abstract: In complex consumer-resource type systems, where diverse individuals are interconnected and interdependent, one can often anticipate what has become known as the tragedy of the commons, i.e., a situation, when overly efficient consumers exhaust the common resource, causing collapse of the entire population. In this dissertation I use mathematical modeling to explore different variations on the consumer-resource type systems, identifying some possible transitional regimes that can precede the tragedy of the commons. I then reformulate it as a game of a multi-player prisoner's dilemma and study two possible approaches for preventing it, namely direct modification of players' payoffs through punishment/reward and modification of the environment in which the interactions occur. I also investigate the questions of whether the strategy of resource allocation for reproduction or competition would yield higher fitness in an evolving consumer-resource type system and demonstrate that the direction in which the system will evolve will depend not only on the state of the environment but largely on the initial composition of the population. I then apply the developed framework to modeling cancer as an evolving ecological system and draw conclusions about some alternative approaches to cancer treatment. / Dissertation/Thesis / Ph.D. Applied Mathematics for the Life and Social Sciences 2012

On constate que la majorité des essais de phase III, conduits après des essais de phase II pourtant prometteurs, sont “négatifs”, la nouvelle thérapeutique se révélant finalement trop toxique ou insuffisamment efficace. L’hétérogénéité de la population participant aux différentes phases de développement est une explication. Elle induirait une estimation erronée de la toxicité et, par dilution de l’effet traitement, conduirait à arrêter l’évaluation thérapeutique alors que peut être un sous-ensemble de cette population, définie à partir d’une caractéristique particulière, pourrait en bénéficier.Dans cette thèse, nous proposons dans un premier temps une réflexion sur les aspects méthodologiques des essais de phase II qui permettraient d’améliorer l’identification précoce des thérapeutiques toxiques et des populations les plus sensibles et donc de ne planifier des essais de phase III que sur des populations encore mieux ciblées. Dans un second temps, nous présentons une nouvelle méthodologie d’essai de phase II que nous avons développée pour prendre en compte l’hétérogénéité de la population et son intérêt en pratique clinique courante. Avec cette méthode, qui est une extension du plan de Fleming à deux étapes, le développement des médicaments est moins fréquemment arrêté pour la population entière et moins de patients non sensibles à la nouvelle thérapeutique sont exposés à des molécules potentiellement toxiques, durant l’étape 2 de l’essai de phase II ou plus tard lors de l’essai de phase III. / The majority of phase III clinical trials, despite being conducted after promising phase II trials, are "negative," with the new therapy determined in the end to be too toxic or insufficiently efficacious. One explanation is the heterogeneity of the populations participating in various phases of development, which results in an erroneous estimation of the toxicity and thus a diluted therapeutic effect. This may lead to termination of evaluation of a therapy, even if a sub-population, defined by a particular characteristic, may stand to benefit from it. In this thesis, we propose a close examination of the methodological aspects of phase II trials which would permit improved early identification of toxic therapies and of responsive populations, so that phase III trials may be designed only with the best targeted populations in mind. We present as well a new phase II clinical trial methodology which we have developed to take into account trial population heterogeneity and its importance in current clinical practice. With this method, drug development is less often stopped for the entire phase II population and less non sensitive patients are exposed to toxic drugs in the second part of phase II trials, and next in phase III trials.

