Orientador: Camila Pires Cremasco Gabriel / Resumo: Para uma satisfatória produtividade, a cultura do rabanete (Raphanus sativus L.) exige principalmente boa qualidade do solo e grande disponibilidade de água. A irrigação é uma técnica artificial utilizada para disponibilizar água as plantas. Seu uso deve ser criterioso e para que se obtenha menores custos de produção, deve-se evitar o uso desnecessário de água, e consequentemente, energia elétrica. Formas de utilização da água são cada vez mais estudadas, entre elas, a água de irrigação tratada magneticamente, que tem mostrado aprimoramentos produtivos em diversas culturas. O objetivo deste trabalho foi o desenvolvimento de um conjunto de sistemas computacionais baseados em regras fuzzy para previsão de componentes de produção de culturas irrigadas. Para tanto, foram utilizados dados de um experimento conduzido com água de irrigação convencional ou tratada magneticamente, sendo avaliado variáveis biométricas, tais como: peso verde do bulbo, número de folhas, comprimento da raiz, diâmetro do bulbo, comprimento do bulbo, peso verde da raiz, peso verde da folha, peso seco da raiz, peso seco da folha e peso seco do bulbo. Como resultado, foi apresentado um conjunto de softwares com uma interface de simples uso e fácil compreensão, que poderá auxiliar os produtores na estimativa dos resultados das variáveis biométricas do rabaneteiro e de outras culturas irrigadas. / Abstract: For satisfactory productivity, the cultivation of radish (Raphanus sativus L.) mainly requires good soil quality and great availability of water. Irrigation is an artificial technique used to make water available to plants. Its use must be judicious and to obtain lower production costs, unnecessary use of water and, consequently, electric energy should be avoided. Ways of using water are increasingly studied, among them, magnetically treated irrigation water, which has shown productive improvements in several cultures. The objective of this work was the development of a set of computational systems based on fuzzy rules for forecasting production components of irrigated crops. For that, data from an experiment conducted with conventional irrigation water or magnetically treated water were used, and biometric variables were evaluated, such as green bulb weight, number of leaves, root length, bulb diameter, bulb length, green weight root weight, green leaf weight, dry root weight, dry leaf weight, and dry bulb weight. As a result, a set of software was presented with a simple to use and easy to understand interface, which can assist producers in estimating the results of the biometric variables of the radish feet and other irrigated crops. / Doutor

In this work, two differential equation models for smallpox are numerically solved to find the optimal intervention policy. In each model we look for the range of values of the parameters that give rise to the worst case scenarios. Since the scale of an epidemic is determined by the number of people infected, and eventually dead, as a result of infection, we attempt to quantify the scale of the epidemic and recommend the optimum intervention policy. In the first case study, we mimic a densely populated city with comparatively big tourist population, and heavily used mass transportation system. A mathematical model for the transmission of smallpox is formulated, and numerically solved. In the second case study, we incorporate five different stages of infection: (1) susceptible (2) infected but asymptomatic, non infectious, and vaccine-sensitive; (3) infected but asymptomatic, noninfectious, and vaccine-in-sensitive; (4) infected but asymptomatic, and infectious; and (5) symptomatic and isolated. Exponential probability distribution is used for modeling this case. We compare outcomes of mass vaccination and trace vaccination on the final size of the epidemic.

<p>    </p> <p>Migration is a ubiquitous phenomenon in biology and is relevant to all scales ranging from bacteria to human beings. It is relevant to fundamental biological processes like bacterial chemotaxis, development, disease progression, etc. So, understanding migration is pivotal to addressing fundamental questions in biology. We address three broad questions relevant to cell migration using models from physics: (i) What are the critical features of cancer cell migration? (ii) Is it possible to explain complex cell migration data using minimal bio- chemical networks? And (iii) how does cell-to-cell communication affect its migration at the population level? To address these questions we performed (i) mathematical analysis using the Cellular Potts model, simulations using the Biased Persistent random walk model, and steady-state analysis of cell response to graded signals to explain cancer cell migration in response to single and multiple chemical and mechanical signals, (ii) rigorous network anal- ysis of ∼ 500,000 minimal networks having features of fundamental biochemical processes like regulation, conversion or molecular binding to understand the origin of antagonism in multiple cue cancer cell migration experiments and (iii) the steady-state analysis of Keller- Segel equations mimicking collective cell migration to understand the role of cell to cell communication on chemotaxis of a bacterial population. From our analysis, we found that (i) persistence and bias in cancer cell migration are decoupled from each other owing to a lack of memory about past movements and for any general cell migration they are inherently constrained to take only a fixed set of values. (ii) Bias in cancer cell migration in response to a combination of chemoattractant gradients can be less than the response to individual gradients (antagonism in bias) while the speed remains unaltered. This antagonism in bias and lack thereof in speed can be explained by several minimal networks having molecular regulation, conversion, or binding as its central feature and all these distinct mechanisms show convergence and saturation of an internal molecule common to both the chemoattrac- tants. (iii) By analyzing the role of cell-cell communication in bacterial chemotaxis using the Keller-Segel model we find that communication enhances chemotaxis only when it is adaptive to its external surroundings and cell-to-cell variability helps in increasing the chemotactic drift in the bacterial population. </p>

