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Thesis (MSc (Biochemistry))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: The Hodgkin-Huxley model, created in 1952, was one of the first models in computational neuroscience and remains the best studied neuronal model to date. Although many other models have a more detailed system description than the Hodgkin-Huxley model, it nonetheless gives an accurate account of various high-level neuronal behaviours. The fields of computational neuroscience and Systems Biology have developed as separate disciplines for a long time and only fairly recently has the neurosciences started to incorporate methods from Systems Biology. Metabolic Control Analysis (MCA), a Systems Biology tool, has not been used in the neurosciences. This study aims to further bring these two fields together, by testing the feasibility of an MCA approach to analyse the Hodgkin-Huxley model. In MCA it is not the parameters of the system that are perturbed, as in the more traditional sensitivity analysis, but the system processes, allowing the formulation of summation and connectivity theorems. In order to determine if MCA can be performed on the Hodgkin-Huxley model, we identified all the discernable model processes of the neuronal system. We performed MCA and quantified the control of the model processes on various high-level time invariant system observables, e.g. the action potential (AP) peak, firing threshold, propagation speed and firing frequency. From this analysis we identified patterns in process control, e.g. the processes that would cause an increase in sodium current, would also cause the AP threshold to lower (decrease its negative value) and the AP peak, propagation speed and firing frequency to increase. Using experimental inhibitor titrations from literature we calculated the control of the sodium channel on AP characteristics and compared it with control coefficients derived from our model simulation. Additionally, we performed MCA on the model’s time-dependent state variables during an AP. This revealed an intricate linking of the system variables via the membrane potential. We developed a method to quantify the contribution of the individual feedback loops in the system. We could thus calculate the percentage contribution of the sodium, potassium and leak currents leading to the observed global change after a system perturbation. Lastly, we compared ion channel mutations to our model simulations and showed how MCA can be useful in identifying targets to counter the effect of these mutations. In this thesis we extended the framework of MCA to neuronal systems and have successfully applied the analysis framework to quantify the contribution of the system processes to the model behaviour. / AFRIKAANSE OPSOMMINMG: Die Hodgkin-Huxley-model, wat in 1952 ontwikkel is, was een van die eerste modelle in rekenaarmagtige neurowetenskap en is vandag steeds een van die bes-bestudeerde neuronmodelle. Hoewel daar vele modelle bestaan met ’n meer uitvoerige sisteembeskrywing as die Hodgkin-Huxley-model gee dié model nietemin ’n akkurate beskrywing van verskeie hoëvlak-sisteemverskynsels. Die twee velde van sisteembiologie en neurowetenskap het lank as onafhanklike dissiplines ontwikkel en slegs betreklik onlangs het die veld van neurowetenskap begin om metodes van sisteembiologie te benut. ’n Sisteembiologiemetode genaamd metaboliese kontrole-analise (MKA) is tot dusver nog nie in die neurowetenskap gebruik nie. Hierdie studie het gepoog om die twee velde nader aan mekaar te bring deurdat die toepasbaarheid van die MKA-raamwerk op die Hodgkin-Huxley-model getoets word. In MKA is dit nie die parameters van die sisteem wat geperturbeer word soos in die meer tradisionele sensitiwiteitsanalise nie, maar die sisteemprosesse. Dit laat die formulering van sommasie- en konnektiwiteitsteoremas toe. Om die toepasbaarheid van die MKA-raamwerk op die Hodgkin-Huxleymodel te toets, is al die onderskeibare modelprosesse van die neurale sisteem geïdentifiseer. Ons het MKA toegepas en die kontrole van die model-prosesse op verskeie hoëvlak, tydsonafhanklike waarneembare sisteemvlak-eienskappe, soos die aksiepotensiaal-kruin, aksiepotensiaal-drempel, voortplantingspoed en aksiepotensiaal-frekwensie, gekwantifiseer. Vanuit hierdie analise kon daar patrone in die proseskontrole geïdentifiseer word, naamlik dat die prosesse wat ’n toename in die natriumstroom veroorsaak, ook sal lei tot ’n afname in die aksiepotensiaal-drempel (die negatiewe waarde verminder) en tot ’n toename in die aksiepotensiaal-kruin, voortplantingspoed en aksiepotensiaalfrekwensie. Deur gebruik te maak van eksperimentele stremmer-titrasies vanuit die literatuur kon die kontrole van die natriumkanaal op die aksiepotensiaaleienskappe bereken en vergelyk word met die kontrole-koëffisiënte vanuit die modelsimulasie. Ons het ook MKA op die model se tydsafhanklike veranderlikes deur die verloop van die aksiepotensiaal uitgevoer. Die analise het getoon dat die sisteemveranderlikes ingewikkeld verbind is via die membraanpotensiaal. Ons het ’n metode ontwikkel om die bydrae van die individuele terugvoerlusse in die sisteem te kwantifiseer. Die persentasie-bydrae van die natrium-, kalium- en lekstrome wat tot die waarneembare globale verandering ná ’n sisteemperturbasie lei, kon dus bepaal word. Laastens het ons ioonkanaalmutasies met ons modelsimulasies vergelyk en getoon hoe MKA nuttig kan wees in die identifisering van teikens om die effek van hierdie mutasies teen te werk. In hierdie tesis het ons die raamwerk van MKA uitgebrei na neurale sisteme en die analise-raamwerk suksesvol toegepas om die bydrae van die sisteemprosesse tot die modelgedrag te kwantifiseer.

