BACKGROUND: Resolution of the link between micro- and macroevolution calls for comparing both processes on the same deterministic landscape, such as genomic, metabolic or fitness networks. We apply this perspective to the evolution of carotenoid pigmentation that produces spectacular diversity in avian colors and show that basic structural properties of the underlying carotenoid metabolic network are reflected in global patterns of elaboration and diversification in color displays. Birds color themselves by consuming and metabolizing several dietary carotenoids from the environment. Such fundamental dependency on the most upstream external compounds should intrinsically constrain sustained evolutionary elongation of multi-step metabolic pathways needed for color elaboration unless the metabolic network gains robustness - the ability to synthesize the same carotenoid from an additional dietary starting point. RESULTS: We found that gains and losses of metabolic robustness were associated with evolutionary cycles of elaboration and stasis in expressed carotenoids in birds. Lack of metabolic robustness constrained lineage's metabolic explorations to the immediate biochemical vicinity of their ecologically distinct dietary carotenoids, whereas gains of robustness repeatedly resulted in sustained elongation of metabolic pathways on evolutionary time scales and corresponding color elaboration. CONCLUSIONS: The structural link between length and robustness in metabolic pathways may explain periodic convergence of phylogenetically distant and ecologically distinct species in expressed carotenoid pigmentation; account for stasis in carotenoid colors in some ecological lineages; and show how the connectivity of the underlying metabolic network provides a mechanistic link between microevolutionary elaboration and macroevolutionary diversification. REVIEWERS: This article was reviewed by Junhyong Kim, Eugene Koonin, and Fyodor Kondrashov. For complete reports, see the Reviewers' reports section.

Establishing metrics of diversification can calibrate the observed scope of diversity within a lineage and the potential for further phenotypic diversification. There are two potential ways to calibrate differences between phenotypes. The first metric is based on the structure of the network of direct and indirect connections between elements, such as the genes, proteins, enzymes and metabolites that underlie a phenotype. The second metric characterizes the dynamic properties that determine the strength of the interactions among elements, and influence which elements are the most likely to interact. Determining how the connectivity and strength of interactions between elements lead to specific phenotypic variations provides insight into the tempo and mode of observed evolutionary changes. In this dissertation, I proposed and tested hypotheses for how the structure and metabolic flux of a biochemical network delineate patterns of phenotypic variation. I first examined the role of structural properties in shaping observed patterns of carotenoid diversification in avian plumage. I found that the diversification of species-specific carotenoid networks was predictable from the connectivity of the underlying metabolic network. The compounds with the most enzymatic reactions, that were part of the greatest number of distinct pathways, were more conserved across species’ networks than compounds associated with the fewest enzymatic reactions. These results established that compounds with the greatest connectivity act as hotspots for the diversification of pathways between species. Next, I investigated how dynamic properties of biochemical networks influence patterns of phenotypic variation in the concentration and occurrence of compounds. Specifically, I examined if the rate of compound production, known as metabolic flux, is coordinated among compounds in relation to their structural properties. I developed predictions for how different distributions of flux could cause distinct diversification patterns in the concentrations and presence of compounds in a biochemical network. I then tested the effect of metabolic network structure on the concentrations of carotenoids in the plumage of male house finches (Haemorhous mexicanus) from the same population. I assessed whether the structure of a network corresponds to a specific distribution of flux among compounds, or if flux is independent of network structure. I found that flux coevolves with network structure; concentrations of metabolically derived compounds depended on the number of reactions per compound. There were strong correlations between compound concentrations within a network structure, and the strengths of these correlations varied among structures. These findings suggest that changes in network structure, and not independent changes in flux, influence local adaptations in the concentrations of compounds. Lastly, the influence of carotenoid network structure in the evolutionary diversification of compounds across species of birds depends on how the structure of the network itself evolves. To test whether the carotenoid metabolic network structure evolves in birds, I examined the patterns of carotenoid co-occurrence across ancestral and extant species. I found that the same groups of compounds are always gained or lost together even as lineages diverge further from each other. These findings establish that the diversification of carotenoids in birds is constrained by the structure of an ancestral network, and does not evolve independently within a lineage. Taken together, the results of this dissertation establish that local adaptations and the evolutionary diversification of carotenoid metabolism are qualitatively predictable from the structure of an ancestral enzymatic network, and this suggests there is significant structural determinism in phenotypic evolution.