We present a mathematical model that describes how cyanobacterial communities use natural light as a source of energy and water as a source of electrons to perform photosynthesis and therefore, grow and co-survive together with other bacterial species. We apply our model to a phototrophic population of bacteria, namely, cyanobacteria. Our model involves the use of light as a source of energy and inorganic carbon as a source of nutrients. First, we study a single species model involving only cyanobacteria, then we include heterotrophs in the two species model. The model consists of ordinary differential equations describing bacteria and chemicals evolution in time. Stability analysis results show that adding heterotrophs to a population of cyanobacteria increases the level of inorganic carbon in the medium, which in turns allows cyanobacteria to perform more photosynthesis. This increase of cyanobacterial biomass agrees with experimental data obtained by collaborators at the Center for Biofilm Engineering at Montana State University. / Mathematics

The hybrid activated sludge-biofilm system called Integrated Fixed Film Activated Sludge (IFAS) has recently become popular for enhanced nitrification and denitrification in aerobic zones because it is an alternative to increasing the volume of treatment plant units to accomplish year round nitrification and nitrogen removal. Biomass is retained on the fixed-film media and remains in the aerobic reactor, thus increasing the effective mean cell resident time (MCRT) of the biomass and providing the temperature sensitive, slow growing nitrifiers a means of staying in the system when they otherwise would washout. While the utilization of media in aerobic zones to enhance nitrification and denitrification has been the subject of several studies and full-scale experiments, the effects and performances of fixed film media integrated into the anoxic zones of biological nutrient removal (BNR) systems have not adequately been evaluated as well as the impacts of integrated media upon enhanced biological phosphorus removal (EBPR). Also, user-friendly software designed specifically to simulate the complex mixture of biological processes that occur in IFAS systems are not available. The purpose of this research was to more fully investigate the effects of integrated fixed film media on EBPR, to evaluate the impacts of media integrated into the anoxic zone on system performance, and to develop a software program that could be used to simulate the effects of integrating the various types of media into suspended growth biological nutrient removal (BNR) systems. The UCT type configuration was chosen for the BNR system, and Accuweb rope-like media was selected for integration into the anoxic zones of two IFAS systems. The media also was integrated into the aerobic reactors of one of the systems for comparison and for further investigation of the performance of the Accuweb media on enhanced nitrification and denitrification in the aerobic zones. The experiments were conducted at 10 day total MCRT during the initial phase, and then at 6 days MCRT for the experimental temperature of 10 oC. A13 hour hydraulic retention time (HRT) was used throughout the study. A high and a low COD/TP ratio were used during the investigation to further study the effects of integrated media on EBPR. The PC Windows based IFAS program began with the concepts of IAWQ model No. 2 and a zero-dimensional biofilm model was developed and added to predict the IFAS processes. Experimental data from the initial study and existing data from similar studies performed at high temperatures (>10oC) indicated that there were no significant differences in BNR performances between IFAS systems with media integrated into the anoxic and aerobic or only aerobic zones and a suspended growth control system maintained at the same relative high MCRT and temperature values. Even though greater biological nitrogen removal could not be achieved for the experimental conditions used, the experimental results indicated that the IFAS systems with fixed film media installed in the anoxic zone have a greater potential for denitrification than conventional BNR systems. As much as 30 percent of the total denitrification was observed to occur in the aerobic zones of the system installed the media only anoxic zones and 37% in the system with integrated media in both anoxic and aerobic zones where as no denitrification was observed in the aerobic zones of the control system when the systems were operated at 6 days MCRT and COD/TP of 52. It is statistically confirmed EBPR can be maintained in IFAS systems as well as Control systems, but the IFAS processes tend to have more phosphorus release in the anoxic zones with integrated fixed film installed. Further, the combination of split flow to the anoxic zone and fixed film media in the anoxic zone resulted in the decreased EBPR performances in the IFAS system relative to the control system. / Ph. D.

In a multi-cellular organism, cells constantly receive signals on their internal condition and surrounding environment. In response to various signals, cells proliferate, move around or even undergo suicide. The signal-response is controlled by complex molecular machinery, understanding of which is an important goal of basic molecular biological research. Such understanding is also valuable for clinical application, since lethal diseases like cancer show maladaptive responses to growth-regulating signals. Because the multiple feedbacks in the molecular regulatory machinery obscure cause-effect relations, it is hard to understand these control systems by intuition alone. Here we translate the molecular interactions into differential equations and recapture the cellular physiological properties with the help of numerical simulations and non-linear dynamical tools. The models address the physiological features of programmed cell death, the cell fate decision by p53 and the dynamics of the NF-?B control system. These models identify key molecular interactions responsible for the observed physiological properties, and they generate experimentally testable predictions to validate the assumptions made in the models. / Ph. D.

