Dans le domaine automobile, intégrer de plus en plus de matériaux composites recyclés tout en améliorant les performances initiales et en diminuant les masses emportées devient un compromis auquel il faut répondre. Par ailleurs, les pièces de structures en matériaux composites destinées au crash sont souvent soumises à des conditions environnementales, notamment des températures modérément élevées, pouvant produire une dégradation physico-chimique progressive. Ainsi, pour assurer une meilleure conception et une durabilité des pièces, il est primordial de bien cerner l’influence du vieillissement thermique sur les propriétés dynamiques des matériaux. Dans ce but, ce travail vise à coupler la physique de la cinétique de dégradation par oxydation et le comportement mécanique multi-échelles d’un nouveau matériau composite totalement issu du recyclage à renfort carbone et matrice à base polypropylène. Le premier axe de l’étude est dédié à l’élaboration, la caractérisation physicochimique, microstructurale et mécanique de plusieurs formulations de composites. Une fois le composite optimal sélectionné, une méthodologie hybride, expérimentale et numérique, visant à caractériser les propriétés dynamiques rapides allant jusqu’à des vitesses de déformation de 100 s-1 est développée. Le deuxième axe de ce travail est focalisé sur l’étude de l’influence de la thermo-oxydation sur les propriétés physico-chimique et mécaniques à différentes vitesses de sollicitation du composite optimal et sa matrice. L’ensemble des données expérimentales issues du vieillissement a permis l’identification d’un modèle cinétique basé sur un schéma mécanistique de l’oxydation des matériaux vieillis. D’autre part, une étude qualitative et quantitative de l’effet du vieillissement sur les mécanismes d’endommagement a été réalisée à l’échelle microscopique visant à mettre en place une loi d’endommagement reliant, pour une déformation imposée donnée, le taux d’endommagement local à la concentration des produits d’oxydation. Les résultats de cette étude mettent en évidence la possibilité de développer des lois de comportement affectés par les paramètres de modèles cinétiques décrivant l’évolution de l’état physico-chimique du composite au cours du vieillissement. / In the automotive sector, integrating more and more recycled composite materials while improving the initial performance and decreasing the carried masses becomes a compromise that needs to be addressed. Moreover, structural parts made of composite materials intended for crash are often subjected to environmental conditions, including moderately high temperatures, capable of causing gradual physico-chemical degradation. Thus, to ensure better design and durability of parts, it is important to understand the influence of thermal aging on the dynamic properties of materials. To this end, this work aims to couple the physics of oxidative degradation kinetics and the multi-scales mechanical behavior of a new fully recycled composite based on a polypropylene matrix and carbon fibers. The first axis of the study is dedicated to the elaboration, the physicochemical, microstructural and mechanical characterization of several formulations of composites. Once the optimal composite is selected, a hybrid experimental and numerical methodology is s is developed in order to characterize the dynamic properties at high strain rates reaching 100 s-1. The second axis of this work is focused on the study of the influence of thermo-oxidation on the physicochemical and mechanical properties at different strain rates of the optimal composite and its matrix. The resulting experimental has allowed the identification of a kinetic model parameters based on a mechanistic scheme. Furthermore, a qualitative and quantitative study of the effect of aging on the damage mechanisms has been carried out at a microscopic scale in order to establish a damage law linking, for a given imposed strain, the local damage density to the concentration of the oxidation products. The results of this study highlight the possibility of developing behavioral laws affected by the parameters of kinetic models describing the evolution of the physicochemical state of the composite during aging.

