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Dissertations / Theses on the topic 'Mathematical biology'
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Mazzag, Barbara Cathrine. "Mathematical models in biology /." For electronic version search Digital dissertations database. Restricted to UC campuses. Access is free to UC campus dissertations, 2002. http://uclibs.org/PID/11984.
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Lewis, Matthew. "Laboratory Experiences in Mathematical Biology for Post-Secondary Mathematics Students." DigitalCommons@USU, 2016. https://digitalcommons.usu.edu/etd/5219.
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In addition to the memorization, algorithmic skills and vocabulary which is the default focus in many mathematics classrooms, professional mathematicians are expected to creatively apply known techniques, construct new mathematical approaches and communicate with and about mathematics. We propose that students can learn these professional, higher level skills through Laboratory Experiences in Mathematical Biology (LEMBs) which put students in the role of mathematics researcher creating mathematics to describe and understand biological data. LEMBs are constructed so they require no specialized equipment and can easily be run in the context of a college math class. Students collect data and develop mathematical models to explain the data. In this work examine how LEMBs are designed with the student as the primary focus. We explain how well-designed LEMBs lead students to interact with mathematics at higher levels of cognition while building mathematical skills sought after in both academia and industry. Additionally, we describe the online repository created to assist in the teaching and further development of LEMBs. Since student-centered teaching is foreign to many post-secondary instructors, we provide research-based, pedagogical strategies to ensure student success while maintaining high levels of cognition.
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Li, Yifei. "Nonlinear diffusion in mathematical biology." Thesis, Queensland University of Technology, 2022. https://eprints.qut.edu.au/234381/1/Yifei_Li_Thesis.pdf.
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Reaction-diffusion models with nonlinear diffusion are widely used for studying population dynamics in biology and ecology. Yet, the relationship between nonlinear diffusion mechanisms in populations and the behaviours of individuals is hard to be intuitively interpreted in classical models. To address this problem, we develop a discrete-continuum modelling framework, where the movement of individuals influenced by crowding effects is connected to the nonlinear diffusivity functions in a well-defined continuum limit. Using this framework, we explore the influence of nonlinear diffusion on population extinction, and analyse the existence and stability of travelling waves in continuous equations which model the invasion process.
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Murphy, Ryan John. "Mechanochemical and experimental models in mathematical biology." Thesis, Queensland University of Technology, 2022. https://eprints.qut.edu.au/228428/1/Ryan%20John_Murphy_Thesis.pdf.
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Experiments that probe epithelial tissue dynamics, cell competition, and tumour growth are fundamental to understand processes in developmental biology, cancer progression and treatment. However, interpreting complex biological experiments is challenging. To address this challenge, we develop and use a range of mathematical models. First, we focus on epithelial tissue dynamics. Second, we use real-time cell cycle imaging to reveal the structure of growing tumour spheroids. We then revisit the seminal Greenspan tumour growth model and use statistical analysis to quantitatively connect it to experimental data for the first time to reveal experimental design choices that lead to reliable biological insight.
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Bozic, Ivana. "Mathematical Models of Cancer." Thesis, Harvard University, 2012. http://dissertations.umi.com/gsas.harvard:10220.
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Major efforts to sequence cancer genomes are now occurring throughout the world. Though the emerging data from these studies are illuminating, their reconciliation with epidemiologic and clinical observations poses a major challenge. Here we present mathematical models that begin to address this challenge. First we present a model of accumulation of driver and passenger mutations during tumor progression and derive a formula for the number of driver mutations as a function of the total number of mutations in a tumor. Fitting this formula to recent experimental data, we were able to calculate the selective advantage provided by a typical driver mutation. Second, we performed a quantitative analysis of pancreatic cancer metastasis genetic data. The results of this analysis define a broad time window for detection of pancreatic cancer before metastatic dissemination. Finally, we model the evolution of resistance to targeted cancer therapy. We apply our model to experimental data on the response to panitumumab, targeted therapy against colorectal cancer. Our modeling suggested that cells resistant to therapy were likely present in patients’ tumors prior to the start of therapy.Mathematics
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Ferrara, Joseph. "A Study of Nonlinear Dynamics in Mathematical Biology." UNF Digital Commons, 2013. http://digitalcommons.unf.edu/etd/448.
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We first discuss some fundamental results such as equilibria, linearization, and stability of nonlinear dynamical systems arising in mathematical modeling. Next we study the dynamics in planar systems such as limit cycles, the Poincaré-Bendixson theorem, and some of its useful consequences. We then study the interaction between two and three different cell populations, and perform stability and bifurcation analysis on the systems. We also analyze the impact of immunotherapy on the tumor cell population numerically.
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Hunt, Gordon S. "Mathematical modelling of pattern formation in developmental biology." Thesis, Heriot-Watt University, 2013. http://hdl.handle.net/10399/2706.
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The transformation from a single cell to the adult form is one of the remarkable wonders of nature. However, the fundamental mechanisms and interactions involved in this metamorphic change still remain elusive. Due to the complexity of the process, researchers have attempted to exploit simpler systems and, in particular, have focussed on the emergence of varied and spectacular patterns in nature. A number of mathematical models have been proposed to study this problem with one of the most well studied and prominent being the novel concept provided by A.M. Turing in 1952. Turing's simple yet elegant idea consisted of a system of interacting chemicals that reacted and di used such that, under certain conditions, spatial patterns can arise from near homogeneity. However, the implicit assumption that cells respond to respective chemical levels, di erentiating accordingly, is an oversimpli cation and may not capture the true extent of the biology. Here, we propose mathematical models that explicitly introduce cell dynamics into pattern formation mechanisms. The models presented are formulated based on Turing's classical mechanism and are used to gain insight into the signi cance and impact that cells may have in biological phenomena. The rst part of this work considers cell di erentiation and incorporates two conceptually di erent cell commitment processes: asymmetric precursor di erentiation and precursor speci cation. A variety of possible feedback mechanisms are considered with the results of direct activator upregulation suggesting a relaxation of the two species Turing Instability requirement of long range inhibition, short range activation. Moreover, the results also suggest that the type of feedback mechanism should be considered to explain observed biological results. In a separate model, cell signalling is investigated using a discrete mathematical model that is derived from Turing's classical continuous framework. Within this, two types of cell signalling are considered, namely autocrine and juxtacrine signalling, with both showing the attainability of a variety of wavelength patterns that are illustrated and explainable through individual cell activity levels of receptor, ligand and inhibitor. Together with the full system, a reduced two species system is investigated that permits a direct comparison to the classical activator-inhibitor model and the results produce pattern formation in systems considering both one and two di usible species together with an autocrine and/or juxtacrine signalling mechanism. Formulating the model in this way shows a greater applicability to biology with fundamental cell signalling and the interactions involved in Turing type patterning described using clear and concise variables.
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Yang, Xige. "MATHEMATICAL MODELS OF PATTERN FORMATION IN CELL BIOLOGY." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1542236214346341.
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Xu, Yiyang. "Topics in population genetics and mathematical evolutionary biology." Thesis, University of Bristol, 2015. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.682366.
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Part A studies the optimal strategies of seed germination problems where the population has a class structure under a fluctuating environment . In particular, a multidimensional age-class model is studied using a dynamical programming method. Numerical results about the so-called optimal stochastic strategy which consists of information about previous environmental states are computed. Comparing the optimal stochastic strategy with the optimal population-based strategy shows that the optimal stochastic strategy is highly effective in genera.l. A potentially useful diffusion approximation for the seed germination problem is also derived with numerical results. For part B, a multi-dimensional Moran model is studied using a diffusion approximation approach. The scaling limit and corresponding governing stochastic partial differential equations (SDEs) are derived. An expansion method is used to approximate the stationary distribution of the SDEs. An approximation formula for the effective migration rate is then derived.
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Buckalew, Richard L. "Mathematical Models in Cell Cycle Biology and Pulmonary Immunity." Ohio University / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1395242276.
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Warne, David James. "Computational inference in mathematical biology: Methodological developments and applications." Thesis, Queensland University of Technology, 2020. https://eprints.qut.edu.au/202835/1/David_Warne_Thesis.pdf.
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Complexity in living organisms occurs on multiple spatial and temporal scales. The function of tissues depends on interactions of cells, and in turn, cell dynamics depends on intercellular and intracellular biochemical networks. A diverse range of mathematical modelling frameworks are applied in quantitative biology. Effective application of models in practice depends upon reliable statistical inference methods for experimental design, model calibration and model selection. In this thesis, new results are obtained for quantification of contact inhibition and cell motility mechanisms in prostate cancer cells, and novel computationally efficient inference algorithms suited for the study of biochemical systems are developed.
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Cole, D. J. "Stochastic branching processes in biology." Thesis, University of Kent, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.270684.
