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Topological Analysis of Metabolic and Regulatory Networks by Decomposition Methods

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Topological Analysis of Metabolic and Regulatory Networks by Decomposition Methods Topological analysis of metabolic and regulatory networks by decomposition methods DISSERTATION zur Erlangung des akademischen Grades doctor rerum naturalium (dr. rer. nat.) im Fach Biophysik eingereicht an der Mathematisch-Naturwissenschaftlichen Fakult¨atI Humboldt-Universit¨atzu Berlin von Frau Dipl.-Inf. Ionela Oancea geboren am 22.02.1977 in Bukarest Pr¨asident der Humboldt-Universit¨at zu Berlin: Prof. Dr. J¨urgen Mlynek Dekan der Mathematisch-Naturwissenschaftlichen Fakult¨atI: Prof. Dr. Michael Linscheid Gutachter: 1. Prof. Dr. Reinhart Heinrich 2. Prof. Dr. Hermann-Georg Holzh¨utter 3. Prof. Dr. Stefan Schuster eingereicht am: 21. Juli 2003 Tag der m¨undlichen Pr¨ufung: 1. Dezember 2003 Zusammenfassung Die lebenden Organismen sind fur¨ eine wissenschaftliche Analyse zu kom- pliziert, wenn man sie als Ganzes und in ihrer vollen Komplexit¨at betrachtet. Die vorliegende Arbeit behandelt die topologischen Eigenschaften von zwei wichtigen Teilen der lebenden Organismen: die metabolischen und die re- gulatorischen Systeme. Topolgische Eigenschaften sind solche, die durch die Netwerkstruktur bedingt werden. Ein Signalsystem ist eine spezielle Art von regulatorischem System. Zwischen den metabolischen und Signalnetzen gibt es wichtige Unterschiede, die ihre Behandlung in unterschiedlicher Weise er- fordert. In der metabolischen Pfadanalyse ist das Konzept der elementaren Flussmoden bereits als ein passendes Instrument fur¨ die Charakterisierung der einfachsten essentiellen Wege in biochemischen Systemen etabliert. Wir untersuchen die Eigenschaften und Vorteile dieses Konzepts in einigen be- sonderen F¨allen. Zuerst untersuchen wir die vielfach vorkommenden Enzyme mit niedri- ger Spezifit¨at (z.B. Nukleosiddiphosphokinase, Uridinkinase, Transketolase, Transaldolase). Sie k¨onnen parallel verschiedene Substrate und Produkte um- wandeln. Auch die Enzym-Mechanismen sind vielf¨altig, wie wir mit dem Re- aktionsschema fur¨ bifunktionelle Enzyme veranschaulichen. Wir betrachten dabei nur den Fall, dass ein bestimmtes aktives Zentrum mehrere Reaktio- nen katalysiert. Der Fall, dass das studierte Enzym mehrere solche aktiven Zentren hat, kann in den Fall mehrerer Enzyme transformiert werden, die nur ein aktives Zentrum haben. Wenn eine Krankheit das Ausgangsenzym ¨andert, werden dann in der Analyse auch alle ersetzenden Enzyme ge¨andert. Es gibt zwei unterschiedliche Betrachtungsweisen, um multifunktionelle En- zyme zu beschreiben. Zum einen kann man die Gesamtreaktionen betrachten und zum anderen die elementaren Reaktionsschritte (Hemireaktionen, Halb- reaktionen). Fur¨ Enzyme mit zwei oder mehr Funktionen ist es wichtig, nur linear unabh¨angige Funktionen zu betrachten, weil sonst zyklische elementare Moden auftreten wurden,¨ die keine Nettoumwandlung durchfuhren.