Células estomáticas e reações metabólicas de plantas foram modelados por meio da teoria dos grafos neste trabalho; a distância entre estômatos vizinhos na folha foi adotada como parâmetro utilizado para a conectividade em redes onde os estômatos foram definidos como nodos. A direção da formação de produtos e substratos em reações metabólicas determinou a conectividade nas redes metabólicas, onde cada metabólito foi definido como um nodo. As redes de estômatos foram capazes de gerar uma grande quantidade de informação geométrica associada à distância entre os estômatos. Estas medidas se mostraram uma poderosa ferramenta para avaliar a plasticidade fenotípica em folhas de plantas. A adaptação de plantas a condições ambientais extremas, como altas taxas de umidade e grandes variações no tempo de exposição à luz, puderam ser quantificadas por parâmetros de redes. Parâmetros topológicos globais das redes metabólicas mostraram que elas possuem propriedades estatísticas e topológicas de redes livre escala, como nos seres vivos em geral. Entretanto, alguns parâmetros topológicos locais das redes como a medida hub-score, geram vetores de características que, se comparados entre plantas, geram informação filogenética. Além disso, nós comprovamos que é possível construir modelos que sugerem uma organização geral para o metabolismo, por meio de algorítmos de conectividade hierárquica. O algorítmo de k-cores foi usado para gerar camadas de conectividade nas redes metabólicas. A atribuição química dos metabólitos ao longo das camadas k-core, mostra que a hierarquia de conexões está associada a especialização do metabolismo. Isto sugere que o algorítimo também gera informação sobre a evolução da maquinaria metabólica. Portanto, o modelo para conectar elementos de uma rede metabólica adotado neste trabalho, traz informações naturais sobre as plantas, o que sugere que exista parâmetros físicos das reações metabólicas representados pelo modelo. / Stomatic cells and metabolic reactions were modeled by graph theory in this work. The distance between stomata was adopted as connectivity parameter in the networks where stomata were defined as nodes. The direction of formation from products and substrates in the metabolic reactions, determined the connectivity from the metabolic networks, where each metabolite was defined as a node. The networks of stomata were able to generate a large amount of geometric information based at distance between the stomata. These measures represented a powerful tool to evaluate the phenotypic plasticity in leaves of plants. Global topological parameters from plant the metabolic networks revealed that plant metabolic networks has the topology of free scale networks, as in living beings in general. However, some local topological parameters of the networks such as the hub-score, can be organized as characteristic vectors with differential phylogenetic information. In addition, we have shown that it is possible to construct models that suggest a general organization for the metabolism through algorithms with iterative percolation from network connectivity. The k-cores algorithm was used to generate layers of connectivity in the metabolic networks. The chemical assignment of the metabolites along the k-core layers shows that the hierarchy of connections is associated with specialization of metabolism. This suggests that the algorithm also generates information about the evolution of the metabolic machinery. Therefore, the model used to connect elements of the metabolic networks adopted in this work, brings natural information about the plants, which suggests that there are physical parameters of the metabolic reactions represented by the model.

