Paralog reduction, the loss of duplicate genes after whole genome duplication (WGD) is a pervasive process. Whether this loss proceeds gene by gene or through deletion of multi-gene DNA segments is controversial, as is the question of fractionation bias, namely whether one homeologous chromosome is more vulnerable to gene deletion than the other. As a null hypothesis, we first assume deletion events, on one homeolog only, excise a geometrically distributed number of genes with unknown mean mu, and these events combine to produce deleted runs of length l, distributed approximately as a negative binomial with unknown parameter r; itself a random variable with distribution pi(.). A biologically more realistic model requires deletion events on both homeologs distributed as a truncated geometric. We simulate the distribution of run lengths l in both models, as well as the underlying pi(r), as a function of mu, and show how sampling l allows us to estimate mu. We apply this to data on a total of 15 genomes descended from 6 distinct WGD events and show how to correct the bias towards shorter runs caused by genome rearrangements. Because of the difficulty in deriving pi(.) analytically, we develop a deterministic recurrence to calculate each pi(r) as a function of mu and the proportion of unreduced paralog pairs. This is based on a computing formula containing nested sums. The parameter mu can be estimated based on run lengths of single-copy regions. We then reduce the computing formulae, at least in the one-sided case, to closed form. This virtually eliminates computing time due to highly nested summations. We formulate a continuous version of the fractionation process, deleting line segments of exponentially distributed lengths in analogy to geometric distributed numbers of genes. We derive nested integrals and discover that the number of previously deleted regions to be skipped by a new deletion event is exactly geometrically distributed. We undertook a large simulation experiment to show how to discriminate between the gene-by-gene duplicate deletion model and the deletion of a geometrically distributed number of genes. This revealed the importance of the effects of genome size N, the mean of the geometric distribution, the progress towards completion of the fractionation process, and whether the data are based on runs of deleted genes or undeleted genes.

In the operation of CMGs there exists a concept called “back drive,” which represents a case where the coupling effects of the angular velocity of the body and the angular momentum of the CMG overwhelm the input torque and result in a lack of control. This effect is known but not well documented or studied in the literature. Starting from first principles, this thesis derives the full nonlinear dynamical equations for CMGs. These equations contain significantly more terms than are found in the literature. As a means to understand the implications of these terms, a reduced order model is derived. The full and reduced models are then validated by means of extensive simulations. Finally, experimental verification of the models confirms the finding that the reduced order model provides a reasonably high fidelity for dynamics.

A crucial step in eukaryotic cell proliferation is the initiation of DNA replication, a tightly regulated process mediated by a multitude of protein factors. In Saccharomyces cerevisiae, this occurs as a result of the concerted action of an assembly of proteins acting at origins of replication, known as the pre-replicative complex (pre-RC). While many of the mechanisms pertaining to the functions of these proteins and the associations amongst them have been explored experimentally, mathematical models are needed to effectively explore the network’s dynamic behaviour. An ordinary differential equation (ODE)-based model of the protein-protein interaction network describing DNA replication initiation was constructed. The model was validated against quantified levels of protein factors determined in vivo and from the literature over a range of cell cycle timepoints. The model behaviour conforms to perturbation trials previously reported in the literature and accurately predicts the results of knockdown experiments performed herein. Furthermore, the DNA replication model was successfully incorporated into an established model of the entire yeast cell cycle, thus providing a comprehensive description of these processes. A screen for novel DNA damage response proteins was investigated using a unique proteomics approach that uses chromatin fractionation samples to enrich for factors bound to the DNA. This form of sub-cellular fractionation was combined with differential-in-gel-electrophoresis (DIGE) to detect and quantify low abundance chromatin proteins in the budding yeast proteome. The method was applied to analyze the effect of the DNA damaging agent methyl methanesulfonate (MMS) on levels of chromatin-associated proteins. Up-regulation of several previously characterized DNA damage checkpoint-regulated proteins, such as Rnr4, Rpa1 and Rpa2, was observed. In addition, several novel DNA damage responsive proteins were identified and assessed for genotoxic sensitivity. A strain in which the expression of the Ran-GTPase binding protein Yrb1 was reduced was found to be hypersensitive to genotoxic stress, pointing to a role for this nuclear import-associated protein in DNA damage response. The model presented in this thesis provides a tool for exploring the biochemical network of DNA replication. This is germane to the exploration of new cancer therapeutics considering the link between this disease (and others) and errors in proper cell cycle regulation. The high functional conservation between cell cycle mechanisms in humans and yeast allows predictive analyses of the model to be extrapolated towards understanding aberrant human cell proliferation. Importantly, the model is useful in identifying potential targets for cancer treatment and provides insights into developing highly specific anti-cancer drugs. Finally, the characterization of factors in the proteomic screen opens the door to further investigation of the roles of potential DNA damage response proteins.

