As a robust system, cells can wisely choose and switch between different signaling programs according to their differentiation stages and external environments. Cancer cells can hijack this plasticity to develop drug resistance. For example, breast cancers that are initially responsive to endocrine therapy often develop resistance robustly. This process is dynamically controlled by interactions of genes, proteins, RNAs and environmental factors at multiple scales. The complexity of this network cannot be understood by studying individual components in the cell. Systems biology focuses on the interactions of basic components, so as to uncover the molecular mechanism of cell physiology with a systemic and dynamical view. Mathematical modeling as a tool in systems biology provides a unique opportunity to understand the underlying mechanisms of endocrine response and resistance in breast cancer. In Chapter 2, I focused on the experimental observations that breast cancer cells can switch between estrogen receptor α (ERα) regulated and growth factor receptor (GFR) regulated signaling pathways for survival and proliferation. A mathematical model based on the signaling crosstalk between ERα and GFR was constructed. The model successfully explains several intriguing experimental findings related to bimodal distributions of GFR proteins in breast cancer cells, which had been lacking reasonable justifications for almost two decades. The model also explains how transient overexpression of ERα promotes resistance of breast cancer cells to estrogen withdrawal. Understanding the non-genetic heterogeneity associated with this survival-signaling switch can shed light on the design of more efficient breast cancer therapies. In Chapter 3, I utilized a novel strategy to model the transitions between the endocrine response and resistance states in breast cancer cells. Using the experimentally observed estrogen sensitivity phenotypes in breast cancer (sensitive, hypersensitive, and supersensitive) as example, I proposed a useful framework of modeling cell state transitions on the energy landscape of breast cancer as a dynamical system. Grounded on the most possible routes of transitions on the breast cancer landscape, a state transition model was developed. By analyzing this model, I investigated the optimum settings of two intuitive strategies, sequential and intermittent treatments, to overcome endocrine resistance in breast cancer. The method used in this study can be generalized to study treatment strategies and improve treatment efficiencies in breast cancer as well as other types of cancer. / Ph. D.

The life cycle of Caulobacter crescentus is of interest because of the asymmetric nature of cell division that gives rise to progeny that have distinct morphology and function. One daughter called the stalked cell is sessile and capable of DNA replication, while the second daughter called the swarmer cell is motile but quiescent. Advances in microscopy combined with molecular biology techniques have revealed that macromolecules are localized in a non-homogeneous fashion in the cell cytoplasm, and that dynamic localization of proteins is critical for cell cycle progression and asymmetry. However, the molecular-level mechanisms that govern protein localization, and enable the cell to exploit subcellular localization towards orchestrating an asymmetric life cycle remain obscure. There are also instances of researchers using intuitive reasoning to develop very different verbal explanations of the same biological process. To provide a complementary view of the molecular mechanism controlling the asymmetric division cycle of Caulobacter, we have developed a mathematical model of the cell cycle regulatory network. Our reaction-diffusion models provide additional insight into specific mechanism regulating different aspects of the cell cycle. We describe a molecular mechanism by which the bifunctional histidine kinase PleC exhibits bistable transitions between phosphatase and kinase forms. We demonstrate that the kinase form of PleC is crucial for both swarmer-to-stalked cell morphogenesis, and for replicative asymmetry in the predivisional cell. We propose that localization of the scaffolding protein PopZ can be explained by a Turing-type mechanism. Finally, we discuss a preliminary model of ParA- dependent chromosome segregation. Our model simulations are in agreement with experimentally observed protein distributions in wild-type and mutant cells. In addition to predicting novel mutants that can be tested in the laboratory, we use our models to reconcile competing hypotheses and provide a unified view of the regulatory mechanisms that direct the Caulobacter cell cycle. / Ph. D.