In dieser Arbeit wird eine detaillierte Analysis des konsistenten kinetischen Modells zum Kornwachstum von Fradkov durchgeführt. Dieses Modell beschreibt - basierend auf dem von Neumann--Mullins Gesetz - die Flächenänderung eines Korns abhängig von seiner Topologieklasse, d.h. der Anzahl der Kanten. Topologieänderungen werden durch Kopplungsterme zwischen den Gleichungen für die Anzahldichten der verschiedenen Topologieklassen beschrieben. Daraus resultiert ein unendlich-dimensionales System von Transportgleichungen mit tridiagonaler Kopplungsstruktur. Durch eine spezielle Wahl des Kopplungsgewichts, welche die Gleichungen nichtlinear und räumlich nichtlokal macht, wird das Modell konsistent. Nach einer Einführung wird das Modell von Fradkov im zweiten Kapitel hergeleitet; formale Rechnungen zeigen die Konsistenz des Modells auf. Im dritten Kapitel wird das Kopplungsgewicht a priori beschränkt. Dadurch kann im ersten Teil des vierten Kapitels Existenz und Eindeutigkeit von Lösungen für endlich-dimensionale Systeme gezeigt werden. Weitere Schranken an die Anzahldichten im fünften Kapitel ermöglichen den Grenzübergang hinsichtlich der Anzahl der Gleichungen im zweiten Teil des vierten Kapitels. Die Existenz von Lösungen des unendlich-dimensionalen Systems wird somit über eine geeignete Approximation gezeigt. Energiemethoden liefern Eindeutigkeit und stetige Abhängigkeit von den Daten. Im sechsten Kapitel wird das Langzeitverhalten untersucht. Besonderes Augenmerk liegt dabei auf stationären Lösungen eines reskalierten Systems als Kandidaten für selbstähnliche Lösungen. Abschließend wird das Lewis''sche Gesetz asymptotisch verifiziert. / The subject matter of this thesis is a detailed analysis of the self--consistent kinetic model for grain growth introduced by Fradkov. The model is based on the von Neumann--Mullins law describing the change of area of grains according to their topological class, i.e. the number of edges they have. Topological events are performed by coupling terms between equations for the number densities of different topological classes. The resulting system of transport equations is infinite-dimensional with a tridiagonal coupling structure. Self-consistency of this kinetic model is achieved by introducing a coupling''s weight making the equations nonlinear and nonlocal in space. We start with an introduction in the first chapter. Afterwards in the second chapter we derive Fradkov''s model and carry out formal calculations to illustrate self-consistency. In the third chapter we present a priori calculations mainly allowing us to bound the nonlinearity. This enables us to prove existence and uniqueness of solutions to finite-dimensional systems in the first part of the fourth chapter. Further bounds on the number densities established in the fifth chapter allow for passing to the limit concerning the number of equations in the second part of the fourth chapter. Therefore we prove existence of solutions to the infinite-dimensional system by a suitable approximation procedure. Uniqueness and continuous dependence on the data is then provided by energy methods. The sixth chapter focusses on long-time behaviour and mainly on stationary solutions of a rescaled system as candidates for self-similar solutions. Finally we prove Lewis'' law asymptotically.

The objective of this study is to investigate the influence of sulfur compounds (S and Na2S) for powdered activated carbon derived from carbon black of pyrolyzed waste tires (CPBAC). Besides, this study investigated the distribution of impregnated sulfur in the inner pores of activated carbon and its effected on the specific surface area and pore size distribution. This study investigated the fundamental mechanisms by analysis of thermodynamic properties and to establish the kinetic models for the adsorption/desorption of HgCl2 by/from sulfur impregnated CBPAC. Furthermore, this study investigated the adsorptive and desorption capacity of HgCl2 onto CPBAC via thermogravimetric analysis (TGA). Experimental results indicated that the specific surface area of sulfur impregnated CBPAC with elemental S (S0) was larger than sulfur impregnated CBPAC with Na2S. Besides, the sulfur content of sulfur impregnated CBPAC increased with increasing the surface area of CBPAC under the same impregnated temperature. And, the adsorptive capacity of CBPAC increased with the increase of influent HgCl2 concentration and surface area of the activated carbon. According to the experimental results of the adsorption capacity under the differential sulfur content, its indicated that the affection of sulfur content for adsorption capacity of HgCl2 was much than HgCl2 concentration and surface area of the activated carbon. The desorption energys were 266 and 282 