During the past decade, many successful deterministic models of macromolecular regulatory networks have been built. Deterministic simulations of these models can show only average dynamics of the systems. However, stochastic simulations of macromolecular regulatory models can account for behaviors that are introduced by the noisy nature of the systems but not revealed by deterministic simulations. Thus, converting an existing model of value from the most common deterministic formulation to one suitable for stochastic simulation enables further investigation of the regulatory network. Although many different stochastic models can be developed and evolved from deterministic models, a direct conversion is the first step in practice. This conversion process is tedious and error-prone, especially for complex models. Thus, we seek to automate as much of the conversion process as possible. However, deterministic models often omit key information necessary for a stochastic formulation. Specifically, values in the model have to be scaled before a complete conversion, and the scaling factors are typically not given in the deterministic model. Several functionalities helping model scaling and converting are introduced and implemented in the JigCell modeling environment. Our tool makes it easier for the modeler to include complete details as well as to convert the model. Stochastic simulations are known for being computationally intensive, and thus require high performance computing facilities to be practical. With parallel computation on Virginia Tech's System X supercomputer, we are able to obtain the first stochastic simulation results for realistic cell cycle models. Stochastic simulation results for several mutants, which are thought to be biologically significant, are presented. Successful deployment of the enhanced modeling environment demonstrates the power of our techniques. / Master of Science

The field of biochemical systems modeling and analysis is faced with an unprecedented flood of data from experimental methodologies of molecular biology. While these techniques continue to leapfrog ahead in the speed, volume and finesse with which they generate data, the methods of data analysis and interpretation, however, are still playing the catch-up game. The notions of systems analysis have found a new foothold, under the banner of Systems Biology, with the promise of uncovering the rationale for the designs of biological systems from their parts lists, as they are generated by experimentation and sorted and managed by bioinformatics tools. With an aim to complement hypothesis-driven and reductionistic biological research, and not replace it, a systems biologist relies on the tools of mathematical and computational modeling to be able to contribute meaningfully to any ongoing bio-molecular systems research. These systems analysis tools, however, should not only have their roots steeped well in the theoretical foundations of biochemistry, mathematics and numerical computation, but they should be married to a framework that facilitates the required systems way of thought for all its users computational scientists, experimentalists and molecular biologists alike. Hopefully, such framework-based tools would go beyond just providing fancy GUIs, numerical packages for integrating ODEs and/or optimization libraries. The intent of this thesis is to present a framework and toolbox for biochemical systems modeling, with an application in metabolic pathway analysis and/or metabolic engineering. The research presented here builds upon the tenets of a very well established and generic approach to biological systems modeling and analysis, called Biochemical Systems Theory (BST), which is almost forty years old. The nuances of modeling and practical hurdles to analysis are presented in the context of a real-time case study of analyzing the glucolytic pathway in the bacterium Lactococcus lactis. Alongside, the thesis presents the features of a MATLAB-based software application that has been built upon the framework of BST and is aptly named as Biochemical Systems Toolbox (BSTBox). The thesis presents novel contributions, made by the author during the course of his research, to state-of-the-art techniques in parameter estimation, and robustness and sensitivity analysis topics that, as this thesis will show, remain to be the most restrictive bottlenecks in the world of biological systems modeling and analysis.

By exploiting the concept of emergent network properties and the hierarchical nature of networks, we have constructed several levels of models facilitating the investigations of issues in the area of respiratory neural control. The first of such models is an intracellular second messenger pathway model, which has been shown to be an important contributor to intracellular calcium metabolism and mediate responses to neuromodulators such as serotonin. At the next level, we have constructed new single neuron models of respiratory-related neurons (e.g. the pre-Btzinger complex neuron and the Hypoglossal motoneuron), where the electrical activities of the neurons are linked to intracellular mechanisms responsible for chemical homeostasis. Beyond the level of individual neurons, we have constructed models of neuron populations where the effects of different component neurons, varying strengths and types of inter-neuron couplings, as well as network topology are investigated. Our results from these simulation studies at different structural levels are in line with experiment observations. The small-world topology, as observed in previous anatomical studies, has been shown here to support rhythm generation along with a variety of other network-level phenomena. The interactions between different inter-neuron coupling types simultaneously manifesting at time-scales orders of magnitude apart suggest possible explanations for variations in the outputs measured from the XII rootlet in experiments. In addition, we have demonstrated the significance of pacemakers, along with the importance of considering neuromodulations and second-messenger pathways in an attempt to understand important physiological functions such as breathing activities.

As an important endogenous source of reactive oxygen species (ROS), NADPH oxidase 1 (Nox1) has received tremendous attention in the past few decades. It has been identified to play a key role as the initial "kindle," whose activation is crucial for amplifying ROS production through several propagation mechanisms in the vascular system. As a consequence, Nox1 has been implicated in the initiation and genesis of many cardiovascular diseases and has therefore been the subject of detailed investigations. The literature on experimental studies of the Nox1 system is extensive. Numerous investigations have identified essential features of the Nox1 system in vasculature and characterized key components, possible regulatory signals and/or signaling pathways, potential activation mechanisms, a variety of Nox1 stimuli, and its potential physiological and pathophysiological functions. While these experimental studies have greatly enhanced our understanding of the Nox1 system, many open questions remain regarding the overall functionality and dynamic behavior of Nox1 in response to specific stimuli. Such questions include the following. What are the main regulatory and/or activation mechanisms of Nox1 systems in different types of vascular cells? Once Nox1 is activated, how does the system return to its original, unstimulated state, and how will its subunits be recycled? What are the potential disassembly pathways of Nox1? Are these pathways equally important for effectively reutilizing Nox1 subunits? How does Nox1 activity change in response to dynamic signals? Are there generic features or principles within the Nox1 system that permit optimal performance? These types of questions have not been answered by experiments, and they are indeed quite difficult to address with experiments. I demonstrate in this dissertation that one can pose such questions and at least partially answer them with mathematical and computational methods. Two specific cell types, namely endothelial cells (ECs) and vascular smooth muscle cells (VSMCs), are used as "templates" to investigate distinct modes of regulation of Nox1 in different vascular cells. By using a diverse array of modeling methods and computer simulations, this research identifies different types of regulation and their distinct roles in the activation process of Nox1. In the first study, I analyze ECs stimulated by mechanical stimuli, namely shear stresses of different types. The second study uses different analytical and simulation methods to reveal generic features of alternative disassembly mechanisms of Nox1 in VSMCs. This study leads to predictions of the overall dynamic behavior of the Nox1 system in VSMCs as it responds to extracellular stimuli, such as the hormone angiotensin II. The studies and investigations presented here improve our current understanding of the Nox1 system in the vascular system and might help us to develop potential strategies for manipulation and controlling Nox1 activity, which in turn will benefit future experimental and clinical studies.