Cell phenotypic transitions, or cell fate decision making processes, are regulated by complex regulatory networks composed of genes, RNAs, proteins and metabolites. The regulation can take place at the epigenetic, transcriptional, translational, and post-translational levels to name a few. Epigenetic histone modification plays an important role in cell phenotype maintenance and transitions. However, the underlying mechanism relating dynamical histone modifications to stable epigenetic cell memory remains elusive. Incorporating key pieces of molecular level experimental information, we built a statistical mechanics model for the inheritance of epigenetic histone modifications. The model reveals that enzyme selectivity of different histone substrates and cooperativity between neighboring nucleosomes are essential to generate bistability of the epigenetic memory. We then applied the epigenetic modeling framework to the differentiation process of olfactory sensory neurons (OSNs), where the observed 'one-neuron-one-allele' phenomenon has remained as a long-standing puzzle. Our model successfully explains this singular behavior in terms of epigenetic competition and enhancer cooperativity during the differentiation process. Epigenetic level events and transcriptional level events cooperate synergistically in the OSN differentiation process. The model also makes a list of testable experimental predictions. In general, the epigenetic modeling framework can be used to study phenotypic transitions when histone modification is a major regulatory element in the system. Post-transcriptional level regulation plays important roles in cell phenotype maintenance. Our integrated experimental and computational studies revealed such a motif regulating the differentiation of definitive endoderm. We identified two RNA binding proteins, hnRNPA1 and KSRP, which repress each other through microRNAs miR-375 and miR-135a. The motif can generate switch behavior and serve as a noise filter in the stem cell differentiation process. Manipulating the motif could enhance the differentiation efficiency toward a specific lineage one desires. Last we performed mathematical modeling on an epithelial-to-mesenchymal transition (EMT) process, which could be used by tumor cells for their migration. Our model predicts that the IL-6 induced EMT is a stepwise process with multiple intermediate states. In summary, our theoretical and computational analyses about cell phenotypic transitions provide novel insights on the underlying mechanism of cell fate decision. The modeling studies revealed general physical principles underlying complex regulatory networks. / Ph. D.

A company's decisions on how to manage its reverse supply chain (RSC) are important for both economic and environmental reasons. From a strategic standpoint, the key decision a manufacturer makes is whether or not to collect products at their end-of-life (EOL) (i.e., when their useful lives are over), and if so, how to recover value from the recovered products. We call this decision as the EOL option of a product, and it determines how the RSC is designed and managed overall. Many EOL options exist for a product such as resale, refurbishment, remanufacturing and part salvage. However, many factors influence the optimal EOL option. These factors include the product's: (i) characteristics, (ii) design, and (iii) pricing. A product's characteristics are its properties that impact the various costs incurred during its production, residual part values, and customer demand. In this work, the product design is viewed as the choice of quality for each of its parts. A part's quality-level determines, among other things, its cost, salvage value, and the likelihood of obtaining it in good condition from a disassembled used product. Finally, the manufacturer must determine how to price its new and used products. This decision depends on many considerations such as whether new and used products compete and whether competition exists from other manufacturers. The choice of appropriate EOL options for products constitutes a foundation of RSC design. In this work, we study how to optimally determine a product's optimal EOL option and consider the impact of product design and product pricing on this decision. We present a full description of the system that details the relationships among all entities. The system description reveals the use of a production planning type of modeling strategy. Additionally, a comprehensive and general mathematical model is presented that takes into consideration multi-period planning and product inventory. A unique aspect of our model over previous production planning models for RSC is that we consider the product returns as being endogenous variables rather than them being exogenous. This model forms the basis of our research, and we use its special cases in our analysis. To begin our analysis of the problem, we study the case in which the product design and price are fixed. Both non-mandated and mandated collection are considered. Our analysis focuses on a special case of the problem involving two stages: in the first stage, new products are produced, and in the second stage, the EOL products are collected for value recovery. For fixed product design and price, our analysis reveals a fundamental mapping of product characteristics onto optimal EOL options. It is germane to our understanding of the problem in general since a multi-period problem is separable into multiple two-stage problems. Necessary and sufficient optimality conditions are also presented for each possible solution of this two-stage problem. For the two-part problem, a graphical mapping of product characteristics onto optimal EOL options is also presented, which reveals how EOL options vary with product characteristics. Additionally, we study the case of product design under mandated collection, as encountered in product leasing. We assume new production cost, part replacement cost, and part salvage value to be functions of the quality-level of a part along with the likelihood of recovering a good-part from a returned product. These are reasonable assumptions for leased products since the customer is paying for the usage of the product over a fixed contract period. In this case, the two-stage model can still be used to gain insights. For the two-part problem, a method for mapping part yields onto optimal EOL options is presented. Closed-form optimality conditions for joint determination of part yields and EOL options are not generally attainable for the two-stage case; however, computationally efficient methods for this problem are developed for some relatively non-restrictive special cases. It is found that, typically, a part may belong to one of three major categories: (i) it is of low quality and will need to be replaced to perform remanufacturing, (ii) it is of high quality and its surplus will be salvaged, or (iii) it is of moderate quality and just enough of its amount is collected to meet remanufactured product demand. Finally, we consider the problem of determining optimal prices for new and remanufactured products under non-mandated manufacturer's choice of collection. New and remanufactured products may or may not compete, depending on market conditions. Additionally, we assume the manufacturer to have a monopoly on the product. Again, the two-stage problem is used and efficient solution methods are developed. Efficient solution methods and key insights are presented. / Ph. D.