kJ/mole for HgCl2 desorption from saturated CBPAC-S0 and CBPAC-Na2S, respectively. The results showed the process of HgCl2 adsorption onto CBPAC was in favor of a physisorbed state of HgCl2 at the adsorption temperature of 150 oC but the process of HgCl2 adsorption onto CBPAC which impregated was in favor of a chemisorbed state of HgCl2 at the adsorption of 150 oC. The value of ∆G for CBPAC at the adsorption temperature of 30 ~150 oC were ranged from -15.28 kJ/mole to -26.63 kJ/mole. The value of ∆G for CBPAC-S0 at the adsorption temperature of 30~150 oC ranged from -23.45 kJ/mole to -32.09 kJ/mole. The value of ∆G for CBPAC-Na2S at the adsorption temperature of 30~150 oC ranged from -22.84 kJ/mole to -32.72 kJ/mole. The results showed negative values of ∆G confirmed the feasibility of adsorption process and the spontaneous nature for the adsorption of HgCl2. The value of ∆H for CBPAC at the adsorption temperature of 30 ~150 oC ranged from -35.58 kJ/mole to -35.82 kJ/mole. The value of ∆H for CBPAC-S0 at the adsorption temperature of 30 ~150 oC ranged from -38.07 kJ/mole to -52.49 kJ/mole. The value of ∆H for CBPAC-Na2S at the adsorption temperature of 30~150 oC was -37.45 kJ/mole to -53.12 kJ/mole. A negative ∆H suggested that the adsorption of HgCl2 is an exothermic process. Besides, the adsorptive behavior of HgCl2 for two activated carbons (CBPAC-Na2S and CBPAC-S0) at high temperature (110 ¢J and 150 ¢J ) was the same chemical reaction mechanism due to the same ∆H. Besides, the results of model simulation indicated that modified adsorption kinetic model based on pore diffusion scheme developed in this study could successfully simulate the transport and adsorption of HgCl2 by considering the chemical reaction within the inner pores of carbon grains at 150 oC.

This study combined photocatalytic technology with activated carbon cellulose-paper filter (ACCF) adsorption to decompose gaseous pollutants. Gaseous pollutants were initially adsorbed by activated carbon and could be further decomposed by photocatalytic technology. This study selected acetone (CH3COCH3) as gaseous pollutants. Two market available photocatalysts (photocatalysts¢¹and¢º) were coated on ACCF by impregnation to decompose acetone in a batch photocatlytic reactor. Operating parameters investigated in this study included initial acetone concentration (4.1~10.2 £gM), reaction temperature (40~70¢J), and water vapor (0~20 %). The incident UV light of 365 nm was irradiated by a 20-watt low-pressure mercury lamp placing above the batch photocatalytic reactor. The ACCF coated with TiO2 was placed at the center of the photocatalytic reactor. Acetone was injected into the reactor by a gasket syringe to conduct the photocatalytic tests. Reactants and products were analyzed quantitatively by a gas chromatography with an electron capture detector (GC/DCD) and a flame ionization detector followed by a methaneizer (GC/FID-Methaneizer). Finally, a Langmiur-Hinshewood (L-H) kinetic model was proposed to describe the rate of photocatalytic reaction. Results obtained from the photocatalytic tests indicated that photocatalyst¢º was better than photocatalyst¢¹ for the decomposition of acetone. Experimental results indicated that the size range of self-produced TiO2 photocatalyst by sol-gel was 20~70 nm. The end products were mainly CO and CO2, which resulted in the mineralization ratio up to 98%. Results obtained from the operating parameter tests revealed that the increase of initial acetone concentration enhanced the amount of acetone adsorbed on ACCF, which however did not increase the reaction rate of acetone. Although the increase of reaction temperature could reduce the amount of acetone adsorbed on ACCF, the decomposition rate of acetone could be promoted, so as the yield rate and mineralization ratio of products (CO and CO2). The increase of water vapor could slightly decrease the amount of acetone adsorbed on ACCF. The competitive adsorption phenomenon between acetone and water molecules on active sites could decelerate the decomposion of acetone. Moreover, the ACCF would not be saturated since the adsorbed acetone could be further decomposed quickly by the photocatalysts, which made the TiO2/ACCF more effective on removing acetone and lasted longer than the conventional ACCF. Finally, a modified bimolecular Langmuir-Hinshelwood kinetic model was developed to investigate the influences of initial acetone concentration reaction, temperature, and relative humidity on the promotion and inhibition for the photocatalytic oxidation of acetone. The modified L-H kinetic model could successfully simulate the photocatalytic reaction rate of acetone. Thus, the reaction rate of acetone over TiO2/ACCF could be described by the modified L-H kinetic model.