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Jones, Jennifer Grace. "A mathematical model of emphysema." Thesis, University of Bristol, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.269229.
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Durney, Clinton H. "A Two-Component Model For Bacterial Chemotaxis." The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1366312981.
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Anderson, Kerri-Ann. "A Mathematical Model of Cytokinetic Morphogenesis." The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1429607984.
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Turner, Katherine Mary Elizabeth. "Mathematical models of gonorrhoea and chlamydia : biology, behaviour and interactions." Thesis, Imperial College London, 2008. http://hdl.handle.net/10044/1/1303.
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Gonorrhoea and chlamydia are curable, bacterial, sexually transmitted infections (STIs) of humans, with important long term consequences for health. Their epidemiology and biology are reviewed in chapter one. The way the biology of the organisms and the behaviour of human hosts interact to influence the patterns of infection and the potential impact of interventions is the subject of the main body of the thesis. Mathematical models are presented, together with empirical data, to gain a better understanding of the epidemiology of gonorrhoea and chlamydia. New approaches are applied, using more complex measures of disease occurrence including reinfection (subsequent infection by the same organism) or coinfection (infection with both organisms simultaneously). Coinfection with gonorrhoea and chlamydia is investigated in chapter two. The third chapter investigates the importance of heterogeneity in human behaviour (i.e. level of sexual activity, mixing patterns within and between populations) on the spread of disease in subpopulations, using a model incorporating race, gender and sexual activity level. This was parameterised and validated using data collected in South East London. In chapter four, models of reinfection are used to investigate the interaction of population level parameters such as degree of assortative mixing and rates of reinfection. In chapter five, the characteristics of individuals coinfected with both organisms are shown to provide additional information useful in determining how infection is distributed across a population. The biology of the organism is demonstrated, in the fifth chapter, to play an important role in the prevalence and incidence of disease within the host population. The impact of the emergence of resistant or asymptomatic phenotypes under selective pressure by different treatment regimens is quantified using a two strain model, including asymptomatic and symptomatic infections. The final chapter considers the contribution of the research and discusses the implications of the results for STI intervention strategies.
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Camacho, Diogo Mayo. "In silico cell biology and biochemistry: a systems biology approach." Diss., Virginia Tech, 2007. http://hdl.handle.net/10919/27960.
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In the post-"omic" era the analysis of high-throughput data is regarded as one of the major challenges faced by researchers. One focus of this data analysis is uncovering biological network topologies and dynamics. It is believed that this kind of research will allow the development of new mathematical models of biological systems as well as aid in the improvement of already existing ones. The work that is presented in this dissertation addresses the problem of the analysis of highly complex data sets with the aim of developing a methodology that will enable the reconstruction of a biological network from time series data through an iterative process.
The first part of this dissertation relates to the analysis of existing methodologies that aim at inferring network structures from experimental data. This spans the use of statistical tools such as correlations analysis (presented in Chapter 2) to more complex mathematical frameworks (presented in Chapter 3). A novel methodology that focuses on the inference of biological networks from time series data by least squares fitting will then be introduced. Using a set of carefully designed inference rules one can gain important information about the system which can aid in the inference process. The application of the method to a data set from the response of the yeast Saccharomyces cerevisiae to cumene hydroperoxide is explored in Chapter 5. The results show that this method can be used to generate a coarse-level mathematical model of the biological system at hand. Possible developments of this method are discussed in Chapter 6.Ph. D.
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Campanelli, Mark Benjamin. "Multicellular mathematical models of somitogenesis." Thesis, Montana State University, 2009. http://etd.lib.montana.edu/etd/2009/campanelli/CampanelliM0809.pdf.
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Somitogenesis is an important pattern formation process in the developmental biology of vertebrates. The phenomenon has received wide attention from experimental, theoretical, and computational biologists. Numerous mathematical models of the process have been proposed, with the clock and wavefront mechanism rising to prominence over the last ten years. This work presents two multicellular mathematical models of somitogenesis. The first is a phenomenological phase oscillator model that reproduces both the clock and wavefront aspects of somitogenesis, but lacks a biological basis. The second is a biologically informed delay differential equation model of the clock-wave that is produced by coordinated oscillatory gene expression across many cells. Careful and efficient model construction, parameter estimation, and model validation identify important nonlinear mechanisms in the genetic control circuit of the somitogenesis clock. In particular, a graded control protein combined with differential decay of clock protein monomers and dimers is found to be a key mechanism for slowing oscillations and generating experimentally observed waves of gene expression. This represents a mode of combinatorial control that has not been previously examined in somitogenesis, and warrants further experimental and theoretical investigation.
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Riposo, Julien. "Computational and Mathematical Methods for Data Analysis in Biology and Finance." Thesis, Paris 6, 2015. http://www.theses.fr/2015PA066177/document.
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Les mathématiques sont comprises en tant qu’ensemble d’idées abstraites, dans le sens où le monde réel – ou plutôt réalité – n’a pas à intervenir. Pourtant, certains faits mathématiques observables dans des données expérimentales ou simulées peuvent être contre-intuitifs. La thèse est divisée en deux parties : premièrement, on étudie mathématiquement les matrices du genre celles dont nous avons discutées en biologie et finance. En particulier, nous mettons en évidence le fait contre-intuitif suivant : pour ces matrices, le vecteur propre associé à la plus haute valeur propre est très proche de la somme de chacune des lignes de la matrice, colonne par colonne. Nous discutons aussi d’applications en théorie des graphes avec bon nombre de simulations numériques. Dans un second temps, nous attaquons le problème des contacts géniques : à partir d’une carte de contact génique, un vrai défi actuel est de retrouver la structure tridimensionnelle de l’ADN. Nous proposons diverses méthodes d’analyse matricielle de données, dont une met en évidence l’existence, dans le noyau, de zones disjointes où les interactions sont de différents types. Ces zones sont des compartiments nucléaires. Avec d’autres données biologiques, nous mettons en évidence la fonction biologique de chacun de ces compartiments. Les outils d’analyses sont ceux utilisés en finance pour analyser des matrices d’auto-corrélation, ou même des séries temporellesMathematics are understood as a set of abstract ideas, in the measure of the real world – or reality – has no way to intervene. However, some observable mathematical facts in experimental or simulated data can be counter-intuitive. The PhD is divided into two parts: first, we mathematically study the matrices of the same type of the ones in biology and finance. In particular, we show the following counter-intuitive fact: for these matrices, the eigenvector associated with the highest eigenvalue is close to the sum of each row, column by column. We also discuss some applications to graph theory with many numerical simulations and data analysis.On the other hand, we will face the genetic contact problem: from a contact map, a real current challenge is to find the DNA 3D-structure. We propose several matrix analysis methods, which one show disjoinct areas in the nucleus where the DNA interactions are different. These areas are nuclear compartments. With other biological features, we characterize the biological function of each of the compartments. The analysis tools are the ones already used in finance to analyze the autocorrelation matrices, or even time series
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Urquiza, García José María Uriel. "Mathematical model in absolute units for the Arabidopsis circadian oscillator." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/31132.
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The Earth’s oblique rotation results in changes in light and temperature across the day and time of year. Living organisms evolved rhythmic behaviours to anticipate these changes and execute appropriate responses at particular times. The current paradigm for the biological clocks in several branches of life is an underlying biochemical oscillator mainly composed by a network of repressive transcription factors. The slow decay in their activity is fundamental for generating anticipatory dynamics. Interestingly, these dynamics can be well appreciated when the biological system is left under constant environmental conditions, where oscillation of several physiological readouts persists with a period close to 24 hours, hence the term “circadian clocks”, circa=around dian=day. In plants the model species Arabidopsis thaliana has served as an invaluable tool for analysing the genetics, biochemical, developmental, and physiological effects of the oscillator. Many of these experimental results have been integrated in mechanistic and mathematical theories for the circadian oscillator. These models predict the timing of gene expression and protein presence in several genetic backgrounds and photoperiodic conditions. The aim of this work is the introduction of a correct mass scale for both the RNA transcript and protein variables of the clock models. The new mass scale is first introduced using published RNA data in absolute units, from qRT-PCR. This required reinterpreting several assumptions of an established clock model (P2011), resulting in an updated version named U2017. I evaluate the performance of the U2017 model in using data in absolute mass units, for the first time for this clock system. Introducing absolute units for the protein variables takes place by generating hypothetical protein data from the existing qRT-PCR data and comparing a data-driven model with western blot data from the literature. I explore the consequences of these predicted protein numbers for the model’s dynamics. The process required a meta-analysis of plant parameter values and genomic information, to interpret the biological relevance of the updated protein parameters. The predicted protein amounts justify, for example, the revised treatment of the Evening Complex in the U2017 model, compared to P2011. The difficulties of introducing absolute units for the protein components are discussed and components for experimental quantification are proposed. Validating the protein predictions required a new methodology for absolute quantification. The methodology is based on translational fusions with a luciferase reporter than has been little used in plants, NanoLUC. Firstly, the characterisation of NanoLUC as a new circadian reporter was explored using the clock gene BOA. The results show that this new system is a robust, sensitive and automatable approach for addressing quantitative biology questions. I selected five clock proteins CCA1, LHY, PRR7, TOC1 and LUX for absolute quantification using the new NanoLUC methodology. Functionality of translation fusions with NanoLUC was assessed by complementation experiments. The closest complementing line for each gene was selected to generate protein time series data. Absolute protein quantities were determined by generation of calibration curves using a recombinant NanoLUC standard. The developed methodology allows absolute quantification comparable to the calibrated qRT-PCR data. These experimental results test the predicted protein amounts and represent a technical resource to understand protein dynamics of Arabidopsis’ circadian oscillator quantitatively. The new experimental, meta-analysis and modelling results in absolute units allows future researchers to incorporate further, quantitative biochemical data.