¨ Jedoch ist die Wahl der linear unabh¨angigen Funktionen nicht a priori eindeutig. Wir stellen eine Methode fur¨ das Treffen dieser Wahl vor, indem wir die kon- vexe Basis des Hemireaktions-Systems betrachten. Eine formale Anwendung des Algorithmus fur¨ das Berechnen der elementaren Flussmoden (Routen) erbringt das Resultat, dass die Zahl solcher Moden manchmal vom Niveau der Beschreibung abh¨angt, wenn einige Reaktionen reversibel sind und die Produkte der multifunktionellen Enzyme externe Metabolite sind, oder ei- nige multifunktionelle Enzyme zum Teil die gleichen Stoffwechselprodukte umwandeln. Jedoch kann dieses Problem durch eine geeignete Deutung der Definition der elementaren Moden und die korrekte Wahl der unabh¨angigen iii Funktionen der Multifunktionsenzyme gel¨ost werden. Die Analyse wird durch einige kleinere Beispiele und ein gr¨oßeres biochemisches Beispiel veranschau- licht, das aus dem Nukleotidmetabolismus stammt und die zwei Arten der Beschreibung fur¨ Nukleosiddiphosphokinase und Adenylatekinase vergleicht. Der Nukleotidmetabolismus spielt eine wichtige Rolle in lebenden Orga- nismen und ist gegenuber¨ allen m¨oglichen St¨orungen in seiner internen Balan- ce sehr empfindlich. Gef¨ahrliche Krankheiten k¨onnen auftreten, wenn einige Enzyme nicht richtig funktionieren. Mit Hilfe des Konzeptes des elementaren Flussmodus erkl¨aren wir das Auftreten und den Schweregrad von Krank- heiten, die auf Enzymdefizienzen basieren. Wenn ein Enzym vollst¨andig ge- hemmt wird, werden einige metabolische Wege blockiert. Wenn jedoch ei- nige alternative Wege noch bestehen, ist die Krankheit weniger gef¨ahrlich. Unsere Analyse ist darauf gerichtet, alternative Wege, wesentliche Enzyme und solche Enzyme, die immer zusammenarbeiten zu finden. Der letzte Be- griff ist auch als ,Enzyme subset “ bekannt und stellt einen intermedi¨aren Schritt im Algorithmus zur Berechnung der elementaren Flussmoden dar. Wir diskutieren bereits bekannte und bisher nur hypothetische Mechanis- men einiger Krankheiten (proliferative Krankheiten, Immundefizienzen), die auf St¨orungen des Nukleotidmetabolismus oder seiner Ausbeutung durch Vi- ren und Parasiten beruhen. Die meisten Strategien, die fur¨ das Bek¨ampfen solcher Krankheiten eingesetzt werden, basieren auf der Unterbrechung des Nukleotidmetabolismus an bestimmten Stellen. Diese Strategien k¨onnen aber auch zur Akkumulation toxischer Stoffe fuhren¨ und dadurch Nebenwirkun- gen hervorrufen. Deswegen hilft ein besseres Verst¨andnis dieses Systems, wir- kungsvollere Medikamente zu entwickeln, und eine gute strukturelle Analyse kann viele experimentelle Bemuhungen¨ ersparen. Konzepte aus der Theorie der Petri-Netze liefern zus¨atzliche Werkzeu- ge fur¨ das Modellieren metabolischer Netzwerke. In Kapitel 4 werden die Ahnlichkeiten¨ zwischen einigen Konzepten in der traditionellen biochemi- schen Modellierung und analogen Konzepten aus der Petri-Netztheorie be- sprochen. Zum Beispiel entspricht die stochiometrische Matrix eines meta- bolischen Netzwerkes der Inzidenzmatrix des Petri-Netzes. Die Flussmoden und die Erhaltungs-Relationen haben die T-Invarianten beziehungsweise P- Invarianten als Gegenstucke.