Pharmacodynamic studies are important for the optimal use of antimicrobial agents. Combination antifungal therapy may be one method to improve outcome in invasive Candida infections. An in vitro kinetic model to study the pharmacodynamic effects of a combination of two antifungal agents with different elimination rates was developed and the pharmacodynamics of amphotericin B (AMB), voriconazole (VRC) or the combination was evaluated. Exposure to VRC inhibited the fungicidal activity of sequential doses of AMB against VRC-susceptible strains of C. albicans. The interaction was VRC dose-dependent. AMB activity was regained once VRC was removed or it increased gradually when the concentration of VRC had fallen below the minimum inhibitory concentration (MIC). The VRC-AMB interaction, however, was also present against strains of C. albicans, C. glabrata and C. krusei despite reduced VRC susceptibility. Against these strains the interaction was not predicted by the MIC value, suggesting that mechanisms of resistance may be of importance. Until more data are available, a reasonable recommendation is probably to avoid the sequential use of VRC followed by AMB and to use the combination of VRC and AMB for the treatment of Candida infections with caution. Only the unbound fraction of a drug is generally accepted as pharmacologically active. The activity of posaconazole (POS) with a protein binding of 98-99% was tested in serum against Candida species and compared with the calculated unbound serum concentration in protein-free media. Significant differences emerged at clinically relevant POS serum concentrations of 1.0 and 0.10 mg/l compared with the serum control regimen against one strain of C. lusitaniae. In RPMI 1640 the corresponding calculated unbound concentrations resulted in no effect for the low dose regimen compared with the RPMI 1640 control regimen. Further, against seven additional Candida strains tested, the effect of POS was greater in serum than in RPMI 1640. A flux from serum protein bound to fungal lanosterol 14α-demethylase bound POS may be the explanatory mechanism.

Abstract In the sugar platform of biorefining, the complex polymeric structure of lignocellulose biomass is degraded into sugars, which are utilized by microbial cells in the further processing steps. The reaction steps in both biomass degradation and microbial fermentation processes involve multiphase reactions in which mass transfer and reaction kinetics often play a key role. The aim of this thesis is to characterize the effect of these conditions on enzymatic hydrolysis of cellulose and utilization of sugars by aerobic microbes. These types of liquid-solid (cellulose hydrolysis) and liquid-gas (microbial cultivation) systems are typically very demanding on the reactors that are used in the process. By the fed-batch process utilized in this work, sufficient mixing in enzymatic hydrolysis of cellulose is achieved even with high final substrate concentration. One of the main outcomes of this work is the kinetic model that concentrates on the kinetics of fed-batch process by discretizing the substrate into subpopulations. By using this approach, the model parameters were identified in an adequate manner, and the poorly identified parameters could be sorted out. Parameter identifiability has been an issue in previous models for enzymatic hydrolysis of cellulose. Based on the experiments and modelling studies, it can be concluded that the enzymes remain intact for time scales relevant for the hydrolysis process. Thus, the decrease in the hydrolysis rate found in many literature studies is probably mostly due to substrate-enzyme interactions rather than denaturation of the enzyme. In aerobic cell cultivations, the mixing and mass transfer conditions are often more critical for the process performance. In this work, we studied the performance and suitability of alternative reactor types to be used in aerobic cell cultivations and obtained some promising results. In addition, the thesis presents a modelling approach to study the effect of process conditions on metabolism and growth rate of Pichia pastoris yeast. The model