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Nurtay, Anel. "Mathematical modelling of pathogen specialisation." Doctoral thesis, Universitat Autònoma de Barcelona, 2019. http://hdl.handle.net/10803/667178.
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L’aparició de nous virus causants de malalties està estretament lligada a l’especialització de subpoblacions virals cap a nous tipus d’amfitrions. La modelització matemàtica proporciona un marc quantitatiu que pot ajudar amb la predicció de processos a llarg termini com pot ser l’especialització. A causa de la naturalesa complexa que presenten les interaccions intra i interespecífiques en els processos evolutius, cal aplicar eines matemàtiques complexes, com ara l’anàlisi de bifurcacions, al estudiar dinàmiques de població. Aquesta tesi desenvolupa una jerarquia de models de població per poder comprendre l’aparició i les dinàmiques d’especialització, i la seva dependència dels paràmetres del sistema. Utilitzant un model per a un virus de tipus salvatge i un virus mutat que competeixen pel mateix amfitrió, es determinen les condicions per a la supervivència únicament de la subpoblació mutant, juntament amb la seva coexistència amb el cep de tipus salvatge. Els diagrames d’estabilitat que representen regions de dinàmiques diferenciades es construeixen en termes de taxa d’infecció, virulència i taxa de mutació; els diagrames s’expliquen en base a les característiques biològiques de les subpoblacions. Per a paràmetres variables, s’observa i es descriu el fenomen d’intersecció i intercanvi d’estabilitat entre diferents solucions sistemàtiques i periòdiques en l’àmbit dels ceps de tipus salvatge i els ceps mutants en competència directa. En el cas de que diversos tipus d’amfitrions estiguin disponibles per a ser disputats per ceps especialitzats i generalistes existeixen regions de biestabilitat, i les probabilitats d’observar cada estat es calculen com funcions de les taxes d’infecció. S’ha trobat un rar atractor caòtic i s’ha analitzat amb l’ús d’exponents de Lyapunov. Això, combinat amb els diagrames d’estabilitat, mostra que la supervivència del cep generalista en un entorn estable és un fet improbable. A més, s’estudia el cas dels diversos ceps N>>1 que competeixen per diferents tipus de cèl·lules amfitriones. En aquest cas s’ha descobert una dependència no monotònica, contraria al que es preveia, del temps d’especialització sobre la mida inicial i la taxa de mutació, com a conseqüència de la realització d’un anàlisi de regressió sobre dades obtingudes numèricament. En general, aquest treball fa contribucions àmplies a la modelització matemàtica i anàlisi de la dinàmica dels patogens i els processos evolutius.La aparición de nuevos virus causantes de enfermedades está estrechamente ligada a la especialización de las subpoblaciones virales hacia nuevos tipos de anfitriones. La modelizaci ón matemática proporciona un marco cuantitativo que puede ayudar a la predicción de procesos a largo plazo como la especialización. Debido a la naturaleza compleja que presentan las interacciones intra e interespecíficas en los procesos evolutivos, aplicar herramientas matemáticas complejas, tales como el análisis de bifurcación, al estudiar dinámicas de población. Esta tesis desarrolla una jerarquía de modelos de población para poder comprender la aparición y las dinámicas de especialización, y su dependencia de los parámetros del sistema. Utilizando un modelo para un virus de tipo salvaje y un virus mutado que compiten por el mismo anfitrión, se determinan las condiciones para la supervivencia únicamente de la subpoblación mutante, junto con su coexistencia con la cepa de tipo salvaje. Los diagramas de estabilidad que representan regiones de dinámicas diferenciadas se construyen en términos de tasa de infección, virulencia y tasa de mutación; los diagramas se explican en base a las características biológicas de las subpoblaciones. Para parámetros variables, se observa y se describe el fenómeno de intersección e intercambio de estabilidad entre diferentes soluciones sistemáticas y periódicas en el ámbito de las cepas de tipo salvaje y las cepas mutantes en competencia directa. En el caso de que varios tipos de anfitriones estén disponibles para ser disputados por cepas especializadas y generalistas existen regiones de biestabilidad, y las probabilidades de observar cada estado se calculan como funciones de las tasas de infección. Se ha encontrado un raro atractor caótico y se ha analizado con el uso de exponentes de Lyapunov. Esto, combinado con los diagramas de estabilidad, muestra que la supervivencia de la cepa generalista en un entorno estable es un hecho improbable. Además, se estudia el caso de los varias cepas N>> 1 que compiten por diferentes tipos de células anfitrionas. En este caso se ha descubierto una dependencia no monotónica, contraria a lo que se preveía, del tiempo de especialización sobre el tamaño inicial y la tasa de mutación, como consecuencia de la realización de un análisis de regresión sobre datos obtenidos numéricamente. En general, este trabajo hace contribuciones amplias a la modelización matemática y el análisis de la dinámica de los patógenos y los procesos evolutivos.
The occurrence of new disease-causing viruses is tightly linked to the specialisation of viral sub-populations towards new host types. Mathematical modelling provides a quantitative framework that can aid with the prediction of long-term processes such as specialisation. Due to the complex nature of intra- and interspecific interactions present in evolutionary processes, elaborate mathematical tools such as bifurcation analysis must be employed while studying population dynamics. In this thesis, a hierarchy of population models is developed to understand the onset and dynamics of specialisation and their dependence on the parameters of the system. Using a model for a wild-type and mutant virus that compete for the same host, conditions for the survival of only the mutant subpopulation, along with its coexistence with the wild-type strain, are determined. Stability diagrams that depict regions of distinct dynamics are constructed in terms of infection rates, virulence and the mutation rate; the diagrams are explained in terms of the biological characteristics of the sub-populations. For varying parameters, the phenomenon of intersection and exchange of stability between different periodic solutions of the system is observed and described in the scope of the competing wild-type and mutant strains. In the case of several types of hosts being available for competing specialist and generalist strains, regions of bistability exist, and the probabilities of observing each state are calculated as functions of the infection rates. A strange chaotic attractor is discovered and analysed with the use of Lyapunov exponents. This, combined with the stability diagrams, shows that the survival of the generalist in a stable environment is an unlikely event. Furthermore, the case of N=1 different strains competing for different types of host cells is studied. For this case, a counterintuitive and non-monotonic dependence of the specialisation time on the burst size and mutation rate is discovered as a result of carrying out a regression analysis on numerically obtained data. Overall, this work makes broad contributions to mathematical modelling and analysis of pathogen dynamics and evolutionary processes.
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Vorwerk, Michael Conrad. "A mathematical study of mimicry and opportunism." Thesis, Georgia Institute of Technology, 1989. http://hdl.handle.net/1853/28944.
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Apostu, Raluca. "Mathematical model of GAL regulon dynamics in «Saccharomyces cerevisiae»." Thesis, McGill University, 2012. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=107676.