Thesis (PhD (Biochemistry))--University of Stellenbosch, 2011. / ENGLISH ABSTRACT: Metabolic Control Analysis (MCA) provides a powerful quantitative framework for understanding and explaining the control and regulation within a cellular system. MCA allows the global control of a steady-state system to be quantified in terms of control coeficients, which we can express in terms of the local properties referred to as elasticity coeficients. MCA relates elasticities to control coeficients through a matrix inversion, thus allowing scientists to predict and quantify how the kinetics of the individual enzymes affect the systemic behaviour of cellular systems. Traditionally we solved this problem numerically, while we used algebraic and symbolic control analysis techniques less frequently. By using symbolic algebraic computation we present a general implementation of the symbolic matrix inversion of MCA, known as SymCA, which requires only the description of any allosteric modifier interactions and the stoichiometry of a cellular system. The algebraic expressions generated allow an in-depth analysis of the distribution of the control within a system and also of the parameters which exhibit the greatest effect on this control distribution. This also applies when the exact values for the elasticities or control coeficients are unknown. We have demonstrated that by quantifying the control patterns, referred to as `routes of regulation', inherent in all control coeficient expressions, we can gain insight into how perturbations are propagated through a cellular system and which regulatory pathways are favoured under changing conditions. / AFRIKAANSE OPSOMMING: Metaboliese Kontrole-Analise (MKA) bied 'n kragtige kwantitatiewe raamwerk om die beheer en regulering binne sellulere sisteme te verstaan en te verduidelik. 'n Sleutelaspek van MKA is dat die globale beheer van 'n sisteem met 'n bestendige toestand gekwantifiseer kan word in terme van kontrole-koefisente en dat hierdie koefisente uitgedruk kan word in terme van die sisteem se lokale eienskappe, genaamd elastisiteitskoefisente. Deur van matriksinversie gebruik te maak kan MKA die verband tussen elastisiteitskoefisente en kontrole-koefisente aflei wat mens in staat stel om te sien hoe die kinetika van die individuele ensiemreaksies die sisteemgedrag op sellulere vlak beinvloed. Die probleem word tradisioneel hoofsaaklik op numeriese wyse bereken terwyl die gebruik van algebraiese en simboliese kontrole-analise minder gereeld gebruik word. In hierdie proefskrif verskaf ons, deur van simboliese algebraiese metodes gebruik te maak, 'n generiese implementasie van die simboliese matriksinversie van MKA, genaamd SymCA, wat slegs 'n beskrywing van 'n sellulere sisteem se allosetriese interaksies en die stoichiometrie benodig. Die algebraiese uitdrukkings sodanig gegenereer stel mens in staat om 'n in-diepte analise te doen om vas te stel waar die beheer binne 'n sisteem le, asook watter parameters die grootste effek op die kontrole-verspreiding het. Dit geld selfs in die geval waar die presiese waardes van die elastisiteitskoefisente of kontrole-koefisente onbekend is. Hierdie proefskrif demonstreer hoe die kwantifisering van kontrole-patrone, ook gesien as 'roetes van regulering', wat inherent is aan kontrole-koefisent vergelykings, mens in staat stel om te sien hoe perturbasies in 'n sellulere sisteem voortplant en watter regulatoriese paaie bevoordeel word onder veranderde kondisies.

