Visual Network Analysis of Dynamic Metabolic Pathways

Abstract. We extend our previous work on the exploration of static metabolic networks to evolving, and therefore dynamic, pathways. We apply our visualization software to data from a simulation of early metabolism. Thereby, we show that our technique allows us to test and argue for or against different scenarios for the evolution of metabolic pathways. This supports a profound and efficient analysis of the structure and properties of the generated metabolic networks and its underlying components, while giving the user a vivid impression of the dynamics of the system. The analysis process is inspired by Ben Shneiderman’s mantra of information visualization. For the overview, user-defined diagrams give insight into topological changes of the graph as well as changes in the attribute set associated with the participating enzymes, substances and reactions. This way, “interesting features” in time as well as in space can be recognized. A linked view implementation enables the navigation into more detailed layers of perspective for in-depth analysis of individual network configuration

Evolution of Metabolic Networks: A Computational Framework

Background: The metabolic architectures of extant organisms share many key pathways such as the citric acid cycle, glycolysis, or the biosynthesis of most amino acids. Several competing hypotheses for the evolutionary mechanisms that shape metabolic networks have been discussed in the literature, each of which finds support from comparative analysis of extant genomes. Alternatively, the principles of metabolic evolution can be studied by direct computer simulation. This requires, however, an explicit implementation of all pertinent components: a universe of chemical reaction upon which the metabolism is built, an explicit representation of the enzymes that implement the metabolism, of a genetic system that encodes these enzymes, and of a fitness function that can be selected for. Results: We describe here a simulation environment that implements all these components in a simplified ways so that large-scale evolutionary studies are feasible. We employ an artificial chemistry that views chemical reactions as graph rewriting operations and utilizes a toy-version of quantum chemistry to derive thermodynamic parameters. Minimalist organisms with simple string-encoded genomes produce model ribozymes whose catalytic activity is determined by an ad hoc mapping between their secondary structure and the transition state graphs that they stabilize. Fitness is computed utilizing the ideas of metabolic flux analysis. We present an implementation of the complete system and first simulation results. Conclusions: The simulation system presented here allows coherent investigations into the evolutionary mechanisms of the first steps of metabolic evolution using a self-consistent toy univers

