Cells generally manage to maintain stable phenotypes in the face of widely varying environmental conditions. This fact is particularly surprising since the key step of gene expression is fundamentally a stochastic process. Many hypotheses have been suggested to explain this robustness. First, the special topology of gene regulatory networks (GRNs) seems to be an important factor as they possess feedforward loops and certain other topological features much more frequently than expected. Second, genes often regulate each other in a canalizing fashion: there exists a dominance order amidst the regulators of a gene, which in silico leads to very robust phenotypes. Lastly, an entirely novel gene regulatory mechanism, discovered and studied during the last two decades, which is believed to play an important role in cancer, is shedding some light on how canalization may in fact take place as part of a cell’s gene regulatory program. Short segments of single-stranded RNA, so-called microRNAs, which are embedded in several different types of feedforward loops, help smooth out noise and generate canalizing effects in gene regulation by overriding the effect of certain genes on others. Boolean networks and their multi-state extensions have been successfully used to model GRNs for many years. In this dissertation, GRNs are represented in the time- and statediscrete framework of Stochastic Discrete Dynamical Systems (SDDS), which captures the cell-inherent stochasticity. Each gene has finitely many different concentration levels and its concentration at the next time step is determined by a gene-specific update rule that depends on the current concentration of the gene’s regulators. The update rules in published gene regulatory networks are often nested canalizing functions. In Chapter 2, this class of functions is introduced, generalized and analyzed with respect to its potential to confer robustness. Chapter 3 describes a simulation study, which supports the hypothesis that microRNA-mediated feedforward loops have a stabilizing effect on GRNs. Chapter 4 focuses on the cellular DNA mismatch repair machinery. A first regulatory network for this machinery is introduced, partly validated and analyzed with regard to the role of microRNAs and certain genes in conferring robustness to this particular network. Due to steady exposure to mutations, GRNs have evolved over time into their current form. In Chapter 5, a new framework for modeling the evolution of GRNs is developed and then used to identify topological features that seem to stabilize GRNs on an evolutionary time-scale. Chapter 6 addresses a completely separate project in Bioinformatics. A novel functional enrichment method is developed and compared to various popular methods. Funding for this work was provided by NSF grant CMMI-0908201 and NSF grant 1062878. / Ph. D.

Chemotherapy is commonly used in cancer treatments, however only 25% of cancers are responsive and a significant proportion develops resistance. The p53 tumour suppressor is crucial for cancer development and therapy, but has been less amenable to therapeutic applications due to the complexity of its action reflected in 67,000 papers describing its function. Here we provide a systematic approach to integrate this information by constructing large-scale logical models of the p53 interactome using extensive database and literature integration. Initially we generated models using manual curation to demonstrate the feasibility of the approach. This was followed by creation of the next generation models by automatic text mining results retrieval. Final model PKT205/G3 was generated by choosing the size of the interactome that could be analysed with current available computing power and by linking upstream nodes to input environmental signals such as DNA damage and downstream nodes to output signal such as apoptosis. This final version of the PKT205/G3 model contains 205 nodes representing genes or proteins, DNA damage input and apoptosis output, and 677 logical interactions. Predictions from in silico knock-outs and steady state model analysis were validated using literature searches and in vitro experiments. We identify an up regulation of Chk1, ATM and ATR pathways in p53 negative cells and 58 other predictions obtained by knockout tests mimicking mutations. The comparison of model simulations with microarray data demonstrated a significant rate of successful predictions ranging between 52 % and 71 % depending on the cancer type. Growth factors and receptors FGF2, IGF1R, PDGFRB and TGFA were identified as factors contributing selectively to the control of U2OS osteosarcoma and HCT116 colon cancer cell growth. In summary, we provide the proof of principle that this versatile and predictive model has vast potential for use in cancer treatment by identifying pathways in individual patients that contribute to tumour growth, defining a sub population of “high” responders and identification of shifts in pathways leading to chemotherapy resistance.

