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.

Gillespie's Stochastic Simulation Algorithm (SSA) provides an elegant simulation approach for simulating models composed of coupled chemical reactions. Although this approach can be used to describe a wide variety biological, chemical, and ecological systems, often systems have external behaviors that are difficult or impossible to characterize using chemical reactions alone. This work extends the applicability of the SSA by adding mechanisms for the inclusion of external events and external triggers. We define events as changes that occur in the system at a specified time while triggers are defined as changes that occur to the system when a particular condition is fulfilled. We further extend the SSA with the efficient implementation of these model parameters. This work allows numerous systems that would have previously been impossible or impractical to model using the SSA to take advantage of this powerful simulation technique.

Cells are able to function and survive due to a delicate orchestration of the expression of genes and their downstream products at the genetic, transcriptomic, proteomic, and metabolic levels. Since metabolites are ultimately the causative agents for physiological responses and responsible for much of the functionality of the organism, a comprehensive understanding of cellular functioning mandates deep insights into how metabolism works. Gaining these insights is impeded by the fact that the regulation and dynamics of metabolic networks are often too complex to allow intuitive predictions, which thus renders mathematical modeling necessary as a means for assessing and understanding metabolic systems. The most difficult step of the modeling process is the extraction of information regarding the structure and regulation of the system from experimental data. The work presented here addresses this "inverse" task with three new methods that are applied to models within Biochemical Systems Theory (BST). Alternating Regression (AR) dissects the nonlinear estimation task into iterative steps of linear regression by utilizing the fact that power-law functions are linear in logarithmic space. Eigenvector Optimization (EO) is an extension of AR that is particularly well suited for the identification of model structure. Dynamic Flux Estimation (DFE) is a more general approach that can involve AR and EO and resolves open issues of model validity and quality beyond residual data fitting errors. The necessity of fast solutions to biological inverse problems is discussed in the context of concept map modeling, which allows the conversion of hypothetical network diagrams into mathematical models.

Lignin polymers provide natural rigidity to plant cell walls by forming complex molecular networks with polysaccharides such as cellulose and hemicellulose. This evolved strategy equips plants with recalcitrance to biological and chemical degradation. While naturally beneficial, recalcitrance complicates the use of inedible plant materials as feedstocks for biofuel production. Genetically modifying lignin biosynthesis is an effective way to generate varieties of bioenergy crops with reduced recalcitrance, but certain lignin-modified plants display undesirable phenotypes and/or unexplained effects on lignin composition, suggesting that the process and regulation of lignin biosynthesis is not fully understood. Given the intrinsic complexities of metabolic pathways in plants and the technical hurdles in understanding them purely with experimental methods, the objective of this dissertation is to develop novel computational tools combining static, constraint-based, and dynamic, kinetics-based modeling approaches for a systematic analysis of lignin biosynthesis in wild-type and genetically engineered plants. Pathway models are constructed and analyzed, yielding insights that are difficult to obtain with traditional molecular and biochemical approaches and allowing the formulation of new, testable hypotheses with respect to pathway regulation. These model-based insights, once they are verified experimentally, will form a solid foundation for the rational design of genetic modification strategies towards the generation of lignin-modified crops with reduced recalcitrance. More generically, the methods developed in this dissertation are likely to have wide applicability in similar studies of complex, ill-characterized pathways where regulation occurring at the metabolic level is not entirely known.

This dissertation addresses the development of integrative modeling strategies capable of combining deterministic and stochastic, discrete and continuous, as well as multi-scale features. The first set of studies combines the purely deterministic modeling methodology of Biochemical Systems Theory (BST) with a hybrid approach, using Functional Petri Nets, which permits the account of discrete features or events, stochasticity, and different types of delays. The efficiency and significance of this combination is demonstrated with several examples, including generic biochemical networks with feedback controls, gene regulatory modules, and dopamine based neuronal signal transduction. A study expanding the use of stochasticity toward systems with small numbers of molecules proposes a rather general strategy for converting a deterministic process model into a corresponding stochastic model. The strategy characterizes the mathematical connection between a stochastic framework and the deterministic analog. The deterministic framework is assumed to be a generalized mass action system and the stochastic analogue is in the format of the chemical master equation. The analysis identifies situations where internal noise affecting the system needs to be taken into account for a valid conversion from a deterministic to a stochastic model. The conversion procedure is illustrated with several representative examples, including elemental reactions, Michaelis-Menten enzyme kinetics, a genetic regulatory motif, and stochastic focusing. The last study establishes two novel, particle-based methods to simulate biochemical diffusion-reaction systems within crowded environments. These simulation methods effectively simulate and quantify crowding effects, including reduced reaction volumes, reduced diffusion rates, and reduced accessibility between potentially reacting particles. The proposed methods account for fractal-like kinetics, where the reaction rate depends on the local concentrations of the molecules undergoing the reaction. Rooted in an agent based modeling framework, this aspect of the methods offers the capacity to address sophisticated intracellular spatial effects, such as macromolecular crowding, active transport along cytoskeleton structures, and reactions on heterogeneous surfaces, as well as in porous media. Taken together, the work in this dissertation successfully developed theories and simulation methods which extend the deterministic, continuous framework of Biochemical Systems Theory to allow the account of delays, stochasticity, discrete features or events, and spatial effects for the modeling of biological systems, which are hybrid and multiscale by nature.

