Mathematical modeling of biological systems can be useful to reveal new insights into biological observations. Here we apply mathematical modeling to study the underlying molecular networks driving observed behaviors of two systems. First, we apply systems biology and dynamic systems theory techniques to reveal new insights into the process of hematopoiesis. More specifically, we search the literature to deduce the underlying molecular mechanism that drives cell fate determination in granulocyte-monocyte progenitor (GMP) cells that are exposed to various cytokines. By converting this molecular mechanism into a set of ordinary differential equations (ODEs), we acquired new insights into the behavior of differentiating GMP cells. Next, we explore the cell cycle of the model prokaryotic organism, Caulobacter crescentus. Caulobacter is a uniquely successful oligotrophic bacterium, found abundantly in freshwater systems. While it is not a pathogenic species, Caulobacter is extremely well studied due to its distinguishable asymmetrical morphology and the ability to synchronize populations by cell cycle stage. We built a detailed mathematical model of the molecular mechanism driving the cell cycle. This research suggests a previously unknown role for the unknown form of the master regulator, CtrA, in regulating the G1-S transition. Furthermore, we incorporate a nutrient signaling model into the cell cycle model to investigate how Caulobacter responds to nutrient deprivation. We find that regulation of DivK phosphorylation is an essential component of the nutrient signaling pathway and demonstrate how starvation signals work together in synergy to manifest in observed cell cycle response. / Doctor of Philosophy / Every cell in the human body has the same DNA, yet there are cells of all kinds with different jobs, appearances and behaviors. This simple concept is a consequence of complex regulatory systems within cells that dictate what genes are expressed and when. This dissertation breaks down the molecular mechanisms that regulate gene expression in cells and how these mechanisms result in the interesting behaviors and morphologies that have been observed experimentally. By deriving mathematical equations to describe the molecular mechanisms, we simulate how cell behavior might change under different conditions to make novel discoveries. More specifically, we utilize these techniques to study the freshwater bacterium, Caulobacter crescentus, and human cells of the white blood cell lineage. We utilize our models to identify previously unknown aspects of the molecular mechanisms, develop explanations for mysterious cell behaviors and provide interesting predictions that have not been explored experimentally.

This study examines the trading activity of a large cross section of American bank holding companies upon various sub-events associated with the introduction of Basel III. An event study methodology was applied to various sub-composite portfolios, as determined by regulatory capitalization and leverage ratios. The results suggest that statically significant abnormal negative returns occurred on the announcement to negotiate due to heightened regulatory uncertainty, especially amongst the least capitalized and highest leveraged banks. However, this effect is complemented by statically significant positive returns upon the release of the initial guidelines. Reactions to subsequent events report to be less significant.

Technology, nowadays, has given us huge computational potential, but computer sciences have major problems tapping into this pool of resources. One of the main issues is how to program and design distributed systems. Biology has solved this issue about half a billion years ago, during the Cambrian explosion: the evolution of multicellularity. The evolution of multicellularity allowed cells to differentiate and so divide different tasks to different groups of cells; this combined with evolution gives us a very good example of how massively parallel distributed computational system can function and be “programmed”. However, the evolution of multicellularity is not very well understood, and most traditional methodologies used in evolutionary theory are not apt to address and model the whole transition to multicellularity. In this thesis I develop and argue for new computational artificial life methodologies for the study of the evolution of multicellularity that are able to address the whole transition, give new insights, and complement existing methods. I argue that these methodologies should have three main characteristics: accessible across scientific disciplines, have potentiality for complex behaviour, and be easy to analyse. To design models, which possess those characteristics, I developed a model of genetic regulatory networks (GRNs) that control artificial cells, which I have used in multiple evolutionary experiments. The first experiment was designed to present some of the engineering problems of evolving multicelled systems (applied to graph-colouring), and to perfect my artificial cell model. The two subsequent experiments demonstrate the characteristics listed above: one model based on a genetic algorithm with an explicit two-level fitness function to evolve multicelled cooperative patterning, and one with freely evolving artificial cells that have evolved some multicelled cooperation as evidenced by novel measures, and has the potential to evolve multicellularity. These experiments show how artificial life models of evolution can discover and investigate new hypotheses and behaviours that traditional methods cannot.

