Novel algorithms for electronic structure based molecular dynamics with linear system-size scaling

Die vorliegende Arbeit behandelt die Entwicklung und Verbesserung von linear skalierenden Algorithmen für Elektronenstruktur basierte Molekulardynamik. Molekulardynamik ist eine Methode zur Computersimulation des komplexen Zusammenspiels zwischen Atomen und Molekülen bei endlicher Temperatur. Ein entscheidender Vorteil dieser Methode ist ihre hohe Genauigkeit und Vorhersagekraft. Allerdings verhindert der Rechenaufwand, welcher grundsätzlich kubisch mit der Anzahl der Atome skaliert, die Anwendung auf große Systeme und lange Zeitskalen. Ausgehend von einem neuen Formalismus, basierend auf dem großkanonischen Potential und einer Faktorisierung der Dichtematrix, wird die Diagonalisierung der entsprechenden Hamiltonmatrix vermieden. Dieser nutzt aus, dass die Hamilton- und die Dichtematrix aufgrund von Lokalisierung dünn besetzt sind. Das reduziert den Rechenaufwand so, dass er linear mit der Systemgröße skaliert. Um seine Effizienz zu demonstrieren, wird der daraus entstehende Algorithmus auf ein System mit flüssigem Methan angewandt, das extremem Druck (etwa 100 GPa) und extremer Temperatur (2000 - 8000 K) ausgesetzt ist. In der Simulation dissoziiert Methan bei Temperaturen oberhalb von 4000 K. Die Bildung von sp²-gebundenem polymerischen Kohlenstoff wird beobachtet. Die Simulationen liefern keinen Hinweis auf die Entstehung von Diamant und wirken sich daher auf die bisherigen Planetenmodelle von Neptun und Uranus aus. Da das Umgehen der Diagonalisierung der Hamiltonmatrix die Inversion von Matrizen mit sich bringt, wird zusätzlich das Problem behandelt, eine (inverse) p-te Wurzel einer gegebenen Matrix zu berechnen. Dies resultiert in einer neuen Formel für symmetrisch positiv definite Matrizen. Sie verallgemeinert die Newton-Schulz Iteration, Altmans Formel für beschränkte und nicht singuläre Operatoren und Newtons Methode zur Berechnung von Nullstellen von Funktionen. Der Nachweis wird erbracht, dass die Konvergenzordnung immer mindestens quadratisch ist und adaptives Anpassen eines Parameters q in allen Fällen zu besseren Ergebnissen führt.

Molecular Dynamics Simulation of a PNA·DNA·PNA Triple Helix in Aqueous Solution

Molecular dynamics simulations have been used to explore the conformational flexibility of a PNA·DNA·PNA triple helix in aqueous solution. Three 1.05 ns trajectories starting from different but reasonable conformations have been generated and analyzed in detail. All three trajectories converge within about 300 ps to produce stable and very similar conformational ensembles, which resemble the crystal structure conformation in many details. However, in contrast to the crystal structure, there is a tendency for the direct hydrogen-bonds observed between the amide hydrogens of the Hoogsteen-binding PNA strand and the phosphate oxygens of the DNA strand to be replaced by water-mediated hydrogen bonds, which also involve pyrimidine O2 atoms. This structural transition does not appear to weaken the triplex structure but alters groove widths and so may relate to the potential for recognition of such structures by other ligands (small molecules or proteins). Energetic analysis leads us to conclude that the reason that the hybrid PNA/DNA triplex has quite different helical characteristics from the all-DNA triplex is not because the additional flexibility imparted by the replacement of sugar−phosphate by PNA backbones allows motions to improve base-stacking but rather that base-stacking interactions are very similar in both types of triplex and the driving force comes from weak but definate conformational preferences of the PNA strands.

Molecular Dynamics Simulations of the d(TAT) Triple Helix

Molecular dynamics (MD) simulations have been used to study the dynamical and time-averaged characteristics of the DNA triple helix d(T)10âd(A)10âd(T)10. The structures sampled during the trajectory resemble closely the B-type model for the DNA triplex proposed on the basis of NMR data, although there are some subtle differences. Alternative P- and A-type conformations for the triplex, suggested from X-ray experiments, are not predicted to contribute significantly to the structure of the DNA triplex in solution. Comparison with the best available experimental data supports the correctnes of the MD-generated structures. The analysis of the collected data gives a detailed picture of the characteristics of triple-helix DNA. A new and interesting pattern of hydration, specific for triplex DNA, is an important observation. The results suggest that molecular dynamics can be useful for the study of novel nucleic acid structures.