The development of human society, which is highly dependent on fossil fuels, is now facing a range of global issues, such as rising energy prices, energy security and climate changes. To successfully tackle the resultant issues, the energy transition from fossil fuels to renewable energy sources, such as solar energy, tide energy, hydroelectric power, geothermal heat and biofuels, is under way. Biodiesel, as an important type of biofuels, has been increasingly produced from vegetable oil or used cooking oil, especially in Europe. Nevertheless, considering the high production cost of biodiesel, there is still much to be done to improve the economics of biodiesel industry. Utilisation of crude glycerol, the main by-product of the biodiesel industry, to produce value-added products appears to be a promising solution. Poly(3-hydroxybutyric acid) (PHB), a biodegradable plastic, can be converted from glycerol by Cupriavidus necator DSM 545 under unbalanced growth conditions, such as nitrogen limitation. One way to enhance the batch production of PHB is to genetically engineer the strain of C. necator, which requires insights of the dynamic impact of extracellular environment on cell phenotypes. Hence in this thesis, we aim to perform metabolic modelling based on experimental measurements to gain a better understanding of the behaviour of the metabolic network of Cupriavidus necator DSM 545 and identify potential bottlenecks of the process. Initially, C. necator DSM 545 is a strain that hardly grows on glycerol, so in a preliminary study, we investigate the process by which the strain was adapted to consume glycerol through serial subcultivation. It is found that the adaptation can be achieved within 15 cell generations over three passages in basal mineral medium, and the acquired phenotype is sufficiently stable upon further passage. The study of metabolism started with the reconstruction of the cell's metabolic network, followed by a thermodynamic analysis to check the feasibility and reversibility of all the biochemical reactions included. Then the static flux balance analysis was extended and applied to analyse the shift of metabolic states during the microbial fermentation in different batch conditions. The resulting patterns of flux distribution reveal the TCA cycle to be the major competitor for PHB synthesis at the ACCoA node. Cells have the potential to enter an efficient PHB-production phase that features minimal TCA/PHB flux split ratio, and the length of the phase can be manipulated by aeration. Although low aeration rate favours optimal flux split ratio, such condition that limits respiration also limits nutrient uptake, leading to low PHB productivity overall. To identify the actual limiting factors of PHB synthesis in the system, we further performed metabolic control analysis based on the calculated flux distributions. The analysis demonstrated how the distribution of the metabolic control can vary widely, depending on the aeration conditions used and the flux split ratios. Glycerolipid pathway, glycolysis, PHB metabolism, as well as the electron transport chain are revealed to be potential engineering targets as they contribute to the great majority of the positive control of PHB flux.

In this study, firstly, bioprocess characteristics for Serine Alkaline Protease (SAP) production, using recombinant Bacillus subtilis carrying pHV1431::subC, were examined. The cell concentration, substrate concentration, SAP activity and SAP synthesis rate profiles demonstrated that the system reaches to a steady state in terms of cell growth and SAP synthesis between t=15-25 h, therefore, this time interval is appropriate to employ both metabolic flux analysis and metabolic control analysis, which apply strictly to steady state systems. After that, three separate perturbations were introduced by addition of aspartate to the production medium at a certain time of the bioprocess. The response of the cells were observed and / by comparing the changes in intracellular reactions of aspartate pathway, Asn, Thr and Ile productions were determined to be the bottlenecks in aspartate pathway and the branchpoints splitting from Asp and AspSa were identified to be weakly rigid branchpoints. Lastly, metabolic control analysis principles were applied to determine the elasticity and flux control coefficients of the simplified aspartate pathway. Aspartate formation reaction and Lys, Thr, Ile, Met producing group share the control of asparagine synthesis. The results revealed that lysine producing branch flux dominates the other branch fluxes, therefore to eliminate bottlenecks and increase SAP production, the activity of the branches leading to the formation of Asn, Thr and Ile should be increased while decreasing the activity of lysine synthesizing branch. This could be achieved either by genetic manipulation or by addition of specific inhibitors or activators to the system.

