Markov State Models from short non-Equilibrium Simulations - Analysis and Correction of Estimation Bias

Many state-of-the-art methods for the thermodynamic and kinetic characterization of large and complex biomolecular systems by simulation rely on ensemble approaches, where data from large numbers of relatively short trajectories are integrated. In this context, Markov state models (MSMs) are extremely popular because they can be used to compute stationary quantities and long-time kinetics from ensembles of short simulations, provided that these short simulations are in “local equilibrium” within the MSM states. However, over the last 15 years since the inception of MSMs, it has been controversially discussed and not yet been answered how deviations from local equilibrium can be detected, whether these deviations induce a practical bias in MSM estimation, and how to correct for them. In this paper, we address these issues: We systematically analyze the estimation of MSMs from short non-equilibrium simulations, and we provide an expression for the error between unbiased transition probabilities and the expected estimate from many short simulations. We show that the unbiased MSM estimate can be obtained even from relatively short non-equilibrium simulations in the limit of long lag times and good discretization. Further, we exploit observable operator model (OOM) theory to derive an unbiased estimator for the MSM transition matrix that corrects for the effect of starting out of equilibrium, even when short lag times are used. Finally, we show how the OOM framework can be used to estimate the exact eigenvalues or relaxation time scales of the system without estimating an MSM transition matrix, which allows us to practically assess the discretization quality of the MSM. Applications to model systems and molecular dynamics simulation data of alanine dipeptide are included for illustration. The improved MSM estimator is implemented in PyEMMA of version 2.3

a swarm intelligence-based optimizer for molecular geometry

We present a stochastic, swarm intelligence-based optimization algorithm for the prediction of global minima on potential energy surfaces of molecular clusterstructures. Our optimization approach is a modification of the artificial bee colony (ABC) algorithm which is inspired by the foraging behavior of honey bees. We apply our modified ABC algorithm to the problem of global geometryoptimization of molecular clusterstructures and show its performance for clusters with 2–57 particles and different interatomic interaction potentials

