Convergence results for stochastic particle systems with social interaction

We consider stochastic individual-based models for social behaviour of groups of animals. In these models the trajectory of each animal is given by a stochastic differential equation with interaction. The social interaction is contained in the drift term of the SDE. We consider a global aggregation force and a short-range repulsion force. The repulsion range and strength gets rescaled with the number of animals N. We show that for N tending to infinity stochastic fluctuations disappear and a smoothed version of the empirical process converges uniformly towards the solution of a nonlinear, nonlocal partial differential equation of advection-reaction-diffusion type. The rescaling of the repulsion in the individual-based model implies that the corresponding term in the limit equation is local while the aggregation term is non-local. Moreover, we discuss the effect of a predator on the system and derive an analogous convergence result. The predator acts as an repulsive force. Different laws of motion for the predator are considered.

Direct and inverse transient eddy current problems

Die vorliegende Arbeit behandelt Vorwärts- sowie Rückwärtstheorie transienter Wirbelstromprobleme. Transiente Anregungsströme induzieren elektromagnetische Felder, welche sogenannte Wirbelströme in leitfähigen Objekten erzeugen. Im Falle von sich langsam ändernden Feldern kann diese Wechselwirkung durch die Wirbelstromgleichung, einer Approximation an die Maxwell-Gleichungen, beschrieben werden. Diese ist eine lineare partielle Differentialgleichung mit nicht-glatten Koeffizientenfunktionen von gemischt parabolisch-elliptischem Typ. Das Vorwärtsproblem besteht darin, zu gegebener Anregung sowie den umgebungsbeschreibenden Koeffizientenfunktionen das elektrische Feld als distributionelle Lösung der Gleichung zu bestimmen. Umgekehrt können die Felder mit Messspulen gemessen werden. Das Ziel des Rückwärtsproblems ist es, aus diesen Messungen Informationen über leitfähige Objekte, also über die Koeffizientenfunktion, die diese beschreibt, zu gewinnen. In dieser Arbeit wird eine variationelle Lösungstheorie vorgestellt und die Wohlgestelltheit der Gleichung diskutiert. Darauf aufbauend wird das Verhalten der Lösung für verschwindende Leitfähigkeit studiert und die Linearisierbarkeit der Gleichung ohne leitfähiges Objekt in Richtung des Auftauchens eines leitfähigen Objektes gezeigt. Zur Regularisierung der Gleichung werden Modifikationen vorgeschlagen, welche ein voll parabolisches bzw. elliptisches Problem liefern. Diese werden verifiziert, indem die Konvergenz der Lösungen gezeigt wird. Zuletzt wird gezeigt, dass unter der Annahme von sonst homogenen Umgebungsparametern leitfähige Objekte eindeutig durch die Messungen lokalisiert werden können. Hierzu werden die Linear Sampling Methode sowie die Faktorisierungsmethode angewendet.

Analytische Ableitungen der Energie für den "Equation-of-Motion-Coupled-Cluster"-Ansatz zur Berechnung von Ionisationspotentialen