combines a kinetic model for yeast growth and a model for the mixing and mass transfer conditions in stirred tank reactor. / Tiivistelmä Biojalostuksen sokerialustassa lignoselluloosapohjaisen biomassan monimutkaista polymeerirakennetta muokataan ja sieltä vapautetaan monomeerisia sokereita, joita voidaan edelleen hyödyntää jatkojalostuksessa. Monet jatkojalostusprosessit käyttävät mikrobeja, joiden aineenvaihdunnassa sokereita voidaan jalostaa arvokkaammiksi tuotteiksi ns. fermentointiprosesseissa. Tämän väitöstyön tarkoitus on tutkia reaktio- ja aineensiirtokinetiikan vaikutusta selluloosan entsymaattiseen hydrolyysiin ja aerobisiin mikrobifermentointeihin. Näistä ensimmäinen on neste-kiintoainesysteemi ja jälkimmäinen neste-kaasusysteemi, ja tällaiset prosessit asettavat tyypillisesti merkittäviä vaatimuksia niissä käytettäville reaktoreille. Tässä työssä hyödynnettiin kiinteän raaka-aineen vähittäistä syöttöä (ns. fed-batch prosessi) selluloosan hydrolyysissä, jolloin sekoitus voidaan pitää riittävänä suurillakin kiintoainemäärillä. Työn merkittävin tuotos on kineettinen malli, jossa hyödynnetään fed-batch prosessia ja koedataa osittamalla mallinnusyhtälöt raaka-aineen syöttöajan perusteella. Tällä tavalla mallin parametrit saatiin identifioitua kohtuullisella tarkkuudella sekä eriteltyä huonosti identifioituneet parametrit. Mallin parametrien identifiointi on ollut ongelmallista monissa vastaavan tyyppisissä malleissa aiemmin. Kokeiden ja mallinnustulosten perusteella voidaan sanoa, että hydrolyysissä käytettävät entsyymit pysyvät aktiivisina prosessin aikana, ja usein todettu hydrolyysin hidastuminen johtuu ennemmin kiinteän kuidun ja entsyymien vuorovaikutuksen muutoksista kuin entsyymin denaturoitumisesta. Aerobisiin mikrobikasvatuksiin liittyen tässä työssä tutkittiin vaihtoehtoisten reaktorityyppien hyödyntämistä, joista saatiin myös lupaavia tuloksia. Lisäksi työssä kehitettiin mallinnustyökaluja, joilla voidaan tutkia prosessiolosuhteiden vaikutusta Pichia pastoris –hiivan metaboliaan ja kasvunopeuteen. Mallissa yhdistetään hiivan kasvun kineettinen malli sekä reaktoriolosuhteiden mallinnus.

Les polyamides sont des thermoplastiques techniques qui entrent dans la conception de pièces destinées à remplacer certains composants métalliques des moteurs automobiles. En dépit de propriétés mécaniques initiales satisfaisantes, leur tenue à long terme est limitée par leur sensibilité à l'oxygène conduisant à des réactions de thermo-oxydation. Ces réactions ont été largement étudiées dans le cas des polyoléfines mais peu dans le cas des polyamides, rendant nécessaire l'élaboration d'un modèle cinétique susceptible de prédire la fragilisation donc la durée de vie des polyamides. Cette thèse est une contribution à la compréhension du processus d'oxydation dans le cas des polyamides aliphatiques et à la construction d'un modèle cinétique. La démarche cinétique réside tout d'abord dans la caractérisation physico-chimique multi-échelle de films de PA11 oxydés dans différentes conditions de températures (90 à 165 °C sous air) et sous différentes pressions partielles d'oxygène. Un modèle cinétique couplant oxydation et post-polycondensation est proposé ici : il permet de simuler les données expérimentales (hydroperoxydes, carbonyles et masse molaires) quelles que soient les conditions d'exposition. Parallèlement, un critère intrinsèque gouvernant la fragilisation du PA11 est identifié afin de prédire cette dernière à partir du modèle cinétique. Enfin, l'influence de l'ajout d'antioxydants phénoliques et des sels de cuivre sur la cinétique d'oxydation est caractérisée. Un premier modèle cinétique prenant en compte la stabilisation du PA11 décrit les tendances spécifiques de la stabilisation du PA11 comme l'apparition de la pseudo-période d'induction contribuant à une augmentation significative de la durée de vie du PA11. / Some metal components of automotive engine are bound to be replaced by polyamide parts. However, despite their thermal resistance polyamides are sensitive to oxygen leading to thermal oxidation chain reactions responsible for their long-term properties. While durability is critical for