Em sistemas biológicos, o estudo da estabilidade das redes de regulação gênica é visto como uma contribuição importante que a Matemática pode proporcionar a pesquisas sobre câncer e outras doenças genéticas. Neste trabalho, utilizamos o conceito de ``canalização\'\' como sinônimo de estabilidade em uma rede biológica. Como as características de uma rede de regulação canalizada ainda são superficialmente compreendidas, estudamos esse conceito sob o ponto de vista computacional: propomos um modelo matemático simplificado para descrever o fenômeno e realizamos algumas análises sobre o mesmo. Mais especificamente, a estabilidade da maior bacia de atração das redes Booleanas - um clássico paradigma para a modelagem de redes de regulação - é analisada. Os resultados indicam que a estabilidade da maior bacia de atração está relacionada com dados biológicos sobre o crescimento de colônias de leveduras e que considerações sobre a interação entre as funções Booleanas e a topologia da rede devem ser realizadas conjuntamente na análise de redes estáveis. / In biological systems, the study of gene regulatory networks stability is seen as an important contribution that Mathematics can make to cancer research and that of other genetic diseases. In this work, we consider the concept of ``canalization\'\' as a consequence of stability in gene regulatory networks. The characteristics of canalized regulatory networks are superficially understood. Hence, we study the canalization concept under a computational framework: a simplified model is proposed to describe the phenomenon using Boolean Networks - a classical paradigm to modeling regulatory networks. Specifically, the stability of the largest basin of attraction in gene regulatory networks is analyzed. Our results indicate that the stability of the largest basin of attraction is related to biological data on growth of yeast colonies, and that thoughts about the interaction between Boolean functions and network topologies must be given in the analysis of stable networks.

All high-level living organisms are made of small cell units, containing DNA, RNA, genes, proteins etc. Genes are important components of the cells and it is necessary to understand the inter-gene relations, in order to comprehend, predict and ultimately intervene in the cells’ dynamics. Genetic regulatory networks (GRN) represent the gene interactions that dictate the cell behavior. Translational genomics aims to mathematically model GRNs and one of the main goals is to alter the networks’ behavior away from undesirable phenotypes such as cancer. The mathematical framework that has been often used for modeling GRNs is the probabilistic Boolean network (PBN), which is a collection of constituent Boolean networks with perturbation, BNp. This dissertation uses BNps, to model gene regulatory networks with an intent of designing stationary control policies (CP) for the networks to shift their dynamics toward more desirable states. Markov Chains (MC) are used to represent the PBNs and stochastic control has been employed to find stationary control policies to affect steady-state distribution of the MC. However, as the number of genes increases, it becomes computationally burdensome, or even infeasible, to derive optimal or greedy intervention policies. This dissertation considers the problem of modeling and intervening in large GRNs. To overcome the computational challenges associated with large networks, two approaches are proposed: first, a reduction mapping that deletes genes from the network; and second, a greedy control policy that can be directly designed on large networks. Simulation results show that these methods achieve the goal of controlling large networks by shifting the steady-state distribution of the networks toward more desirable states. Furthermore, a new inference method is used to derive a large 17-gene Boolean network from microarray experiments on gastrointestinal cancer samples. The new algorithm has similarities to a previously developed well-known inference method, which uses seed genes to grow subnetworks, out of a large network; however, it has major differences with that algorithm. Most importantly, the objective of the new algorithm is to infer a network from a seed gene with an intention to derive the Gene Activity Profile toward more desirable phenotypes. The newly introduced reduction mappings approach is used to delete genes from the 17-gene GRN and when the network is small enough, an intervention policy is designed for the reduced network and induced back to the original network. In another experiment, the greedy control policy approach is used to directly design an intervention policy on the large 17-gene network to beneficially change the long-run behavior of the network. Finally, a novel algorithm is developed for selecting only non-isomorphic BNs, while generating synthetic networks, using a method that generates synthetic BNs, with a prescribed set of attractors. The goal of the new method described in this dissertation is to discard isomorphic networks.