Doctor of Philosophy / Collective actions of large animal groups result in elaborate behaviour, whose nature can be breathtaking in their complexity. Social organisation is the key to the origin of this behaviour and the mechanisms by which this organisation occurs are of particular interest. In this thesis, these mechanisms of social interactions and their consequences for group-level behaviour are explored. Social interactions amongst individuals are based on simple rules of attraction, alignment and orientation amongst neighbouring individuals. As part of this study, we will be interested in data that takes the form of a set of directions in space. In Chapter 2, we discuss relevant statistical measure and theory which will allow us to analyse directional data. These statistical tools will be employed on the results of the simulations of the mathematical models formulated in the course of the thesis. The first mathematical model for collective group behaviour is a Lagrangian self-organising model, which is formulated in Chapter 3. This model is based on basic social interactions between group members. Resulting collective behaviours and other related issues are examined during this chapter. Once we have an understanding of the model in Chapter 3, we use this model in Chapter 4 to investigate the idea of guidance of large groups by a select number of individuals. These individuals are privy to information regarding the location of a specific goal. This is used to explore a mechanism proposed for honeybee (Apis mellifera) swarm migrations. The spherical theory introduced in Chapter 2 will prove to be particularly useful in analysing the results of the modelling. In Chapter 5, we introduce a second mathematical model for aggregative behaviour. The model uses ideas from electromagnetic forces and particle physics, reinterpreting them in the context of social forces. While attraction and repulsion terms have been included in similar models in past literature, we introduce an orientation force to our model and show the requirement of a dissipative force to prevent individuals from escaping from the confines of the group.

Ce travail de thèse vise à améliorer notre compréhension des effets l'entraînement en résistance sur la performance et le muscle strié squelettique. La dynamique de ces effets de l'entraînement a été appréhendée de façon systématique grâce à des outils issus de la théorie des systèmes, auprès de 26 rongeurs entraînés en résistance dans un protocole d'escalade avec charges additionnelles. Le modèle classique (Banister et coll, 1975) a permis de décrire les variations de performance de manière significative (R2 = 0,53, P<0,001). L'origine des gains de performance très marqués (+136% par rapport au groupe contrôle) a été recherchée parmi les mécanismes adaptatifs musculaires potentiels. A l'issue de l'entraînement, une augmentation de l'activité de la myosine ATPase de 123 ± 61% indépendante du phénotype a été observée par rapport aux animaux contrôles. Cette augmentation de la puissance chimique consommée semble liée à une augmentation de la vitesse des étapes d'hydrolyse de l'ATP et surtout de celle de la libération des produits de cette hydrolyse (i.e. ADP et Pi) accompagnant la bascule de la tête de myosine. Une nouvelle forme de plasticité musculaire semble avoir été identifiée. Sur la base des mécanismes adaptatifs musculaires, une nouvelle formulation mathématique plus physiologique du modèle des effets de l'entraînement a été proposée et a aboutit à une meilleure qualité d'ajustement (R2 = 0,71, P<0,001). La fonction impulsionnelle du modèle classique a été remplacée par une fonction exponentielle de croissance qui semble plus appropriée pour rendre compte à la fois des variations de performance mais aussi des adaptations qui surviennent au sein du tissu musculaire comme au sein des unités contractiles elles-mêmes. / This thesis work aims to improve our understanding of the effects of resistance training on performance and skeletal muscle. The dynamic of these effects of training has been apprehended systematically trough tools from systems theory, with 26 rodents resistance trained on a climbing protocol with additional weights. The classical model (Banister et al, 1975) was suitable to analyze the training response (R2 = 0.53, P <0.001). The origin of the very marked performance gains (+ 136% compared to the control group) was investigated among the potential muscle adaptive mechanisms. At the end of the training program, an increase of 123 ± 61% in myosin ATPase activity independent of the phenotype was observed compared to control animals. This increase in myosin ATPase activity seems to occur precisely during the main myosin head isomerization step (i.e. powerstroke) that includes the liberation of the hydrolysis products, and to a lesser extent, during ATP hydrolysis step. A new form of muscular plasticity seems identified. Based on muscle adaptive mechanisms, a new mathematical formulation, more physiological, of the model of the training effects has been proposed and resulted in a better fit (R2 = 0.71, P <0.001). The impulse function of the traditional model has been replaced by an exponential growth function that seems more suitable to analyze both the training response and the adaptations that occur within the muscle tissue as in the contractile units themselves.