Development of the nervous system is a highly organized process that utilizes genetic mechanisms conserved across the animal kingdom. Components of the nervous system such as inhibitory GABAergic neural networks are common among most multicellular animals. The nematode Caenorhabditis elegans, utilizes similar genetic pathways to that of mice and humans to develop its GABAergic neural networks. These GABAergic neural networks are composed of two types of GABAergic motor neurons: the VD and DD sub-classes. The GABAergic differentiation of both these sub-classes requires the conserved transcription factor, Pitx/UNC-30. The VD sub-class is differentiated from the DD motor neurons by the expression of another transcription factor, COUP TFII/UNC-55. The transcriptional mechanisms regulating the expression of Pitx/UNC-30 and Coup TFII are unknown. We sought to determine how Pitx/UNC-30 and COUP TF-II/UNC-55 were transcriptionally regulated in an attempt to understand how mechanisms of GABAergic fate specification and class specification may be connected. We hypothesized there would be different mechanisms regulating the GABAergic differentiation and sub-class specification of the two sub-classes of GABAergic motor neurons. To test this, we dissected the transcriptional mechanisms responsible for the expression of Pitx/UNC-30 and COUP TFII/UNC-55. We found that different isoforms of the Hox cofactor Meis/UNC-62 stabilize and activate the expression of UNC-55. Furthermore, we conclude that Pitx/UNC-30 expression is regulated differently between the two motor neuron sub-classes by Meis/UNC-62, Hox-B7/MAB-5 and NeuroD/CND-1, each of which are vital to the development of different components of the nervous system in vertebrates. Our findings suggest that the GABAergic identity and the sub-class specification of neurons are under the control of multiple conserved transcription factors responsible for neuron fate determination and post mitotic identities.

Esta dissertação de mestrado tem como finalidade descrever o trabalho realizado em uma pesquisa que envolve a análise de expressões gênicas provenientes de microarrays com o objetivo de encontrar genes importantes em um organismo ou em uma determinada doença, como o câncer. Acreditamos que a descoberta desses genes, que chamamos aqui de genes de predição intrinsicamente multivariada (genes IMP), possa levar a descobertas de importantes processos biológicos ainda não conhecidos na literatura. A busca por genes IMP foi realizada em conjunto com estudos de modelos e conceitos matemáticos e estatísticos como redes Booleanas, cadeias de Markov, Coeficiente de Determinação (CoD), Classificação em análise de expressões gênicas e métodos de estimação de erro. No modelo de redes Booleanas, introduzido na Biologia por Kauffman, as expressões gênicas são quantizadas em apenas dois níveis: \"ligado\'\' ou \"desligado\'\'. O nível de expressão (estado) de cada gene, está relacionado com o estado de alguns outros genes através de uma função lógica. Adicionando uma perturbação aleatória a este modelo, temos um modelo mais geral conhecido como redes Booleanas com perturbação. O sistema dinâmico representado pela rede é uma cadeia de Markov ergódica e existe então uma distribuição de probabilidade estacionária. Temos a hipótese de que os experimentos de microarray seguem esta distribuição estacionária. O CoD é uma medida normalizada de quanto a expressão de um gene alvo pode ser melhor predita observando-se a expressão de um conjunto de genes preditores. Uma determinada configuração de CoDs caracteriza um gene alvo como sendo um gene IMP. Podemos trabalhar não somente com genes alvo, mas também com fenótipos alvo, onde o fenótipo de um sistema biológico poderia ser representado por uma variável aleatória binária. Por exemplo, podemos estar interessados em saber quais genes estão relacionados ao fenótipo de vida/morte de uma célula. Como a distribuição de probabilidade das amostras de microarray é desconhecida, o estudo dos CoDs é feito através de estimativas. Entre os métodos de estimação de erro estudados para este propósito podemos citar: Holdout, Resubstituição, Cross-validation, Bootstrap e .632 Bootstrap. Os métodos foram implementados para calcular os CoDs, permitindo então a busca por genes IMP. Os programas implementados na pesquisa foram usados em conjunto com uma pesquisa realizada pelo Prof. Dr. Hugo A. Armelin do Instituto de Química da USP. Este estudo em particular envolve a busca de genes importantes relacionados à morte de células tumorigênicas de camundongo disparada por FGF2 (Fibroblast Growth Factor 2). Nesta pesquisa observamos sub-redes de genes envolvidos no processo biológico em questão e também encontramos genes que podem estar relacionados ao fenômeno de morte das células de camundongo ou que estão, de fato, participando de alguma via disparada pelo FGF2. Esta abordagem de análise de expressões gênicas, juntamente com a pesquisa realizada pelo Prof. Armelin, resulta em uma metodologia para buscas de genes envolvidos em novos mecanismos de células tumorigênicas, ativados pelo FGF2. Na realidade esta metodologia pode ser aplicada em qualquer processo biológico de interesse científico, desde que seja possível modelar o problema proposto no contexto de redes Booleanas, coeficientes de determinação e genes IMP. / This Master\'s degree dissertation describes a research that involves an analysis of gene expression data from microarray experiments with the purpose to find important genes in certain organisms or diseases such as cancer. We believe that these type of genes, called intrinsically multivariately predictive genes (IMP genes), can lead to the discovery of important biological process that are unknown in the literature. The search for IMP genes was done with the study of mathematical and statistical models such as Boolean Networks, Markov Chains, Coefficient of Determination (CoD), Classification and Error Estimation Methods. In the Boolean network model, introduced in Biology by Kauffman, the gene expression is quantized in only two levels: ON and OFF. The expression level (state) of each gene is related with the state of some other genes through a logical function. Adding a random perturbation to this model, we have a more general Boolean-type model called Boolean network with perturbation. The dynamical system represented by this network is an ergodic Markov chain and thereby it possesses a steady-state distribution. We have the hypothesis that the microarray experiments follow this steady-state distribution. The CoD is a normalized measure of how much a gene expression of a target gene can be better predicted observing the expression of a set of predictor genes. A certain configuration of CoDs characterizes a target gene as an IMP gene. We can deal not only with target genes, but also with target phenotypes, where the phenotype of a biological system could be represented by a binary random variable. For example, we could be interested in knowing which genes are related to a life/death cell phenotype. Since the joint probability distribution of the gene expressions is unknown, the CoDs must be computed through estimated values. Among the error estimation methods studied we can cite: Holdout, Resubstitution, Cross-validation, Bootstrap and .632 Bootstrap. Those methods were implemented as a software in order to compute the CoDs and thereby allowing us to search for IMP genes. The software we implemented in this research was used within a research developed by Professor Dr. Hugo A. Armelin from the Instituto de Química - University of Sao Paulo. This particular research involves the search for important genes related to the death of tumorigenic mouse cells triggered by FGF2 (Fibroblast Growth Factor 2). From this research cooperation, we built some gene subnetworks involved in the target biological process and we found some genes that could be related to the death phenotype of mouse cells. This approach of gene expression analysis, together with the research developed by Professor Armelin, results in a methodology to search for important genes that could be involved in new mechanisms of tumorigenic cells triggered by FGF2. Actually, this methodology can be applied to any biological process of scientific interest, if one can model the proposed problem in the context of Boolean Networks, Coefficient of Determination and IMP genes.