Computational Studies on the Evolution of Metabolism

Living organisms throughout evolution have developed desired properties, such as the ability of maintaining functionality despite changes in the environment or their inner structure, the formation of functional modules, from metabolic pathways to organs, and most essentially the capacity to adapt and evolve in a process called natural selection. It can be observed in the metabolic networks of modern organisms that many key pathways such as the citric acid cycle, glycolysis, or the biosynthesis of most amino acids are common to all of them. Understanding the evolutionary mechanisms behind this development of complex biological systems is an intriguing and important task of current research in biology as well as artificial life. Several competing hypotheses for the formation of metabolic pathways and the mecha- nisms that shape metabolic networks have been discussed in the literature, each of which finds support from comparative analysis of extant genomes. However, while being powerful tools for the investigation of metabolic evolution, these traditional methods do not allow to look back in evolution far enough to the time when metabolism had to emerge and evolve to the form we can observe today. To this end, simulation studies have been introduced to discover the principles of metabolic evolution and the sources for the emergence of metabolism prop- erties. These approaches differ considerably in the realism and explicitness of the underlying models. A difficult trade-off between realism and computational feasibility has to be made and further modeling decisions on many scales have to be taken into account, requiring the combination of knowledge from different fields such as chemistry, physics, biology and last but not least also computer science. In this thesis, a novel computational model for the in silico evolution of early metabolism is introduced. It comprises all the components on different scales to resemble a situation of evolving metabolic protocells in an RNA-world. Therefore, the model contains a minimal RNA-based genetics and an evolving metabolism of catalytic ribozymes that manipulate a rich underlying chemistry. To allow the metabolic organization to escape from the confines of the chemical space set by the initial conditions of the simulation and in general an open- ended evolution, an evolvable sequence-to-function map is used. At the heart of the metabolic subsystem is a graph-based artificial chemistry equipped with a built-in thermodynamics. The generation of the metabolic reaction network is realized as a rule-based stochastic simulation. The necessary reaction rates are calculated from the chemical graphs of the reactants on the fly. The selection procedure among the population of protocells is based on the optimal metabolic yield of the protocells, which is computed using flux balance analysis. The introduced computational model allows for profound investigations of the evolution of early metabolism and the underlying evolutionary mechanisms. One application in this thesis is the study of the formation of metabolic pathways. Therefore, four established hypothe- ses, namely the backwards evolution, forward evolution, patchwork evolution and the shell hypothesis, are discussed within the realms of this in silico evolution study. The metabolic pathways of the networks, evolved in various simulation runs, are determined and analyzed in terms of their evolutionary direction. The simulation results suggest that the seemingly mutually exclusive hypotheses may well be compatible when considering that different pro- cesses dominate different phases in the evolution of a metabolic system. Further, it is found that forward evolution shapes the metabolic network in the very early steps of evolution. In later and more complex stages, enzyme recruitment supersedes forward evolution, keeping a core set of pathways from the early phase. Backward evolution can only be observed under conditions of steady environmental change. Additionally, evolutionary history of enzymes and metabolites were studied on the network level as well as for single instances, showing a great variety of evolutionary mechanisms at work. The second major focus of the in silico evolutionary study is the emergence of complex system properties, such as robustness and modularity. To this end several techniques to analyze the metabolic systems were used. The measures for complex properties stem from the fields of graph theory, steady state analysis and neutral network theory. Some are used in general network analysis and others were developed specifically for the purpose introduced in this work. To discover potential sources for the emergence of system properties, three different evolutionary scenarios were tested and compared. The first two scenarios are the same as for the first part of the investigation, one scenario of evolution under static conditions and one incorporating a steady change in the set of ”food” molecules. A third scenario was added that also simulates a static evolution but with an increased mutation rate and regular events of horizontal gene transfer between protocells of the population. The comparison of all three scenarios with real world metabolic networks shows a significant similarity in structure and properties. Among the three scenarios, the two static evolutions yield the most robust metabolic networks, however, the networks evolved under environmental change exhibit their own strategy to a robustness more suited to their conditions. As expected from theory, horizontal gene transfer and changes in the environment seem to produce higher degrees of modularity in metabolism. Both scenarios develop rather different kinds of modularity, while horizontal gene transfer provides for more isolated modules, the modules of the second scenario are far more interconnected