Le sujet général de cette thèse est la modélisation mathématique des systèmes biologiques. Le principal modèle étudié est le réseau métabolique: une collection d'objets - métabolites, réactions biochimiques, enzymes et gènes - et les relations entre eux, généralement organisées sous forme de graphe.Trois sujets distincts sont couverts. Dans le premier chapitre principal, un algorithme appelé MOOMIN pour «Mathematical explOration of Omics data on a MetabolIc Network» est présenté. C'est un outil informatique permettant d'interpréter les résultats d'une analyse d'expression différentielle à l'aide d'un réseau métabolique. Le résultat de l'algorithme est un changement métabolique, exprimé en termes de réactions supposées avoir subi un changement d'activité, qui correspond le mieux aux données d'expression génique. Le deuxième chapitre principal traite de l'intersection de la théorie des jeux et de l'étude du métabolisme cellulaire. Un nouveau type de modèle est proposé, combinant les principes de la théorie des jeux évolutive à la modélisation par contraintes pour prédire le comportement métabolique. Dans le troisième et dernier chapitre principal, un modèle épidémiologique de l'agent pathogène de la vigne Xylella fastidiosa est présenté et analysé. À l'aide d'une analyse de sensibilité, l'importance relative des paramètres du modèle est évaluée et les résultats sont discutés du point de vue de la lutte contre la maladie / The overall subject of this thesis is mathematical modelling of biological systems. The main model under study is the metabolic network: a collection of objects — metabolites, biochemical reactions, enzymes, and genes — and the relations amongst them, usually organised to form a graph.Three distinct topics are covered. In the first main chapter, an algorithm called MOOMIN for “Mathematical explOration of Omics data on a MetabolIc Network” is presented. It is a computational tool to interpret the results of a differential expression analysis with the help of a metabolic network. The output of the algorithm is a metabolic shift, expressed in terms of reactions that were inferred to have undergone a change in activity, that best aligns with the gene expression data. In the second main chapter, the intersection of game theory and the study of cellular metabolism is discussed. A new type of model is proposed, one that combines the principles behind evolutionary game theory with constraint-based modelling to predict metabolic behaviour. In the third and last main chapter, an epidemiological model of the Xylella fastidiosa grapevine pathogen is presented and analysed. Using sensitivity analysis, the relative importance of the model parameters is evaluated, and the results discussed from the point of view of disease control

Células estomáticas e reações metabólicas de plantas foram modelados por meio da teoria dos grafos neste trabalho; a distância entre estômatos vizinhos na folha foi adotada como parâmetro utilizado para a conectividade em redes onde os estômatos foram definidos como nodos. A direção da formação de produtos e substratos em reações metabólicas determinou a conectividade nas redes metabólicas, onde cada metabólito foi definido como um nodo. As redes de estômatos foram capazes de gerar uma grande quantidade de informação geométrica associada à distância entre os estômatos. Estas medidas se mostraram uma poderosa ferramenta para avaliar a plasticidade fenotípica em folhas de plantas. A adaptação de plantas a condições ambientais extremas, como altas taxas de umidade e grandes variações no tempo de exposição à luz, puderam ser quantificadas por parâmetros de redes. Parâmetros topológicos globais das redes metabólicas mostraram que elas possuem propriedades estatísticas e topológicas de redes livre escala, como nos seres vivos em geral. Entretanto, alguns parâmetros topológicos locais das redes como a medida hub-score, geram vetores de características que, se comparados entre plantas, geram informação filogenética. Além disso, nós comprovamos que é possível construir modelos que sugerem uma organização geral para o metabolismo, por meio de algorítmos de conectividade hierárquica. O algorítmo de k-cores foi usado para gerar camadas de conectividade nas redes metabólicas. A atribuição química dos metabólitos ao longo das camadas k-core, mostra que a hierarquia de conexões está associada a especialização do metabolismo. Isto sugere que o algorítimo também gera informação sobre a evolução da maquinaria metabólica. Portanto, o modelo para conectar elementos de uma rede metabólica adotado neste trabalho, traz informações naturais sobre as plantas, o que sugere que exista parâmetros físicos das reações metabólicas representados pelo modelo. / Stomatic cells and metabolic reactions were modeled by graph theory in this work. The distance between stomata was adopted as connectivity parameter in the networks where stomata were defined as nodes. The direction of formation from products and substrates in the metabolic reactions, determined the connectivity from the metabolic networks, where each metabolite was defined as a node. The networks of stomata were able to generate a large amount of geometric information based at distance between the stomata. These measures represented a powerful tool to evaluate the phenotypic plasticity in leaves of plants. Global topological parameters from plant the metabolic networks revealed that plant metabolic networks has the topology of free scale networks, as in living beings in general. However, some local topological parameters of the networks such as the hub-score, can be organized as characteristic vectors with differential phylogenetic information. In addition, we have shown that it is possible to construct models that suggest a general organization for the metabolism through algorithms with iterative percolation from network connectivity. The k-cores algorithm was used to generate layers of connectivity in the metabolic networks. The chemical assignment of the metabolites along the k-core layers shows that the hierarchy of connections is associated with specialization of metabolism. This suggests that the algorithm also generates information about the evolution of the metabolic machinery. Therefore, the model used to connect elements of the metabolic networks adopted in this work, brings natural information about the plants, which suggests that there are physical parameters of the metabolic reactions represented by the model.