Protein regulatory networks are the hallmark of many important biological functionalities. Two of these functionalities are mammalian cell cycle progression and near-perfect adaptive responses. Modeling and simulating these functionalities are crucial stages to understanding and predicting them as systems-level properties of cells. In the context of the mammalian cell cycle, the timing of DNA synthesis, mitosis and cell division is regulated by a complex network of biochemical reactions that control the activities of a family of cyclin-dependent kinases. The temporal dynamics of this reaction network is typically modeled by nonlinear differential equations describing the rates of the component reactions. This approach provides exquisite details about molecular regulatory processes but is hampered by the need to estimate realistic values for the many kinetic constants that determine the reaction rates. To avoid this problem, modelers often resort to "qualitative" modeling strategies, such as Boolean switching networks, but these models describe only the coarsest features of cell cycle regulation. In this work, we describe a hybrid approach that combines features of continuous and discrete networks. The model is evaluated in terms of flow cytometry measurements of cyclin proteins in asynchronous populations of human cell lines. Using our hybrid approach, modelers can quickly create quantitatively accurate, computational models of protein regulatory networks found in various contexts within cells. Large-scale protein regulatory networks, such as the one that controls the progression of the mammalian cell cycle, also contain small-scale motifs or modules that carry out specific dynamical functions. Systematic characterization of smaller, interacting, network motifs whose individual behavior is well known under certain conditions is therefore of great interest to systems biologists. We model and simulate various 3-node network motifs to find near-perfect adaptation behavior. This behavior entails that a system responds to a change in its environmental cues, or signals, by coming back nearly to its pre-signal state even in the continued presence of the signal. We let various topologies evolve in their parameter space such that they eventually stumble upon a region where they score well under a pre-defined scoring metric. We find many such parameter sample sets across various classes of topologies. / Ph. D.

Mathematical modeling of biological systems has improved the knowledge of scientists for many years. In virology, particularly in the study of hepatitis B virus, mathematical models were used to explain interactions between hepatitis B virus and the human host in the absence and presence of interventions such as drug therapy and vaccines. This thesis seeks to explain the role of e-Antigen, a particle produced by hepatitis B virus, in the pathogenesis of hepatitis B infection. To accomplish this goal, I will provide biological background as well as previous modeling work on the role of e-Antigen in hepatitis B virus infection, before finally developing a new model adapted specifically for connecting hepatitis B progression with e-Antigen and drug therapy. I will analyze the model both analytically and numerically, fit it to virus data from humans chronically infected with hepatitis B that undergo drug therapy, and draw conclusions about the relation between drugs, immune activation, and loss of e-Antigen. / Master of Science

In recent years, dengue viral infection has become one of the most widely-spread mosquito-borne diseases in the world, with an estimated 50-100 million cases annually, resulting in 500,000 hospitalizations. Due to the nature of the immune response to each of the four serotypes of dengue virus, secondary infections of dengue put patients at higher risk for more severe infection as opposed to primary infections. The current hypothesis for this phenomenon is antibody-dependent enhancement, where strain-specific antibodies from the primary infection enhance infection by a heterologous serotype. To determine the mechanisms responsible for the increase in disease severity, we develop mathematical models of within-host virus-cell interaction, epidemiological models of virus transmission, and a combination of the within-host and between-host models. The main results of this thesis focus on the within-host model. We model the effects of antibody responses against primary and secondary virus strains. We find that secondary infections lead to a reduction of virus removal. This is slightly different than the current antibody-dependent enhancement hypothesis, which suggests that the rate of virus infectivity is higher during secondary infections due to antibody failure to neutralize the virus. We use the results from the within-host model in an epidemiological multi-scale model. We start by constructing a two-strain SIR model and vary the parameters to account for the effect of antibody-dependent enhancement. / Master of Science

Stochastic modeling to represent intrinsic and extrinsic noise is an important challenge in molecular systems biology. There are numerous ways to model intrinsic noise. One framework for intrinsic noise in gene regulatory networks was recently proposed within the discrete setting. In contrast, extrinsic perturbations were rarely modeled due to the complex mechanisms that contribute to its emergence. Here a discrete framework to model extrinsic noise is proposed. The interacting species of the model are represented by discrete variables and are perturbed to represent extrinsic noise. In particular, they are subject to a discretized lognormal distribution. Additionally, a delay is imposed on the update with a certain probability. These two perturbations represent global extrinsic noise and pathway-specic extrinsic noise. It leads to large variations in the concentration of proteins, which is consistent with an existing continuous way of modeling extrinsic fluctuations. The framework is applied to three different published discrete models: the cell fate of lambda phage infection of bacteria, the lactose utilization system in E. coli, and a signaling network in melanoma cells. The framework captures factors that signicantly contribute to the random decision between lysis and lysogeny as well as explains the bistable switch in the model of the lac operon. Finally, a feed-forward loop analysis is conducted by measuring and comparing the noise level in the target protein of feed-forward loops. This analysis reveals the ability of certain feed-forward loops to attenuate or amplify fluctuations, dependent upon various levels of noise. In conclusion, this thesis aims to resolve the question of how the extrinsic noise can be modeled and how biological systems are able to maintain functionality in the wake of such large variations. / Master of Science