Orientational alignment of amyloidogenic proteins in pre-aggregated solutions.

In the present study we combine dielectric relaxation spectroscopy with generalized Born simulations to explore the role of orientational order for protein aggregation in solutions of bovine pancreatic insulin at various pH conditions. Under aggregation-prone conditions at low pH, insulin monomers prefer antiparallel dipole alignments, which are consistent with the orientation of the monomeric subunits in the dimer structure. This alignment is also true for two dimers, suggesting that already at moderate protein concentrations the species assemble in equilibrium clusters, in which the molecules adopt preferred orientations also found for the protomers of the corresponding oligomers.

Relaxation of Voronoi shells in hydrated molecular ionic liquids.

The relaxation of solvation shells is studied following a twofold strategy based on a direct analysis of simulated data as well as on a solution of a Markovian master equation. In both cases solvation shells are constructed by Voronoi decomposition or equivalent Delaunay tessellation. The theoretical framework is applied to two types of hydrated molecular ionic liquids, 1-butyl-3-methyl-imidazolium tetrafluoroborate and 1-ethyl-3-methyl-imidazolium trifluoromethylsulfonate, both mixed with water. Molecular dynamics simulations of both systems were performed at various mole fractions of water. A linear relationship between the mean residence time and the system's viscosity is found from the direct analysis independent of the system's type. The complex time behavior of shell relaxation can be modeled by a Kohlrausch-Williams-Watts function with an almost universal stretching parameter of 1/2 indicative of a square root time law. The probabilistic model enables an intuitive interpretation of essential motional parameters otherwise not accessible by direct analysis. Even more, incorporating the square root time law into the probabilistic model enables a quantitative prediction of shell relaxation from very short simulation studies. In particular, the viscosity of the respective systems can be predicted.

On the collective network of ionic liquid/water mixtures. III. Structural analysis of ionic liquids on the basis of Voronoi decomposition.

Three different mixtures of 1-butyl-3-methyl-imidazolium tetrafluoroborate with water have been studied by means of molecular dynamics simulations. Based on the classical Lopes-Padua force field trajectories of approximately 60 ns were computed. This is the third part of a series concerning the collective network of 1-butyl-3-methyl-imidazolium tetrafluoroborate/water mixtures. The first part [C. Schröder et al., J. Chem. Phys. 127, 234503 (2007)] dealt with the orientational structure and static dielectric constants. The second part [C. Schröder et al., J. Chem. Phys. 129, 184501 (2008)] was focused on the decomposition of the dielectric spectrum of these mixtures. In this work the focus lies on the characterization of the neighborhood of ionic liquids by means of the Voronoi decomposition. The Voronoi algorithm is a rational tool to uniquely decompose the space around a reference molecule without using any empirical parameters. Thus, neighborhood relations, direct and indirect ones, can be extracted and were used in combination with g-coefficients. These coefficients represent the generalization of the traditional radial distribution function in order to include the mutual positioning and orientation of anisotropic molecules. Furthermore, the Voronoi method provides, as a by-product, the mutual coordination numbers of molecular species.

On the collective network of ionic liquid/water mixtures. II. Decomposition and interpretation of dielectric spectra.

This study deals with the dielectric spectra of mixtures of the ionic liquid 1-butyl-3-methyl-imidazolium (BMIM(+)) tetrafluoroborate with water at three selected mole fractions 0.767

The influence of electrostatic forces on the structure and dynamics of molecular ionic liquids.

The vast majority of molecular dynamics simulations are based on nonpolarizable force fields with fixed partial charges for all atoms. The traditional way to obtain these charges are quantum-mechanical calculations performed prior to simulation. Unfortunately, the set of the partial charges heavily relies on the method and the basis set used. Therefore, investigations of the influence of charge variation on simulation data are necessary in order to validate various charge sets. This paper elucidates the consequences of different charge sets on the structure and dynamics of the ionic liquid: 1-ethyl-3-methyl-imidazolium dicyanoamide. The structural features seem to be more or less independent of the partial charge set pointing to a dominance of shape force as modeled by Lennard-Jones parameters. This can be seen in the radial distribution and orientational correlation functions. The role of electrostatic forces comes in when studying dynamical properties. Here, significant deviations between different charge sets can be observed. Overall, dynamics seems to be governed by viscosity. In fact, all dynamical parameters presented in this work can be converted from one charge set to another by viscosity scaling.

