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Graph theory and networks in biology
 IET Systems Biology, 1:89 – 119
, 2007
"... In this paper, we present a survey of the use of graph theoretical techniques in Biology. In particular, we discuss recent work on identifying and modelling the structure of biomolecular networks, as well as the application of centrality measures to interaction networks and research on the hierarch ..."
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In this paper, we present a survey of the use of graph theoretical techniques in Biology. In particular, we discuss recent work on identifying and modelling the structure of biomolecular networks, as well as the application of centrality measures to interaction networks and research on the hierarchical structure of such networks and network motifs. Work on the link between structural network properties and dynamics is also described, with emphasis on synchronization and disease propagation. 1
Observing local and global properties of metabolic pathways: ‘load points’ and ‘choke points’ in the metabolic networks
, 2006
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Using the Topology of Metabolic Networks to Predict Viability of Mutant Strains
"... ABSTRACT Understanding the relationships between the structure (topology) and function of biological networks is a central question of systems biology. The idea that topology is a major determinant of systems function has become an attractive and highly disputed hypothesis. Although structural analy ..."
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ABSTRACT Understanding the relationships between the structure (topology) and function of biological networks is a central question of systems biology. The idea that topology is a major determinant of systems function has become an attractive and highly disputed hypothesis. Although structural analysis of interaction networks demonstrates a correlation between the topological properties of a node (protein, gene) in the network and its functional essentiality, the analysis of metabolic networks fails to find such correlations. In contrast, approaches utilizing both the topology and biochemical parameters of metabolic networks, e.g., flux balance analysis, are more successful in predicting phenotypes of knockout strains. We reconcile these seemingly conflicting results by showing that the topology of the metabolic networks of both Escherichia coli and Saccharomyces cerevisiae are, in fact, sufficient to predict the viability of knockout strains with accuracy comparable to flux balance analysis on large, unbiased mutant data sets. This surprising result is obtained by introducing a novel topologybased measure of network transport: synthetic accessibility. We also show that other popular topologybased characteristics such as node degree, graph diameter, and node usage (betweenness) fail to predict the viability of E. coli mutant strains. The success of synthetic accessibility demonstrates its ability to capture the essential properties of the metabolic network, such as the branching of chemical reactions and the directed transport of material from inputs to outputs. Our results strongly support a link between the topology and function of biological networks and, in agreement with recent genetic studies, emphasize the minimal role of flux rerouting in providing robustness of mutant strains.
Highly optimised global organisation of metabolic networks
 IEE Proceedings: Systems Biology 152
, 2005
"... Abstract: Highlevel, mathematically precise descriptions of the global organisation of complex metabolic networks are necessary for understanding the global structure of metabolic networks, the interpretation and integration of large amounts of biologic data (sequences, various omics) and ultim ..."
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Abstract: Highlevel, mathematically precise descriptions of the global organisation of complex metabolic networks are necessary for understanding the global structure of metabolic networks, the interpretation and integration of large amounts of biologic data (sequences, various omics) and ultimately for rational design of therapies for disease processes. Metabolic networks are highly organised to execute their function efficiently while tolerating wide variation in their environment. These networks are constrained by physical requirements (e.g. conservation of energy, redox and small moieties) but are also remarkably robust and evolvable. The authors use wellknown features of the stoichiometry of bacterial metabolic networks to demonstrate how network architecture facilitates such capabilities, and to develop a minimal abstract metabolism which incorporates the known features of the stoichiometry and respects the constraints on enzymes and reactions. This model shows that the essential functionality and constraints drive the tradeoffs between robustness and fragility, as well as the largescale structure and organisation of the whole network, particularly high variability. The authors emphasise how domainspecific constraints and tradeoffs imposed by the environment are important factors in shaping stoichiometry. Importantly, the consequence of these highly organised tradeoffs and tolerances is an architecture that has a highly structured modularity that is selfdissimilar and scalerich. Introduction Metabolic networks, which have been extensively studied for decades, are emblematic of how evolution has sculpted biologic systems for optimal function. In addition to unambiguous functional descriptions of core metabolism, this conserved network has been recently described in detail in terms of its stoichiometry (mass and energy balance). A higher level, mathematically defined description of the global organisation of complex metabolic networks