The fitness and macromolecular composition of the gram-negative bacterium E.coli are governed by a seemingly insurmountable level of complexity. However, simple phenomenological measures may be found that describe its systems-level response to a variety of inputs. This thesis explores phenomenological approaches providing accurate quantitative descriptions of complex systems in E.coli. Chapter 1 examines the relationship between unnecessary protein production and growth rate in E.coli. It was previously unknown whether the negative effects on growth rate due to multiple unnecessary protein fractions would add linearly or collectively to produce a nonlinear response. Within the regime of this thesis, it appears that the interplay between growth rate and protein is consistent with a non-interacting model. We do not need to account for complex interaction between system components. Appendix A describes a novel technique for real-time measurement of messenger RNA in single living E.coli cells. Using this technique, one may accurately describe the transcriptional response of gene networks in single cells. / Physics

In this study we assessed growth laws of sub-delta crevasses in the Mississippi River delta plain, experimental laboratory deltas, and compared them to previously studied river dominated large deltas worldwide. Metrics for channel and delta geometry for each system were obtained using a combination of geospatial tools, bathymetric datasets, sediment size, and hydrodynamic observations. Most crevasses and experimental deltas appear to obey delta growth laws suggesting that they exhibit planform metrics similar to larger deltas. However, some channels within each system, exhibit outlier behavior (e.g. asymmetric growth) where channel length is much larger than channel width. Hydrodynamic observations and morphodynamic modeling results, support the role of confinement in governing this response, through direct lateral confinement of the receiving basin width and depth thus guiding channels, and indirect confinement caused by sediment cohesion, whereby natural levees guide the systems asymmetric channel growth.

Une méthode améliorant le calcul des facteurs d’intensité de contrainte en mode I par hybridation de deux fonctions de poids est présentée et appliquée aux cas de fissures elliptiques sous différents chargements. L'hybridation consiste à utiliser l'une ou l'autre des deux fonctions dans la zone de la fissure où la fonction est la plus efficace. La délimitation des zones est faite après optimisation des paramètres géométriques de la fissure. Afin d’étendre l’utilisation de cette approche à la modélisation des fissures semi-elliptiques, son couplage avec la PWFM (Point Weight Function Method) pour tenir compte de l’effet de la surface libre a été réalisé. L’utilisation des lois de propagation de fissure (de Paris et de Sih) a permis l’extension de l’application de l’approche d’hybridation aux problèmes de fatigue. La qualité des résultats trouvés pour les fissures elliptiques et semi-elliptiques est bonne aussi bien pour les chargements quasi-statiques que pour ceux de fatigue. / A method improving the evaluation of the stress intensity factor by hybridization of two weight functions is presented and applied for embedded elliptical cracks under various loadings. The hybridization consists in using one or another function in the zone of the crack where it is the most efficient. The delimitation of the zones is achieved after optimizing the geometrical parameters of the crack. In order to extend the use of this approach to the modeling of semi-elliptical surface cracks, its coupling with the PWFM (Point Weight Function Method) to take account of the free edge effect were carried out. The use of the fatigue crack growth laws (Paris law and Sih law) allowed the extension of the application of the hybrid approach to the fatigue problems. The quality of the results found for the elliptical and the semi-elliptical cracks is good for the static loads as well as for the fatigue ones.

Cyanobakterien sind die einzig bekannten Prokaryoten, die in der Lage sind oxygene Photosynthese zu betreiben. Sie besitzen ein großes Potenzial als nachhaltige Ressourcen für die Herstellung zahlreicher industriell und medizinisch relevanter Wirkstoffe. Trotz ihrer essentiellen Bedeutung ist jedoch das Wachstum von Cyanobakterien bis jetzt nur unzureichend verstanden. Im Rahmen dieser Arbeit habe ich daher ein mathematisches Modell entwickelt, das das Wachstum von Cyanobakterien auf der Grundlage von intrazellulärer Proteinverteilung beschreibt. Dabei wurde das Proteom in wenige relevante Protein-Klassen unterteilt, die an fundamentalen zellulären Prozessen beteiligt sind, darunter Kohlenstoffaufnahme, -fixierung und -stoffwechsel, sowie Photosynthese und Proteintranslation. Besonders interessant sind die aus dem Modell resultierenden sogenannten mikrobiellen Wachstumsgesetze, sprich die Korrelationen zwischen der Wachstumsrate und der Proteinverteilung, die im stationären Zustand des Wachstums beobachtet werden. Das Modell prognostiziert eine charakteristische Krümmung für die Wachstumsgesetze jener Proteine, welche mit Lichtabsorption und Proteintranslation assoziiert werden. Verursacht wird diese Krümmung durch hohe Lichtintensitäten, die eine Abnahme der Wachstumsrate zur Folge haben. Die prognostizierten Wachstumsgesetze werden durch Proteindaten, die mittels Massenspektrometrie erhoben wurden, vom Cyanobakterium Synechocystis sp. PCC 6803 gestützt. Des Weiteren bietet das Modell einen geeigneten Ausgangspunkt für die Erweiterung von der Charakterisierung von Einzelzellen zu einer Population von Zellen in einem lichtlimitierten Chemostat. Das erweiterte Modell stellt einen Zusammenhang her zwischen intrazellulärer Proteinverteilung, Wachstum der Population und Kultivierungseigenschaften, und bietet somit einen neuartigen Ansatz zur Untersuchung und Verbesserung der Kultivierung von phototrophen Organismen und die Optimierung der photosynthetischen Produktivität. / Cyanobacteria are the only known prokaryotes that perform oxygenic photosynthesis, and therefore, hold significant potential as sustainable resources for the production of numerous industrially and medically relevant compounds. Despite their importance, however, the (molecular) limits and cellular economy of photoautotrophic growth are still insufficiently understood. In this thesis, I present a mathematical model based on a coarse-grained description of cellular protein allocation to describe cyanobacterial growth. The model describes cellular trade-offs considering only proteins that are involved in key cellular processes (carbon uptake, fixation, and metabolism, as well as photosynthesis and protein translation). Of particular interest are the resulting microbial growth laws, i.e., correlations between the growth rate and the protein distribution observed during balanced growth. The model predicts a characteristic kink for the growth laws of the light harvesting components and the translational machinery induced by photoinhibition, a decrease in growth rate due to high light intensities. The resulting growth laws are supported by quantitative mass spectrometry-based proteomics data of the cyanobacterium Synechocystis sp. PCC 6803. The proteomics data shows that the mathematical model has intrinsic predictive power, and thus, provides a suitable starting point for extending it from describing single cells to describe a growing population in a light-limited chemostat. The extended modeling framework goes beyond current models using phenomenological growth equations and establishes a mechanistic link between intracellular protein allocation, population growth and cultivation properties. The extended model provides a novel approach to study and guide phototrophic cultivation improvements that maximize photosynthetic productivity.