The elucidation of molecular function of proteins encoded by genes is a major challenge in biology today. Genes regulate the amount of proteins (enzymes) needed to catalyse a metabolic reaction. There are several works on either the modelling of gene expression or metabolic network. However, an integrative model of both is not well understood and researched. The integration of both gene expression and metabolic network could increase our understanding of cellular functions and aid in analysing the effects of genes on metabolism. It is now possible to build genome-scale models of cellular processes due to the availability of high-throughput genomic, metabolic and fluxomic data along with thermodynamic information. Integrating biological information at various layers into metabolic models could also improve the robustness of models for in silico analysis. In this study, we provide a software tool for the in silico reconstruction of genome-scale integrative models of gene expression and metabolic network from relevant database(s) and previously existing stoichiometric models with automatic generation of kinetic equations of all reactions involved. To reduce computational complexity, compartmentalisation of the cell as well as enzyme inhibition is assumed to play a negligible role in metabolic function. Obtaining kinetic parameters needed to fully define and characterise kinetic models still remains a challenge in systems biology. Parameters are either not available in literature or unobtainable in the lab. Consequently, there have been numerous methods developed to predict biological behaviour that do not require the use of detailed kinetic parameters as well as techniques for estimation of parameter values based on experimental data. We present an algorithm for estimating kinetic parameters which uses fluxes and metabolites to constrain values. Our results show that our genetic algorithm is able to find parameters that fit a given data set and predict new biological states without having to re-estimate kinetic parameters.

Metabolic networks are naturally represented as directed hypergraphs in such a way that metabolites are nodes and enzyme-catalyzed reactions form (hyper)edges. The familiar operations from set algebra (union, intersection, and difference) form a natural basis for both the pairwise comparison of networks and identification of distinct metabolic features of a set of algorithms. We report here on an implementation of this approach and its application to the procaryotes. We demonstrate that metabolic networks contain valuable phylogenetic information by comparing phylogenies obtained from network comparisons with 16S RNA phylogenies. We then used the same software to study metabolic innovations in two sets of organisms, free living microbes and Pyrococci, as well as obligate intracellular pathogens.