The gene regulatory network (GRN) controls the expression of genes providing phenotypic traits in living organisms. In particular, transcriptional regulation is essential to life, as it governs all levels of gene products that enable cell survival and numerous cellular functions. However, there is still poor understanding of how shifts in gene regulation alter the underlying evolutionary dynamics and consequently generate evolutionary innovations. By employing Wagner's GRN model, this dissertation investigates how the interplay of simple evolutionary forces (mutation and recombination) with natural selection acting on gene regulatory dynamics can generate major evolutionary innovations. In this dissertation, firstly, I review all currently available research papers using Wagner's GRN model, which is also employed as the computational model used extensively in the remaining chapters. I then describe how Wagner's GRN model and its variants are implemented. Finally, network properties such as stability, robustness and path length in initial populations are investigated. In the first study, I explore the characteristics of compensatory mutation in the context of genetic networks. Specifically, I find that 1) compensatory mutations are relatively insensitive to the size and connectivity of the network, 2) compensatory mutations are more likely to occur in genes at or adjacent to the site of a previous deleterious mutation and 3) compensatory mutations are more likely to be driven by mutations with a relatively large regulatory impact. In the second study, I further investigate the evolutionary consequences of the properties of compensatory mutation discovered previously. Specifically, I find that 1) compensatory mutations can occur regardless of patterns of selection, 2) networks with compensatory mutations exhibit proportionately higher robustness when compensatory mutations interact closely with deleterious mutations or have large effects on gene regulation, and 3) regulatory complexity can arise as a consequence of the propensity for co-localised and large-effect compensatory mutations. In the third study, I provide a mechanistic understanding of how recombination benefits sexual lineages. Specifically, I find that 1) recombination together with selection for developmental stability can drive populations towards the optimum, 2) recombination does not frequently disrupt well-adapted lineages as conventionally expected, and 3) recombination facilitates finding good genetic combinations which are robust to disruption, although it also rapidly purges weaker configurations. In the final study, I show that the selection pressure acting on rewiring gene regulation is critical to increasing benefits for sexual lineages whilst mitigating costs of sex and recombination. Specifically, I find that 1) strong selection strength can greatly benefit low-fitness sexual lineages, especially at the early stage, 2) recombination is initially costly, but it can rapidly evolve to compensate for costs of sex and recombination, and 3) sexual lineages with low levels of sex and recombination can outcompete strictly asexual populations under higher selection pressure and lower mutation rates. The results presented for all of the studies are important for mechanistically understanding evolutionary innovations through altering transcriptional regulatory dynamics. These innovations include 1) facilitating alternative pathway evolution, 2) driving regulatory complexity, 3) benefiting sexual reproduction, and 4) resisting invasion against asexual lineages.