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Genetic switches are prevalent in nature, and provide cells with a strategy to adapt to changing environmental conditions. This thesis focuses on an intriguing example which is not understood in complete detail: the GAL switch. The GAL switch allows organisms to metabolize the sugar galactose, and controls whether the machinery responsible for the galactose metabolism is turned ON or OFF. Currently, it is not known exactly how the galactose signal is sensed by the transcriptional machinery. Moreover, there are two contradictory hypotheses concerning the regulatory mechanism at GAL promoters in galactose induced cells: the dissociation and non-dissociation models. This work uses quantitative tools to understand the Saccharomyces cerevisiae cell response to galactose challenge, and to analyze the plausible molecular mechanisms underlying its operation. The thesis proposes a novel dynamic mathematical model which is based on the interplay of the key regulatory proteins Gal4p, Gal80p, and Gal3p, in a cell population. To my knowledge, the deterministic model presented here is the first to reproduce qualitatively the bistable GAL network behavior found experimentally. Given the current understanding of the GAL circuit induction (Wightman et al., 2008; Jiang et al., 2009), this work proposes that the most likely in vivo mechanism leading to the transcriptional activation of the GAL genes is the physical interaction between galactose-activated Gal3p and Gal80p, with the complex Gal3p-Gal80p remaining bound at the GAL promoters. The mathematical model is in agreement with the flow cytometry profiles of wild type, gal3∆ and gal80∆ mutant strains from Acar et al. (2005), and involves a fraction of actively transcribing cells with the same qualitative features as in the data set collected by Acar et al. (2010). Furthermore, the computational modelling provides an explanation for the contradictory results obtained by independent laboratories when tackling experimentally the issue of binary versus graded GAL response to galactose induction.Les signaux génétiques binaires sont répandues dans la nature, et fournissent aux cellules une stratégie pour s'adapter à des environnements variables. Cette thése cherche a comprendre un example intéressant qui n'est pas compris complètement: le commutateur GAL. Le commutateur GAL en est un exemple fascinant qui n'est pas pas compris dans tous ses détails. Le commutateur GAL permet aux organismes de métaboliser du galactose, et contrôle si les mécanismes responsables du métabolisme du galactose sont en marche ou non. Actuellement, on ne connaît pas exactement comment le signal galactose est senti par les mécanismes de transcription. En fait, il y a deux hypothèses qui s'opposent à propos du mécanisme régulatoire au site du promoteur de GAL dans les cellules qui étaient induites avec galactose: le modèle de dissociation et le modèle de non-dissociation. Ce travail utilise des outils quantitatifs pour comprendre la réponse de la cellule S. cerevisiae au stimuli de galactose et pour analyser les mécanismes moléculaires possibles à la base de son fonctionnement. Cette thèse propose un modèle dynamique à l'échelle de population de cellules basé sur l'interaction des protéines régulatrices clées Gal4p, Gal80p et Gal3p. À notre connaissance, le modèle présenté ici est le premier à reproduire qualitativement le comportement bistable du réseau observé expérimentalement. Étant donné la compréhension actuelle du circuit d'induction GAL (Wightman et al., 2008; Jiang et al., 2009), ce travail propose que le mécanisme in vivo le plus probable menant à l'activation de la transcription des gènes GAL soit l'interaction physique entre la protéine galactose-activé Gal3p et la protéine Gal80p, avec le complexe Gal3p-Gal80p attaché aux promoteurs des gènes GAL. Notre modèle mathématique est en accord avec les profils de cytométrie en flux des souches sauvages, des souches mutées gal3∆ et gal80∆ d'Acar et al. (2005), et implique une fraction de cellules qui transcrit activement avec les mêmes caractéristiques qualitatives que dans le jeu de données rassemblées par Acar et al. (2010). En outre, les simulations informatiques du modèle fournissent une explication des résultats contradictoires obtenus par des laboratoires indépendants qui abordent expérimentalement la question de la réponse binaire ou graduelle à l'induction de galactose.
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Kumbhari, Adarsh. "Mathematical models of cellular dysfunction." Thesis, University of Sydney, 2020. https://hdl.handle.net/2123/23711.
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Mathematical models provide a framework to confirm or reject hypotheses via the generation of quantitative predictions and offer rich insights into the processes that drive complex biological phenomena. In this thesis, we develop mathematical models that integrate experimental data and use these models to explore cellular dysfunction at different scales. The core of this thesis focuses on the selection of high-avidity T cells in cancer vaccines. High-avidity T cells, unlike low-avidity T cells, are adept at killing cancer cells and are essential for durable anti-tumour immunity. Using an ordinary differential equation (ODE) model, we show that we can optimise dosages to elicit high-avidity T cells. We find that increased numbers of immune cells known as immature dendritic cells, can also promote high-avidity T cells. We then reduce the complexity of our model and perform a thorough sensitivity analysis. We then study how immune cells regulate PD-L1 in the tumour niche. PD-L1 is an immunosuppressive molecule that tumours upregulate. Intriguingly, PD-L1 expression does not always correlate with tumour progression. To understand why we develop an ODE model that we calibrate to in vitro data. Using this model, we show that PD-L1 expression equilibrates in response to changes in immune activity via a feedforward circuit. This finding explains why some patients may respond to therapies targeting PD-L1 despite being PD-L1 negative. The last part of this thesis tests whether the spatial arrangement of cardiac mitochondria affects bioenergetics, as speculated by scholars. To test this, we develop an agent-based model of mitochondrial structure linked to a validated model of energy production and show that cardiac bioenergetics are robust to changes in fission and fusion over a physiological range. This thesis contains several foundational models. We expect the findings from this thesis to be a starting point for further interdisciplinary modelling and experimental work.
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Dyson, Louise. "Mathematical models of cranial neural crest cell migration." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:66955fb9-691f-4d27-ad26-39bb2b089c64.
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From the developing embryo to the evacuation of football stadiums, the migration and movement of populations of individuals is a vital part of human life. Such movement often occurs in crowded conditions, where the space occupied by each individual impacts on the freedom of others. This thesis aims to analyse and understand the effects of occupied volume (volume exclusion) on the movement of the individual and the population. We consider, as a motivating system, the rearrangement of individuals required to turn a clump of cells into a functioning embryo. Specifically, we consider the migration of cranial neural crest cells in the developing chick embryo. Working closely with experimental collaborators we construct a hybrid model of the system, consisting of a continuum chemoattractant and individual-based cell description and find that multiple cell phenotypes are required for successful migration. In the crowded environment of the migratory system, volume exclusion is highly important and significantly enhances the speed of cell migration in our model, whilst reducing the numbers of individuals that can enter the domain. The developed model is used to make experimental predictions, that are tested in vivo, using cycles of modelling and experimental work to give greater insight into the biological system. Our formulated model is computational, and is thus difficult to analyse whilst considering different parameter regimes. The second part of the thesis is driven by the wish to systematically analyse our model. As such, it concentrates on developing new techniques to derive continuum equations from diffusive and chemotactic individual-based and hybrid models in one and two spatial dimensions with the incorporation of volume exclusion. We demonstrate the accuracy of our techniques under different parameter regimes and using different mechanisms of movement. In particular, we show that our derived continuum equations almost always compare better to data averaged over multiple simulations than the equivalent equations without volume exclusion. Thus we establish that volume exclusion has a substantial effect on the evolution of a migrating population.
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Morin, Benjamin R. "The Effect of Static and Dynamic Spatially Structured Disturbances on a Locally Dispersing Population Model." Fogler Library, University of Maine, 2006. http://www.library.umaine.edu/theses/pdf/MorinBR2006.pdf.
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Cong, Yang, and 丛阳. "Optimization models and computational methods for systems biology." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2012. http://hub.hku.hk/bib/B47752841.
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Systems biology is a comprehensive quantitative analysis of the manner in
which all the components of a biological system interact functionally along with
time. Mathematical modeling and computational methods are indispensable
in such kind of studies, especially for interpreting and predicting the complex
interactions among all the components so as to obtain some desirable system
properties. System dynamics, system robustness and control method are three
crucial properties in systems biology. In this thesis, the above properties are
studied in four different biological systems.
The outbreak and spread of infectious diseases have been questioned and
studied for years. The spread mechanism and prediction about the disease could
enable scientists to evaluate isolation plans to have significant effects on a particular
epidemic. A differential equation model is proposed to study the dynamics
of HIV spread in a network of prisons. In prisons, screening and quarantining
are both efficient control manners. An optimization model is proposed to study
optimal strategies for the control of HIV spread in a prison system.
A primordium (plural: primordia) is an organ or tissue in its earliest recognizable
stage of development. Primordial development in plants is critical to the
proper positioning and development of plant organs. An optimization model and
two control mechanisms are proposed to study the dynamics and robustness of primordial systems.
Probabilistic Boolean Networks (PBNs) are mathematical models for studying
the switching behavior in genetic regulatory networks. An algorithm is proposed
to identify singleton and small attractors in PBNs which correspond to
cell types and cell states. The captured problem is NP-hard in general. Our
algorithm is theoretically and computationally demonstrated to be much more
efficient than the naive algorithm that examines all the possible states.
The goal of studying the long-term behavior of a genetic regulatory network is
to study the control strategies such that the system can obtain desired properties.
A control method is proposed to study multiple external interventions meanwhile
minimizing the control cost.