The understanding of cellular metabolism has been an intriguing challenge in classical cellular biology for decades. Essentially, cellular metabolism can be viewed as a complex system of enzyme-catalysed biochemical reactions that produces the energy and material necessary for the maintenance of life. In modern biochemistry, it is well-known that these reactions group into metabolic pathways so as to accomplish a particular function in the cell. The identification of these metabolic pathways is a key step to fully understanding the metabolic capabilities of a given organism. Typically, metabolic pathways have been elucidated via experimentation on different organisms. However, experimental findings are generally limited and fail to provide a complete description of all pathways. For this reason it is important to have mathematical models that allow us to identify and analyze metabolic pathways in a computational fashion. This is precisely the main theme of this thesis. We firstly describe, review and discuss existent mathematical/computational approaches to metabolic pathways, namely stoichiometric and path finding approaches. Then, we present our initial mathematical model named the Beasley-Planes (BP) model, which significantly improves on previous stoichiometric approaches. We also illustrate a successful application of the BP model to optimally disrupt metabolic pathways. The main drawback of the BP model is that it needs as input extra pathway knowledge. This is especially inappropriate if we wish to detect unknown metabolic pathways. As opposed to the BP model and stoichoimetric approaches, this issue is not found in path finding approaches. For this reason a novel path finding approach is built and examined in detail. This analysis serves us as inspiration to build the Improved Beasley-Planes (IBP) model. The IBP model incorporates elements of both stoichometric and path finding approaches. Though somewhat less accurate than the BP model, the IBP model solves the issue of extra pathway knowledge. Our research clearly demonstrates that there is a significant chance of developing a mathematical optimisation model that underlies many/all metabolic pathways.

This work presents mathematical and computational approaches to cover various aspects of metabolic network modelling, especially regarding the limited availability of detailed kinetic knowledge on reaction rates. It is shown that precise mathematical formulations of problems are needed i) to find appropriate and, if possible, efficient algorithms to solve them, and ii) to determine the quality of the found approximate solutions. Furthermore, some means are introduced to gain insights on dynamic properties of metabolic networks either directly from the network structure or by additionally incorporating steady-state information. Finally, an approach to identify key reactions in a metabolic networks is introduced, which helps to develop simple yet useful kinetic models. The rise of novel techniques renders genome sequencing increasingly fast and cheap. In the near future, this will allow to analyze biological networks not only for species but also for individuals. Hence, automatic reconstruction of metabolic networks provides itself as a means for evaluating this huge amount of experimental data. A mathematical formulation as an optimization problem is presented, taking into account existing knowledge and experimental data as well as the probabilistic predictions of various bioinformatical methods. The reconstructed networks are optimized for having large connected components of high accuracy, hence avoiding fragmentation into small isolated subnetworks. The usefulness of this formalism is exemplified on the reconstruction of the sucrose biosynthesis pathway in Chlamydomonas reinhardtii. The problem is shown to be computationally demanding and therefore necessitates efficient approximation algorithms. The problem of minimal nutrient requirements for genome-scale metabolic networks is analyzed. Given a metabolic network and a set of target metabolites, the inverse scope problem has as it objective determining a minimal set of metabolites that have to be provided in order to produce the target metabolites. These target metabolites might stem from experimental measurements and therefore are known to be produced by the metabolic network under study, or are given as the desired end-products of a biotechological application. The inverse scope problem is shown to be computationally hard to solve. However, I assume that the complexity strongly depends