On the computation and contribution of conductivity in molecular ionic liquids.

In this study we present the results of the molecular dynamics simulation of the ionic liquids: 1-butyl-3-methyl-imidazolium tetrafluoroborate and trifluoromethylacetate as well as 1-ethyl-3-methyl-imidazolium dicyanamide. Ionic liquids are characterized by both a molecular dipole moment and a net charge. Thus, in contrast to a solution of simple ions in a (non-) polar solvent, rotational and translational effects influence the very same molecule. This study works out the theoretical framework necessary to compute the conductivity spectrum and its low frequency limit of ionic liquids. Merging these computed conductivity spectra with previous simulation results on the dielectric spectra of ionic liquids yields the spectrum of the generalized dielectric constant, which may be compared to experiments. This spectrum was calculated for the three ionic liquids over six orders of magnitude in frequency ranging from 10 MHz to 50 THz. The role of rotation and translation and their coupling term on the generalized dielectric constant is discussed in detail with a special emphasis on the zero-frequency limit. Thereby, the frequency dependence of the cross correlation between the collective rotational dipole moment and the current is discussed.

On the collective network of ionic liquid/water mixtures. I. Orientational structure.

In this work, the collective structure of aqueous solutions of ionic liquids was studied by means of molecular dynamics simulations. Various concentrations of 1-butyl-3-methyl-imidazolium tetrafluoroborate and TIP3P water were simulated at the very same size of the simulation box. For the analysis, the ternary system cation/anion/water was subdivided into binary networks. The local structure of each of these six networks is investigated by atom-atom radial distribution functions as well as by the so-called g coefficients, which reveal the mutual orientation of the network constituting partners. Furthermore, the collective structure of the whole samples was characterized by the contribution of each species to the static dielectric constant epsilon(omega=0) and to the Kirkwood G(K) factor. The combination of the analysis tools mentioned above provides knowledge about the cross-linking of the ionic species with the dipolar water. Thereby, the interplay between charge-charge and hydrogen bond networks is analyzed in detail.

Impact of anisotropy on the structure and dynamics of ionic liquids: a computational study of 1-butyl-3-methyl-imidazolium trifluoroacetate.

The complex ionic network of 1-butyl-3-methyl-imidazolium trifluoroacetate was simulated by means of the molecular dynamics methods over a time period of 100 ns. The influence of the anisotropy of the shape and charge distribution of both the cations and the anions on the local (molecular) and global (collective) structure and dynamics is analyzed. The distance-dependent g coefficients of the orientational probability function g(r,Omega) were found to be an excellent way to interpret local structure. Thereby, the combination and interrelation of individual g coefficients elucidate the mutual orientation. Dynamics at the molecular level is characterized by the time correlation function of the center-of-mass corrected molecular dipole moment mucm. Upon uniting the set of molecular dipoles to a single collective rotational dipole moment, MD, dynamics on a global level is studied. Decomposing into subsets of cations and anions respective self terms as well as the prominent cross term can be extracted. This decomposition also enables a detailed peak assignment in dielectric spectra.

Collective rotational dynamics in ionic liquids: a computational and experimental study of 1-butyl-3-methyl-imidazolium tetrafluoroborate.

The aim of this study is the analysis of the rotational motion in ionic liquids, in particular, 1-butyl-3-methyl-imidazolium tetrafluoroborate. By comparing single-particle and collective motion it is found that the Madden-Kivelson relation is fairly fulfilled in long-term simulation studies (>100 ns), i.e., the collective reorientation can be predicted by the corresponding single-particle property and the static dipolar correlation factor, GK. Furthermore, simulated reorientation is in accordance with hydrodynamic theories yielding hydrodynamic radii comparable to van der Waals radii. Since viscosity is the central quantity entering hydrodynamic formulas, we calculated and measured the viscosity of our system in order to have two independent cycles of hydrodynamic evaluation, a computational and an experimental one. While the static dielectric constant agrees with dielectric reflectance experiment, the hydrodynamic radii derived from the experiments are much lower as a consequence of enhanced rotational motion. Even more, a considerable dynamic broadening is observed in the experiments.

Simulation studies of the protein-water interface. II. Properties at the mesoscopic resolution.