In der vorliegenden Arbeit wird die Theorie der analytischen zweiten Ableitungen für die EOMIP-CCSD-Methode formuliert sowie die durchgeführte Implementierung im Quantenchemieprogramm CFOUR beschrieben. Diese Ableitungen sind von Bedeutung bei der Bestimmung statischer Polarisierbarkeiten und harmonischer Schwingungsfrequenzen und in dieser Arbeit wird die Genauigkeit des EOMIP-CCSD-Ansatzes bei der Berechnung dieser Eigenschaften für verschiedene radikalische Systeme untersucht. Des Weiteren können mit Hilfe der ersten und zweiten Ableitungen vibronische Kopplungsparameter berechnet werden, welche zur Simulation von Molekülspektren in Kombination mit dem Köppel-Domcke-Cederbaum (KDC)-Modell - in der Arbeit am Beispiel des Formyloxyl (HCO2)-Radikals demonstriert - benötigt werden.rnrnDer konzeptionell einfache EOMIP-CC-Ansatz wurde gewählt, da hier die Wellenfunktion eines Radikalsystems ausgehend von einem stabilen geschlossenschaligen Zustand durch die Entfernung eines Elektrons gebildet wird und somit die Problematik der Symmetriebrechung umgangen werden kann. Im Rahmen der Implementierung wurden neue Programmteile zur Lösung der erforderlichen Gleichungen für die gestörten EOMIP-CC-Amplituden und die gestörten Lagrange-Multiplikatoren zeta zum Quantenchemieprogramm CFOUR hinzugefügt. Die unter Verwendung des Programms bestimmten Eigenschaften werden hinsichtlich ihrer Leistungsfähigkeit im Vergleich zu etablierten Methoden wie z.B. CCSD(T) untersucht. Bei der Berechnung von Polarisierbarkeiten und harmonischen Schwingungsfrequenzen liefert die EOMIP-CCSD-Theorie meist gute Resultate, welche nur wenig von den CCSD(T)-Ergebnissen abweichen. Einzig bei der Betrachtung von Radikalen, für die die entsprechenden Anionen nicht stabil sind (z.B. NH2⁻ und CH3⁻), liefert der EOMIP-CCSD-Ansatz aufgrund methodischer Nachteile keine aussagekräftige Beschreibung. rnrnDie Ableitungen der EOMIP-CCSD-Energie lassen sich auch zur Simulation vibronischer Kopplungen innerhalb des KDC-Modells einsetzen.rnZur Kopplung verschiedener radikalischer Zustände in einem solchen Modellpotential spielen vor allem die Ableitungen von Übergangsmatrixelementen eine wichtige Rolle. Diese sogenannten Kopplungskonstanten können in der EOMIP-CC-Theorie besonders leicht definiert und berechnet werden. Bei der Betrachtung des Photoelektronenspektrums von HCO2⁻ werden zwei Alternativen untersucht: Die vertikale Bestimmung an der Gleichgewichtsgeometrie des HCO2⁻-Anions und die Ermittlung adiabatischer Kraftkonstanten an den Gleichgewichtsgeometrien des Radikals. Lediglich das adiabatische Modell liefert bei Beschränkung auf harmonische Kraftkonstanten eine qualitativ sinnvolle Beschreibung des Spektrums. Erweitert man beide Modelle um kubische und quartische Kraftkonstanten, so nähern sich diese einander an und ermöglichen eine vollständige Zuordnung des gemessenen Spektrums innerhalb der ersten 1500 cm⁻¹. Die adiabatische Darstellung erreicht dabei nahezu quantitative Genauigkeit.