[pt] Introdução: A capacidade para realização das atividades instrumentais da vida diária (AIVDs) é um importante marcador dentro um envelhecimento, uma vez que reflete o grau de independência para atuação no mundo real. No entanto, há uma escassez de estudos que se proponham a investigar os diferentes perfis de desempenho entre idosos. Objetivo: investigar a heterogeneidade presente em idosos da comunidade, agrupando-os a partir de características e padrões observados através de uma avaliação objetiva baseada em desempenho. Método: Participantes foram selecionados conforme critérios de inclusão: fluência no Português; 60 ou mais anos; participação regular no programa de casas de convivência do Rio de Janeiro e ausência de cuidador. A avaliação das AIVDs foi determinada pelo UPSA e UPSA-B e Escala de Lawton e Brody. A Bateria Breve de Rastreio Cognitivo foi utilizada para caracterização da amostra, além da Escala de Depressão Geriátrica. Um total de 61 idosos com idade média de 72,5 anos, predominantemente do sexo feminino (85,2 por cento), e escolaridade média de 11,2 foram avaliados e agrupados de acordo com o seu desempenho no UPSA por meio de uma análise de cluster. Resultados: A análise revelou três padrões de agrupamento de alto médio e baixo funcionamento, subdividindo a amostra em subgrupos que se diferenciaram significativamente em termos de idade, escolaridade, cognição global e todas as atividades instrumentais avaliadas pelo UPSA – planejamento, finanças, comunicação, transporte e habilidades domésticas. Conclusão: O presente estudo foi capaz de identificar a heterogeneidade presente na população idosa entre os diferentes fatores que compõe as AIVDs através de uma avaliação baseada em desempenho. / [en] Introduction: The ability to perform instrumental activities of daily living (IADLs) is an important marker within the aging process, as it reflects the level of independence to act and permorme in the real world. However, there is a scarcity of studies that investigate the different performance profiles among older adults. Objective: to investigate the heterogeneity present in the community s elderly, grouping them based on characteristics and patterns observed through an objective performance-based assessment. Method: Participants were selected according to inclusion criteria: fluency in Portuguese; 60 or more years; regular participation in a social program offered by the government of Rio de Janeiro, and absence of a caregiver. The evaluation of IADLs was determined by UPSA, UPSA-B, and the Lawton IADL scale.The Brief Cognitive Screening Battery was used to characterize the sample, in addition to the Geriatric Depression Scale. A total of 61 elderly people with an average age of 72.5 years, predominantly female (85.2 percent), and average education of 11.2 were evaluated and grouped according to their performance at UPSA through clustering analysis. Results: The analysis revealed three grouping patterns, subdividing the sample into subgroups that differed significantly in terms of age, education, global cognition, and all instrumental activities assessed by UPSA - planning, finance, communication, transportation, and household chores. Conclusion: The present study was able to identify the heterogeneity present between the elderly in the different factors that composes the IADLs through a performance-based assessment.

The overall objective of this work has been to adopt new developments and techniques in the area of measurement, modelling and control of fermentation processes. Flow cytometry and software sensors are techniques which were considered ready for application and the focus was set on developing tools for research aiming at understanding the relationship between measured variables and process quality parameters. In this study fed-batch cultivations have been performed with two different strains of Escherichia coli (E.coli) K12 W3110 with and without a gene for the recombinant protein promegapoietin. Inclusion body formation was followed during the process with flow cytometric detection by labelling the inclusion bodies with first an antibody against the protein promegapoietin and then a second fluorescent anti-antibody. The approach to label inclusion bodies directly in disintegrated and diluted cell slurry could be adopted as a method to follow protein production during the process, although the labelling procedure with incubation times and washings was somewhat time-consuming (1.5 h). The labelling of inclusion bodies inside the cells to follow protein production was feasible to perform, although an unexplained decrease in the relative fluorescence intensity occurred late in process. However, it is difficult to translate this qualitative measurement into a quantitative one, since a quantitative protein analysis should give data proportional to the volume, while the labelling of the spheric inclusion bodies gives a signal corresponding to the area of the body, and calibration is not possible. The methods were shown to be useful for monitoring inclusion body formation, but it seems difficult to get quantitative information from the analysis. Population heterogeneity analysis was performed, by using flow cytometry, on a cell population, which lost 80-90% viability according to viable count analysis. It was possible to show that the apparent cell death was due to cells incapable of dividing on agar plates after induction. These cells continued to produce the induced recombinant protein. It was shown that almost all cells in the population (≈97%) contained PMP, and furthermore total protein analysis of the medium indicated that only about 1% of the population had lysed. This confirms that the "non-viable" cells according to viable count by cfu analysis produced product. The software sensors XNH3 and µNH3, which utilises base titration data to estimate biomass and specific growth rate was shown to correlate well with the off-line analyses during cultivation of E. coli W3110 using minimal medium. In rich medium the µNH3 sensor was shown to give a signal that may be used as a fingerprint of the process, at least from the time of induction. The software sensor KLaC* was shown to respond to foaming in culture that probably was caused by increased air bubble dispersion. The RO/S coefficient, which describes the oxygen to substrate consumption, was shown to give a distinct response to stress caused by lowered pH and addition of the inducing agent IPTG. The software sensor for biomass was applied to a highly automated 6-unit multi-bioreactor system intended for fast process development. In this way also specific rates of substrate and oxygen consumption became available without manual sampling. / QC 20100819