We report molecular dynamics (MD) simulations of three protein-water systems (ubiquitin, apo-calbindin D(9K), and the C-terminal SH2 domain of phospholipase C-gamma1), from which we compute the dielectric properties of the solutions. Since two of the proteins studied have a net charge, we develop the necessary theory to account for the presence of charged species in a form suitable for computer simulations. In order to ensure convergence of the time correlation functions needed for the analysis, the minimum length of the MD simulations was 20 ns. The system sizes (box length, number of waters) were chosen so that the resulting protein concentrations are comparable to experimental conditions. A dielectric component analysis was carried out to analyze the contributions from protein and water to the frequency-dependent dielectric susceptibility chi(omega) of the solutions. Additionally, an even finer decomposition into protein, two solvation shells, and the remaining water (bulk water) was carried out. The results of these dielectric decompositions were used to study protein solvation at mesoscopic resolution, i.e., in terms of protein, first and second solvation layers, and bulk water. This study, therefore, complements the structural and dynamical analyses at molecular resolution that are presented in the companion paper. The dielectric component contributions from the second shell and bulk water are very similar in all three systems. We find that the proteins influence the dielectric properties of water even beyond the second solvation shell, in agreement with what was observed for the mean residence times of water molecules in protein solutions. By contrast, the protein contributions, as well as the contributions of the first solvation shell, are system specific. Most importantly, the protein and the first water shell around ubiquitin and apo-calbindin are anticorrelated, whereas the first water shell around the SH2 domain is positively correlated.

Simulation studies of the protein-water interface. I. Properties at the molecular resolution.

We report molecular dynamics simulations of three globular proteins: ubiquitin, apo-calbindin D(9K), and the C-terminal SH2 domain of phospholipase C-gamma1 in explicit water. The proteins differ in their overall charge and fold type and were chosen to represent to some degree the structural variability found in medium-sized proteins. The length of each simulation was at least 15 ns, and larger than usual solvent boxes were used. We computed radial distribution functions, as well as orientational correlation functions about the surface residues. Two solvent shells could be clearly discerned about charged and polar amino acids. Near apolar amino acids the water density near such residues was almost devoid of structure. The mean residence time of water molecules was determined for water shells about the full protein, as well as for water layers about individual amino acids. In the dynamic properties, two solvent shells could be characterized as well. However, by comparison to simulations of pure water it could be shown that the influence of the protein reaches beyond 6 A, i.e., beyond the first two shells. In the first shell (r < or =3.5 A), the structural and dynamical properties of solvent waters varied considerably and depended primarily on the physicochemical properties of the closest amino acid side chain, with which the waters interact. By contrast, the solvent properties seem not to depend on the specifics of the protein studied (such as the net charge) or on the secondary structure element in which an amino acid is located. While differing considerably from the neat liquid, the properties of waters in the second solvation shell (3.5< r < or =6 A) are rather uniform; a direct influence from surface amino acids are already mostly shielded.

Simulation studies of ionic liquids: orientational correlations and static dielectric properties.

The ionic liquids BMIM+I-, BMIM+BF4-, and BMIM+PF6- were simulated by means of the molecular dynamics method over a time period of more than 100 ns. Besides the common structural analysis, e.g., radial distribution functions and three dimensional occupancy plots, a more sophisticated orientational analysis was performed. The angular correlation functions g(00)110(r) and g(00)101(r) are the first distance dependent coefficients of the pairwise orientational distribution function g(rij,Omega1,Omega2,Omega12). These functions help to interpret the three dimensional plot and reveal interesting insights into the local structure of the analyzed ionic liquids. Furthermore, the collective network of ionic liquids can be characterized by the Kirkwood factor Gkappa(r) [J. Chem. Phys. 7, 911 (1939)]. The short-range behavior (r<10 A) of this factor may be suitable to predict the water miscibility of the ionic liquid. The long-range limit of Gkinfinity is below 1 which demonstrates the strongly coupled nature of the ionic liquid networks. In addition, this factor relates the orientational structure and the dielectric properties of the ionic liquids. The static dielectric constant epsilon(omega=0) for the simulated system is 8.9-9.5. Since in ionic liquids the very same molecule contributes to the total dipole moment as well as carries a net charge, a small, but significant contribution of the cross term between the total dipole moment and the electric current to epsilon(omega=0) is observed.

