This dissertation is concerned with the application of mathematical modeling and statistical signal processing into the rapidly expanding fields of proteomics and genomics. The research is guided by a translational goal which drives the problem formalization and experimental design, and leads to optimization, prediction and control of the underlying system. The dissertation is comprised of three interconnected subjects. In the first part of the dissertation, two Bayesian peptide detection algorithms are proposed to optimize the feature extraction step, which is the most fundamental step in mass spectrometry-based proteomics. The algorithms are designed to tackle data processing challenges that are not satisfactorily addressed by existing methods. In contrast to most existing methods, the proposed algorithms perform deisotoping and deconvolution of mass spectra simultaneously, which enables better identification of weak peptide signals. Unlike greedy template-matching algorithms, the proposed methods have the capability to handle complex spectra where features overlap. The proposed methods achieve better sensitivity and accuracy compared to many popular software packages such as msInspect. In the second part of the dissertation, we consider modeling and assessing the entire mass spectrometry-based proteomic data analysis pipeline. Different modules are identified and analyzed, resulting in a framework that captures key factors in system performance. The effects of various model parameters on protein identification rates and quantification errors, differential expression results, and classification performance are examined. The proposed pipeline model can be used to aid experimental design, pinpoint critical bottlenecks, optimize the work flow, and predict biomarker discovery results. Finally, the same system methodology is extended to analyze the work flow in DNA microarray experiments. A model-based approach is developed to explore the relationship among microarray data properties, missing value imputation, and sample classification in a complicated data analysis pipeline. The situations when it is suitable to apply missing value imputation are identified and recommendations regarding imputation are provided. In addition, a missing value rate-related peaking phenomenon is uncovered.

Trunk instability is a major problem for people with spinal cord injury (SCI); it not only limits their independence, but also leads to secondary health complications such as kyphosis, pressure sores, and respiratory dysfunction. In exploring mechanisms that may facilitate or compromise postural stability, dynamic models are very useful because the spine dynamics are difficult to study in vivo compared to other structures of the body. Therefore, one objective of this work was to develop a detailed three-dimensional dynamic model of the human trunk as a tool for investigating the neural-mechanical control strategy that healthy people apply to maintain trunk stability during various tasks. Since trunk control is fairly complex, however, another objective of this work was to provide insights into the balance control strategy of a simpler neuro-musculo-skeletal system that may facilitate future studies on trunk control. For this purpose, the control of the ankle joint complex during quiet standing (anterior-posterior degree of freedom) was studied in place of the trunk. The obtained results reveal that a neural-mechanical control scheme using a proportional-derivative controller as the neural control strategy can overcome a large sensory-motor (feedback) time delay and stabilize the ankle joint during quiet standing. Moreover, a detailed dynamic model of the trunk has been developed that is: (1) based on highly accurate geometric models; and (2) universally applicable. Thus, this work also responds to the postulation that structurally more complex models are needed to better characterize the biomechanics of multifaceted systems. Combining the developed biomechanical tools for the trunk with the postural control insights for the ankle joint during standing will be beneficial for: (1) understanding the neural-mechanical control strategy that facilitates trunk stability in healthy people; and for (2) developing neuroprostheses for trunk stability after SCI and other neurological disorders.

Trunk instability is a major problem for people with spinal cord injury (SCI); it not only limits their independence, but also leads to secondary health complications such as kyphosis, pressure sores, and respiratory dysfunction. In exploring mechanisms that may facilitate or compromise postural stability, dynamic models are very useful because the spine dynamics are difficult to study in vivo compared to other structures of the body. Therefore, one objective of this work was to develop a detailed three-dimensional dynamic model of the human trunk as a tool for investigating the neural-mechanical control strategy that healthy people apply to maintain trunk stability during various tasks. Since trunk control is fairly complex, however, another objective of this work was to provide insights into the balance control strategy of a simpler neuro-musculo-skeletal system that may facilitate future studies on trunk control. For this purpose, the control of the ankle joint complex during quiet standing (anterior-posterior degree of freedom) was studied in place of the trunk. The obtained results reveal that a neural-mechanical control scheme using a proportional-derivative controller as the neural control strategy can overcome a large sensory-motor (feedback) time delay and stabilize the ankle joint during quiet standing. Moreover, a detailed dynamic model of the trunk has been developed that is: (1) based on highly accurate geometric models; and (2) universally applicable. Thus, this work also responds to the postulation that structurally more complex models are needed to better characterize the biomechanics of multifaceted systems. Combining the developed biomechanical tools for the trunk with the postural control insights for the ankle joint during standing will be beneficial for: (1) understanding the neural-mechanical control strategy that facilitates trunk stability in healthy people; and for (2) developing neuroprostheses for trunk stability after SCI and other neurological disorders.