on the number of directed cycles within the metabolic network. This might guide the development of efficient approximation algorithms. Assuming mass-action kinetics, chemical reaction network theory (CRNT) allows for eliciting conclusions about multistability directly from the structure of metabolic networks. Although CRNT is based on mass-action kinetics originally, it is shown how to incorporate further reaction schemes by emulating molecular enzyme mechanisms. CRNT is used to compare several models of the Calvin cycle, which differ in size and level of abstraction. Definite results are obtained for small models, but the available set of theorems and algorithms provided by CRNT can not be applied to larger models due to the computational limitations of the currently available implementations of the provided algorithms. Given the stoichiometry of a metabolic network together with steady-state fluxes and concentrations, structural kinetic modelling allows to analyze the dynamic behavior of the metabolic network, even if the explicit rate equations are not known. In particular, this sampling approach is used to study the stabilizing effects of allosteric regulation in a model of human erythrocytes. Furthermore, the reactions of that model can be ranked according to their impact on stability of the steady state. The most important reactions in that respect are identified as hexokinase, phosphofructokinase and pyruvate kinase, which are known to be highly regulated and almost irreversible. Kinetic modelling approaches using standard rate equations are compared and evaluated against reference models for erythrocytes and hepatocytes. The results from this simplified kinetic models can simulate acceptably the temporal behavior for small changes around a given steady state, but fail to capture important characteristics for larger changes. The aforementioned approach to rank reactions according to their influence on stability is used to identify a small number of key reactions. These reactions are modelled in detail, including knowledge about allosteric regulation, while all other reactions were still described by simplified reaction rates. These so-called hybrid models can capture the characteristics of the reference models significantly better than the simplified models alone. The resulting hybrid models might serve as a good starting point for kinetic modelling of genome-scale metabolic networks, as they provide reasonable results in the absence of experimental data, regarding, for instance, allosteric regulations, for a vast majority of enzymatic reactions. / In dieser Arbeit werden mathematische und informatische Ansätze zur Behandlung diverser Probleme im Zusammenhang mit der Modellierung metabolischer Netzwerke vorgestellt, insbesondere unter Berücksichtigung der eingeschränkten Verfügbarkeit detaillierter Enzymkinetiken. Es wird gezeigt, dass präzise mathematische Formulierungen der Probleme notwendig sind, um erstens angemessene und, falls möglich, effiziente Algorithmen zur Lösung zu entwickeln. Und zweitens, um die Güte der so gefundenen Lösungen zu bewerten. Des weiteren werden Methoden zur Analyse dynamischer Eigenschaften metabolischer Netzwerke eingeführt, welche entweder nur auf der Struktur der Netzwerke basieren oder zusätzlich noch Informationen über stationäre Zustände mit berücksichtigen. Außerdem wird eine Strategie zur Bestimmung von Schlüsselreaktionen eines Netzwerkes vorgestellt, welche die Entwicklung kinetischer Modelle vereinfacht. Der Erfolg neuer Technologien ermöglicht eine immer billigere und schnellere Sequenzierung des Genoms. Dies wird in naher Zukunft die Analyse biologischer Netzwerke nicht nur für Spezies, sondern auch für einzelne Individuen ermöglichen. Die automatische Rekonstruktion metabolischer Netzwerke ist bestens dafür geeignet, diese großen Datenmengen auszuwerten. Eine mathematische Formulierung der Rekonstruktion als Optimierungsproblem wird vorgestellt, die sowohl bereits vorhandenes Wissen als auch theoretische Vorhersagen verschiedenster bioinformatischer Methoden berücksichtigt. Die rekonstruierten Netzwerke sind hinsichtlich möglichst großer und plausibler Zusammenhangskomponenten hin optimiert, um fragmentierte und isolierte Teilnetzwerke zu vermeiden. Als Beispiel dient die Rekonstruktion der Saccharosesynthese in Chlamydomonas reinhardtii. Es wird gezeigt, dass das Problem sehr rechenintensiv ist und somit Approximationsalgorithmen erforderlich macht. Das 'inverse scope' Problem hat als Optimierungsziel, für ein gegebenes metabolisches Netzwerk die