Biotechnological processes are distinguished from classical chemistry by employing bio-molecules or whole cells as the catalytic element, providing unique reaction mechanisms with unsurpassed specificity. Whole cells are the most versatile \'factories\' for natural or non-natural products, however, the conversion of e.g. hydrophobic substrates can quickly become cytotoxic. One host organism with the potential to handle such conditions is the gram-negative bacterium Pseudomonas putida, which distinguishes itself by solvent tolerance, metabolic flexibility, and genetic amenability. However, whole cell bioconversions are highly complex processes. A typical bottleneck compared to classical chemistry is lower yield and reproducibility owing to cell-to-cell variability. The intention of this work was therefore to characterize a model producer strain of P. putida KT2440 on the single cell level to identify non-productive or impaired subpopulations. Flow cytometry was used in this work to discriminate subpopulations regarding DNA content or productivity, and further mass spectrometry or digital PCR was employed to reveal differences in protein composition or plasmid copy number. Remarkably, productivity of the population was generally bimodally distributed comprising low and highly producing cells. When these two subpopulations were analyzed by mass spectrometry, only few metabolic changes but fundamental differences in stress related proteins were found. As the source for heterogeneity remained elusive, it was hypothesized that cell cycle state may be related to production capacity of the cells. However, subpopulations of one, two, or higher fold DNA content were virtually identical providing no clear hints for regulatory differences. On the quest for heterogeneity the loss of genetic information came into focus. A new work flow using digital PCR was created to determine the absolute number of DNA copies per cell and, finally, lack of expression could be attributed to loss of plasmid in non-producing cells. The average plasmid copy number was shown to be much lower than expected (1 instead of 10-20). In conclusion, this work established techniques for the quantification of proteins and DNA in sorted subpopulations, and by these means provided a highly detailed picture of heterogeneity in a microbial population.