Gliomas are the most common and aggressive primary brain tumors. The most common treatment protocols for these brain tumors are combinations of surgery, chemotherapy and radiotherapy. However, even with the most aggressive combination of surgery and radiotherapy and/or chemotherapy schedules, gliomas almost always recur resulting in a median survival time for patients of not more than 12 months. This highly diffusive and invasive nature of brain tumors makes it very important to study the effects of these combined therapeutic strategies in an effort to improve the survival time of patients. It is also important to study the tumor microenvironment, since the complex nature of the cerebral vasculature, including the blood brain barrier and several other tumor-induced conditions such as hypoxia, high interstitial pressure, and cerebral edema affect drug delivery as well as the effectiveness of radiotherapy. Recently, a novel strategy using antiangiogenic therapy has been studied for the treatment of brain tumors. Antiangiogenic therapy interferes with the development of tumor vasculature and indirectly helps in the control of tumor growth. Recent clinical trials suggest that anti-angiogenic therapy is usually more effective when given in combination with other therapeutic strategies. In an effort to study the effects of the aforementioned therapeutic strategies, a spatio-temporal model is considered here that incorporates the tumor cell growth and the effects of radiotherapy and chemotherapy. The effects of different schedules of radiation therapy is then studied using a generalized linear quadratic model and compared against the published clinical data. The model is then extended to include the interactions of tumor vasculature and oxygen concentration, to explain tumor hypoxia and to study various methods of hypoxia characterizations including biomarker estimates and needle electrode measurements. The model predicted hypoxia is also used to analyze the effects of tumor oxygenation status on radiation response as it is known that tumor hypoxia negatively influences the radiotherapy outcome. This thesis also presents a detailed analysis of the effects of heterogenous tumor vasculature on tumor interstitial fluid pressure and interstitial fluid velocity. A mathematical modeling approach is then used to analyze the changes in interstitial fluid pressure with or without antiangiogenic therapy.

Gliomas are the most common and aggressive primary brain tumors. The most common treatment protocols for these brain tumors are combinations of surgery, chemotherapy and radiotherapy. However, even with the most aggressive combination of surgery and radiotherapy and/or chemotherapy schedules, gliomas almost always recur resulting in a median survival time for patients of not more than 12 months. This highly diffusive and invasive nature of brain tumors makes it very important to study the effects of these combined therapeutic strategies in an effort to improve the survival time of patients. It is also important to study the tumor microenvironment, since the complex nature of the cerebral vasculature, including the blood brain barrier and several other tumor-induced conditions such as hypoxia, high interstitial pressure, and cerebral edema affect drug delivery as well as the effectiveness of radiotherapy. Recently, a novel strategy using antiangiogenic therapy has been studied for the treatment of brain tumors. Antiangiogenic therapy interferes with the development of tumor vasculature and indirectly helps in the control of tumor growth. Recent clinical trials suggest that anti-angiogenic therapy is usually more effective when given in combination with other therapeutic strategies. In an effort to study the effects of the aforementioned therapeutic strategies, a spatio-temporal model is considered here that incorporates the tumor cell growth and the effects of radiotherapy and chemotherapy. The effects of different schedules of radiation therapy is then studied using a generalized linear quadratic model and compared against the published clinical data. The model is then extended to include the interactions of tumor vasculature and oxygen concentration, to explain tumor hypoxia and to study various methods of hypoxia characterizations including biomarker estimates and needle electrode measurements. The model predicted hypoxia is also used to analyze the effects of tumor oxygenation status on radiation response as it is known that tumor hypoxia negatively influences the radiotherapy outcome. This thesis also presents a detailed analysis of the effects of heterogenous tumor vasculature on tumor interstitial fluid pressure and interstitial fluid velocity. A mathematical modeling approach is then used to analyze the changes in interstitial fluid pressure with or without antiangiogenic therapy.