Biofilms are communities of microorganisms that can form in the human microbiome and on medical implants among other locations. These communities provide greater protection for their member cells resulting in an increase in resistance to antibiotic treatment and persistent infections. There are several factors that may contribute to antibiotic resistance of biofilms. These studies were done concurrently with biological experiments to test the hypothesis that dense, rigid structures within the biofilm may be an additional mechanism for protection from antibiotics. A computational tool and workflow was developed to analyze bead movement for the characterization of biofilm biomaterial properties including rigidity. With this tool, the analysis revealed that the amyloid, curli, confers rigidity in biofilms, thereby restricting bead movement. Greater movement of the beads is seen in biofilms lacking curli and biofilms that produced complex heterogeneous rigid structures. A new model was also developed that uses microscopy imaging data to simulate diffusion-reaction of antibiotics within heterogeneous biofilms. This model was used to investigate the effect of the dense, rigid structures on antibiotic treatment through test simulations and simulations using biological imaging data. These studies reveal various properties about the dense, rigid structures that confer protection. / Mathematics

Breakthroughs in molecular and synthetic biology through de novo gene synthesis are stimulating new vaccines, pharmaceutical applications, and functionalized biomaterials, and advancing the knowledge of the function of cells. This evolution in biological processing motivates the study of a class of manufacturing systems, defined here as genetic manufacturing systems, which produce a final product with a genetic construct. Genetic manufacturing systems rely on rare molecular events for success, resulting in waste and repeated work during the deoxyribonucleic acid (DNA) fabrication process. Inspection and real time monitoring strategies are possible as mitigation tools, but it is unclear if these techniques are cost efficient and value added for the successful creation of custom genetic constructs. This work investigates resource allocation strategies for DNA fabrication environments, with an emphasis on inspection allocation. The primary similarities and differences between traditional manufacturing systems and genetic manufacturing systems are described. A serial, multi-stage inspection allocation mathematical model is formulated for a genetic manufacturing system utilizing gene synthesis. Additionally, discrete event simulation is used to evaluate inspection strategies for a fragment synthesis process and multiple fragment assembly operation. Results from the mathematical model and discrete event simulation provide two approaches to determine the appropriate inspection strategies with respect to total cost or total flow time of the genetic manufacturing system. / Ph. D. / Breakthroughs in molecular and synthetic biology through <i>de novo</i> gene synthesis are stimulating new vaccines, pharmaceutical applications, and functionalized biomaterials, and advancing the knowledge of the function of cells. This evolution in biological processing motivates the study of a class of manufacturing systems, defined here as genetic manufacturing systems, which produce a final product with a genetic construct. Genetic manufacturing systems rely on rare molecular events for success, resulting in waste and repeated work during the deoxyribonucleic acid (DNA) fabrication process. Inspection and real time monitoring strategies are possible as mitigation tools, but it is unclear if these techniques are cost efficient and value added for the successful creation of custom genetic constructs. This work investigates resource allocation strategies for DNA fabrication environments, with an emphasis on inspection allocation. The primary similarities and differences between traditional manufacturing systems and genetic manufacturing systems are described. A serial, multi-stage inspection allocation mathematical model is formulated for a genetic manufacturing system utilizing gene synthesis. Additionally, discrete event simulation is used to evaluate inspection strategies for a fragment synthesis process and multiple fragment assembly operation. Results from the mathematical model and discrete event simulation provide two approaches to determine the appropriate inspection strategies with respect to total cost or total flow time of the genetic manufacturing system.

