Correlation induced electrostatic effects in biomolecular systems

An understanding of electrostatic interactions in biomolecular systems is crucial for many applications in molecular biology. This thesis focuses on the theoretical modeling of two effects: first, the change in the dielectric properties of water due to hydrogen bond formation and second, the reentrant condensation of proteins induced by protein-metal ion complexation. A nonlocal response theory is necessary to describe the dielectric effects of hydrogen bond formation. Correctly formulating this theory for a solvated biomolecule is challenging, because the biomolecule\u27s cavity poses an obstacle for the water network. We develop a theory explicitly incorporating boundary conditions to describe the water network on the molecular surface. We implement an accurate and efficient finite difference solver, which offers the possibility to easily investigate different physically motivated boundary effects. A detailed analysis of different nonlocal models reveals that, for the macroscopic behavior, the boundary conditions are of minor importance, while for a detailed understanding of the electrostatics near the molecular surface the correct modeling of the hydrogen bond formation is crucial. Recent experimental findings describe a reentrant condensation of proteins in solutions of varying metal ion concentration. We present a heuristic model to account for the metal ion binding on the molecular surface which qualitatively and quantitatively explains the phase diagram of this condensation effect.In der vorliegenden Arbeit konzentrieren wir uns auf die Beschreibung elektrostatischer Phänomene in biomolekularen Systemen. Zuerst untersuchen wir den Einfluss von Wasserstoffbrückenbindungen auf die dielektrischen Eigenschaften von Wasser. Dafür ist die Einführung eines nichtlokalen dielektrischen Operators notwendig. Die nichtlokale Reaktion des Wassers wird durch das gelöste Protein und der damit entstandenen Kavität maßgeblich beeinflusst.Wir entwickeln ein Differentialgleichungssystem, welches Veränderungen der dielektrischen Eigenschaften an der Moleküloberfläche explizit berücksichtigt. Um diese Randeffekte genauer zu analysieren und um unsere Modellgleichungen auf ionische Lösungen zu erweitern, implementieren wir ein modifiziertes Finite-Differenzen-Verfahren, welches sich, neben Effizienz, durch hohe Genauigkeit auszeichnet. Mit diesem Lösungsverfahren untersuchen wir erstmals verschiedene Wassermodelle. Die Analyse zeigt, dass die Veränderungen der Randbedingung an der Moleküloberfläche auf makroskopische Größen von untergeordneter Bedeutung sind, jedoch einen signifikanten Einfluss auf das elektrostatische Potential in der Nähe des Moleküls hat. Des Weiteren betrachten wir einen kürzlich entdeckten Effekt in Proteinlösungen: die Bindungsaffinität von gelösten Metallionen induziert die Bildung von Protein-Metallionen-Komplexen. Diese können in Abhängigkeit der gelösten Ionenkonzentration kondensieren und wieder in Lösung gehen. In Analogie zu Protonierungsmodellen entwickeln wir eine Theorie zur Beschreibung der Komplexbildung. Erste Vergleiche mit Experimenten zeigen, dass das vorgeschlagene Modell den Kondensationseffekt qualitativ und quantitativ erklären kann

Deterministic and statistical methods for inverse problems with partial data

Inverse problems with partial data have many applications in science and engineering. They are more challenging than the complete data cases since the lack of data increases ill-posedness and nonlinearity. The use of only deterministic or statistical methods might not provide satisfactory results. We propose to combine the deterministic and statistical methods to treat such inverse problems. The thesis is organized as follows. In Chapter 1, we briefly introduce the inverse problems and their applications. The classical deterministic methods and Bayesian inversion are discussed. The chapter is concluded with a summary of contributions. Chapter 2 considers the reconstruction of the unknown acoustic sources using partial data. First, we extend the direct sampling method to approximate the source locations. Second, the inverse problem is formulated as a statistical inference problem using the Bayes\u27 formula. The source locations obtained in the first step are coded in the priors. Then a Metropolis-Hastings algorithm is used to explore the posterior density. In Chapter 3, a two-step deterministic-statistical approach is proposed to recover the trajectories of moving sources using partial measured data. In the first step, an approximate direct sampling method is developed to obtain the locations of the sources at different times. Such information is coded in the priors, which is critical for the success of the Bayesian method in the second step. The combined approach inherits the merits of the deterministic method and Bayesian inversion as demonstrated by the numerical examples. Chapter 4 studies the reconstruction of Stekloff eigenvalues and the index of refraction of an inhomogeneous medium from Cauchy data. The inverse spectrum problem of Stekloff eigenvalues is investigated by the reciprocity gap method. Then a Bayesian approach is proposed to estimate the index of refraction using a few reconstructed eigenvalues. In Chapter 5, we consider the inverse spectral problem to determine the material properties given a few transmission eigenvalues. The lack of theoretical results motivates us to propose a Bayesian approach to formulate a statistical inference problem. The MCMC algorithm is used to explore the posterior density. Due to the non-uniqueness nature of the problem, we adopt the local conditional means (LCM) to characterize the posterior density function