The type of regional dynamics of a species can provide information on how to manage the species, and may be the only way that some rare species may persist in a given region. A metapopulation is a type of regional dynamic in which local extinction is counterbalanced by recruitment from nearby patches. Metapopulation studies were originally conducted on animals, but have been adapted to plants, and are generally restricted to single-season studies. Plant species may persist as a metapopulation in patchy habitats, such as in forest openings. Forest openings (commonly called barrens, hill prairies, or glades) are habitats found on ridgetops which are characterized by having thin or nutrient-poor soil, high sunlight exposure, and relatively low soil moisture when compared to nearby forest habitats. Forest openings commonly contain plant species more frequently found in prairies, and are often maintained by natural fires that prevents woody species encroachment. In the absence of natural fires due to human management and suppression, woody species have invaded some forest openings, dividing them into a series of patches. To determine whether it is possible for each species to persist as a metapopulation in forest openings, five studies were carried out at each of three sites within the Shawnee National Forest in southern Illinois: a plant survey and ordination using environmental variables, the use of incidence function models to determine which of the species had the potential to form a metapopulation, a metacommunity study to examine overall patterns at each site, a seed bank study, and a seed dispersal study. Forest openings were found to be separate habitats from the surrounding forest based upon canopy openness. Approximately 30% of the species fit the metapopulation model, and the metacommunities at each of the sites exhibited a Clementsian pattern, characterized by groups of co-occurring species that replace each other over the region due to turnover between the groups of species. Species that fit the metapopulation model tended to have seeds that emerge more frequently from the seed bank if annuals and less frequently in the seed bank than species not fitting the metapopulation model (non-metapopulation species) if longer-lived. Species fitting the metapopulation model dispersed equal numbers of seeds as non-metapopulation species at short (5m) and medium (10m) distances, and in some cases dispersed more seeds to longer distances than non-metapopulation species. These studies show that forest openings can be treated as islands of suitable habitat for some species, and that numerous (~30%) species (such as Scleria pauciflora, Stylosanthes biflora, and Manfreda virginica) may assume a metapopulation dynamic in any given year. Many species may have incidence patterns consistent with those of a metapopulation in multiple years; however, the exact habitat patches in which species occur in any given year may change from year to year. Species in forest openings tend to co-occur in groups (a Clementsian pattern), which means that management plans should consider the entire community rather than a single species.

abstract: One solution to mitigating global climate change is using cyanobacteria or single-celled algae (collectively microalgae) to replace petroleum-based fuels and products, thereby reducing the net release of carbon dioxide. This work develops and evaluates a mechanistic kinetic model for light-dependent microalgal growth. Light interacts with microalgae in a variety of positive and negative ways that are captured by the model: light intensity (LI) attenuates through a microalgal culture, light absorption provides the energy and electron flows that drive photosynthesis, microalgae pool absorbed light energy, microalgae acclimate to different LI conditions, too-high LI causes damage to the cells’ photosystems, and sharp increases in light cause severe photoinhibition that inhibits growth. The model accounts for all these phenomena by using a set of state variables that represent the pooled light energy, photoacclimation, PSII photo-damage, PSII repair inhibition and PSI photodamage. Sets of experiments were conducted with the cyanobacterium Synechocystis sp. PCC 6803 during step-changes in light intensity and flashing light. The model was able to represent and explain all phenomena observed in the experiments. This included the spike and depression in growth rate following an increasing light step, the temporary depression in growth rate following a decreasing light step, the shape of the steady-state growth-irradiance curve, and the “blending” of light and dark periods under rapid flashes of light. The LI model is a marked improvement over previous light-dependent growth models, and can be used to design and interpret future experiments and practical systems for generating renewable feedstock to replace petroleum. / Dissertation/Thesis / Doctoral Dissertation Civil and Environmental Engineering 2017

