how the force field can be made self-consistent by adapting the parameters for calculation of surface and polarization free energies closely to the molecular mechanics force field used in the dynamics simulation, using established simulation methods to compute free energies for cavity formation and a charging process with the molecular mechanics force field to provide a set of (quasi-experimental) reference data that can be used to refine the parameters of the continuum models. The molecular surface area together with a microscopic surface free energy near 70 cal/(mol Å2) is found to be a consistent descriptor of the cavity free energy. Preliminary results indicate that a linear-response approximation for the polarization of water solvent reaction near typical polar and charged protein groups is accurate to within approximately 90%.
Biophysical Chemistry.