polyamide users, only a few studies deal with the elaboration of a kinetic model capable of predicting polyamide lifetime (time to embrittlement) in contrary to polyolefins (especially polyethylene). This PhD thesis is a contribution to the understanding of aliphatic polyamide thermal degradation by considering chemical and physical aspects of oxidation process in order to build a kinetic model. Our approach is based on a multi-scale physicochemical characterization of oxidized PA11 film samples under air between 90 and 165 °C but also under oxygen pressure. The proposed kinetic model coupling oxidation and solid state polymerization is able to simulate the whole experimental data (hydroperoxides, carbonyls and molar mass changes). In a same time, an intrinsic criterion for embrittlement is assessed to predict lifetime whatever the exposure conditions. Finally, the influence of phenols and copper salts on the oxidation kinetic is investigated. A first kinetic model including the phenol stabilizing effect is capable of simulating the main observed trends for stabilized PA11 such as the appearance of the pseudo induction period which contributes to the significant improvement of PA11 durability.

Le butadiène est une molécule d’intérêt industriel qui peut être produite par le procédé dit Ostromislensky, avec l’éthanol en tant que matière première. Cette étude a pour objectif de développer un modèle cinétique pour expliquer la transformation d’un mélange éthanol/acétaldéhyde en butadiène, dans le cadre de la seconde étape de ce procédé. Le modèle cinétique est basé sur un schéma réactionnel et un modèle de réacteur. Le schéma proposé comprend la voie de Gorin Jones, communément acceptée dans la littérature, et une toute nouvelle voie impliquant un intermédiaire buténone. Les étapes clés ont été étudiées spécifiquement via des tests dédiés. Le schéma décrit aussi les étapes amenant aux principaux produits secondaires. Il a été validé à partir d’une base de données expérimentale, générée en amont de l’étude sur une unité de type gaz/solide, lit fixe, isobare (3 bara) et isotherme, avec un catalyseur Ta2O5 SiO2. L’influence des conditions opératoires sur l’effluent a été observée pour trois ratios éthanol/acétaldéhyde et sur des gammes de PPH (1,1 à 8,1 g·gcata 1·h-1) et de températures (320 à 370 °C). Le réacteur (piston dispersif sans limitations diffusionnelles) intégrant des lois cinétiques d’ordre, a été modélisé à l’état permanent via un solveur LSODE. Les paramètres cinétiques ont été estimés via un optimiseur Levenberg Marquardt à partir de la base de données expérimentale. Le modèle cinétique obtenu, basé sur un schéma réactionnel inédit, est en capacité de représenter et de prédire les débits des composés principaux et les tendances et ordre de grandeurs des débits des composés minoritaires selon les effets de PPH, de charge et de température, excepté dans certaines conditions opératoires limites isolées / Butadiene is a molecule of industrial interest that can be produced by the so-called Ostromislensky process, with ethanol as raw material. This study aims to develop a kinetic model to explain the transformation of an ethanol/acetaldehyde mixture into butadiene, as part of the second step of this process. The kinetic model is based on a reaction scheme and a reactor model. The proposed scheme includes the commonly accepted Gorin Jones pathway and a new pathway involving a butenone intermediate. The key steps were specifically studied via dedicated experiments. The scheme describes also steps leading to by products. It was validated from an experimental database, generated upstream of the study on a gas / solid type unit, fixed bed, isobaric (3 bara) and isothermal, with a Ta2O5 SiO2 catalyst. The influence of the operating conditions on the effluent was observed for three ethanol/acetaldehyde ratios and over ranges of PPH (1.1 to 8.1 g·gcata 1·h-1) and temperatures (320 to 370 °C). The reactor (plug flow without diffusional limitations) integrating kinetic laws of order, was modeled in the permanent state via a solver LSODE. Kinetic parameters were estimated via a Levenberg Marquardt optimizer from the experimental database. The kinetic model obtained, based on a brand new reaction scheme, is able to represent and predict the flow rates of the main compounds and the trends and orders of magnitude of the flow rates of the minority compounds according to the effects of PPH, charge and temperature, except under certain isolated operating conditions