Robustness is a paramount property for living organisms. The impact degree
is a measure of robustness of a metabolic system against the deletion of single
or multiple reaction(s). An algorithm is proposed to study the impact degree
in Escherichia coli metabolic system. Moreover, approximation method based
on Branching process is proposed for estimating the impact degree of metabolic
networks. The effectiveness of our method is assured by testing with real-world
Escherichia coli, Bacillus subtilis, Saccharomyces cerevisiae and Homo Sapiens
metabolic systems.published_or_final_version
Mathematics
Doctoral
Doctor of Philosophy
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Vaskan, Pavel. "Development of advanced mathematical programming methods for sustainable engineering and system biology." Doctoral thesis, Universitat Rovira i Virgili, 2014. http://hdl.handle.net/10803/145250.
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The main goal of this thesis is to develop advanced mathematical programming tools to address the design and planning of sustainable engineering systems and the modeling and optimization of biological systems. First we introduce a novel framework for the coupled use of Geographical Information Systems (GIS), Mixed-Integer Linear Programming (MILP) and decomposition algorithm for GIS based MILP models. Our approaches combine optimization tools, spatial decision support tools, economic and environmental analysis. Second we propose the general framework for sustainable design of energy systems like heat exchanger networks and utility plant. Our method is based on the combined use of the multi-objective optimization tools, Life Cycle Assessment methodology (LCA) and a rigorous dimensionality reduction method that allows identifying key environmental metrics. Finally we introduce multi-objective Mixed-Integer Non-Linear Programming (MINLP) based method for identifying in a rigorous and systematic manner the most probable biological objective functions explaining the operation of metabolic networks.El objetivo principal de esta tesis es el desarrollo de herramientas de programación matemática para abordar el diseño y planificación de procesos industriales sostenibles y la optimización en el área de la biología de sistemas. Primeramente se establece un nuevo marco para el uso simultáneo de Sistemas de Información Geográfica (GIS), Programación Lineal Entera Mixta (MILP) y algoritmos de descomposición para modelo basados en MILP-GIS. Nuestros enfoques combinan herramientas de optimización, herramientas espaciales para la toma de decisiones y análisis económicos y medioambientales. En segundo lugar, se propone el marco general para el diseño de sistemas de energía sostenibles, como las redes de intercambio de calor y plantas de servicio para la industria del proceso. Nuestro método se basa en el uso combinado de herramientas de optimización multiobjetivo, metodología de Análisis de Ciclo de Vida (LCA) y un riguroso método de reducción de dimensionalidad que permite la identificación de indicadores ambientales clave. Finalmente introducimos un método basado en Programación Multiobjetivo Mixta Entera no Lineal (MINLP) aplicado a la identificación rigurosa y sistemática de las funciones objetivo biológicas más probables que explican el funcionamiento de las redes metabólicas
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Rosado, Linares Jesús. "Analysis of some diffusive and kinetic models in mathematical biology and physics." Doctoral thesis, Universitat Autònoma de Barcelona, 2010. http://hdl.handle.net/10803/3113.
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Wearing, Helen Jane. "Mathematical modelling of cell-cell signalling in developmental biology and wound healing." Thesis, Heriot-Watt University, 2001. http://hdl.handle.net/10399/1184.
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Cobbold, Christina Anne. "Mathematical modelling of problems in human biology : dermal wound healing and atherosclerosis." Thesis, Heriot-Watt University, 2001. http://hdl.handle.net/10399/471.
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Donaghy, Josephine. "Researchers' assumptions and mathematical models : a philosophical study of metabolic systems biology." Thesis, University of Exeter, 2014. http://hdl.handle.net/10871/16001.
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This thesis examines the philosophical implications of the assumptions made by researchers involved in the development of mathematical models of metabolism. It does this through an analysis of several detailed historical case studies of models between the 1960’s and the present day, thus also contributing to the growing literature on the historiography of biochemical systems biology. The chapters focus on four main topics: the relationship between models and theory, temporal decomposition as a simplifying strategy for building models of complex metabolic systems, interactions between modellers and experimental biochemists, and the role of biochemical data. Four categories of assumptions are shown to play a significant role in these different aspects of model development; ontological assumptions, idealising assumptions, assumptions about data, and researchers’ commitments. Building on this analysis, the thesis brings to light the importance of researcher’s ontological and idealising assumptions about the temporal organisation, alongside the spatial organisation, of metabolic systems. It also offers an account of different forms of interactions between research groups – hostile interactions, closed collaboration, and open collaboration – on the basis of differences in the characteristics of researcher’s commitments. Throughout the case studies, biological data play a powerful role in model development by virtue of the contents of available data sets, as well as researchers’ perceptions of those data, which are in turn influenced by their ontological assumptions. The historical trajectories explored illustrate how the relationships between different facets of model building, and their associated philosophical abstractions, are often best understood as transient features within a highly dynamic research process, whose role depends on the specific stage of modelling in which they are enacted. This thesis provides an expanded perspective on the different types and roles of assumptions in the development of mathematical models of metabolism, which is firmly grounded in a historical analysis of scientific practice.
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Jin, Wang. "Investigating the reproducibility of in vitro cell biology assays using mathematical models." Thesis, Queensland University of Technology, 2017. https://eprints.qut.edu.au/109790/1/Wang_Jin_Thesis.pdf.
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In vitro cell biology assays are routinely used to study cancer spreading, drug design and tissue repair. However, issues associated with reproducibility are reported in literature. In this thesis we investigate the overlooked source of variability that affects the reproducibility of cell biology assays, using a combined mathematical and experimental approach. By calibrating mathematical models to experimental data, we find that the initial degree of confluence significantly affects cell motility. Following the similar approach, we identify the two-phase growth in scratch assays. We then propose a proliferation mechanism for lattice-based, random walk models, which accounts for biologically more realistic crowding effects. At last, we use a lattice-based, random walk model to mimic the passaging process and find that the passage number could significantly affect the wound closure in scratch assays.
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Matsiaka, Oleksii. "New mathematical models for cell biology assays incorporating realistic cell size dynamics." Thesis, Queensland University of Technology, 2020. https://eprints.qut.edu.au/198192/1/Oleksii_Matsiaka_Thesis.pdf.
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This thesis provides novel insights into several contemporary problems in the mathematical biology involving migration of living cells. Primarily, we focus on cell motility and how dynamic changes in cell size affect collective cell migration. Additionally, this thesis investigates the importance of cellular heterogeneity and how it might affect the choice of modelling techniques we use to describe in vitro cell cultures.
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Misselbeck, Karla. "Computational Systems Biology Applied To Human Metabolism. Mathematical Modelling and Network Analysis." Doctoral thesis, Università degli studi di Trento, 2019. https://hdl.handle.net/11572/369023.
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Human metabolism, an essential and highly organized process, which is required to run and maintain cellular processes and to respond to shifts in external and internal conditions, can be described as a complex and interconnected network of metabolic pathways.
Computational systems biology provides a suitable framework to study the mechanisms and interactions of this network and to address questions that are difficult to reproduce in vitro or in vivo.
This dissertation contributes to the development of computational strategies which help to investigate aspects of human metabolism and metabolic-related disorders.
In the first part, we introduce mathematical models of folate-mediated one-carbon metabolism in the cytoplasm and subsequently in the nucleus.
A hybrid-stochastic framework is applied to investigate the behavior and stability of the complete metabolic network in response to genetic and nutritional factors.
We analyse the effect of a common polymorphism of MTHFR, B12 and folate deficiency, as well as the role of the 5-formyltetrahydrofolate futile cycle on network dynamics.
Furthermore, we study the impact of multienzyme complex formation and substrate channelling, which are key aspects related to nuclear folate-mediated one-carbon metabolism.
Model simulations of the nuclear model highlight the importance of these two factors for normal functioning of the network and further identify folate status and enzyme levels as important influence factors for network dynamics.
In the second part, we focus on metabolic syndrome, a highly prevalent cluster of metabolic disorders.
We develop a computational workflow based on network analysis to characterise underlying molecular mechanisms of the disorder and to explore possible novel therapeutic strategies by means of drug repurposing.
To this end, genetic data, text mining results, drug expression profiles and drug target information are integrated in the setting of tissue-specific background networks and a proximity score based on topological distance and functional similarity measurements is defined to identify potential new therapeutic applications of already approved drugs. A filtering and prioritization analysis allow us to identify ibrutinib, an inhibitor of bruton tyrosine kinase, as the most promising repurposing candidate.
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Misselbeck, Karla. "Computational Systems Biology Applied To Human Metabolism. Mathematical Modelling and Network Analysis." Doctoral thesis, University of Trento, 2019. http://eprints-phd.biblio.unitn.it/3546/1/Thesis_Misselbeck_20190314.pdf.