In the aerobic cell, oxygen can be converted into a series of reactive metabolites, together called as "reactive oxygen species" (ROS). This large group include both radical and non-radical species such as superoxide anion (02"), hydroxyl radical ("0H), H202, nitric oxide (N0') and lipid hydroperoxides (LOOH). ROS are generated in very small amounts at all stages of aerobic life, and probably have a role in cellular regulation. However, their formation in excess leads to toxicity and damage to tissues. This situation, called 'oxidative stress', is responsible, atleast in part, to the pathophysioiogy of a number of disease states such as inflammation, arthritis, cancer, ageing, ischemia-reperfusion and several neurodegenerative disorders. Compared to other organs in the animal body, brain tissue is more vulnerable to oxidative stress. This is due to three major reasons; (1) brain has a high oxygen consumption (2) high content of polyunsaturated fatty acids and iron, that can promote lipid peroxidation, and (3) low levels of antioxidant enzymes such as catalase and glutathione peroxidase. The inability of neurons to regenerate also contributes to exacerbate an oxidant damage in the brain. The main objective of this investigation was to identify biochemical systems in the brain that are susceptible to ROS, on the following two issues: 1. What are the targets for the action of H2O2 and NO in the glycolytic cycle, the major route for the oxidation of glucose in brain? 2. What are the targets for the action of polyunsaturated fatty acids and their oxidative metabolites among the enzymes of phosphoinositide cycle (PI cycle), the ubiquitous signal transduction event in the brain? Using sheep brain cytosol , it was found that among the various glycolytic enzymes, only glyceraldehyde 3-phosphate dehydrogenase (GAPD) was inhibited by H2O2. The enzyme was purified to homogeneity from sheep brain and its inactivation with H202 was studied in detail. Commercial preparations of rabbit skeletal muscle GAPD was also used in this study. An unusual requirement of glutathione for the complete inactivtion of the enzyme by H2O2 was observed. The H2O2-inactivated GAPD was partially reactivated by prolonged treatment with thiol compounds. Using CD-spectral analysis, a significant change was found in the secondary structure in H2O2-treated GAPD. GAPD was inactivated by NO only in presence of high concentrations of DTT and after prolonged incubation. The N0-inactivated GAPD was partially reactivated by treatment with thiol compounds. A new activity, namely ADP-ribosylation (ADPR) emerged in the NO-treated mammalian, but not in yeast. GAPD, ADPR activity could be generated in GAPD through NO-independent treatments such as incubation with NADPH and aerobic dialysis. During NADPH treatment no loss of dehydrogenase activity occurred. Thus, it was concluded that loss of dehydrogenase activity and emergence of ADPR in NO-treated GAPD were not correlated but coincidental, and that NO treatment yielded small amounts of modified-GAPD that had ADPR activity. In the brain, onset of ischemia is characterized by a significant elevation in free fatty acid (FFA) levels, predominantly, arachidonic acid (AA). It is suggested that AA can be oxidised to its metabolites like prostaglandins and 15-hydroperoxy arachidonic acid (15-HPETE) and some of these might exert toxic effects during reperfusion. Using whole membranes or tissue slices prepared from rat brain, effects of polyunsaturated fatty acids and their oxidative metabolites on five enzymes of PI cycle namely PI synthase, PI and PIP kinases, agonist-stimulated PLC and DG kinase was studied. Hydroperoxides of linoleic- and arachidonic acids inactivated PI synthase selectively among the PI cycle enzymes. Interestingly, AA selectively stimulated DG kinase in neural membranes. Docasahexaenoic acid (DHA) a highly unsaturated fatty acid found in the brain, also stimulated DG kinase activity while saturated, mono-and di-unsaturated fatty acids were ineffective. It was concluded that AA and DHA have a role in modulating neural DG kinase. The data presented in the thesis indicate that ROS have selective targets in cells and the consequent protein modifications can be used to modulate cellular functions under normal and oxidative stress conditions.