minimale Menge notwendiger Metabolite zu bestimmen, um eine ebenfalls gegebene Menge von gewünschten Zielmetaboliten zu produzieren. Diese Zielmetabolite können entweder durch experimentellen Messungen festgelegt werden, oder sie sind die gewünschten Endprodukte einer biotechnologischen Anwendung. Es wird gezeigt, dass das 'inverse scope' Problem rechenintensiv ist. Allerdings wird angenommen, dass die Berechnungskomplexität stark von der Anzahl gerichteter Zyklen innerhalb des metabolischen Netzwerkes abhängt. Dies könnte die Entwicklung effizienter Approximationsalgorithmen ermöglichen. Unter der Annahme von Massenwirkungskinetiken erlaubt es die 'chemical reaction network theory' (CRNT), anhand der Struktur metabolischer Netzwerke Rückschlüsse auf Multistabilität zu ziehen. Auch weitere Kinetiken können durch Modellierung von Enzymmechanismen mit berücksichtigt werden. CRNT wird zum Vergleich von mehreren Modellen des Calvinzyklus, welche sich in Größe und Abstraktionsniveau unterscheiden, verwendet. Obwohl für kleinere Modelle Ergebnisse erzielt werden, erlauben es die verfügbaren Theoreme und Algorithmen der CRNT nicht, Aussagen für größere Modelle zu machen, da die gegenwärtigen Implementierungen der Algorithmen an ihre Berechnungsgrenzen stoßen. Sind sowohl die Stoichiometrie eines metabolischen Netzwerkes, als auch die Metabolitkonzentrationen und Flüsse im stationären Zustand bekannt, so kann 'structural kinetic modelling' angewandt werden, um das dynamische Verhalten des Netzwerkes zu analysieren, selbst wenn die expliziten Ratengleichung unbekannt sind. Dieser Ansatz wird verwendet, um den stabilisierenden Einfluss allosterischer Regulation in menschlichen Erythrozyten zu untersuchen. Des weiteren werden die Reaktionen anhand ihrer Bedeutung hinsichtlich Stabilität im stationären Zustand angeordnet. Die wichtigsten Reaktionen bezüglich dieser Ordnung sind Hexokinase, Phosphofructokinase und Pyruvatkinase, welche bekanntermaßen stark reguliert und irreversibel sind. Kinetische Modelle, die auf generischen Ratengleichung beruhen, werden mit detaillierten Referenzmodellen für Erythrozyten und Hepatozyten verglichen. Die generischen Modelle simulieren das Verhalten nur in der Nähe eines gegebenen stationären Zustandes recht gut. Der zuvor erwähnte Ansatz, wichtige Reaktionen bezüglich Stabilität zu identifizieren, wird zur Bestimmung von Schlüsselreaktionen genutzt. Diese Schlüsselreaktionen werden im Detail modelliert, während für alle anderen Reaktionen weiterhin generische Ratengleichung verwendet werden. Die so entstandenen Hybridmodelle können das Verhalten des Referenzmodells signifikant besser beschreiben. Die Hybridmodelle können als Ausgangspunkt zur Erstellung genomweiter kinetischer Modelle dienen.

Complex networks have been successfully employed to represent different levels of biological systems, ranging from gene regulation to protein-protein interactions and metabolism. Network-based research has mainly focused on identifying unifying structural properties, including small average path length, large clustering coefficient, heavy-tail degree distribution, and hierarchical organization, viewed as requirements for efficient and robust system architectures. Existing studies estimate the significance of network properties using a generic randomization scheme - a Markov-chain switching algorithm - which generates unrealistic reactions in metabolic networks, as it does not account for the physical principles underlying metabolism. Therefore, it is unclear whether the properties identified with this generic approach are related to the functions of metabolic networks. Within this doctoral thesis, I have developed an algorithm for mass-balanced randomization of metabolic networks, which runs in polynomial time and samples networks almost uniformly at random. The properties of biological systems result from two fundamental origins: ubiquitous physical principles and a complex history of evolutionary pressure. The latter determines the cellular functions and abilities required for an organism’s survival. Consequently, the functionally important properties of biological systems result from evolutionary pressure. By employing randomization under physical constraints, the salient structural properties, i.e., the smallworld property, degree distributions, and biosynthetic capabilities of six metabolic networks from all kingdoms of life are shown to be independent of physical constraints, and thus likely to be related to evolution and functional organization of metabolism. This stands in stark