Computational Studies on the Evolution of Metabolism

Living organisms throughout evolution have developed desired properties, such as the ability of maintaining functionality despite changes in the environment or their inner structure, the formation of functional modules, from metabolic pathways to organs, and most essentially the capacity to adapt and evolve in a process called natural selection. It can be observed in the metabolic networks of modern organisms that many key pathways such as the citric acid cycle, glycolysis, or the biosynthesis of most amino acids are common to all of them. Understanding the evolutionary mechanisms behind this development of complex biological systems is an intriguing and important task of current research in biology as well as artificial life. Several competing hypotheses for the formation of metabolic pathways and the mecha- nisms that shape metabolic networks have been discussed in the literature, each of which finds support from comparative analysis of extant genomes. However, while being powerful tools for the investigation of metabolic evolution, these traditional methods do not allow to look back in evolution far enough to the time when metabolism had to emerge and evolve to the form we can observe today. To this end, simulation studies have been introduced to discover the principles of metabolic evolution and the sources for the emergence of metabolism prop- erties. These approaches differ considerably in the realism and explicitness of the underlying models. A difficult trade-off between realism and computational feasibility has to be made and further modeling decisions on many scales have to be taken into account, requiring the combination of knowledge from different fields such as chemistry, physics, biology and last but not least also computer science. In this thesis, a novel computational model for the in silico evolution of early metabolism is introduced. It comprises all the components on different scales to resemble a situation of evolving metabolic protocells in an RNA-world. Therefore, the model contains a minimal RNA-based genetics and an evolving metabolism of catalytic ribozymes that manipulate a rich underlying chemistry. To allow the metabolic organization to escape from the confines of the chemical space set by the initial conditions of the simulation and in general an open- ended evolution, an evolvable sequence-to-function map is used. At the heart of the metabolic subsystem is a graph-based artificial chemistry equipped with a built-in thermodynamics. The generation of the metabolic reaction network is realized as a rule-based stochastic simulation. The necessary reaction rates are calculated from the chemical graphs of the reactants on the fly. The selection procedure among the population of protocells is based on the optimal metabolic yield of the protocells, which is computed using flux balance analysis. The introduced computational model allows for profound investigations of the evolution of early metabolism and the underlying evolutionary mechanisms. One application in this thesis is the study of the formation of metabolic pathways. Therefore, four established hypothe- ses, namely the backwards evolution, forward evolution, patchwork evolution and the shell hypothesis, are discussed within the realms of this in silico evolution study. The metabolic pathways of the networks, evolved in various simulation runs, are determined and analyzed in terms of their evolutionary direction. The simulation results suggest that the seemingly mutually exclusive hypotheses may well be compatible when considering that different pro- cesses dominate different phases in the evolution of a metabolic system. Further, it is found that forward evolution shapes the metabolic network in the very early steps of evolution. In later and more complex stages, enzyme recruitment supersedes forward evolution, keeping a core set of pathways from the early phase. Backward evolution can only be observed under conditions of steady environmental change. Additionally, evolutionary history of enzymes and metabolites were studied on the network level as well as for single instances, showing a great variety of evolutionary mechanisms at work. The second major focus of the in silico evolutionary study is the emergence of complex system properties, such as robustness and modularity. To this end several techniques to analyze the metabolic systems were used. The measures for complex properties stem from the fields of graph theory, steady state analysis and neutral network theory. Some are used in general network analysis and others were developed specifically for the purpose introduced in this work. To discover potential sources for the emergence of system properties, three different evolutionary scenarios were tested and compared. The first two scenarios are the same as for the first part of the investigation, one scenario of evolution under static conditions and one incorporating a steady change in the set of ”food” molecules. A third scenario was added that also simulates a static evolution but with an increased mutation rate and regular events of horizontal gene transfer between protocells of the population. The comparison of all three scenarios with real world metabolic networks shows a significant similarity in structure and properties. Among the three scenarios, the two static evolutions yield the most robust metabolic networks, however, the networks evolved under environmental change exhibit their own strategy to a robustness more suited to their conditions. As expected from theory, horizontal gene transfer and changes in the environment seem to produce higher degrees of modularity in metabolism. Both scenarios develop rather different kinds of modularity, while horizontal gene transfer provides for more isolated modules, the modules of the second scenario are far more interconnected

Visualization of Metabolic Networks

The metabolism constitutes the universe of biochemical reactions taking place in a cell of an organism. These processes include the synthesis, transformation, and degradation of molecules for an organism to grow, to reproduce and to interact with its environment. A good way to capture the complexity of these processes is the representation as metabolic network, in which sets of molecules are transformed into products by a chemical reaction, and the products are being processed further. The underlying graph model allows a structural analysis of this network using established graphtheoretical algorithms on the one hand, and a visual representation by applying layout algorithms combined with information visualization techniques on the other. In this thesis we will take a look at three different aspects of graph visualization within the context of biochemical systems: the representation and interactive exploration of static networks, the visual analysis of dynamic networks, and the comparison of two network graphs. We will demonstrate, how established infovis techniques can be combined with new algorithms and applied to specific problems in the area of metabolic network visualization. We reconstruct the metabolic network covering the complete set of chemical reactions present in a generalized eucaryotic cell from real world data available from a popular metabolic pathway data base and present a suitable data structure. As the constructed network is very large, it is not feasible for the display as a whole. Instead, we introduce a technique to analyse this static network in a top-down approach starting with an overview and displaying detailed reaction networks on demand. This exploration method is also applied to compare metabolic networks in different species and from different resources. As for the analysis of dynamic networks, we present a framework to capture changes in the connectivity as well as changes in the attributes associated with the network’s elements