The utilization of mathematical tools within biology and medicine has traditionally been less widespread compared to other hard sciences, such as physics and chemistry. However, an increased need for tools such as data processing, bioinformatics, statistics, and mathematical modeling, have emerged due to advancements during the last decades. These advancements are partly due to the development of high-throughput experimental procedures and techniques, which produce ever increasing amounts of data. For all aspects of biology and medicine, these data reveal a high level of inter-connectivity between components, which operate on many levels of control, and with multiple feedbacks both between and within each level of control. However, the availability of these large-scale data is not synonymous to a detailed mechanistic understanding of the underlying system. Rather, a mechanistic understanding is gained first when we construct a hypothesis, and test its predictions experimentally. Identifying interesting predictions that are quantitative in nature, generally requires mathematical modeling. This, in turn, requires that the studied system can be formulated into a mathematical model, such as a series of ordinary differential equations, where different hypotheses can be expressed as precise mathematical expressions that influence the output of the model. Within specific sub-domains of biology, the utilization of mathematical models have had a long tradition, such as the modeling done on electrophysiology by Hodgkin and Huxley in the 1950s. However, it is only in recent years, with the arrival of the field known as systems biology that mathematical modeling has become more commonplace. The somewhat slow adaptation of mathematical modeling in biology is partly due to historical differences in training and terminology, as well as in a lack of awareness of showcases illustrating how modeling can make a difference, or even be required, for a correct analysis of the experimental data. In this work, I provide such showcases by demonstrating the universality and applicability of mathematical modeling and hypothesis testing in three disparate biological systems. In Paper II, we demonstrate how mathematical modeling is necessary for the correct interpretation and analysis of dominant negative inhibition data in insulin signaling in primary human adipocytes. In Paper III, we use modeling to determine transport rates across the nuclear membrane in yeast cells, and we show how this technique is superior to traditional curve-fitting methods. We also demonstrate the issue of population heterogeneity and the need to account for individual differences between cells and the population at large. In Paper IV, we use mathematical modeling to reject three hypotheses concerning the phenomenon of facilitation in pyramidal nerve cells in rats and mice. We also show how one surviving hypothesis can explain all data and adequately describe independent validation data. Finally, in Paper I, we develop a method for model selection and discrimination using parametric bootstrapping and the combination of several different empirical distributions of traditional statistical tests. We show how the empirical log-likelihood ratio test is the best combination of two tests and how this can be used, not only for model selection, but also for model discrimination. In conclusion, mathematical modeling is a valuable tool for analyzing data and testing biological hypotheses, regardless of the underlying biological system. Further development of modeling methods and applications are therefore important since these will in all likelihood play a crucial role in all future aspects of biology and medicine, especially in dealing with the burden of increasing amounts of data that is made available with new experimental techniques. / Användandet av matematiska verktyg har inom biologi och medicin traditionellt sett varit mindre utbredd jämfört med andra ämnen inom naturvetenskapen, såsom fysik och kemi. Ett ökat behov av verktyg som databehandling, bioinformatik, statistik och matematisk modellering har trätt fram tack vare framsteg under de senaste decennierna. Dessa framsteg är delvis ett resultat av utvecklingen av storskaliga datainsamlingstekniker. Inom alla områden av biologi och medicin så har dessa data avslöjat en hög nivå av interkonnektivitet mellan komponenter, verksamma på många kontrollnivåer och med flera återkopplingar både mellan och inom varje nivå av kontroll. Tillgång till storskaliga data är emellertid inte synonymt med en detaljerad mekanistisk förståelse för det underliggande systemet. Snarare uppnås en mekanisk förståelse först när vi bygger en hypotes vars prediktioner vi kan testa experimentellt. Att identifiera intressanta prediktioner som är av kvantitativ natur, kräver generellt sett matematisk modellering. Detta kräver i sin tur att det studerade systemet kan formuleras till en matematisk modell, såsom en serie ordinära differentialekvationer, där olika hypoteser kan uttryckas som precisa matematiska uttryck som påverkar modellens output. Inom vissa delområden av biologin har utnyttjandet av matematiska modeller haft en lång tradition, såsom den modellering gjord inom elektrofysiologi av Hodgkin och Huxley på 1950‑talet. Det är emellertid just på senare år, med ankomsten av fältet systembiologi, som matematisk modellering har blivit ett vanligt inslag. Den något långsamma adapteringen av matematisk modellering inom biologi är bl.a. grundad i historiska skillnader i träning och terminologi, samt brist på medvetenhet om exempel som illustrerar hur modellering kan göra skillnad och faktiskt ofta är ett krav för en korrekt analys av experimentella data. I detta arbete tillhandahåller jag sådana exempel och demonstrerar den matematiska modelleringens och hypotestestningens allmängiltighet och tillämpbarhet i tre olika biologiska system. I Arbete II visar vi hur matematisk modellering är nödvändig för en korrekt tolkning och analys av dominant-negativ-inhiberingsdata vid insulinsignalering i primära humana adipocyter. I Arbete III använder vi modellering för att bestämma transporthastigheter över cellkärnmembranet i jästceller, och vi visar hur denna teknik är överlägsen traditionella kurvpassningsmetoder. Vi demonstrerar också frågan om populationsheterogenitet och behovet av att ta hänsyn till individuella skillnader mellan celler och befolkningen som helhet. I Arbete IV använder vi matematisk modellering för att förkasta tre hypoteser om hur fenomenet facilitering uppstår i pyramidala nervceller hos råttor och möss. Vi visar också hur en överlevande hypotes kan beskriva all data, inklusive oberoende valideringsdata. Slutligen utvecklar vi i Arbete I en metod för modellselektion och modelldiskriminering med hjälp av parametrisk ”bootstrapping” samt kombinationen av olika empiriska fördelningar av traditionella statistiska tester. Vi visar hur det empiriska ”log-likelihood-ratio-testet” är den bästa kombinationen av två tester och hur testet är applicerbart, inte bara för modellselektion, utan också för modelldiskriminering. Sammanfattningsvis är matematisk modellering ett värdefullt verktyg för att analysera data och testa biologiska hypoteser, oavsett underliggande biologiskt system. Vidare utveckling av modelleringsmetoder och tillämpningar är därför viktigt eftersom dessa sannolikt kommer att spela en avgörande roll i framtiden för biologi och medicin, särskilt när det gäller att hantera belastningen från ökande datamängder som blir tillgänglig med nya experimentella tekniker.