Greenhill et al. (2011) developed a gene regulatory network of the main genes and interactions known to play a role in melanocyte biology, and generated a mathematical model to describe the behaviour of this complex network using semi quantitative data (ISH expression data). In this project we sought to collect expression data from four genes of the melanocyte GRN (sox10, kit, mitfa and dct) to develop a quantitative model that is able to describe the data more accurately. Moreover, we intended to identify more genes that are part of the melanocyte development process to be incorporated to the GRN. We analysed microarray data that compared differentially expressed genes between sox10 mutant and wild type embryos and validated five genes with a key role in melanocyte biology as downregulated in mitfa mutant embryos, which are downstream of mitfa in the GRN. We suggest that kit plays the role of factor Y in the Greenhill et al. (2011) GRN: Mitfa drives kit expression, and kit expression is transiently driven by Sox10 at early stages of development. As part of the feedback loop, kit seems to drive and maintain mitfa expression, however this needs to be validated. Finally we developed an experimental set up to obtain an estimate of gene expression per melanocyte from sox10, kit, mitfa and dct, using both qPCR and ISH cell count measurements. With this estimate we performed a parameter optimisation procedure, and found a set of parameters for the mathematical model that predicted the experimental data very accurately. The new model suggests that low expression values of sox10 are sufficient to drive mitfa expression in high levels. It also predicts that high expression of sox9b is needed to achieve the high expression levels of dct seen in the data, although these predictions need to be experimentally tested. This study represents the first attempt to obtain fine-scale gene expression data from melanocytes for the development of a quantitative mathematical model in zebrafish.

Many organisms can acclimate to new environments through phenotypic plasticity, a complex trait that can be heritable, be subject to selection, and evolve. However, the rate and genetic basis of plasticity evolution remain largely unknown. Experimentally evolved populations of the nematode Caenorhabditis remanei were created by selecting for stress resistance under different environmental conditions. This resource was used to address key questions about how phenotypic plasticity evolves and what the genetic basis of plasticity is. Here, I highlight ways in which a fuller understanding of the environmental context influences our interpretation of the evolution of phenotypic plasticity. In a population selected to withstand heat stress, an apparent case of genetic assimilation did not show correlated changes in global gene regulation. However, further investigation revealed that the induced plasticity was not fixed across environments, but rather the threshold for the response was shifted over evolutionary time. Similarly, the past environment experienced by populations can play a role in directing the multivariate response to selection. Correlated responses to selection between traits and across environments were examined. The pattern of covariation in the evolutionary response among traits differed depending on the environment in which selection occurred, indicating that there exists variation in pleiotropy across the stress response network that is highly sensitive to the external environment. To understand how the patterns of pleiotropy are altered by environment and evolution, there is a pressing need to determine the structure of the molecular networks underlying plastic phenotypes. Using RNA-sequencing, the structure of the gene regulatory network is examined for a subset of evolved populations from one environment. Key modules within this network were identified that are strong candidates for the evolution of phenotypic plasticity in this system. Together, the data presented in this dissertation provide a comprehensive view of the myriad ways in which the environment shapes the genetic architecture of stress response phenotypes and directs the evolution of phenotypic plasticity. Additionally, the structure of transcriptional network provides valuable insight into the genetic basis of adaptation to environmental change and the evolution of phenotypic plasticity. This dissertation includes both previously published and co-authored material.