Full textAbstract:
Human metabolism, an essential and highly organized process, which is required to run and maintain cellular processes and to respond to shifts in external and internal conditions, can be described as a complex and interconnected network of metabolic pathways.
Computational systems biology provides a suitable framework to study the mechanisms and interactions of this network and to address questions that are difficult to reproduce in vitro or in vivo.
This dissertation contributes to the development of computational strategies which help to investigate aspects of human metabolism and metabolic-related disorders.
In the first part, we introduce mathematical models of folate-mediated one-carbon metabolism in the cytoplasm and subsequently in the nucleus.
A hybrid-stochastic framework is applied to investigate the behavior and stability of the complete metabolic network in response to genetic and nutritional factors.
We analyse the effect of a common polymorphism of MTHFR, B12 and folate deficiency, as well as the role of the 5-formyltetrahydrofolate futile cycle on network dynamics.
Furthermore, we study the impact of multienzyme complex formation and substrate channelling, which are key aspects related to nuclear folate-mediated one-carbon metabolism.
Model simulations of the nuclear model highlight the importance of these two factors for normal functioning of the network and further identify folate status and enzyme levels as important influence factors for network dynamics.
In the second part, we focus on metabolic syndrome, a highly prevalent cluster of metabolic disorders.
We develop a computational workflow based on network analysis to characterise underlying molecular mechanisms of the disorder and to explore possible novel therapeutic strategies by means of drug repurposing.
To this end, genetic data, text mining results, drug expression profiles and drug target information are integrated in the setting of tissue-specific background networks and a proximity score based on topological distance and functional similarity measurements is defined to identify potential new therapeutic applications of already approved drugs. A filtering and prioritization analysis allow us to identify ibrutinib, an inhibitor of bruton tyrosine kinase, as the most promising repurposing candidate.
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El, Moustaid Fadoua. "MATHEMATICAL MODELING OF CYANOBACTERIAL DYNAMICS IN A CHEMOSTAT." Master's thesis, Temple University Libraries, 2015. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/335727.
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MathematicsM.S.
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.
Temple University--Theses
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趙崇諾 and Sung-nok Chiu. "Stochastic models of molecular mechanisms in biology." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1992. http://hub.hku.hk/bib/B31210752.
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Rata, Scott. "Mathematical modelling of mitotic controls." Thesis, University of Oxford, 2018. https://ora.ox.ac.uk/objects/uuid:7bef862c-2025-4494-a2bb-4fe93584d92a.
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The mitotic cell cycle is fundamental to eukaryotic life. In mitosis, replicated chromosomes are segregated to form two new nuclei. This is essential to ensure the maintenance of chromosome number between parent and daughter cells. In higher eukaryotes, numerous cytological changes occur to facilitate the separation of the genetic material: the nuclear envelope breaks down, the mitotic spindle assembles, and the cell rounds-up. There is a well-conserved control network that regulates these processes to bring about the entry into mitosis, the separation of the genetic material, and the reversal of these processes during mitotic exit. To build a coherent model of these regulatory networks requires us to write the biochemical reactions in mathematical form. The work in this Thesis pertains to three fundamental switches: entry into mitosis, the metaphase-to-anaphase transition, and exit from mitosis. I present three studies from a systems-level perspective. The first investigates a novel bistable mechanism controlling mitotic entry/exit in vitro using purified proteins. Dephosphorylation of Greatwall kinase by the phosphatase PP2A-B55 creates a double negative feedback loop that gives a bistable system response with respect to cyclin-dependent kinase 1 (Cdk1) activity. The second looks at hysteresis between mitotic entry and mitotic exit in HeLa cells. Hysteresis persists when either of the regulatory loops of Cdk1 or its counter-acting phosphatase PP2A-B55 is removed, but is diminished when they are both removed. Finally, the regulation of separase in the metaphase-to-anaphase transition is analysed. Separase that is liberated from securin inhibition is isomerised by Pin1 into a conformation that can bind to cyclin B1. This binding peaks after separase has cleaved cohesin and initiated anaphase.
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Nguyen, An. "Mathematical model of competence regulation circuit." Thesis, University of Southampton, 2014. https://eprints.soton.ac.uk/374173/.
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Gene expression regulatory networks are molecular networks which describe interactions among gene products in terms of biochemical reactions. This helps us understand the molecular mechanisms underlying important biological processes as well as cell functioning as a whole. For instance, the phenomenon of bacterial competence, whereby a bacterium enters a transiently differentiated state, incorporating DNA fragments from its environment into its genome, has been studied with the help of such gene regulatory circuits (Suel et al., 2006; Maamar and Dubnau, 2005). As a result, a genetic circuit has been taken into account in order to describe the transition from a vegetative state to a transient state of competence and vice versa. In this work, we are going to study a genetic circuit presented by Suel et al. (2007) to describe this dynamical behaviour. The authors introduce model reduction techniques to study the behaviour of stochastic chemical system of X species by means of an adiabatic two dimensional model. While the adiabatic model helps us understand about the dynamics near the steady state, it gives an incorrect description of the time-scales of the competent state. For this reason, it is necessary to build up a model which better describes the system realistically. In the thesis, I propose an approximate two-dimensional model of the full high-dimensional system and from that, the dynamics of the system can be simulated more accurately compared to that of Suel et al. (2007). I then show how to put the noise back into the approximate model to be able come up with a stochastic model which can mathematically describe the dynamical behaviour of the original high dimensional system. I also found out that the evolution of the system is not well approximated by a Langevin process. This leads to a gap between the real behavior which is described by Gillespie's stochastic simulation and the Langevin approximation. To overcome this, I have fixed the stochastic Langevin model by incorporating empirically tunable noise into the model so as to obtain a similar behaviour as observed in the original system. I also introduce the chemical Fokker-Planck equation aimed to estimate the probability density function of species concentrations which are involved in the biochemical system.
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Chapman, Lloyd A. C. "Mathematical modelling of cell growth in tissue engineering bioreactors." Thesis, University of Oxford, 2015. https://ora.ox.ac.uk/objects/uuid:7c9ee131-7d9b-4e5d-8534-04a059fbd039.
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Expanding cell populations extracted from patients or animals is essential to the process of tissue engineering and is commonly performed in laboratory incubation devices known as bioreactors. Bioreactors provide a means of controlling the chemical and mechanical environment experienced by cells to ensure growth of a functional population. However, maximising this growth requires detailed knowledge of how cell proliferation is affected by bioreactor operating conditions, such as the flow rate of culture medium into the bioreactor, and by the initial cell seeding distribution in the bioreactor. Mathematical modelling can provide insight into the effects of these factors on cell expansion by describing the chemical and physical processes that affect growth and how they interact over different length- and time-scales. In this thesis we develop models to investigate how cell expansion in bioreactors is affected by fluid flow, solute transport and cell seeding. For this purpose, a perfused single-fibre hollow fibre bioreactor is used as a model system. We start by developing a model of the growth of a homogeneous cell layer on the outer surface of the hollow fibre in response to local nutrient and waste product concentrations and fluid shear stress. We use the model to simulate the cell layer growth with different flow configurations and operating conditions for cell types with different nutrient demands and responses to fluid shear stress. We then develop a 2D continuum model to investigate the influence of oxygen delivery, fluid shear stress and cell seeding on cell aggregate growth along the outer surface of the fibre. Using the model we predict operating conditions and initial aggregate distributions that maximise the rate of growth to confluence over the fibre surface for different cell types. A potential limitation of these models is that they do not explicitly consider individual cell interaction, movement and growth. To address this, we conclude the thesis by assessing the suitability of a hybrid framework for modelling bioreactor cell aggregate growth, with a discrete cell model coupled to a continuum nutrient transport model. We consider a simple set-up with a 1D cell aggregate growing along the base of a 2D nutrient bath. Motivated by trying to reduce the high computational cost of simulating large numbers of cells with a cell-based model, and to assess the validity of our previous continuum description of cell aggregate growth, we derive a continuum approximation of the discrete model in the large cell number limit and determine whether it agrees with the discrete model via numerical simulations.
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Baxley, Dana Ali. "A MATHEMATICAL STUDY OF TWO RETROVIRUSES, HIV AND HTLV-I." Master's thesis, University of Central Florida, 2007. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/2369.