Differential cell type-specific transcriptional regulation of the CYP1A1 gene

Cytochrome P450 1A1 (CYP1A1) monooxygenase plays an important role in the metabolism of environmental pollutants such as polycyclic aromatic hydrocarbons (PAHs) and halogenated polycyclic aromatic hydrocarbons (HAHs). Oxidation of these compounds converts them to the metabolites that subsequently can be conjugated to hydrophilic endogenous entities e.g. glutathione. Derivates generated in this way are water soluble and can be excreted in bile or urine, which is a defense mechanism. Besides detoxification, metabolism by CYP1A1 may lead to deleterious effects since the highly reactive intermediate metabolites are able to react with DNA and thus cause mutagenic effects, as it is in the case of benzo(a) pyrene (B[a]P). CYP1A1 is normally not expressed or expressed at a very low level in the cells but it is inducible by many PAHs and HAHs e.g. by B[a]P or 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD). Transcriptional activation of the CYP1A1 gene is mediated by aryl hydrocarbon receptor (AHR), a basic-helix-loop-helix (bHLH) transcription factor. In the absence of a ligand AHR stays predominantly in the cytoplasm. Ligand binding causes translocation of AHR to the nuclear compartment, its heterodimerization with another bHLH protein, the aryl hydrocarbon nuclear translocator (ARNT) and binding of the AHR/ARNT heterodimer to a DNA motif designated dioxin responsive element (DRE). This process leads to the transcriptional activation of the responsive genes containing DREs in their regulatory regions, e.g. that coding for CYP1A1. TCDD is the most potent known agonist of AHR. Since it is not metabolized by the activated enzymes, exposure to this compound leads to a persisting activation of AHR resulting in diverse toxic effects in the organism. To enlighten the molecular mechanisms that mediate the toxicity of xenobiotics like TCDD and related compounds, the AHR-dependent regulation of the CYP1A1 gene was investigated in two cell lines: human cervix carcinoma (HeLa) and mouse hepatoma (Hepa). Study of AHR activation and its consequence concerning expression of the CYP1A1 enzyme confirmed the TCDD-dependent formation of the AHR/ARNT complex on DRE leading to an increase of the CYP1A1 transcription in Hepa cells. In contrast, in HeLa cells formation of the AHR/ARNT heterodimer and binding of a protein complex containing AHR and ARNT to DRE occurred naturally in the absence of TCDD. Moreover, treatment with TCDD did not affect the AHR/ARNT dimer formation and binding of these proteins to DRE in these cells. Even though the constitutive complex on DRE exists in HeLa, transcription of the CYP1A1 gene was not increased. Furthermore, the CYP1A1 level in HeLa cells remained unchanged in the presence of TCDD suggesting repressional mechanism of the AHR complex function which may hinder the TCDD-dependent mechanisms in these cells. Similar to the native, the mouse CYP1A1-driven reporter constructs containing different regulatory elements were not inducible by TCDD in HeLa cells, which supported a presence of cell type specific trans-acting factor in HeLa cells able to repress both the native CYP1A1 and CYP1A1-driven reporter genes rather than species specific differences between CYP1A1 genes of human and rodent origin. The different regulation of the AHR-mediated transcription of CYP1A1 gene in Hepa and HeLa cells was further explored in order to elucidate two aspects of the AHR function: (I) mechanism involved in the activation of AHR in the absence of exogenous ligand and (II) factor that repress function of the exogenous ligand-independent AHR/ARNT complex. Since preliminary studies revealed that the activation of PKA causes an activation of AHR in Hepa cells in the absence of TCDD, the PKA-dependent signalling pathway was the proposed endogenous mechanism leading to the TCDD-independent activation of AHR in HeLa cells. Activation of PKA by forskolin or db-cAMP as well as inhibition of the kinase by H89 in both HeLa and Hepa cells did not lead to alterations in the AHR interaction with ARNT in the absence of TCDD and had no effect on binding of these proteins to DRE. Moreover, the modulators of PKA did not influence the CYP1A1 activity in these cells in the presence and in the absence of TCDD. Thus, an involvement of PKA in the regulation of the CYP1A1 Gen in HeLa cells was not evaluated in the course of this study. Repression of genes by transcription factors bound to their responsive elements in the absence of ligands has been described for nuclear receptors. These receptors interact with protein complex containing histone deacetylase (HDAC), enzyme responsible for the repressional effect. Thus, a participation of histone deacetylase in the transcriptional modulation of CYP1A1 gene by the constitutively DNA-bound AHR/ARNT complex was supposed. Inhibition of the HDAC activity by trichostatin A (TSA) or sodium butyrate (NaBu) led to an increase of the CYP1A1 transcription in the presence but not in the absence of TCDD in Hepa and HeLa cells. Since amount of the AHR and ARNT proteins remained unchanged upon treatment of the cells with TSA or NaBu, the transcriptional upregulation of CYP1A1 gene was not due to an increased expression of the regulatory proteins. These findings strongly suggest an involvement of HDAC in the repression of the CYP1A1 gene. Similar to the native human CYP1A1 also the mouse CYP1A1-driven reporter gene transfected into HeLa cells was repressed by histone deacetylase since the presence of TSA or NaBu led to an increase in the reporter activity. Induction of reporter gene did not require a presence of the promoter or negative regulatory regions of the CYP1A1 gene. A promoter-distal fragment containing three DREs together with surrounding sequences was sufficient to mediate the effects of the HDAC inhibitors suggesting that the AHR/ARNT binding to its specific DNA recognition site may be important for the CYP1A1 repression. Histone deacetylase is recruited to the specific genes by corepressors, proteins that bind to the transcription factors and interact with other members of the HDAC complex. Western blot analyses revealed a presence of HDAC1 and the corepressors mSin3A (mammalian homolog of yeast Sin3) and SMRT (silencing mediator for retinoid and thyroid hormone receptor) in both cell types, while the corepressor NCoR (nuclear receptor corepressor) was expressed exclusively in HeLa cells. Thus the high inducibility of CYP1A1 in Hepa cells may be due to the absence of NCoR in these cells in contrast to the non-responsive HeLa cells, where the presence of NCoR would support repression of the gene by histone deacetylase. This hypothesis was verified in reporter gene experiments where expression constructs coding for the particular members of the HDAC complex were cotransfected in Hepa cells together with the TCDD-inducible reporter constructs containing the CYP1A1 regulatory sequences. An overexpression of NCoR however did not decrease but instead led to a slight increase of the reporter gene activity in the cells. The expected inhibition was observed solely in the case of SMRT that slightly reduced constitutive and TCDD-induced reporter gene activity. A simultaneous expression of NCoR and SMRT shown no further effects and coexpression of HDAC1 with the two corepressors did not alter this situation. Thus, additional factors that are likely involved in the repression of CYP1A1 gene by HDAC complex remained to be identified. Taking together, characterisation of an exogenous ligand independent AHR/ARNT complex on DRE in HeLa cells that repress transcription of the CYP1A1 gene creates a model system enabling investigation of endogenous processes involved in the regulation of AHR function. This study implicates HDAC-mediated repression of CYP1A1 gene that contributes to the xenobiotic-induced expression in a tissue specific manner. Elucidation of these processes gains an insight into mechanisms leading to deleterious effects of TCDD and related compounds.