contrast to the results obtained from the commonly applied switching algorithm. In addition, a novel network property is devised to quantify the importance of reactions by simulating the impact of their knockout. The relevance of the identified reactions is verified by the findings of existing experimental studies demonstrating the severity of the respective knockouts. The results suggest that the novel property may be used to determine the reactions important for viability of organisms. Next, the algorithm is employed to analyze the dependence between mass balance and thermodynamic properties of Escherichia coli metabolism. The thermodynamic landscape in the vicinity of the metabolic network reveals two regimes of randomized networks: those with thermodynamically favorable reactions, similar to the original network, and those with less favorable reactions. The results suggest that there is an intrinsic dependency between thermodynamic favorability and evolutionary optimization. The method is further extended to optimizing metabolic pathways by introducing novel chemically feasibly reactions. The results suggest that, in three organisms of biotechnological importance, introduction of the identified reactions may allow for optimizing their growth. The approach is general and allows identifying chemical reactions which modulate the performance with respect to any given objective function, such as the production of valuable compounds or the targeted suppression of pathway activity. These theoretical developments can find applications in metabolic engineering or disease treatment. The developed randomization method proposes a novel approach to measuring the significance of biological network properties, and establishes a connection between large-scale approaches and biological function. The results may provide important insights into the functional principles of metabolic networks, and open up new possibilities for their engineering. / In der Systembiologie und Bioinformatik wurden in den letzten Jahren immer komplexere Netzwerke zur Beschreibung verschiedener biologischer Prozesse, wie Genregulation, Protein-Interaktionen und Stoffwechsel (Metabolismus) rekonstruiert. Ein Hauptziel der Forschung besteht darin, die strukturellen Eigenschaften von Netzwerken für Vorhersagen über deren Funktion nutzbar zu machen, also eine Verbindung zwischen Netzwerkeigenschaften und Funktion herzustellen. Die netzwerkbasierte Forschung zielte bisher vor allem darauf ab, gemeinsame Eigenschaften von Netzwerken unterschiedlichen Ursprungs zu entdecken. Dazu zählen die durchschnittliche Länge von Verbindungen im Netzwerk, die Häufigkeit redundanter Verbindungen, oder die hierarchische Organisation der Netzwerke, welche als Voraussetzungen für effiziente Kommunikationswege und Robustheit angesehen werden. Dabei muss zunächst bestimmt werden, welche Eigenschaften für die Funktion eines Netzwerks von besonderer Bedeutung (Signifikanz) sind. Die bisherigen Studien verwenden dafür eine Methode zur Erzeugung von Zufallsnetzwerken, welche bei der Anwendung auf Stoffwechselnetzwerke unrealistische chemische Reaktionen erzeugt, da sie physikalische Prinzipien missachtet. Es ist daher fraglich, ob die Eigenschaften von Stoffwechselnetzwerken, welche mit dieser generischen Methode identifiziert werden, von Bedeutung für dessen biologische Funktion sind, und somit für aussagekräftige Vorhersagen in der Biologie verwendet werden können. In meiner Dissertation habe ich eine Methode zur Erzeugung von Zufallsnetzwerken entwickelt, welche physikalische Grundprinzipien berücksichtigt, und somit eine realistische Bewertung der Signifikanz von Netzwerkeigenschaften ermöglicht. Die Ergebnisse zeigen anhand der Stoffwechselnetzwerke von sechs Organismen, dass viele der meistuntersuchten Netzwerkeigenschaften, wie das Kleine-Welt-Phänomen und die Vorhersage der Biosynthese von Stoffwechselprodukten, von herausragender Bedeutung für deren biologische Funktion sind, und somit für Vorhersagen und Modellierung verwendet werden können. Die Methode ermöglicht die Identifikation von chemischen Reaktionen, welche wahrscheinlich von lebenswichtiger Bedeutung für den Organismus sind. Weiterhin erlaubt die Methode die Vorhersage von bisher unbekannten, aber physikalisch möglichen Reaktionen, welche spezifische Zellfunktionen, wie erhöhtes Wachstum in Mikroorganismen, ermöglichen könnten. Die Methode bietet einen neuartigen Ansatz zur Bestimmung der funktional relevanten Eigenschaften biologischer Netzwerke, und eröffnet neue Möglichkeiten für deren Manipulation.