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In this thesis, we examine epidemiological models of two different retroviruses, which infect the human body. The two viruses under study are HIV or the human immunodefiency virus and HTLV-I, which is the human T lymphotropic virus type I. A retrovirus is a virus, which injects its RNA into the host, rather than it's DNA. We will study each of the different mathematical models for each of the viruses separately. Then we use MATLAB-SIMULINK to analyze the models by studying the reproductive numbers in each case and the disease progression by examining the graphs. In Chapter 1, we mention basic ideas associated with HIV and HTLV-I. In Chapter 2 some of the basic mathematical model of epidemiology is presented. Chapter 3 is devoted to a model describing the intra-host dynamics of HIV. Here, we take into account how HIV infects and replicates in the CD4+ T cells. The model studied in this thesis examines the difference between cells, which are susceptible to the virus, and cells, which are not susceptible. Through the graphs associated with this model, we are able to see how this difference affects disease progression. In Chapter 4, we examine the effect of HTLV-I virus on human body. The HTLV-I virus causes a chronic infection in humans and may eventually lead to other diseases. In particular, the development of Adult T-cell Leukemia or ATL is studied in this thesis. The T-cell dynamics and progression to ATL is described using a mathematical model with coupled differential equations. Using mathematical analysis and SIMULINK, we obtain results on stability, asymptotic stability and the manner of progression of the disease. In Chapter 5 and appendices, we mention our inference and the MATLAB-SIMULINK codes used in this thesis, so that a reader can verify the details of the work carried out in this thesis.M.S.
Department of Mathematics
Sciences
Mathematical Science MS
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Catt, Christopher Joseph. "Mathematical modelling of tissue metabolism and growth." Thesis, University of Southampton, 2010. https://eprints.soton.ac.uk/176447/.
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The work presented in this thesis is concerned with modelling the growth of tissue constructs, with particular focus on the effects the local micro environment has on the cell cycle and metabolism. We consider two cases; multicellular tumour spheroids and orthopaedic tissue constructs. This thesis is divided into two parts. In the first part we will present a multispecies model of an avascular tumour that studies how a cell’s metabolism affects the cell cycle, spheroid growth and the mechanical forces that arise during growth. The second part consists of a study of the growth of an engineered cartilaginous tissue layer. Experimental observations will be compared to a model of the distribution of cells and extracellular matrix. The efficiency of cancer treatments such as radiotherapy and chemotherapy are sensitive to the local environment of a cell. Therefore an essential task in tumour biology is to understand the microenvironment within a tumour. Many mathematical models study the effects of nutrients and waste products, usually assuming growth is limited by the diffusion of a single nutrient. We will look in detail at the metabolic pathways from which cells obtain energy (ATP). A multispecies model is presented that considers the transition from aerobic to anaerobic respi- ration and includes relevant chemical and ionic buffering reactions and transport mechanisms. Results show that potential ATP production affects the cell cycle and consequently the rate of growth. This model is simplified using mathematical analysis and is integrated with a morphoelastic model to study the development of mechanical forces. The model shows that mechanical effects are particularly important during necrosis, where large tensile forces are shown to develop. A review of the equations governing nutrient conservation is given, by developing alternative macroscopic equations based on the microscopic features of a tumour using homogenization techniques. The second part of this thesis studies the growth of cartilaginous tissue. Bio-materials are being engineered in an attempt to replace dysfunctional tissue in the human body using cells extracted from living organisms. We model the growth of a cartilaginous tissue construct that has been grown from expanded chondrocytes seeded onto collagen coated filters. A model is developed to explain the distribution of cells and the concentration and distribution of collagen and GAGs. This is achieved by studying the local environment of the cells. Model predictions are compared to a range of experimental data and show most of the growth takes place in the upper region of the construct.
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Modhara, Sunny. "Mathematical modelling of vascular development in zebrafish." Thesis, University of Nottingham, 2015. http://eprints.nottingham.ac.uk/29125/.
Full textAbstract:
The Notch signalling pathway is pivotal in ensuring that the processes of arterial specification, angiogenic sprouting and haematopoietic stem cell (HSC) specification are correctly carried out in the dorsal aorta (DA), a primary arterial blood vessel in developing vertebrate embryos. Using the zebrafish as a model organism, and additional experimental observations from mouse and cell line models to guide mathematical modelling, this thesis aims to better understand the mechanisms involved in the establishment of a healthy vasculature in the growing embryo. We begin by studying arterial and HSC specification in the zebrafish DA. Mathematical models are used to analyse the dose response of arterial and HSC genes to an input Notch signal. The models determine how distinct levels of Notch signalling may be required to establish arterial and HSC identity. Furthermore, we explore how Delta-Notch coupling, which generates salt-and-pepper patterns, may drive the average gene expression levels higher than their homogeneous levels. The models considered here can qualitatively reproduce experimental observations. Using laboratory experiments, I was able to isolate DA cells from transgenic zebrafish embryos and generate temporal gene expression data using qPCR. We show that it is possible to fit ODE models to such data but more reliable data and a greater number of replicates at each time point is required to make further progress. The same VEGF-Delta-Notch signalling pathway is involved in tip cell selection in angiogenic sprouting. Using an ODE model, we rigourously study the dynamics of a VEGF-Delta-Notch feedback loop which is capable of amplifying differences betwen cells to form period-2 spatial patterns of alternating tip and stalk cells. The analysis predicts that the feeback strengths of Delta ligand and VEGFR-2 production dictate the onset of patterning in the same way, irrespective of the parameter values used. This model is extended to incorporate feedback from filopodia, growing in a gradient of extracellular VEGF, which are capable of facilitating tip cell selection by amplifying the resulting patterns. Lastly, we develop a PDE model which is able to properly account for VEGF receptor distributions in the cell membrane and filopodia. Receptors can diffuse and be advected due to domain growth, defined by a constitutive law, in this model. Our analysis and simulations predict that when receptor diffusivity is large, the ODE model for filopodia growth is an excellent approximation to the PDE model, but that for smaller diffusivity, the PDE model provides valuable insight into the pattern forming potential of the system.
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Bakshi, Suruchi D. "Mathematical modelling of Centrosomin incorporation in Drosophila centrosomes." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:baefde65-bc38-4a11-bd92-e2e4cccad784.
Full textAbstract:
Centrosomin (Cnn) is an integral centrosomal protein in Drosophila with orthologues in several species, including humans. The human orthologue of Cnn is required for brain development with Cnn hypothesised to play a similar role in Drosophila. Control of Cnn incorporation into centrosomes is crucial for controlling asymmetric division in certain types of Drosophila stem cells. FRAP experiments on Cnn show that Cnn recovers in a pe- culiar fashion, which suggest that Cnn may be incorporated closest to the centrioles and then spread radially outward, either diffusively or ad- vectively. The aim of this thesis is to understand the mechanism of Cnn incorporation into the Drosophila centrosomes, to determine the mode of transport of the incorporated Cnn, and to obtain parameter estimates for transport and biochemical reactions. A crucial unknown in the modelling process is the distribution of Cnn receptors. We begin by constructing coupled partial differential equation models with either diffusion or advection as the mechanism for incorpo- rated Cnn transport. The simplest receptor distribution we begin with involves a spherical, infinitesimally thick, impermeable shell. We refine the diffusion models using the insights gained from comparing the model out- put with data (gathered during mitosis) and through careful assessment of the behaviour of the data. We show that a Gaussian receptor distribution is necessary to explain the Cnn FRAP data and that the data cannot be explained by other simpler receptor distributions. We predict the exact form of the receptor distribution through data fitting and present pre- liminary experimental results from our collaborators that suggest that a protein called DSpd2 may show a matching distribution. Not only does this provide strong experimental support for a key prediction from our model, but it also suggests that DSpd2 acts as a Cnn receptor. We also show using the mitosis FRAP data that Cnn does not exhibit appreciable radial movement during mitosis, which precludes the use of these data to distinguish between diffusive and advective transport of Cnn. We use long time Cnn FRAP data gathered during S-phase for this purpose. We fit the S-phase FRAP data using the DSpd2 profiles gath- ered for time points corresponding to the Cnn FRAP experiments. We also use data from FRAP experiments where colchicine is injected into the embryos to destroy microtubules (since microtubules are suspected to play a role in advective transport of Cnn). From the analysis of all these data we show that Cnn is transported in part by advection and in part by diffusion. Thus, we are able to provide the first mechanistic description of the Cnn incorporation process. Further, we estimate parameters from the model fitting and predict how some of the parameters may be altered as nuclei progress from S-phase to mitosis. We also generate testable predic- tions regarding the control of the Cnn incorporation process. We believe that this work will be useful to understand the role of Cnn incorporation in centrosome function, particularly in asymmetrically dividing stem cells.
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Lumpkin, Robert. "Parameter Classification and Analysis of Neuronal Systems with Astrocytic Modulation of Behaviour." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1563206513875333.
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Meyer, Gigi. "A SYSTEMS BIOLOGY APPROACH FOR UNDERSTANDING INFLAMMATION IN THE GASTROINTESTINAL TRACT OF A CROHN’S PATIENT." VCU Scholars Compass, 2013. http://scholarscompass.vcu.edu/etd/3153.