The bracket geometry of statistics

In this thesis we build a geometric theory of Hamiltonian Monte Carlo, with an emphasis on symmetries and its bracket generalisations, construct the canonical geometry of smooth measures and Stein operators, and derive the complete recipe of measure-constraints preserving dynamics and diffusions on arbitrary manifolds. Specifically, we will explain the central role played by mechanics with symmetries to obtain efficient numerical integrators, and provide a general method to construct explicit integrators for HMC on geodesic orbit manifolds via symplectic reduction. Following ideas developed by Maxwell, Volterra, Poincaré, de Rham, Koszul, Dufour, Weinstein, and others, we will then show that any smooth distribution generates considerable geometric content, including ``musical" isomorphisms between multi-vector fields and twisted differential forms, and a boundary operator - the rotationnel, which, in particular, engenders the canonical Stein operator. We then introduce the ``bracket formalism" and its induced mechanics, a generalisation of Poisson mechanics and gradient flows that provides a general mechanism to associate unnormalised probability densities to flows depending on the score pointwise. Most importantly, we will characterise all measure-constraints preserving flows on arbitrary manifolds, showing the intimate relation between measure-preserving Nambu mechanics and closed twisted forms. Our results are canonical. As a special case we obtain the characterisation of measure-preserving bracket mechanical systems and measure-preserving diffusions, thus explaining and extending to manifolds the complete recipe of SGMCMC. We will discuss the geometry of Stein operators and extend the density approach by showing these are simply a reformulation of the exterior derivative on twisted forms satisfying Stokes' theorem. Combining the canonical Stein operator with brackets allows us to naturally recover the Riemannian and diffusion Stein operators as special cases. Finally, we shall introduce the minimum Stein discrepancy estimators, which provide a unifying perspective of parameter inference based on score matching, contrastive divergence, and minimum probability flow.Open Acces

Computational workflow management for conceptual design of complex systems : an air-vehicle design perspective

The decisions taken during the aircraft conceptual design stage are of paramount importance since these commit up to eighty percent of the product life cycle costs. Thus in order to obtain a sound baseline which can then be passed on to the subsequent design phases, various studies ought to be carried out during this stage. These include trade-off analysis and multidisciplinary optimisation performed on computational processes assembled from hundreds of relatively simple mathematical models describing the underlying physics and other relevant characteristics of the aircraft. However, the growing complexity of aircraft design in recent years has prompted engineers to substitute the conventional algebraic equations with compiled software programs (referred to as models in this thesis) which still retain the mathematical models, but allow for a controlled expansion and manipulation of the computational system. This tendency has posed the research question of how to dynamically assemble and solve a system of non-linear models. In this context, the objective of the present research has been to develop methods which significantly increase the flexibility and efficiency with which the designer is able to operate on large scale computational multidisciplinary systems at the conceptual design stage. In order to achieve this objective a novel computational process modelling method has been developed for generating computational plans for a system of non-linear models. The computational process modelling was subdivided into variable flow modelling, decomposition and sequencing. A novel method named Incidence Matrix Method (IMM) was developed for variable flow modelling, which is the process of identifying the data flow between the models based on a given set of input variables. This method has the advantage of rapidly producing feasible variable flow models, for a system of models with multiple outputs. In addition, criteria were derived for choosing the optimal variable flow model which would lead to faster convergence of the system. Cont/d.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Transactive Control of Coupled Electric Power and District Heating Networks

The aim to decarbonize the energy supply represents a major technical and social challenge. The design of approaches for future energy network operation faces the technical challenge of needing to coordinate a vast number of new network participants spatially and temporally, in order to balance energy supply and demand, while achieving secure network operation. At the same time these approaches should ideally provide economic optimal solutions. In order to meet this challenge, the research field of transactive control emerged, which is based on an appropriate interaction of market and control mechanisms. These approaches have been extensively studied for electric power networks. In order to account for the strong differences between the operation of electric power networks and other energy networks, new approaches need to be developed. Therefore, within this work a new transactive control approach for Coupled Electric Power and District Heating Networks (CEPDHNs) is presented. As this is built upon a model-based control approach, a suitable model is designed first, which enables to operate coupled electric power and district heating networks as efficient as possible. Also, for the transactive control approach a new fitted procedure is developed to determine market clearing prices in the multi-energy system. Further, a distributed form of district heating network operation is designed in this context. The effectiveness of the presented approach is analyzed in multiple simulations, based on real world networks

Computing binary black hole merger waveforms using openGR

textOne of the most important predictions of General Relativity, Einstein’s theory of gravity, is the existence of gravitational radiation. The strongest source of such radiation is expected to come from the merging of black holes. Upgrades to large ground based interferometric detectors (LIGO, VIRGO, GEO 600) have increased their sensitivity to the point that the first direct observation of a gravitational wave is expected to occur within the next few years. The chance of detection is greatly improved by the use of simulated waveforms which can be used as templates for signal processing. Recent advances in numerical relativity have allowed for long stable evolution of black hole mergers and the generation of expected waveforms. openGR is a modular, open framework black hole evolution code developed at The University of Texas at Austin Center for Relativity. Based on the BSSN (strongly hyperbolic) formulation of Einstein’s equations and the moving puncture method, we are able to model the evolution of a binary black hole system through the merger and extract the gravitational radiation produced. Although we are generally interested in binary interactions, openGR is capable of handling any number of black holes. This work serves as an overview of the capabilities of openGR and a demonstration of the physics it can be used to explore.Physic