In this work three different approaches for deriving genetic association networks were tested. The three approaches were Pearson correlation, an algorithm based on the Boolean network approach and prior knowledge. Pearson correlation and the algorithm based on the Boolean network approach derived associations from gene expression data. In the third approach, prior knowledge from a known genetic network of a related organism was used to derive associations for the target organism, by using homolog matching and mapping the known genetic network to the related organism. The results indicate that the Pearson correlation approach gave the best results, but the prior knowledge approach seems to be the one most worth pursuing

<p>In this work three different approaches for deriving genetic association networks were tested. The three approaches were Pearson correlation, an algorithm based on the Boolean network approach and prior knowledge. Pearson correlation and the algorithm based on the Boolean network approach derived associations from gene expression data. In the third approach, prior knowledge from a known genetic network of a related organism was used to derive associations for the target organism, by using homolog matching and mapping the known genetic network to the related organism. The results indicate that the Pearson correlation approach gave the best results, but the prior knowledge approach seems to be the one most worth pursuing</p>

Em sistemas biológicos, o estudo da estabilidade das redes de regulação gênica é visto como uma contribuição importante que a Matemática pode proporcionar a pesquisas sobre câncer e outras doenças genéticas. Neste trabalho, utilizamos o conceito de ``canalização\'\' como sinônimo de estabilidade em uma rede biológica. Como as características de uma rede de regulação canalizada ainda são superficialmente compreendidas, estudamos esse conceito sob o ponto de vista computacional: propomos um modelo matemático simplificado para descrever o fenômeno e realizamos algumas análises sobre o mesmo. Mais especificamente, a estabilidade da maior bacia de atração das redes Booleanas - um clássico paradigma para a modelagem de redes de regulação - é analisada. Os resultados indicam que a estabilidade da maior bacia de atração está relacionada com dados biológicos sobre o crescimento de colônias de leveduras e que considerações sobre a interação entre as funções Booleanas e a topologia da rede devem ser realizadas conjuntamente na análise de redes estáveis. / In biological systems, the study of gene regulatory networks stability is seen as an important contribution that Mathematics can make to cancer research and that of other genetic diseases. In this work, we consider the concept of ``canalization\'\' as a consequence of stability in gene regulatory networks. The characteristics of canalized regulatory networks are superficially understood. Hence, we study the canalization concept under a computational framework: a simplified model is proposed to describe the phenomenon using Boolean Networks - a classical paradigm to modeling regulatory networks. Specifically, the stability of the largest basin of attraction in gene regulatory networks is analyzed. Our results indicate that the stability of the largest basin of attraction is related to biological data on growth of yeast colonies, and that thoughts about the interaction between Boolean functions and network topologies must be given in the analysis of stable networks.