Cette thèse traite de la synchronisation et de la désynchronisation des systèmes dynamiques. Dans une première partie nous abordons, sous l’angle de la biologie systémique, le problème de la désynchronisation qui consiste à induire un comportement chaotique dans un système ayant une dynamique stable. Nous étudions ce problème sur un réseau génétique appelé V-système, inventé afin de coupler le plus simplement possible une bifurcation de Hopf et une hystérèse. Après avoir démontré qu’un champ de vecteurs de R^n présentant un tel couplage peut, sous certaines conditions, avoir un comportement chaotique, nous donnons un ensemble de paramètres pour lequel le V-système associé satisfait ces conditions et vérifions numériquement que le mécanisme responsable du chaos prend place dans ce système. Dans une deuxième partie, nous nous intéressons à la synchronisation de systèmes organisés hiérarchiquement. Nous commençons par définir une structure hiérarchique pour un ensemble de 2^n systèmes par une matrice représentant les étapes d’un processus de regroupement deux par deux. Cela nous amène naturellement au cas d’un ensemble de Cantor de systèmes, pour lequel nous obtenons un résultat de synchronisation globale généralisant le cas fini. Enfin nous traitons de la situation où certains défauts apparaissent dans la hiérarchie, i.e que certains liens entre les systèmes sont brisés. Nous montrons que l’on peut accepter un nombre infini de liens brisés, tout en gardant une synchronisation locale, à condition que ces liens soient uniquement présents aux N premiers étages de la hiérarchie (pour un N fixé) et qu’ils soient suffisamment espacés dans ces étages. / This thesis deals with the synchronization and desynchronization of dynamical systems. In a first part we tackle (under a biological viewpoint) the desynchronization problem, which consists in the induce- ment of a chaotic behavior in a stable dynamical system. We study this problem on a gene regulatory network called V-system, invented in order to couple in a very simple way, a Hopf bifurcation and a hysteresis-type dynamics. After having proved that a vector field on Rn admitting such a coupling may, under some condi- tions, show a chaotic dynamics, we give a set of parameters for which the associated V-system satisfies these conditions and verify numerically that the mechanism responsible of the chaotic motion occurs in this system. In a second part, we take interest in the synchronization of hierarchically organized dynamical systems. We first define a hierarchical structure for a set of 2^n systems by a matrix representing the steps of a matching process in groups of size two. This leads us naturally to the case of a Cantor set of systems, for which we obtain a global synchronization result generalizing the finite case. Finally, we deal with the situation where some defects appear in the hierarchy, that is to say when some links between certain systems are broken. We prove we can afford an infinite number of such broken links while keeping a local synchronization, providing they are only present at the first N stages of the hierarchy (for a fixed integer N) and they are enough spaced out in these stages.

RNA sequencing (RNA-seq) technologies facilitate the characterisation of genes and transcripts in different cell types as well as their expression analysis across various conditions. Due to its ability to provide in-depth insights into transcription and post-transcription mechanisms, RNA-seq has been extensively used in functional genetics and transcriptomics, system biology and developmental biology in animals, plants, diseases, etc. The aim of this project is to use mathematical and computational models to integrate big genomic and transcriptomic data from high-throughput technologies in plant biology and develop new methods to identify which genes or transcripts have significant expression variation across experimental conditions of interest, then to interpret the regulatory causalities of these expression changes by distinguishing the effects from the transcription and alternative splicing. We performed a high resolution ultra-deep RNA-seq time-course experiment to study Arabidopsis in response to cold treatment where plants were grown at 20^oC and then the temperature was reduced to 4^oC. We have developed a high quality <i>Arabidopsis thaliana</i> Reference Transcript Dataset (AtRTD2) transcriptome for accurate transcript and gene quantification. This high quality time-series dataset was used as the benchmark for novel method development and downstream expression analysis. The main outcomes of this project include three parts. i) A pipeline for differential expression (DE) and differential alternative splicing (DAS) analysis at both gene and transcript levels. Firstly, we implemented data pre-processing to reduce the noise/low expression, batch effects and technical biases of read counts. Then we used the limma-voom pipeline to compare the expression at corresponding time-points of 4^oC to the time-points of 20^oC. We identified 8,949 genes with altered expression of which 2,442 showed significant DAS and 1,647 were only regulated by AS. Compared with current publications, 3,039 of these genes were novel cold-responsive genes. In addition, we identified 4,008 differential transcript usage (DTU) transcripts of which the expression changes were significantly different to their cognate DAS genes. ii) A TSIS R package for time-series transcript isoform switch (IS) analysis was developed. IS refers to the time-points when a pair of transcript isoforms from the same gene reverse their relative expression abundances. By using a five metric scheme to evaluate robustly the qualities of each switch point, we identified 892 significant ISs between the high abundance transcripts in the DAS genes and about 57% of these switches occurred very rapidly between 0-6h following transfer to 4^oC. iii) A RLowPC R package for co-expression network construction was generated. The RLowPC method uses a two-step approach to select the high-confidence edges first by reducing the search space by only picking the top ranked genes from an initial partial correlation analysis, and then computes the partial correlations in the confined search space by only removing the linear dependencies from the shared neighbours, largely ignoring the genes showing lower association. In future work, we will construct dynamic transcriptional and AS regulatory networks to interpret the causalities of DE and DAS. We will study the coupling and de-coupling of expression rhythmicity to the Arabidopsis circadian clock in response to cold. We will develop new methods to improve the statistical power of expression comparative analysis, such as by taking into account the missing values of expression and by distinguishing the technical and biological variabilities.