Protonenleitung mittels großskaliger atomistischer Simulationen

The simulation of large and complex molecular systems is a very challenging task, especially under realistic conditions. A case in point is the phenomenon of proton conduction in fuel cell membranes, which is the main topic addressed in this work. The computational modeling of this transport phenomenon is still far from being a routine problem, despite the fast development of computational infrastructure. The general phenomenon of ion conduction in condensed matter consists of a multitude of facets. In this thesis, I address several aspects of this phenomenon for the specific case of the proton transport in hexakis(p-phosphonatophenyl)benzene, an organic compound that is a promising material for high temperature fuel cell membranes. I have performed large-scale atomistic simulations with electronic structure methods to elucidate the proton conduction mechanism in this material. The simulations show that this compound self-organizes in supramolecular columnar stacks with a tight intermolecular/interstack hydrogen bond network, which is in good agreement with experimental results. In particular, the simulations show the direct motion of individual protons in the dynamically fluctuating hydrogen bond network. Interestingly, the hydrogen bond network forms quasi-one- dimensional channels in the interstice of adjacent supramolecular stacks and parallel to the columnar axis. The observed motion of the protons shows that the diffusion is most pronounced in these channels. The applied part of my work is a case in point for large-scale simulations under realistic conditions. Such large-scale simulations, however, also require large-scale methods. The second and more theoretical part of my thesis addresses the development of such large-scale methods, specifically, for quantum-classical calculations. Hybrid quantum-classical (QM/MM) calculations combine the ability of classical methods to treat large molecular systems with the advantage of quantum methods to model chemical processes within smaller fragments of the system. I have developed an approach to increase the accuracy of QM/MM calculations with a particular emphasis on spectroscopic parameters; this approach aims at extending the applicability of first-principles spectroscopy calculations to large-scale systems. The second development subproject targets molecular structure prediction by means of numerical calculations. This is one of the evergreen problems in chemical physics but also one of the most difficult challenges. Specifically the determination of the global minimum structure is a field of intense research. For this aim, I have developed a stochastic, swarm intelligence-based optimization algorithm to the problem of global geometry optimization.Die Simulation von großskaligen und komplexen molekularen Systemen ist eine große Herausforderung, insbesondere, wenn die Simulation unter realistischen Bedingungen durchgeführt werden soll. Das zentrale Thema dieser Dissertation ist die Protonenleitung in Brennstoffzellmembranen und ein typisches Beispiel für solch eine Simulation. Die numerische Modellierung dieses Transportphänomens ist allerdings ausgesprochen aufwendig, trotz der rasanten Leistungsfähigkeitssteigerung modernen Computer. Das allgemeine Phänomen der Ionenleitung in kondensierter Materie hat viele Facetten. Im Rahmen dieser Dissertation untersuche ich einige dieser Aspekte für den speziellen Fall von Protonenleitung in Hexakis(p-Phosphonatophenyl)benzol, einer organischen Verbindung mit großem Potential für die Anwendung in Brennstoffzellmembranen. In meiner Arbeit habe ich großskalige, atomistische Simulationen auf Basis der Elektronenstrukturtheorie durchgeführt, um den Leitungsmechanismus in diesem Material zu untersuchen. Die Simulationen zeigen, dass sich dieses Material selbst in supramolekularen Stapeln anordnet und ein dichtes intermolekulares Netzwerk aus Wasserstoffbrücken ausbildet; diese Resultate stimmen gut mit experimentellen Beobachtungen überein. Inbesondere erlauben die Simulationen, die Bewegung der einzelnen Protonen im dynamisch fluktuierenden Wasserstoffbrückennetzwerk direkt zu beobachten. Interessanterweise bildet das Wasserstoffbrückennetzwerk quasi-eindimensionale Kanäle im Zwischenraum benachbarter Stapel, die parallel zu den Stapelachsen angeordnet sind. Die Analyse der direkten Protonenbewegung zeigt, dass die Protonendiffusion innerhalb dieser Kanäle besonders ausgeprägt ist. Dieses anwendungsorientierte Projekt meiner Arbeit ist ein typisches Beispiel für großskalige Simulationen unter realistischen Umgebungsbedingungen. Solch großskalige Simulationen stützen sich allerdings auch auf großskalige Simulationemethoden, deren Entwicklung den zweiten, methodisch orientierten Teil dieser Dissertation ausmachen: Hybrid-quantenmechanisch-klassische (QM/MM) Simulationsmethoden erlauben es, die Vorteile klassischer und quantenmechanischer Methoden zu kombinieren. Dabei wird ein großskaliges System klassisch modelliert und nur ein Fragment auf Basis der Elektronenstrukturtheorie behandelt. Hierfür habe ich ein Verfahren zur Verbesserung der Genauigkeit dieser Methode entwickelt, die insbesondere die Qualität von spektroskopischen Berechnungen erhöht. Dieses Teilprojekt hat zum Ziel, die Anwendbarkeit von Spektroskopieberechnungen auf großskalige Systeme auzudehnen. Das zweite Teilprojekt betrifft die Vorhersage molekularer Struktur mittels numerischer Rechnungen. Dies stellt eine der zentralen Fragestellungen im Feld der chemischen Physik dar und ist gleichzeitig eine der größten Herausforderungen. Insbesondere die Bestimmung des globalen Minimums ist ein vielbeachtetes Feld. Für dieses Problem habe ich einen stochastischen Algorithmus aus dem Feld der Schwarmintelligenz adaptiert und daraus einen globalen Optimierer für molekulare Geometrien entwickelt

Moving Program Objects to Scratch-Pad Memory for Energy Reduction £

This paper presents a new approach for improving energy consumption of compiler generated software by using on-chip Scratch-Pad RAM more efficiently. This memory allocation technique moves program parts (functions or basic blocks and global data objects) into the limited Scratch-Pad RAM. Experimental results show that this technique saves up to 80 % of the total energy consumption depending on the application, the system architecture and the size of the Scratch-Pad RAM

A Coupled Molecular Dynamics/Kinetic Monte Carlo Approach for Protonation Dynamics in Extended Systems

We propose a multiscale simulation scheme that combines first-principles Molecular Dynamics (MD) and kinetic Monte Carlo (kMC) simulations to describe ion transport processes. On the one hand, the molecular dynamics trajectory provides an accurate atomistic structure and its temporal evolution, and on the other hand, the Monte Carlo part models the long-time motion of the acidic protons. Our hybrid approach defines a coupling scheme between the MD and kMC simulations that allows the kMC topology to adapt continuously to the propagating atomistic microstructure of the system. On the example of a fuel cell membrane material, we validate our model by comparing its results with those of the pure MD simulation. We show that the hybrid scheme with an evolving topology results in a better description of proton diffusion than a conventional approach with a static kMC transfer rate matrix. Furthermore, we show that our approach can incorporate additional dynamical features such as the coupling of the rotation of a side group in the molecular building blocks. In the present implementation, we focus on ion conduction, but it is straightforward to generalize our approach to other transport phenomena such as electronic conduction or spin diffusion