Ramachandran-type Plots for Glycosidic Linkages: Examples from Molecular Dynamics Simulations using the Glycam06 Force Field

The goals of this article are to (1) provide further validation of the Glycam06 force field, specifically for its use in implicit solvent molecular dynamic (MD) simulations, and (2) to present the extension of G.N. Ramachandran's idea of plotting amino acid phi and psi angles to the glycosidic phi, psi, and omega angles formed between carbohydrates. As in traditional Ramachandran plots, these carbohydrate Ramachandran-type (carb-Rama) plots reveal the coupling between the glycosidic angles by displaying the allowed and disallowed conformational space. Considering two-bond glycosidic linkages, there are 18 possible conformational regions that can be defined by (α, ϕ, ψ) and (β, ϕ, ψ), whereas for three-bond linkages, there are 54 possible regions that can be defined by (α, ϕ, ψ, ω) and (β, ϕ, ψ, ω). Illustrating these ideas are molecular dynamic simulations on an implicitly hydrated oligosaccharide (700 ns) and its eight constituent disaccharides (50 ns/disaccharide). For each linkage, we compare and contrast the oligosaccharide and respective disaccharide carb-Rama plots, validate the simulations and the Glycam06 force field through comparison to experimental data, and discuss the general trends observed in the plots.

Predicting the Mechanical Properties of Carbon-Based Materials Using Molecular Dynamics

The development of innovative carbon-based materials can be greatly facilitated by molecular modeling techniques. Although molecular modeling has been used extensively to predict elastic properties of materials, modeling of more complex phenomenon such as fracture has only recently been possible with the development of new force fields such as ReaxFF, which is used in this work. It is not fully understood what molecular modeling parameters such as thermostat type, thermostat coupling, time step, system size, and strain rate are required for accurate modeling of fracture. Selection of modeling parameters to model fracture can be difficult and non-intuitive compared to modeling elastic properties using traditional force fields, and the errors generated by incorrect parameters may be non-obvious. These molecular modeling parameters are systematically investigated and their effects on the fracture of well-known carbon materials are analyzed. It is determined that for coupling coefficients of 250 fs and greater do not result in substantial differences in the stress-strain response of the materials using any thermostat type. A time step of 0.5 fs of smaller is required for accurate results. Strain rates greater than 2.2 ns-1 are sufficient to obtain repeatable results with slower strain rates for the materials studied. The results of this study indicate that further refinement of the Chenoweth parameter set is required to accurately predict the mechanical response of carbon-based systems. The ReaxFF has been used extensively to model systems in which bond breaking and formation occur. In particular ReaxFF has been used to model reactions of small molecules. Some elastic and fracture properties have been successfully modeled using ReaxFF in materials such as silicon and some metals. However, it is not clear if current parameterizations for ReaxFF are able to accurately reproduce the elastic and fracture properties of carbon materials. The stress-strain response of a new ReaxFF parameterization is compared to the previous parameterization and density functional theory results for well-known carbon materials. The new ReaxFF parameterization makes xv substantial improvements to the predicted mechanical response of carbon materials, and is found to be suitable for modeling the mechanical response of carbon materials. Finally, a new material composed of carbon nanotubes within an amorphous carbon (AC) matrix is modeled using the ReaxFF. Various parameters that may be experimentally controlled are investigated such as nanotube bundling, comparing multi-walled nanotube with single-walled nanotubes, and degree of functionalization of the nanotubes. Elastic and fracture properties are investigated for the composite systems and compared to results of pure-nanotube and pure-AC models. It is found that the arrangement of the nanotubes and degree of crosslinking may substantially affect the properties of the systems, particularly in the transverse directions.

Supramolecular Organization of Heptapyrenotide Oligomers—An in Depth Investigation by Molecular Dynamics Simulations

We present a molecular modeling study based on ab initio and classical molecular dynamics calculations, for the investigation of the tridimensional structure and supramolecular assembly formation of heptapyrenotide oligomers in water solution. Our calculations show that free oligomers self-assemble in helical structures characterized by an inner core formed by π- stacked pyrene units, and external grooves formed by the linker moieties. The coiling of the linkers has high ordering, dominated by hydrogen-bond interactions among the phosphate and amide groups. Our models support a mechanism of longitudinal supramolecular oligomerization based on interstrand pyrene intercalation. Only a minimal number of pyrene units intercalate at one end, favoring formation of very extended longitudinal chains, as also detected by AFM experiment. Our results provide a structural explanation of the mechanism of chirality amplification in 1:1 mixtures of standard heptapyrenotides and modified oligomers with covalently linked deoxycytidine, based on selective molecular recognition and binding of the nucleotide to the groove of the left-wound helix.