Single polymers at surfaces: adsorption and detachment

This thesis is concerned with the adsorption and detachment of polymers at planar, rigid surfaces. We have carried out a systematic investigation of adsorption of polymers using analytical techniques as well as Monte Carlo simulations with a coarse grained off-lattice bead spring model. The investigation was carried out in three stages. In the first stage the adsorption of a single multiblock AB copolymer on a solid surface was investigated by means of simulations and scaling analysis. It was shown that the problem could be mapped onto an effective homopolymer problem. Our main result was the phase diagram of regular multiblock copolymers which shows an increase in the critical adsorption potential of the substrate with decreasing size of blocks. We also considered the adsorption of random copolymers which was found to be well described within the annealed disorder approximation. In the next phase, we studied the adsorption kinetics of a single polymer on a flat, structureless surface in the regime of strong physisorption. The idea of a ’stem-flower’ polymer conformation and the mechanism of ’zipping’ during the adsorption process were used to derive a Fokker-Planck equation with reflecting boundary conditions for the time dependent probability distribution function (PDF) of the number of adsorbed monomers. The numerical solution of the time-dependent PDF obtained from a discrete set of coupled differential equations were shown to be in perfect agreement with Monte Carlo simulation results. Finally we studied force induced desorption of a polymer chain adsorbed on an attractive surface. We approached the problem within the framework of two different statistical ensembles; (i) by keeping the pulling force fixed while measuring the position of the polymer chain end, and (ii) by measuring the force necessary to keep the chain end at fixed distance above the adsorbing plane. In the first case we treated the problem within the framework of the Grand Canonical Ensemble approach and derived analytic expressions for the various conformational building blocks, characterizing the structure of an adsorbed linear polymer chain, subject to pulling force of fixed strength. The main result was the phase diagram of a polymer chain under pulling. We demonstrated a novel first order phase transformation which is dichotomic i.e. phase coexistence is not possible. In the second case, we carried out our study in the “fixed height” statistical ensemble where one measures the fluctuating force, exerted by the chain on the last monomer when a chain end is kept fixed at height h over the solid plane at different adsorption strength ε. The phase diagram in the h − ε plane was calculated both analytically and by Monte Carlo simulations. We demonstrated that in the vicinity of the polymer desorption transition a number of properties like fluctuations and probability distribution of various quantities behave differently, if h rather than the force, f, is used as an independent control parameter.