is critical for a deep understanding of metabolism, from the interpretation of huge amounts of biologic data (sequences, various omics) to design of therapies for disease processes. The stakes are high for obtaining the big picture right: biologic data plugged into a distorted model or interpreted in the context of a flawed universal law propagates misinterpretations. In flux analyses [1], stoichiometry is considered as a constraint, and fluxes are optimised to satisfy a global objective, typically growth. Previous studies, however, have not directly addressed whether the stoichiometry itself is highly optimal or organised in any sense and contributes to the origins and purpose of complexity in biological networks. Yet biochemistry textbooks describe metabolism as having evolved to be 'highly integrated' with the appearance of a 'coherent design' [2]. Here we explore both important 'design' (with no implication of a 'designer') features of metabolism and the sense in which stoichiometry itself has highly organised and optimised tolerances and tradeoffs (HOT) Basic features of metabolic networks Metabolism is essentially a linked series of chemical reactions, which function to synthesise building blocks for usable cellular components and to extract energy and reducing power from the cellular environment, in the context of total organism homeostasis. Constraints on the network are imposed by highly unpredictable intracellular and extracellular environments as well as the details of enzyme molecular structure, the cost of making enzymes and the conservation of atoms, energy and small moieties. The simplest model of metabolic networks is a stoichiometry matrix (smatrix for short) of chemical reactions with the metabolites in rows and reactions in columns and is defined unambiguously except for permutations of rows # IEE, 2005
A bilevel optimization algorithm to identify enzymatic capacity constraints in metabolic networks
, 2008
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Minimal Cut Sets and Their Use in
"... This thesis may be consulted by you, provided you comply with the provisions of the Act and the following conditions of use: you will use the copy only for the purposes of research or private study you will recognise the author's right to be identified as the author of the thesis and due ack ..."
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This thesis may be consulted by you, provided you comply with the provisions of the Act and the following conditions of use: you will use the copy only for the purposes of research or private study you will recognise the author's right to be identified as the author of the thesis and due acknowledgement will be made to the author where appropriate you will obtain the author's permission before publishing any material from the thesis.
doi:10.1155/2010/415148 Research Article Optimal Fluxes, Reaction Replaceability, and Response to
, 2010
"... which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Characterizing the capabilities, key dependencies, and response to perturbations of genomescale metabolic networks is a basic problem with important applications. A key questi ..."
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which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Characterizing the capabilities, key dependencies, and response to perturbations of genomescale metabolic networks is a basic problem with important applications. A key question concerns the identification of the potentially most harmful reaction knockouts. The integration of combinatorial methods with sampling techniques to explore the space of viable flux states may provide crucial insights on this issue. We assess the replaceability of every metabolic conversion in the human red blood cell by enumerating the alternative paths from substrate to product, obtaining a complete map of he potential damage of single enzymopathies. Sampling the space of optimal steady state fluxes in the healthy and in the mutated cell reveals both correlations and complementarity between topologic and dynamical aspects. 1.
CURRENT PERSPECTIVE ESSAY SPECIAL SERIES ON LARGESCALE BIOLOGY Network Inference, Analysis, and Modeling in Systems Biology
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CURRENT PERSPECTIVE ESSAY SPECIAL SERIES ON LARGESCALE BIOLOGY Network Inference, Analysis, and Modeling in Systems Biology
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An Overview of Systems Biology
"... This chapter provides an overview of three crucial aspects of systems biology: constructing biological networks, analyzing and modeling the structure of biological networks, and modeling the dynamics of biological networks. We describe the types of intracellular networks most often studied, and the ..."
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This chapter provides an overview of three crucial aspects of systems biology: constructing biological networks, analyzing and modeling the structure of biological networks, and modeling the dynamics of biological networks. We describe the types of intracellular networks most often studied, and the “omic ” information available to synthesize these networks, with a special focus on plant biology. We review the computational methods used to construct or infer (reverse engineer) intracellular networks. We present the graph theoretical measures most useful for understanding the organization of biological networks, from the single node level to the global properties of the whole network. A representative sample of biological network models is provided, ranging from static models to dynamic models that incorporate how the status of the nodes changes in time. Throughout the chapter we focus on the biological predictions possible by combining experimental, theoretical and computational methods.