Unraveling the Conformational Determinants of Peptide Dendrimers Using Molecular Dynamics Simulations

Peptide dendrimers are synthetic tree-like molecules composed of amino acids. There are at least two kinds of preferential structural behaviors exhibited by these molecules, which acquire either compact or noncompact shapes. However, the key structural determinants of such behaviors remained, until now, unstudied. Herein, we conduct a comprehensive investigation of the structural determinants of peptide dendrimers by employing long molecular dynamics simulations to characterize an extended set of third generation dendrimers. Our results clearly show that a trade-off between electrostatic effects and hydrogen bond formation controls structure acquisition in these systems. Moreover, by selectively changing the dendrimers charge we are able to manipulate the exhibited compactness. In contrast, the length of branching residues does not seem to be a major structural determinant. Our results are in accordance with the most recent experimental evidence and shed some light on the key molecular level interactions controlling structure acquisition in these systems. Thus, the results presented constitute valuable insights that can contribute to the development of truly tailor-made dendritic systems.

Mechanisms of recognition and binding of α-TTP to the plasma membrane by multi-scale molecular dynamics simulations

We used multiple sets of simulations both at the atomistic and coarse-grained level of resolution to investigate interaction and binding of α-tochoperol transfer protein (α-TTP) to phosphatidylinositol phosphate lipids (PIPs). Our calculations indicate that enrichment of membranes with such lipids facilitate membrane anchoring. Atomistic models suggest that PIP can be incorporated into the binding cavity of α-TTP and therefore confirm that such protein can work as lipid exchanger between the endosome and the plasma membrane. Comparison of the atomistic models of the α-TTP-PIPs complex with membrane-bound α-TTP revealed different roles for the various basic residues composing the basic patch that is key for the protein/ligand interaction. Such residues are of critical importance as several point mutations at their position lead to severe forms of ataxia with vitamin E deficiency (AVED) phenotypes. Specifically, R221 is main residue responsible for the stabilization of the complex. R68 and R192 exchange strong interactions in the protein or in the membrane complex only, suggesting that the two residues alternate contact formation, thus facilitating lipid flipping from the membrane into the protein cavity during the lipid exchange process. Finally, R59 shows weaker interactions with PIPs anyway with a clear preference for specific phosphorylation positions, hinting a role in early membrane selectivity for the protein. Altogether, our simulations reveal significant aspects at the atomistic scale of interactions of α-TTP with the plasma membrane and with PIP, providing clarifications on the mechanism of intracellular vitamin E trafficking and helping establishing the role of key residue for the functionality of α-TTP.

Parameterizing a Simple Potential Energy Function Appropriate for Vibrational Frequencies Using Molecular Dynamics

A Maple scheme for quickly parameterizing vibrational potential energy functions is presented. As an example, the potential energy function's parameters for the vibrational motions in H_2O_2 are obtained assuming the simplest potential energy function. This paper was originally written as a research paper, but rejected by the referees. It is therefore being edited into an ``educational'' paper for student usage.

Molecular Dynamics and the Diatomic Molecule as Harmonic Oscillator and Rigid Rotor

The HCl molecule is simulated (using Maple) in its dynamics, for both vibrational (and implied) rotational motions. A discussion of the center of mass transformations involved is part of the total presentation.

Molecular Dynamics Simulations of Lead and Lithium in Liquid Phase

Pb17Li is today a reference breeder material in diverse fusion R&D programs worldwide. Extracting dynamic and structural properties of liquid LiPb mixtures via molecular dynamics simulations, represent a crucial step for multiscale modeling efforts in order to understand the suitability of this compound for future Nuclear Fusion technologies. At present a Li-Pb cross potential is not available in the literature. Here we present our first results on the validation of two semi-empirical potentials for Li and Pb in liquid phase. Our results represent the establishment of a solid base as a previous but crucial step to implement a LiPb cross potential. Structural and thermodynamical analyses confirm that the implemented potentials for Li and Pb are realistic to simulate both elements in the liquid phase.