Thesis (PhD (Biochemistry))--University of Stellenbosch, 2009. / ENGLISH ABSTRACT: The multiplication of cells proceeds through consecutive phases of growth and division (G1, S, G2 and M phases), in a process known as the cell cycle. The transition between these phases is regulated by so-called checkpoints, which are important to ensure proper functioning of the cell cycle. For instance, mutations leading to faulty regulation of the G1/S transition point are seen as one of the main causes of cancer. Traditionally, models for biological systems that show rich dynamic behavior, such as the cell cycle, are studied using dynamical systems analysis. However, using this analysis method one cannot quantify the extent of control of an individual process in the system. To understand system properties at the process level, one needs to employ methods such as metabolic control analysis (MCA). MCA was, however, developed for steady-state systems, and is thus limited to the analysis of such systems, unless the necessary extensions would be made to the framework. The central question of this thesis focuses on quantifying the control in mathematical models of the G1/S transition by the individual cell cycle processes. Since MCA was never applied to the cell cycle, several new methods needed to be added to the framework. The most important extension made it possible to follow and quantify, during a single cell cycle, the control properties of the individual system processes. Subsequently, these newly developed methods were used to determine the control by the individual processes of an important checkpoint in mammalian cells, the restriction point. The positioning of the restriction point in the cell cycle was distributed over numerous system processes, but the following processes carried most of the control: reactions involved in the interplay between retinoblastoma protein (Rb) and E2F transcription factor, reactions responsible for the synthesis of Delayed Response Genes and Cyclin D/Cdk4 in response to growth signals, the E2F dependent Cyclin E/Cdk2 synthesis reaction, as well as the reactions involved in p27 formation. In addition it was shown that these reactions exhibited their control on the restriction point via the Cyclin E/Cdk2/p27 complex. Any perturbation of the system leading to a change in the restriction point could be explained via its e ect on the Cyclin E/Cdk2/p27 complex, showing a causal relation between restriction point positioning and the concentration of the Cyclin E/Cdk2/p27 complex. Finally, we applied the new methods, with a modular approach, to compare a number of cell cycle models for Saccharomyces cerevisiae (budding yeast) and mammalian cells with respect to the existence of a mass checkpoint. Such a checkpoint ensures that cells would have a critical mass at the G1/S transition point. Indeed, in budding yeast, a correction mechanism was observed in the G1 phase, which stabilizes the size of cells at the G1/S transition point, irrespective of changes in the specific growth rate. This in contrast to the mammalian cell cycle models in which no such mass checkpoint could be observed in the G1 phase. In this thesis it is shown that by casting specific questions on the regulation and control of cell cycle transition points in the here extended framework of MCA, it is possible to derive consensus answers for subsets of mathematical models. / AFRIKAANSE OPSOMMING: Die selsiklus bestaan uit agtereenvolgende groei- en delingsiklusse wat tot selvermeerdering lei. Die siklus word gekenmerk deur onderskeie fases (G1, S, G2 en M) wat deur sogenaamde beheerpunte gereguleer word. Hierdie beheerpunte verseker dat selvermeerdering nie ongekontroleerd kan plaasvind nie en mutasies wat lei tot foutiewe regulering van die G1/S transisiepunt