X-ray structure and conformational dynamics of the HIV-1 protease in complex with the inhibitor SDZ283-910: agreement of time-resolved spectroscopy and molecular dynamics simulations.

Based on the X-ray structure of the human immunodeficiency virus type-1 (HIV-1) protease in complex with the statine-derived inhibitor SDZ283-910, a 542 ps molecular dynamics trajectory was computed. For comparison with the 805 ps trajectory obtained for the uncomplexed enzyme, the theoretical fluorescence anisotropy decay of the unliganded protease and the inhibitor complex was calculated from the trajectories of the Trp6A/Trp6B and Trp42A/Trp42B transition dipole moments. This enabled us to directly compare the simulated data with the experimental picosecond time-resolved fluorescence data. Fitting both experimental and simulated data to the Kohlrausch-Williams-Watts (KWW) function exp(-t/tauk)beta revealed a very good agreement for the uncomplexed protease as well as for the SDZ283-910 complex. Binding of the inhibitor induced a faster decay of both the experimental and the computed protease fluorescence anisotropy decay. By this integrative approach, the atomic detail of inhibitor-induced changes in the conformational dynamics of the HIV-1 protease was experimentally verified and will be used for further inhibitor optimisation.

Towards a better description and understanding of biomolecular solvation.

We introduce a flexible framework for the correct description of the solvation of biological macromolecules, the dielectric field equation (DFE). The formalism permits the use of any combination of quantum mechanical (QM), molecular mechanical (MM) and continuum electrostatic (CE) based techniques. For the CE region a method that yields the electric field rather than the potential is outlined. The DFE formalism makes clear the need to consider and to calibrate a dielectric boundary region surrounding the simulation system. The details of how to do this are presented for the case of the Ewald summation method; the effects are demonstrated by calculations of the dielectric properties and the spatially resolved Kirkwood G-factor, G(K)(r), of TIP3P water. Computing the dielectric properties of a multi-component system provides a sensitive method to better understand the solvation of biological macromolecules. Towards this goal a rigorous analysis of the dielectric properties of solvated biomolecules based on a decomposition of the frequency-dependent dielectric constant (or susceptibility) of the full system is presented. The meaning of our approach is investigated, and the results of a first application are reported. Using the method of Voronoi polyhedra, the dielectric properties of the first two solvation shells and bulk water are compared by re-analyzing a 12-ns trajectory of a zinc finger peptide in water [Löffler et al. J. Mol. Biol. 270 (1997) 520]. It is found that the first shell behaves considerably different; in addition, there is a non-negligible contribution to the total susceptibility of the system from coupling between the protein and the bulk water phase, i.e. the water molecules not in the immediate vicinity of the solute.

Calculation of the dielectric properties of a protein and its solvent: theory and a case study.

This paper presents a rigorous derivation of a theory for the calculation of the frequency-dependent dielectric properties of each component of the system protein/water/ions with the aim of enabling comparison to experimentally determined dielectric properties. We apply this theory to a very long (13.1 ns) molecular dynamics simulation of an HIV1 zinc finger peptide, its co-ordinated zinc ion, and two chloride ions in a box of SPC/E water molecules. We find the dielectric relaxation of the water molecules restricted compared to pure water, giving rise to a static dielectric constant for the water-component of only 47. The peptide is found to have a complicated dielectric relaxation behaviour, with a static dielectric constant of 15. We also calculate the frequency-dependent conductivity of the ions in this system. We analyze all contributions to the calculation of these dielectric properties and find that the coupling between the dielectric relaxation of the peptide and that of the water-component is particularly important for correctly describing the dielectric constant of the peptide.

The influence of a protein on water dynamics in its vicinity investigated by molecular dynamics simulation.

A system containing the globular protein ubiquitin and 4,197 water molecules has been used for the analysis of the influence exerted by a protein on solvent dynamics in its vicinity. Using Voronoi polyhedra, the solvent has been divided into three subsets, i.e., the first and second hydration shell, and the remaining bulk, which is hardly affected by the protein. Translational motion in the first shell is retarded by a factor of 3 in comparison to bulk. Several molecules in the first shell do not reach the diffusive regime within 100 ps. Shell-averaged orientational autocorrelation functions, which are also subject to a retardation effect, cannot be modeled by a single exponential time law, but are instead well-described by a Kohlrausch-Williams-Watts (KWW) function. The underlying distribution of single-molecule rotational correlation times is both obtained directly from the simulation and derived theoretically. The temperature dependence of reorientation is characterized by a strongly varying correlation time, but a virtually temperature-independent KWW exponent. Thus, the coupling of water structure relaxation with the respective environment, which is characteristic of each solvation shell, is hardly affected by temperature. In other words, the functional form of the distributions of single-molecule rotational correlation times is not subject to a temperature effect. On average, a correlation between reorientation and lifetimes of neighborhood relations is observed.