¨ Wir decken die biologische Bedeutung einiger weiterer Begriffe aus der Theorie der Petri-Netze auf, n¨amlich ,,traps“, ,,si- phons“, ,,deadlocks “ und ,,Lebendigkeit“. Wir konzentrieren uns auf der topologischen Analyse anstatt auf die Analyse des dynamischen Verhaltens. Die geeignete Behandlung der externen Stoffwechselprodukte wird ebenfalls besprochen. Zur Illustration werden einige einfache theoretische Beispiele vorgestellt. Außerdem werden einige Petri-Netze pr¨asentiert, die konkreten biochemischen Netzen entsprechen, um unsere Resultate zu belegen. Zum iv Beispiel wird die Rolle der Triosephosphatisomerase (TPI) im Metabolismus von Trypanosoma brucei ausgewertet, indem traps und siphons ermittelt wer- den. Alle behandelten Eigenschaften von Petri-Netzen werden anhand eines Systems illustriert, das aus dem Nukleotidmetabolismus stammt. W¨ahrend viele Bemuhungen¨ fur¨ das Zerlegen metabolischer Systeme, (ele- mentare Flußmoden, extreme Wege) erfolgt sind, sind bisher unseres Wissens keine Versuche in dieser Richtung fur¨ Signalubertragungssysteme¨ unternom- men worden. Eine spezielle Eigenschaft von Signalnetzwerken in lebenden Zellen ist, dass Aktivierungen, Hemmungen und biochemische Reaktionen normalerweise gleichzeitig anwesend sind. Selbst wenn sie nicht Reaktionen enthalten, machen Mehrfach-Aktivierungen oder Mehrfach-Hemmungen die Netzwerke in hohem Grade verzweigt. Es ist eine schwierige und sehr zeit- raubende Aufgabe, alle Faktoren, die einen Einfluss auf ein gegebenes Ziel haben, ohne eine automatische Methode zu ermitteln. Bereits in Kapitel 1 heben wir die Ahnlichkeiten¨ und Unterschiede zwischen den metabolischen und Signal-Netzwerken hervor. In Kapitel 5 errichten wir einen Rahmen und pr¨asentieren einen Algorithmus fur¨ die Zerlegung von Signalnetzwerken in kleinere Einheiten, die einfacher zu studieren und zu verstehen sind. Zwei F¨alle werden untersucht: ein einfacheres, wenn nur monomolekulare Aktivie- rungen oder Reaktionen anwesend sind, und ein komplizierterer Fall, wenn die Aktivierungen und die Reaktionen multimolekular sein k¨onnen. Ihre Be- schreibung erfordert unterschiedliche Methoden: klassische Graphen bzw. Pe- trinetze. Wir besprechen die Probleme, die in unserem Modell wegen des Vorhandenseins von Hemmungen oder von unbekannten Effekten im Netz auftreten. Der vorgeschlagene Algorithmus ermittelt die Faktoren, die zu- sammenwirken und die Zielsubstanzen, die auf dem gleichen Weg beeinflusst werden. Die Zyklen, die im System auftreten, und m¨ogliche fehlende Reak- tionen werden ebenfalls ermittelt . Theoretische Beispiele veranschaulichen unsere Resultate. Anhand der T-Zell-Antigen-Rezeptor-Signalkaskade zeigen wir, wie die Methoden in realen Systemen angewendet werden k¨onnen. Schlagw¨orter: Enzyme niedriger Spezifit¨at, multifunktionelle Enzyme, Halbreaktionen, En- zymdefizienzen, Nukleotidstoffwechsel, proliferative Krankheiten, Immuno- defizienz, Petri-Netze, Elementarmoden,Signalnetzwerk, Signaltransduktion, Computermodellierung. v Summary The living organisms are too complex when considering them as a whole. The present thesis deals with the topological properties of two important parts of living organisms: the metabolic and the regulatory systems. The topological properties are those features that are determined by the network structure. A classification in metabolic and regulatory systems is often used. A signalling system is a special kind of regulatory system. Between metabolic and signalling networks, there are important differences that impose their treatment in different ways. In metabolic pathway analysis, the
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