word as een van die hoofoorsake van kanker beskou. Die hoofdoel van hierdie studie was om die beheer wat selsiklusprosesse op die G1/S transisie uitoefen met behulp van wiskundige modelle te kwantifiseer. Omdat biologiese sisteme soos die selsiklus ryk dinamiese gedrag vertoon, word hulle tradisioneeldeur middel van dinamiese sisteemanalise bestudeer. Die analisemetode beskik egter nie oor die vermoë om die hoeveelheid beheer wat afsonderlike sisteemprosesse op 0n sisteemeienskap uitoefen te kwantifiseer nie. Om sisteemeienskappe op prosesvlak te verstaan moet metodes soos metaboliese kontrole analise (MKA) ingespan word. MKA was egter ontwikkel om sisteme in 0n bestendige toestand te analiseer en aangesien MKA nog nooit vantevore vir selsiklus analises gebruik was nie, moes nuwe MKA tegnieke gedurende die studie ontwikkel word. Die belangrikste van die metodes maak dit moontlik om beheer (soos uitgeoefen deur die onderskeie sisteemprosesse) oor 0n enkele selsiklus na te volg en te kwantifiseer. Die nuut-ontwikkelde metodes was vervolgens gebruik om te bepaal hoe een so 0n beheerpunt in soogdierselle - die restriksiepunt - deur die onderskeie sisteemprosesse beheer word. Die studie het aangedui dat die posisie van die restriksiepunt tydens die selsiklus deur ’n verskeidenheid sisteemprosesse beheer word. Die bevinding was dat vier prosesse beduidend meer beheer op die posisie van die restriksiepunt uitoefen: Reaksies wat betrekking het op die wisselwerking tussen retinoblastoma proteïen (Rb) en E2F transkripsiefaktor; reaksies verantwoordelik vir die sintese van vertraagde responsgene en Siklien D/Cdk4 in respons tot groeiseine; die E2F afhanklike Siklien E/Cdk2 sintesereaksie; sowel as die reaksies betrokke in p27 vorming. Daar was ook aangetoon dat hierdie reaksies hul beheer op die posisie van die restriksiepunt deur die Siklien E/Cdk2/p27 kompleks uitoefen, siende enige sisteemversteuringe (wat tot veranderinge in die restriksiepuntposisie aanleiding gee) deur veranderinge in die kompleks verklaar kon word - 0n observasie wat aandui dat daar 0n kousale verhouding is tussen die posisie van die restriksiepunt en die Siklien E/Cdk2/p27 kompleks. Die nuut-ontwikkelde metodes was verder gebruik om 0n verskeidenheid selsiklusmodelle van Saccharomyces cerevisiae (bakkersgis) en soogdierselle met 0n modulêre aanpak te vergelyk om te bepaal of daar 0n massa beheerpunt in beide soogdier- en bakkersgisselle bestaan. Daar word gepostuleer dat hierdie beheerpunt verseker dat selle 0n kritiese massa by die G1/S transisiepunt bereik. Die resultate van die studie dui daarop dat bakkersgis, anders as soogdierselle, oor so 0n korreksiemeganisme beskik. Die meganisme stabiliseer die grootte van selle in die G1 fase ondanks veranderinge in die groeitempo van die selle, sodat massa homeostaties by die G1/S transisiepunt gehandhaaf word. Die studie het getoon dat moeilike vrae met betrekking tot die selsiklus beantwoord kan word deur van wiskundige modelle gebruik te maak en die probleme in die nuut-ontwikkelde metaboliese kontrole analise raamwerk te giet.

Plant cell and tissue cultivations are of growing interest for the production of structurally complex and expensive plant-derived products, especially in pharmaceutical production. Problems with up-scaling, low yields and high-priced process conditions result in an increased demand for models to provide comprehension, simulation, and optimization of production processes. In the last 25 years, many models have evolved in plant biotechnology; the majority of them are specialized models for a few selected products or nutritional conditions. In this article we review, delineate, and discuss the concepts and characteristics of the most commonly used models. Therefore, the authors focus on models for plant suspension and submerged hairy root cultures. The article includes a short overview of modeling and mathematics and integrated parameters, as well as the application scope for each model. The review is meant to help researchers better understand and utilize the numerous models published for plant cultures, and to select the most suitable model for their purposes.