NMR cross-relaxation investigated by molecular dynamics simulation: a case study of ubiquitin in solution.

A one nanosecond molecular dynamics simulation of ubiquitin in solution has been used for the calculation of the total dipolar, the radial and the reorientational correlation functions of 174 interproton NOEs and the 76 peptide chain NH vectors. The NOEs have been classified according to the structural elements they are associated with. Using multiexponential fits of the raw data spectral densities and cross-relaxation rate constants have been determined. Statistical distributions of correlation function parameters are given. On the basis of these data the assumptions underlying the standard method for distance measurement using NOE enhancements have been scrutinized. The separability of elongation and reorientation is verified for the vast majority of NOEs, but the rigid-body assumption is not supported by the simulation results. Relying on a spectral density expression that neither makes use of the product approximation nor neglects spatially restricted motion, a "bias-free" (with regard to molecular motion) distance measurement method is suggested and compared with the standard method. Errors in distances up to 24% and 50% occur due to the neglect of the dispersion of order parameters and correlation times, respectively. The preconditions for a class-specific calibration method have been investigated. Within the framework of the product approximation a method for decomposing the total cross-relaxation rate constant into contributions from radial and angular motion has been developed and applied. In several cases distance fluctuation contributes significantly to cross-relaxation with both amplitude and time behaviour.

Taming cut-off induced artifacts in molecular dynamics studies of solvated polypeptides. The reaction field method.

In this paper we present a model system of a solvated polypeptide, which is a suitable reference platform for the systematic exploration of methods for taming artifacts introduced by an incorrect treatment of long-range Coulomb forces. The essential feature of the system composed of an alpha-helical peptide and 1021 water molecules is the strict neutrality of all charge groups. The dynamical properties of the peptide, i.e. unfolding or maintenance of the helix, already give first hints on the influence of boundary effects. A rigorous and deeper insight is gained, however, if analyzing the system by means of the generalized Kirkwood g-factor, which projects the net dipole moment of concentric spheres onto the respective dipole moment of the reference charge group. The g-factor is a global measure for, and a sensitive probe of, the orientational structure, which in its turn reflects even the smallest inconsistencies in the treatment of long-range forces. While the cut-off scheme failed the g-factor test, the "reaction field" method, the simplest cut-off correction scheme, enables a consistent description. In other words, with the aid of the reaction field, the correct orientational structure is restored. As a consequence, the helix stability is regained and we were able to calculate the dielectric constant epsilon approximately 55 to 60 for our system, which is slightly below the corresponding value epsilon SPC = 66 of the pure solvent.

Cutoff size does strongly influence molecular dynamics results on solvated polypeptides.

The behavior of a 17-residue model peptide is analyzed by means of molecular dynamics simulations including explicitly more than a thousand water molecules. On the basis of the charge-group concept, Coulomb interactions are truncated for three values of the cutoff radius: 0.6, 1.0, and 1.4 nm. It is found that the stability of an alpha-helix, which acts as a common starting configuration, is a function of the cutoff size. While the overall stability of the helix is conserved in a simulation using a cutoff of 1.0 nm, it is lost within a very short period of 100 ps when the cutoff is increased to 1.4 nm. This demonstrates that the commonly used cutoff size of 1.0 nm is inappropriate because it does not ensure the convergence of Coulomb interactions. In order to permit an independent judgment, we have performed a 225-ps simulation using the Ewald summation technique, which is more elaborate but circumvents the problem to find an appropriate cutoff value. In contrast to the 1.4-nm cutoff trajectory, the Ewald technique simulation conserves the helical character of the peptide conformation. This demonstrates that even 1.4 nm is too short a cutoff. Due to the fundamental uncertainty introduced by the use of a simple cutoff, this truncation scheme seems questionable for molecular dynamics simulations of solvated biomolecules.