The need to tailor release-rate profiles from polymeric microspheres remains one of the leading challenges in controlled drug delivery. Microsphere size, which has a significant effect on drug release rate, can potentially be varied to design a controlled drug delivery system with desired release profile. In addition, drug release rate from polymeric microspheres is dependent on material properties such as polymer molecular weight. Mathematical modeling provides insight into the fundamental processes that govern the release, and once validated with experimental results, it can be used to tailor a desired controlled drug delivery system. To these ends, PLG microspheres were fabricated using the oil-in-water emulsion technique. A quantitative study that describes the size distribution of poly(lactide-coglycolide) (PLG) microspheres is presented. A fluid mechanics-based correlation that predicts the mean microsphere diameter is formulated based on the theory of emulsification in turbulent flow. The effects of microspheres’ mean diameter, polydispersity, and polymer molecular weight on therapeutic drug release rate from poly(lactide-co-glycolide) (PLG) microspheres were investigated experimentally. Based on the experimental results, a suitable mathematical theory has been developed that incorporates the effect of microsphere size distribution and polymer degradation on drug release. In addition, a numerical optimization technique, based on the least squares method, was developed to achieve desired therapeutic drug release profiles by combining individual microsphere populations. The fluid mechanics-based mathematical correlation that predicts microsphere mean diameter provided a close fit to the experimental results. We show from in vitro release experiments that microsphere size has a significant effect on drug release rate. The initial release rate decreased with an increase in microsphere size. In addition, the release profile changed from first order to concave-upward (sigmoidal) as the microsphere size was increased. The mathematical model gave a good fit to the experimental release data. Using the numerical optimization technique, it was possible to achieve desired release profiles, in particular zero-order and pulsatile release, by combining individual microsphere populations at the appropriate proportions. Overall, this work shows that engineering polymeric microsphere populations having predetermined characteristics is an effective means to obtain desired therapeutic drug release patterns, relevant for controlled drug delivery.

Increasing environmental legislations on pollutant emissions originated from fossil fuel combustion and intention of increasing the life of existing fossil fuels give rise to the use of renewable sources. Biomass at this juncture, with its renewable nature and lower pollutant emission levels becomes an attractive energy resource. However, only seasonal availability of biomass and operation problems caused by high alkaline content of biomass ash restrict its combustion alone. These problems can be overcome by co-combustion of biomass with lignite. With its high fuel flexibility and high combustion efficiency, fluidized bed combustion is the most promising technology for co-firing. To improve and optimize the operation of co-firing systems a detailed understanding of co-combustion of coal and biomass is necessary, which can be achieved both with experiments and modeling studies. For this purpose, a comprehensive system model of fluidized bed combustor, previously developed and tested for prediction of combustion behaviour of fluidized bed combustors fired with lignite was extended to co-firing lignite with biomass by incorporating volatile release, char combustion and population balance for biomass. The model predictions were validated against experimental measurements taken on METU 0.3 MWt AFBC fired with lignite only, lignite with limestone addition and about 50/50 lignite/olive residue mixture with limestone addition. Predicted and measured temperatures and concentrations of gaseous species along the combustor were found to be in good agreement. Introduction of biomass to lignite was found to decrease SO2 emissions but did not affect NO emissions significantly.

This thesis concerns the development, evaluation, comparison and testing of a UH-1H helicopter simulation model with various fidelity levels. In particular, the well known minimum complexity simulation model is updated with various higher fidelity simulation components, such as the Peters-He inflow model, horizontal tail contribution, improved tail rotor model, control mapping, ground eect, fuselage interactions, ground reactions etc. Results are compared with available flight test data. The dynamic model is integrated into the open source simulation environment called Flight Gear. Finally, the model is cross-checked through evaluations using test pilots.