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-03-07T11:11:33Z No. of bitstreams: 1 carlosrobertolimaladeira.pdf: 2482685 bytes, checksum: b90ffa199573e38ddbce8d8ac0283585 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-03-07T15:03:08Z (GMT) No. of bitstreams: 1 carlosrobertolimaladeira.pdf: 2482685 bytes, checksum: b90ffa199573e38ddbce8d8ac0283585 (MD5) / Made available in DSpace on 2017-03-07T15:03:08Z (GMT). No. of bitstreams: 1 carlosrobertolimaladeira.pdf: 2482685 bytes, checksum: b90ffa199573e38ddbce8d8ac0283585 (MD5) Previous issue date: 2014-02-28 / Estimar parâmetros de modelos dinâmicos de sistemas biológicos usando séries temporais é cada vez mais importante, pois uma quantidade imensa de dados experimentais está sendo mensurados pela biologia molecular moderna. Uma abordagem de resolução baseada em problemas inversos pode ser utilizada na solução deste tipo de problema. A escolha do modelo matemático é uma tarefa importante, pois vários modelos podem ser utilizados, apresentando níveis diversos de precisão em suas representações. A Teoria dos Sistemas Bioquímicos (TSB) faz uso de equações diferenciais ordinárias e expansões de séries de potências para representar processos bioquímicos. O Sistema S é um dos modelos usados pela TSB que permite a transformação do sistema original de equações diferenciais em um sistema algébrico desacoplado, facilitando a solução do problema inverso. Essa transformação pode comprometer a qualidade da resposta se o valor das derivadas nos pontos das séries temporais não for obtidos com precisão. Para estimar as derivadas pretende-se explorar o método do passo complexo, que apresenta vantagens em relação ao método das diferenças finitas, mais conhecido e utilizado. A partir daí pode então ser realizada a busca pelas variáveis que definirão as equações do sistema. O método da Regressão Alternada é um dos mais rápidos para esse tipo de problema, mas a escolha inicial dos parâmetros possui influência em seu resultado, que pode até mesmo não ser encontrado. Pretende-se avaliar o método da Entropia Cruzada, que possui a vantagem de realizar buscas globais e talvez por esse motivo a escolha dos parâmetros inicias não cause tanta influência nos resultados. Além disso, será avaliado um método híbrido que fará uso das principais vantagens do método da Regressão Alternada e do Entropia Cruzada para resolver o problema. Experimentos numéricos sistematizados serão realizados tanto para a etapa de estimativa das derivadas quanto para a etapa de otimização para obtenção dos parâmetros das equações do sistema. / Estimating parameters of dynamic models of biological systems using time series is becoming very important because a huge amount of experimental data is being measured by modern molecular biology. A resolution-based approach on inverse problems can be used in solving this type of problem. The choice of the mathematical model is an important task, since many models can be used, with varying levels of accuracy in their representations. The Biochemical Systems Theory (BST) makes use of ordinary differential equations and power series expansions to represent biochemical processes. The S-system is one of the models used by BST that allows the transformation of the original system of differential equations in a decoupled system of algebric equations, favouring the solution of the inverse problem. This transformation can compromise the quality of the response if the value of the derivatives at points of time series are not obtained accurately. To estimate the derivatives we intend to explore the complex-step method, which has advantages over the finite difference method, best known and used . So the search for the variables that define the equations of the system can be performed. The Alternating Regression method is one of the fastest for this type of problem, but the initial choice of parameters has influence on its performance, which may not even be found. We intend to evaluate the Cross-entropy method, which has the advantage of performing global searches and for this reason the choice of the initial search parameters does not cause as much influence on the results. Also, will be assessed a hybrid method that makes use of the main advantages of Alternating Regression and Cross-entropy to solve the problem. Systematic numerical experiments will be conducted for both the step of estimating derivatives as for the optimization step to estimate the variables of the equations of the system.

In 2019, Adams, Ehlting, and Edwards developed a four-variable system of ordinary differential equations modelling phenylalanine metabolism in plants according to Michaelis-Menten kinetics. Analysis of the model suggested that when a series of reactions known as the Shikimate Ester Loop (SEL) is included, phenylalanine flux into primary metabolic pathways is prioritized over flux into secondary metabolic pathways when the availability of shikimate, a phenylalanine precursor, is low. Adams et al. called this mechanism of metabolic regulation the Precursor Shutoff Valve (PSV). Here, we attempt to simplify Adams and colleagues’ model by reducing the system to three variables and replacing the Michaelis-Menten terms with piecewise-defined approximations we call ramp functions. We examine equilibria and stability in this simplified model, and show that PSV-type regulation is still present in the version with the SEL. Then, we define a class of systems structurally similar to the simplified Adams model called biochemical ramp systems. We study the properties of the Jacobian matrices of these systems and then explore equilibria and stability in systems of n ≥ 2 variables. Finally, we make several suggestions regarding future work on biochemical ramp systems. / Graduate

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.