With a continuing and rising demand for hydrocarbons, the energy companies are installing infrastructure ever further offshore, where such infrastructure is often exposed to extreme waves. This thesis explores some aspects of wave-structure interaction, particularly the maximum water surface elevation increase in severe storms due to these local interactions. The effects on wave-structure interactions of column cross-sectional shape are investigated using linear and second-order wave diffraction theory. For multi-column structures, the excitation of locally resonant wave modes (near-trapping) is studied for several column cross-sectional shapes, and a simple method for estimating the surface elevation mode shape is given. The structure of the quadratic transfer functions for second-order sum wave elevation is investigated and an approximation assuming these QTFs are flat perpendicular to the leading diagonal is shown to be adequate for the first few lowest frequency modes. NewWave-type focused wave groups can be used as a more realistic model of extreme ocean waves. A Net Amplification Factor based on the NewWave model is given as an efficient tool for finding the incident frequencies most likely to cause a violent wave-structure interaction and where these violent responses are likely to occur. Statistics are collected from Monte Carlo type simulations of random waves to verify the use of the Net Amplification Factor. Going beyond linear calculations, surface elevation statistics are collected to second-order and a `designer' wave is found to model the most extreme surface elevation responses. A `designer' wave can be identified at required levels of return period to help to understand the relative size of harmonic components in extreme waves. The methods developed with a fixed body are then applied to an identical hull which is freely floating, and the responses between the fixed and moving cases are compared. The vertical heave motion of a semi-submersible in-phase with the incident wave crests is shown to lead to a much lower probability of water-deck impact for the same hull shape restrained vertically. The signal processing methods developed are also applied to a single column to allow comparison with experimental results. Individual harmonic components of the hydrodynamic force are identified up to at least the fifth harmonic. Stokes scaling is shown to hold even for the most violent interactions. It is also shown that the higher harmonic components of the hydrodynamic force can be reconstructed from just the fundamental force time history, and a transfer function in the form of a single phase and an amplitude for each harmonic. The force is also reconstructed well to second-order from the surface elevation time history using diffraction transfer functions. Finally, possible causes of damage to a platform high above mean water level in the North Sea are investigated.

This DPhil project is set in the context of single crystal elasticity-plasticity finite element modelling. Its core objective was to develop and implement a methodology for predicting the evolution of texture in single and dual-phase material systems. This core objective has been successfully achieved. Modelling texture evolution entails essentially modelling large deformations (as accurately as possible) and taking account of the deformation mechanisms that cause texture to change. The most important deformation mechanisms are slip and twinning. Slip has been modelled in this project and care has been taken to explore conditions where it is the dominant deformation mechanism for the materials studied. Modelling slip demands that one also models dislocations since slip is assumed to occur by the movement of dislocations. In this project a model for geometrically necessary dislocations has been developed and validated against experimental measurements. A texture homogenisation technique which relies on interpretation of EBSD data in order to allocate orientation frequencies based on representative area fractions has been developed. This has been coupled with a polycrystal plasticity RVE framework allowing for arbitrarily sized RVEs and corresponding allocation of crystallographic orientation. This has enabled input of experimentally measured initial textures into the CPFE model allowing for comparison of predictions against measured post-deformation textures, with good agreement obtained. The effect of texture on polycrystal physical properties has also been studied. It has been confirmed that texture indeed has a significant role in determining the average physical properties of a polycrystal. The thesis contributes to the following areas of micro-mechanics materials research: (i) 3D small deformation crystal plasticity finite element (CPFE) modelling, (ii) geometrically necessary dislocation modelling, (iii) 3D large deformation CPFE modelling, (iv) texture homogenisation methods, (v) single and dual phase texture evolution modelling, (vi) prediction of polycrystal physical properties, (vii) systematic calibration of the power law for slip based on experimental data, and (viii) texture analysis software development (pole figures and Kearns factors).

Magnetic resonance imaging (MRI) of the liver is an important non-invasive tool for diagnosing liver disease. A key application is dynamic contrast enhanced magnetic resonance imaging (DCE-MRI). With the use of the hepatocyte specific contrast agent (CA) Gd-EOB-DTPA it is now possible to evaluate the liver function. Beyond traditional qualitative evaluation of the DCE-MRI images, parametric quantitative techniques are on the rise which yields more objective evaluations. Systems biology is a gradually expanding field using mathematical modeling to gain deeper mechanistic understanding in complex biological systems. The aim of this thesis to combine these two fields in order to derive a physiologically accurate minimal whole body model that can be used to quantitatively evaluate liver function using clinical DCE-MRI examinations.  The work is based on two previously published sources of data using Gd-EOB-DTPA in healthy humans; i) a region of interest analysis of the liver using DCE-MRI ii) a pre-clinical evaluation of the contrast agent using blood sampling.  The modeling framework consists of a system of ordinary differential equations for the contrast agent dynamics and non-linear models for conversion of contrast agent concentrations to relaxivity values in the DCE-MRI image volumes. Using a χ2-test I have shown that the model, with high probability, can fit the experimental data for doses up to twenty times the clinically used one, using the same parameters for all doses. The results also show that some of the parameters governing the hepatocyte flux of CA can be numerically identifiable. Future applications with the model might be as a basis for regional liver function assessment. This can lead to disease diagnosis and progression evaluation for physicians as well as support for surgeons planning liver resection.

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