Protein homo-oligomerization is the process through which identical peptides bind together to form higher order complexes. Self-interactions in many cases are constitutive and stable, used as building blocks for biological structures, such as rings, filaments and membranes. Further, homo-oligomerization can also be a regulatory process that influences the proteins' function such as change in transcriptional activities for transcription factors. Innovative methods to measure oligomerization in live cells are needed in order to understand regulation and function of homooligomerization in the native cellular context. This thesis examines the case of the tumor suppressor p53, whose homo-tetramerization greatly influences its activity as a transcription factor. We develop methods to quantify p53's self-interaction in individual living cells and follow it in time after DNA damage. The two methods we developed have complementary qualities and different applications. We first use fluorescent correlation spectroscopy to study the molecular events occurring in the first three hours of the p53 in response to double strand breaks. We find that in the absence of stress p53 is present in a mixture of, monomers, dimers and tetramers. When damage is sensed, oligomerization is rapidly induced and nearly all p53 is found bound in tetramers. We combine our data with a mathematical framework to propose the existence of a dedicated mechanism triggering p53 oligomerization independently of protein stabilization. Next, we use bimolecular fluorescent complementation to probe for tetramerization in the longer timescales of p53's response to ultraviolet radiation. In this context we find that even though the rate of p53 accumulation increases with the dose of radiation, p53 tetramers are formed at a steady rate. We hence propose the existence of an inhibitory mechanism that prevents the oligomerization reaction from following a linear input-output relation. We identify ARC, a known cofactor of p53, as part of this inhibitory mechanism. Downregulation of ARC restore the linear relation between to total and tetrameric p53. Finally, in both experimental setups higher oligomerization lead to an increase in p53 activity, underscoring the connection between regulation of oligomerization and the transcriptional activity of p53 in cancer cells. Collectively, this work emphasizes the importance of precise measurements to investigate the regulation and function of higher order complexes and provides generally applicable methods to quantify homo-oligomerization in live single cells.

In this research a variety of drug delivery systems were synthesized and characterized. For the most part, these consisted of a matrix of poly(lactic-co-glycolic acid) (PLGA), polyethylene glycol (PEG), and polyvinyl alcohol (PVA) containing encapsulated anticancer drugs as chemotherapy agents. The drug release from biodegradable nanoparticles was analyzed mathematically using new approaches that simultaneously incorporates the three major mechanisms of release: initial burst, nanoparticle degradation-relaxation, and diffusion. The theoretical release studies were corroborated experimentally by evaluating the cytotoxicity effectiveness of PHT-427-loaded nanoparticles over pancreatic cancer cells in vitro. These studies showed that the encapsulated PHT-427 drug in the nanoparticles is more accessible and thus more effective when compared with the drug alone. Also, the PHT-427-loaded nanoparticles cytotoxicity was evaluated in vivo studies with pancreatic tumors. The results show that the drug is more effective when is loaded into polymeric nanoparticles compared to drug alone, by reducing orthotopic pancreatic tumor growth. In addition, a selection of hydrophobic to hydrophilic drugs were encapsulated into polymeric nanoparticles to find optimal drug loadings by using single or double emulsification techniques. The release of these drugs from PLGA nanoparticles was evaluated to determine the overall release profile characteristics. The encapsulation of the drug pemetrexed was improved by using polyethileneimine. The high positive charge density of polyethileneimine causes a strong electrostatic interaction with the carboxylic acids of pemetrexed; this complex decreases the solubility of pemetrexed and boosts the encapsulation efficiency. Additionally, a drug release mathematical analysis that considers the effects of the temperature of release was effectively established. The analysis was performed by using two different models: the first one simultaneously incorporates the mechanisms of initial burst and nanoparticle degradation - relaxation, and the second model, besides of the mechanisms of the first model, includes the diffusion of the drug. Both models were successfully employed to describe the experimental release of rhodamine 6G from PEGylated nanoparticles at different temperatures. From the parameters obtained by the fit using each model, it was possible to define a set of new relations of the form of Arrhenius to estimate the parameters of release at other temperatures.