Na busca por soluções que maximizem a produção de etanol, o melhoramento genético de diferentes linhagens de levedura tornou-se foco de investigação em diversos centros de pesquisa. Com o recente sequenciamento de uma linhagem selvagem utilizada nas usinas sucroalcooleiras brasileiras, a linhagem PE-2 da espécie Saccharomyces cerevisiae, surgiu o interesse em estudar sua dinâmica durante o processo de fermentação a fim de encontrar aspectos que possam explicar como estas se tornaram mais adaptadas às dornas de fermentação mantendo a alta produtividade de bioetanol. A partir da análise transcricional da linhagem PE-2, Buscamos por métodos de inferência de redes que possam representar a dinâmica dessa levedura. Propomos nesse trabalho a modelagem de dados experimentais temporais das linhagens PE-2 e S288c (utilizada como referência) baseado em um modelo de Redes Booleanas. Trata-se de um modelo onde convertemos dados contínuos em dados discretos (0 or 1) no qual, de acordo com restrições ditadas pelo modelo, são inferidas redes que representem interações gênicas ao longo do tempo baseados nas amostras temporais. Conseguimos modelar, com sucesso, algumas redes utilizando conjuntos com 11 e 12 genes relacionados a genes pertencentes à via da glicólise e fermentação da levedura. / Ethanol production improvements give rise to the breeding of yeast strains, that became the investigation focus in several research centers. Recently, a wild strain used in Brazilian sugarcane industry was sequenced, the PE-2 strain of Saccharomyces cerevisiae, and this event brought an interest in studying the dynamics of the fermentation of this strain in order to understand which aspects this strain become more adapted to the fermentation conditions, maintaining a high capacity to produce bioethanol. From the analysis of transcriptional strain PE-2, we seek for inference networks methods that can represent the dynamics of this yeast.In this work, we model an experimental temporal data of strain PE-2 and strain S288c (used as a reference) based on Boolean networks model. In this model, the data are converted from continuous into discrete data (0 or 1) and, based on constraints rules of Boolean Network model, networks are inferred to represent gene interactions over time based on temporal data. We successfully model networks using a set with 11 and 12 genes related to yeast glycolysis and fermentation pathways.

Na busca por soluções que maximizem a produção de etanol, o melhoramento genético de diferentes linhagens de levedura tornou-se foco de investigação em diversos centros de pesquisa. Com o recente sequenciamento de uma linhagem selvagem utilizada nas usinas sucroalcooleiras brasileiras, a linhagem PE-2 da espécie Saccharomyces cerevisiae, surgiu o interesse em estudar sua dinâmica durante o processo de fermentação a fim de encontrar aspectos que possam explicar como estas se tornaram mais adaptadas às dornas de fermentação mantendo a alta produtividade de bioetanol. A partir da análise transcricional da linhagem PE-2, Buscamos por métodos de inferência de redes que possam representar a dinâmica dessa levedura. Propomos nesse trabalho a modelagem de dados experimentais temporais das linhagens PE-2 e S288c (utilizada como referência) baseado em um modelo de Redes Booleanas. Trata-se de um modelo onde convertemos dados contínuos em dados discretos (0 or 1) no qual, de acordo com restrições ditadas pelo modelo, são inferidas redes que representem interações gênicas ao longo do tempo baseados nas amostras temporais. Conseguimos modelar, com sucesso, algumas redes utilizando conjuntos com 11 e 12 genes relacionados a genes pertencentes à via da glicólise e fermentação da levedura. / Ethanol production improvements give rise to the breeding of yeast strains, that became the investigation focus in several research centers. Recently, a wild strain used in Brazilian sugarcane industry was sequenced, the PE-2 strain of Saccharomyces cerevisiae, and this event brought an interest in studying the dynamics of the fermentation of this strain in order to understand which aspects this strain become more adapted to the fermentation conditions, maintaining a high capacity to produce bioethanol. From the analysis of transcriptional strain PE-2, we seek for inference networks methods that can represent the dynamics of this yeast.In this work, we model an experimental temporal data of strain PE-2 and strain S288c (used as a reference) based on Boolean networks model. In this model, the data are converted from continuous into discrete data (0 or 1) and, based on constraints rules of Boolean Network model, networks are inferred to represent gene interactions over time based on temporal data. We successfully model networks using a set with 11 and 12 genes related to yeast glycolysis and fermentation pathways.

This master's thesis introduces the Random Boolean Networks as a developmental model in the evolutionary design. The representation of the Random Boolean Networks is described. This representation is combined with an evolutionary algorithm. The genetic operators are described too. The Random Boolean Networks are used as the developmental model for  the evolutionary design of the combinational circuits and the sorting networks. Moreover a representation of the Random Boolean Networks for the design of image filters is introduced. The proposed methods are evaluated in different case-studies. The results of the experiments are discussed together with the potential improvements  and topics of the next research.