Full textAbstract:
A system of ordinary differential equations is developed to model the effect of fatty acids on chronic intestinal inflammation that is typical of a Crohn’s patient. Several murine studies have shown an anti-inflammatory response when specific polyunsaturated fatty acids are included regularly in the diet. It is believed that the fatty acids serve as a specific ligand that activates the Peroxisome Proliferator Activated Receptor (PPAR) which is located on multiple cell types that are active in the inflammatory response. The binding of the PPAR results in a suppression of the inflammatory pathway. Results of the model indicate a muted inflammatory response when fatty acids are added regularly to the diet in mild to moderate cases of Crohn’s. Results of mathematical analysis show a stable fixed point with decreased inflammatory markers and pathogen levels when fatty acids are added regularly to the diet.
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González, Flo Eva 1993. "Engineering living biomedical devices : Mathematical and experimental tools for the rational design of cellular devices." Doctoral thesis, TDX (Tesis Doctorals en Xarxa), 2020. http://hdl.handle.net/10803/670358.
Full textAbstract:
The engineering of biology strives on the creation of biological devices concerning society-impact applications. In this PhD thesis, we developed mathematical and experimental tools for the standard and rational design of living devices for biomedical purposes, offering robust and reliable responses. By breaking-up cellular device complexity into functional modules, we have analysed how extracellular information is detected, processed and transformed thanks to re-engineering intrinsic cellular components. We show how the desired range of action of a biosensor could be tuned by modifying the relative levels from two-component receptors’ biosensors. Regarding information processing, combining multicellularity and space permits to develop a 2D multi-branch approach inspired from printed electronics, allowing to perform logic computation by transferring device complexity into the geometrical arrangement. Sensing and processing capabilities have been applied as a proof-of-concept for the design of cellular devices for Diabetes Mellitus. Treating the cellular device closed-loop response as the fourth-functional module allowed to in silico decipher device characteristics on glycaemia regulation and design novel strategies based on dietary modulation, putting the manifest the need to combine both experimental and computational tools for living device application-based designs.L’aplicació de principis d’enginyeria en biologia permet somniar en l’ús de dispositius biològics per abordar problemes de la societat. Concretament, en aquesta tesi doctoral, s’ha abordat el disseny de dispositius biològics per aplicacions biomèdiques mitjançant la combinació d’eines experimentals i computacionals. La creació d’aquests dispositius demana d’un disseny racional que ofereixi respostes robustes i fiables. L’estudi de la creació de dispositius biològics s’ha fet seguint una aproximació modular, on s’ha analitzat com es poden re-enginyeritzar components cel·lulars per obtenir una resposta que s’adeqüi a l’aplicació requerida. Hem demostrat com podem modular el rang de detecció de la capa sensora a través de la modulació de l’element receptor de sensors bastats en dos components. Hem analitzat com integrar informació de diferents fonts de manera sistemàtica i robusta introduint com a nou element de computació l’espai i la divisió de tasques; tot desenvolupant un marc teòric i validant experimentalment per un seguit de funcions lògiques. Finalment, hem desenvolupat dispositius biològics que responen a molècules fisiològiques. Concretament, hem abordat el disseny de dispositius biològics pel tractament de la Diabetes Mellitus. Una primera validació experimental ens ha permès establir l’ús d’aquests dispositius in vitro. Seguidament, hem aprofundit en l’estudi de la seva aplicació mitjançant l’ús d’un simulador de pacient diabètic que ens ha permès el seu tractament virtual i l’anàlisi de les característiques del dispositiu per la regulació de la glicèmia. Finalment, hem explorat com la combinació dels dispositius cel·lulars amb la regulació del patró d’ingestes introdueix millores en els nivells de glucosa en sang. Posant de manifest el potencial que ofereix la creació d’una plataforma hibrida pel disseny de dispositius cel·lulars per una determinada aplicació.
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Taylor, David G. "A mathematical model of interstitial transport and microvascular exchange." Thesis, University of British Columbia, 1990. http://hdl.handle.net/2429/31031.
Full textAbstract:
A generalized mathematical model is developed to describe the transport of fluid and plasma proteins or other macromolecules within the interstitium. To account for the effects of plasma protein exclusion and interstitial swelling, the interstitium is treated as a multiphase deformable porous medium. Fluid flow is assumed proportional to the gradient in fluid chemical potential and therefore depends not only on the local hydrostatic pressure but also on the local plasma protein concentrations through appropriate colloid osmotic pressure relationships. Plasma protein
transport is assumed to occur by restricted convection, molecular diffusion, and convective dispersion.
A simplified version of the model is used to investigate microvascular exchange of fluid and a single 'aggregate' plasma protein species in mesenteric tissue. The interstitium is approximated by a rigid, rectangular, porous slab displaying two fluid pathways, only one of which is available to plasma proteins.
The model is first used to explore the effects the interstitial plasma protein diffusivity, the tissue hydraulic conductivity, the restricted convection of plasma proteins, and the mesothelial transport characteristics have on the steady-state distribution and transport of plasma proteins and flow of fluid in the tissue. The simulations predict significant convective plasma protein transport and complex fluid flow patterns within the interstitium. These flow patterns can produce local regions of high fluid and plasma protein exchange along the mesothelium which might be erroneously identified as 'leaky sites'. Further, the model predicts significant interstitial osmotic gradients in some instances, suggesting that the Darcy expression invoked in a number of previous models appearing in the literature, in which fluid flow is assumed to be driven by hydrostatic pressure gradients alone, may be inadequate.
Subsequent transient simulations of hypoproteinemia within the model tissue indicate that the interstitial plasma protein content decreases following this upset. The simulations therefore support (qualitatively, at least) clinical observations of hypoproteinemia. Simulations of venous congestion, however, demonstrate that changes in the interstitial plasma protein content following this upset depends, in part, on the relative sieving properties of the filtering and draining vessels. For example, when the reflection coefficients of these two sets of boundaries are similar, the interstitial plasma protein content increases with time due to an increased plasma protein exchange rate across the filtering boundaries and sieving of interstitial plasma proteins at the draining boundaries. (This effect is supported by the clinical observation that interstitial plasma protein content in liver increases during venous congestion.) As the reflection coefficient of the draining boundaries decreases relative to that of the filtering boundaries, there is a net loss of plasma proteins from the interstitium, resulting in a decrease in the total interstitial plasma protein content over time (i.e., the familiar 'plasma protein washout'). Further, the model predicts increased fluid transfer from the interstitium to the peritoneum during venous congestion, supporting the clinical observation of ascites.
Finally, the model is used to study the effects of interstitial plasma protein convection and diffusion, plasma protein exclusion, and the capillary transport properties on the transit times of two macromolecular tracers representative of albumin and γ-globulin within a hypothetical, one-dimensional tissue. As was expected, the transit times of each of the tracers through the model tissue varied inversely with the degree of convective transport. Increasing the interstitial diffusivity of the albumin tracer also led to a moderate decrease in the transit time for that tracer. The capillary wall transport properties, meanwhile, had only a marginal effect on the transit time for the range of capillary permeabilities and reflection coefficients considered. However, these properties (and, in particular, the reflection coefficient) had a more pronounced effect on the ultimate steady-state concentration of the tracer in the outlet stream.
It was the interstitial distribution volume of a given tracer that had the greatest impact on the time required for the outlet tracer concentration to reach 50 % of its steady-state value. This was attributed to the increased filling times associated with larger interstitial distribution volumes. These findings suggest that the 'gel chromatographic effect' observed in some tissues could possibly be explained on the basis of varying distribution volumes.Applied Science, Faculty of
Chemical and Biological Engineering, Department of
Graduate
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Erwin, Samantha H. "Mathematical Models of Immune Responses to Infectious Diseases." Diss., Virginia Tech, 2017. http://hdl.handle.net/10919/77026.
Full textAbstract:
In this dissertation, we investigate the mechanisms behind diseases and the immune responses required for successful disease resolution in three projects: i) A study of HIV and HPV co-infection, ii) A germinal center dynamics model, iii) A study of monoclonal antibody therapy. We predict that the condition leading to HPV persistence during HIV/HPV co-infection is the permissive immune environment created by HIV, rather than the direct HIV/HPV interaction. In the second project, we develop a germinal center model to understand the mechanisms that lead to the formation of potent long-lived plasma. We predict that the T follicular helper cells are a limiting resource and present possible mechanisms that can revert this limitation in the presence of non-mutating and mutating antigen. Finally, we develop a pharmacokinetic model of 3BNC117 antibody dynamics and HIV viral dynamics following antibody therapy. We fit the models to clinical trial data and conclude that antibody binding is delayed and that the combined effects of initial CD4 T cell count, initial HIV levels, and virus production are strong indicators of a good response to antibody immunotherapy.Ph. D.