Biotechnological processes are distinguished from classical chemistry by employing bio-molecules or whole cells as the catalytic element, providing unique reaction mechanisms with unsurpassed specificity. Whole cells are the most versatile \''factories\'' for natural or non-natural products, however, the conversion of e.g. hydrophobic substrates can quickly become cytotoxic. One host organism with the potential to handle such conditions is the gram-negative bacterium Pseudomonas putida, which distinguishes itself by solvent tolerance, metabolic flexibility, and genetic amenability. However, whole cell bioconversions are highly complex processes. A typical bottleneck compared to classical chemistry is lower yield and reproducibility owing to cell-to-cell variability. The intention of this work was therefore to characterize a model producer strain of P. putida KT2440 on the single cell level to identify non-productive or impaired subpopulations. Flow cytometry was used in this work to discriminate subpopulations regarding DNA content or productivity, and further mass spectrometry or digital PCR was employed to reveal differences in protein composition or plasmid copy number. Remarkably, productivity of the population was generally bimodally distributed comprising low and highly producing cells. When these two subpopulations were analyzed by mass spectrometry, only few metabolic changes but fundamental differences in stress related proteins were found. As the source for heterogeneity remained elusive, it was hypothesized that cell cycle state may be related to production capacity of the cells. However, subpopulations of one, two, or higher fold DNA content were virtually identical providing no clear hints for regulatory differences. On the quest for heterogeneity the loss of genetic information came into focus. A new work flow using digital PCR was created to determine the absolute number of DNA copies per cell and, finally, lack of expression could be attributed to loss of plasmid in non-producing cells. The average plasmid copy number was shown to be much lower than expected (1 instead of 10-20). In conclusion, this work established techniques for the quantification of proteins and DNA in sorted subpopulations, and by these means provided a highly detailed picture of heterogeneity in a microbial population.

An object-oriented framework is presented for developing and simulating individual-based models of cell populations. The framework supplies classes to define objects called simulation channels that encapsulate the algorithms that make up a simulation model. These may govern state-updating events at the individual level, perform global state changes, or trigger cell division. Simulation engines control the scheduling and execution of collections of simulation channels, while a simulation manager coordinates the engines according to one of two scheduling protocols. When the ensemble of cells being simulated reaches a specified maximum size, a procedure is introduced whereby random cells are ejected from the simulation and replaced by newborn cells to keep the sample population size constant but representative in composition. The framework permits recording of population snapshot data and/or cell lineage histories. Use of the framework is demonstrated through validation benchmarks and two case studies based on experiments from the literature.

An object-oriented framework is presented for developing and simulating individual-based models of cell populations. The framework supplies classes to define objects called simulation channels that encapsulate the algorithms that make up a simulation model. These may govern state-updating events at the individual level, perform global state changes, or trigger cell division. Simulation engines control the scheduling and execution of collections of simulation channels, while a simulation manager coordinates the engines according to one of two scheduling protocols. When the ensemble of cells being simulated reaches a specified maximum size, a procedure is introduced whereby random cells are ejected from the simulation and replaced by newborn cells to keep the sample population size constant but representative in composition. The framework permits recording of population snapshot data and/or cell lineage histories. Use of the framework is demonstrated through validation benchmarks and two case studies based on experiments from the literature.

An object-oriented framework is presented for developing and simulating individual-based models of cell populations. The framework supplies classes to define objects called simulation channels that encapsulate the algorithms that make up a simulation model. These may govern state-updating events at the individual level, perform global state changes, or trigger cell division. Simulation engines control the scheduling and execution of collections of simulation channels, while a simulation manager coordinates the engines according to one of two scheduling protocols. When the ensemble of cells being simulated reaches a specified maximum size, a procedure is introduced whereby random cells are ejected from the simulation and replaced by newborn cells to keep the sample population size constant but representative in composition. The framework permits recording of population snapshot data and/or cell lineage histories. Use of the framework is demonstrated through validation benchmarks and two case studies based on experiments from the literature.