Dynamical Models of biological networks

In der Molekularbiologie sind mathematische Modelle von regulatorischen und metabolischen Netzwerken essentiell, um von einer Betrachtung isolierter Komponenten und Interaktionen zu einer systemischen Betrachtungsweise zu kommen. Genregulatorische Systeme eignen sich besonders gut zur Modellierung, da sie experimentell leicht zugänglich und manipulierbar sind. In dieser Arbeit werden verschiedene genregulatorische Netzwerke unter Zuhilfenahme von mathematischen Modellen analysiert. Weiteres wird ein Modell einer in silico Zelle vorgestellt und diskutiert. Zunächst werden zwei zyklische genregulatorische Netzwerke - der klassische Repressilator und ein Repressilator mit zusätzlicher Autoaktivierung – im Detail mit analytischen Methoden untersucht. Um den Einfluß zufällig schwankender Molekülzahlen auf die Dynamik der beiden Systeme zu untersuchen, werden stochastische Modelle erstellt und die beiden oszillierenden Systeme verglichen. Weiteres werden mögliche Auswirkungen von Genduplikationen auf ein einfaches genregulatorisches Netzwerk untersucht. Dazu wird zunächst ein kleines Netzwerk von GATA Transkriptionsfaktoren, das eine zentrale Rolle in der Regulation des Stickstoffmetabolismus in Hefe spielt, modelliert und das Modell mit experimentellen Daten verglichen, um Parameterregionen einschränken zu können. Außerdem werden potentielle Topologien genregulatorischer Netzwerke von GATA Transkriptionsfaktoren in verwandten Fungi mittels sequenzbasierender Methoden gesucht und verglichen. Im letzten Teil der Arbeit wird MiniCellSim vorgestellt, ein Modell einer selbständigen in silico Zelle. Es erlaubt ein dynamisches System, das eine Protozelle mit einem genregulatorischen Netzwerk, einem einfachen Metabolismus und einer Zellmembran beschreibt, aus einer Sequenz abzuleiten. Nachdem alle Parameter, die zur Berechnung des dynamischen Systems benötigt werden, ohne zusätzliche Eingabe nur aus der Sequenzinformation abgeleitet werden, kann das Modell für Studien zur Evolution von genregulatorischen Netzwerken verwendet werden.In this thesis different types of gene regulatory networks are analysed using mathematical models. Further a computational framework of a novel, self-contained in silico cell model is described and discussed. At first the behaviour of two cyclic gene regulatory systems - the classical repressilator and a repressilator with additional auto-activation - are inspected in detail using analytical bifurcation analysis. To examine the behaviour under random fluctuations, stochastic versions of the systems are created. Using the analytical results sustained oscillations in the stochastic versions are obtained, and the two oscillating systems compared. In the second part of the thesis possible implications of gene duplication on a simple gene regulatory system are inspected. A model of a small network formed by GATA-type transcription factors, central in nitrogen catabolite repression in yeast, is created and validated against experimental data to obtain approximate parameter values. Further, topologies of potential gene regulatory networks and modules consisting of GATA-type transcription factors in other fungi are derived using sequence-based approaches and compared. The last part describes MiniCellSim, a model of a self-contained in silico cell. In this framework a dynamical system describing a protocell with a gene regulatory network, a simple metabolism, and a cell membrane is derived from a string representing a genome. All the relevant parameters required to compute the time evolution of the dynamical system are calculated from within the model, allowing the system to be used in studies of evolution of gene regulatory and metabolic networks