Orientador: Hyun Mo Yang / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-12T03:04:36Z (GMT). No. of bitstreams: 1 Pinheiro_Andressa_M.pdf: 1109369 bytes, checksum: 4cae928d860fd4d141699ffe961e8140 (MD5) Previous issue date: 2008 / Resumo: Os rotavírus são considerados, atualmente, um dos mais importantes agentes causadores de gastroenterites e óbitos em crianças com menos de 5 anos no mundo. Ocorrem globalmente cerca de 125 milhões de episódios diarréicos por rotavírus a cada ano, causando entre 600.000 e 870.000 óbitos. Esses números alarmantes estimularam a busca por um controle desse vírus, mas para combatê -lo é necessário estudar seu comportamento, como ele penetra no organismo humano, como age dentro dele e como se espalha. Nesse trabalho apresenta-se um breve estudo sobre a biologia do rotavírus e os mecanismos de defesa apresentados pelo sistema imunológico. O principal objetivo é, utilizando métodos quantitativos, estudar a interação entre o rotavírus e o sistema imunológico e avaliar, comparativamente, o desempenho das respostas imunológicas humoral e celular. Seguindo esse intuito apresenta-se um modelo matemático, composto de equações diferenciais ordinárias não lineares de primeira ordem, que descreve a ação do sistema imunológico a fim de eliminar o rotavírus. A partir deste modelo nós encontramos os pontos de equilíbrio trivial e não-trivial e analisamos sua estabilidade. Também discutimos sobre a ação das respostas imunológicas humoral e celular. / Abstract: In infants and young children, rotavirus is the major cause of severe inflammation of the intestine (gastroenteritis). Rotavirus infection frequently results in fever, vomiting and diarrhea, wich symptoms are so intense that they can lead to death. This virus causes nearly a million deaths each year worldwide, mostly in developing countries. Rotavirus attacks the epithelial cells of the thin intestine and replicates in the cytoplasm and do not fully uncoat during the process of replication. The reason for their failure to fully uncoat is that the coat is resistant to protease digestion, which prevents them from being completely destroyed by the infected cell and of readily being seen by the immune system. This complex biology of rotavirus and its interaction with the immune system are the motivation of this work, that presents a model for this interaction, structured by non-linear ordinary differential equations of first-order that describes the action of the innate immune system to eliminate rotavirus. From this model, we find the trivial and non-trivial equilibrium points and analyze their stabilities, as well we analyze, comparatively, the humoral and cellular responses. / Mestrado / Biomatematica / Mestre em Matemática Aplicada

This dissertation addresses a simple puzzle: why do governments use indiscriminate violence against civilians? To deter a population from rebelling, a government should make rebellion costlier than the alternatives. Yet indiscriminate violence can make neutrality costlier than rebellion. With the help of mathematical modeling, archival data and micro-comparative evidence from dozens of armed conflicts, I show that indiscriminate violence makes civilians less likely to remain neutral, but not necessarily more likely to support the opponent. There is a threshold level of violence, beyond which it can become safer for civilians to cooperate with the more indiscriminate side. As long as civilians believe that supporting the rebels will be costlier than supporting the government, they will generally support or not actively resist the government -- even if the government is responsible for more civilian deaths overall. The amount of violence needed to meet this threshold depends on the combatants' relative informational endowments. If a combatant can selectively punish her opponents, she can employ a relatively low level of violence. Where she lacks the information for selective punishment, she will use methods more indiscriminate in targeting and more massive in scale. Violence is a substitute for intelligence. / Government

Paralog reduction, the loss of duplicate genes after whole genome duplication (WGD) is a pervasive process. Whether this loss proceeds gene by gene or through deletion of multi-gene DNA segments is controversial, as is the question of fractionation bias, namely whether one homeologous chromosome is more vulnerable to gene deletion than the other. As a null hypothesis, we first assume deletion events, on one homeolog only, excise a geometrically distributed number of genes with unknown mean mu, and these events combine to produce deleted runs of length l, distributed approximately as a negative binomial with unknown parameter r; itself a random variable with distribution pi(.). A biologically more realistic model requires deletion events on both homeologs distributed as a truncated geometric. We simulate the distribution of run lengths l in both models, as well as the underlying pi(r), as a function of mu, and show how sampling l allows us to estimate mu. We apply this to data on a total of 15 genomes descended from 6 distinct WGD events and show how to correct the bias towards shorter runs caused by genome rearrangements. Because of the difficulty in deriving pi(.) analytically, we develop a deterministic recurrence to calculate each pi(r) as a function of mu and the proportion of unreduced paralog pairs. This is based on a computing formula containing nested sums. The parameter mu can be estimated based on run lengths of single-copy regions. We then reduce the computing formulae, at least in the one-sided case, to closed form. This virtually eliminates computing time due to highly nested summations. We formulate a continuous version of the fractionation process, deleting line segments of exponentially distributed lengths in analogy to geometric distributed numbers of genes. We derive nested integrals and discover that the number of previously deleted regions to be skipped by a new deletion event is exactly geometrically distributed. We undertook a large simulation experiment to show how to discriminate between the gene-by-gene duplicate deletion model and the deletion of a geometrically distributed number of genes. This revealed the importance of the effects of genome size N, the mean of the geometric distribution, the progress towards completion of the fractionation process, and whether the data are based on runs of deleted genes or undeleted genes.