Thesis (PhD (Biochemistry))--University of Stellenbosch, 2009. / ENGLISH ABSTRACT: With the recent advances in the field of molecular biology, there is an increased need to integrate data on the various constituents of the cell in kinetic models that can predict and describe cellular behavior. When working towards a description of the entire cell using such kinetic models, the question arises: How do we compare different models for a given biological network? This is the central question addressed in my thesis and I developed and applied mathematical and computational methods for comparing dozens of existing models of erythrocyte and yeast glycolysis. To compare the steady-state behavior in models of erythrocyte glycolysis, I focussed on the function of the pathway, which is to supply the cell with Gibbs-free energy (γ- phosphate of ATP). I used supply-demand analysis in the framework of metabolic control analysis to make this comparison, which revealed that the ATP concentrations were homeostatically buffered at varying supply rates. I also applied this approach to compare steady-state behavior in models of yeast glycolysis, finding that they were not necessarily optimized for homeostatic maintenance of the ATP concentration and that in models for this organism the rate of ATP production is often determined by the supply reactions of glycolysis. In addition, I tested whether a kinetic model can describe novel behavior if it is adjusted to conditions different from those for which the model was originally constructed. More specifically, using a model of steady-state yeast glycolysis, I showed that small adjustments to the original enzyme concentrations are enough to obtain an oscillating model, which shows a remarkable resemblance to the experimentally observed oscillations. Importantly, some of these enzyme concentrations changes are known to occur during the pre-treatment of the cells which is necessary to obtain oscillatory behavior. To the best of my knowledge, the resulting model is the first detailed kinetic model that describes the experimentally observed strong synchronization of glycolytic oscillations in yeast populations. To analyze the dynamic behavior of yeast glycolytic models and to compare different models in terms of dynamics, I introduced a framework used in physics and engineering to create a vector based, two dimensional graphical representation of the oscillating metabolites and reactions of glycolysis. Not only was it possible to make a concise comparison of the set of models, but with the method I could also quantify the contribution of the interactions in the network to the transduction of the oscillations. Furthermore I could distinguish between different mechanisms of oscillation for each of the models, and demonstrated how the framework can be used to create such representations for experimental data sets. / AFRIKAANSE OPSOMMING: Met die onlangse vooruitgang in die veld van molekulere biologie, is daar ?n toenemende behoefte om data rakende die verskeie komponente van die sel in kinetiese modelle te integreer, om sodanig selgedrag te voorspel en te beskryf. As daar gepoog word om ’n beskrywing van die sel as geheel te verkry d.m.v. sulke kinetiese modelle, onstaan die vraag: Hoe vergelyk ons verskillende modelle van ’n gegewe biologiese netwerk? Dit is die sentrale vraag wat my tesis aanspreek en ek het wiskundige en numeriese metodes ontwikkel en toegepas om talle bestaande modelle van gis- en eritrosietglikolise te vergelyk. Om die bestendige-toestand gedrag in modelle van eritrosietglikolise te vergelyk, het ek gefokus op die funksie van die padweg, naamlik om die sel met Gibbs-vrye energie (γ-fosfaat van ATP) te voorsien. Ek het vraag-aanbod analiese in die raamwerk van metaboliese kontrole analiese gebruik om hierdie vergelyking te maak, wat getoon het dat die ATP konsentrasies homeostaties gebuffer was by verskillende aanbod tempos. Ek het ook hierdie aanpak gebruik om die bestendige-toestand gedrag in modelle van gisglikolise te vergelyk, en het bevind dat hulle nie noodwendig geoptimiseer is om ?n homeostatiese balans in die ATP konsentrasie te handhaaf nie, en dat in modelle vir hierdie organisme, die tempo van ATP produksie dikwels bepaal word deur die aanbod reaksies van glikoliese. Ek het verder ook bepaal of so ?n kinetiese model nuwe soorte gedrag kan beskryf, as dit aangepas word aan omstandighede wat verskil van dié waarvoor die model oorspronklik gekonstrueer was. Meer spesifiek, deur ?n model van bestendige-toestand gisglikolise te gebruik, kon ek wys dat klein veranderinge aan die oorspronkline ensiem konsentrasies genoeg was om ?n ossilerende model te verkry, wat opmerklik ooreenstem met die eksperimenteel waargenome ossilasies. Let ook daarop dat sommige van hierdie ensiem konsentrasie veranderinge plaasvind tydens die voorafbehandeling van die selle, wat essensieel is om die ossilasies waar te neem. Tot die beste van my kennis is die model wat ek met hierdie prosedures verkry het, die eerste gedetaileerde kinetiese model wat die eksperimenteel waargenome sterk sinkronisasie in ossilerende gis populasies voorspel. Om gis glikolitiese modelle te vergelyk in terme van hul dinamiese gedrag, het ek ?n raamwerk wat in fisika en ingeneurswese gebruik word, ingespan om ?n vektor-gebasseerde, twee dimensionele grafiese voorstelling van die ossilerende metaboliete en reaksies te maak. Hierdie raamwerk het dit nie net moontlik gemaak om ?n kompakte vergelyking van ?n stel modelle te maak nie, maar ek kon ook die bydrae van interaksies in die netwerk tot transduksie van die ossilasies kwantifiseer. Ek kon verder onderskeid tref tussen die verskillende ossilasiemeganismes vir elk van die modelle, en het ook gedemonstreer hoe die raamwerk gebruik kan word om sulke voorstellings vir eksperimentele datastelle te skep.

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.