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Model-Based Characterization of Intrinsic Noise in Multistable Genetic Circuits

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Model-Based Characterization of Intrinsic Noise in Multistable Genetic Circuits Fakultat¨ fur¨ Maschinenwesen Technische Universitat¨ Munchen¨ Technische Universit¨atM¨unchen Professur f¨urSystembiotechnologie Model-based Characterization of Intrinsic Noise in Multistable Genetic Circuits Sayuri Katharina Hortsch Vollst¨andigerAbdruck der von der Fakult¨atf¨urMaschinenwesen der Technischen Universit¨atM¨unchen zur Erlangung des akademischen Grades eines Doktor-Ingenieurs (Dr.-Ing.) genehmigten Dissertation. Vorsitzende: Prof. Dr. rer. nat. Sonja Berensmeier Pr¨ufendeder Dissertation: 1. Prof. Dr.-Ing. Andreas Kremling 2. Prof. Dr. rer. nat. Christina Kuttler Die Dissertation wurde am 02.07.2018 bei der Technischen Universit¨atM¨unchen eingereicht und durch die Fakult¨atf¨urMaschinenwesen am 03.09.2018 angenommen. Meiner Familie Danksagung Die vorliegende Arbeit entstand w¨ahrendmeiner Zeit als wissenschaftliche Mitarbeiterin an der Professur f¨urSystembiotechnologie der Technischen Universit¨atM¨unchen. Diese Zeit war gepr¨agtvon der Besch¨aftigungmit vielen spannenden Forschungsthemen, von neuartigen inte- ressanten Herausforderungen und Erfahrungen, und von den vielen wunderbaren Menschen, die ich kennenlernen durfte. Dies alles w¨arenicht m¨oglich gewesen ohne meinen Doktorvater, Herrn Prof. Dr.-Ing. Andreas Kremling. Vielen Dank f¨urIhr großes Vertrauen, f¨urIhre Unterst¨utzungund f¨urden n¨otigen Raum zu meiner fachlichen und pers¨onlichen Weiterentwicklung. Wenn ich mich festgefahren hatte, brachten Sie mich mit Geduld und Zuversicht dazu, den weiteren Weg doch zu meistern. Ganz herzlich m¨ochte ich auch meiner Mentorin und Zweitpr¨uferin,Frau Prof. Dr. Christina Kuttler, meinen außerordentlichen Dank aussprechen. Sie waren schon w¨ahrenddes Studiums eine wichtige Ansprechpartnerin f¨urmich, vom Proseminar bis hin zu meiner Masterarbeit. Vielen Dank, dass Sie mir immer so hilfsbereit mit Rat und Tat zur Seite standen! Frau Prof. Dr. Sonja Berensmeier danke ich herzlich f¨urdie Ubernahme¨ des Pr¨ufungsvorsitzes. Bei den Partnern des e:biofilm-Projekts, vor allem bei Prof. Dr. Irene Wagner-D¨oblerund bei Dr. Michael Reck vom HZI Braunschweig, m¨ochte ich mich f¨urdie Zusammenarbeit und die vielen spannenden und sehr angenehmen Projekttreffen bedanken. Es war eine Freude, Einblicke in so viele verschiedene Bereiche zu bekommen und dar¨uber diskutieren zu k¨onnen. Nun zum vielleicht sch¨onstenBestandteil meines Arbeitsalltags { meinen lieben Kollegen aus der Systembiotechnologie, der Selektiven Trenntechnik und der Bioverfahrenstechnik: Danke f¨urden tollen Zusammenhalt ¨uber die Grenzen der Uni hinweg, den intensiven Austausch, Eure Hilfe, Eure Ratschl¨ageund den vielen Spaß, den wir immer hatten. Ihr habt mir jeden Tag vers¨ußtund Ihr wisst ja, wie sehr ich S¨ußessch¨atze!Ein Extra-Dankesch¨ongeb¨uhrtDr. Alberto Mar´ın-Sanguinof¨urdas Korrekturlesen von Teilen der Arbeit und f¨urseine sonstigen fachlichen und auch nicht-fachlichen Hilfestellungen. W¨ahrendder turbulenten Promotionsphase gab es eine Konstante, und sie geht weit ¨uber diese Zeit hinaus: Meine Familie. Danke an meine Eltern, dass Ihr immer f¨urmich da seid, dass Ihr immer mit mir mitgefiebert, mitgelitten und mitgejubelt habt, und Euch immer begeistern konntet f¨urdas, was ich mache, egal, was es war. Und an Ralf { meine Dankbarkeit f¨urDeine immerw¨ahrendeUnterst¨utzungund Geduld, mit der Du mich durch die Promotion begleitet hast, l¨asstsich kaum in Worte fassen. Abstract In biological cells, the stochasticity of biochemical reactions inevitably causes so-called cellular noise, resulting in fluctuating copy numbers of mRNA and protein species. In multistable gene expression systems, large noise may lead to random transitions between distinct cellular states and thus to heterogeneous population behavior. The aim of this work was to use mathematical methods to predict and to gain control over the magnitude and the effects of gene expression noise. In a preliminary study, an analytical comparison between deterministic and stochastic model descriptions was performed and it was shown that the reliability of deterministic models in the context of gene expression is limited: Under common conditions, neither the average cel- lular behavior, nor the preferred states of the system were depicted correctly. In particular, deterministic bistability was not always associated with stochastic bimodality (and thus with phenotypic heterogeneity). Criteria for the occurrence of such discrepancies could be identified and visualized through a systematic graphical model analysis. Among these criteria are large protein bursts combined with nonlinear reaction kinetics. The usage of deterministic approaches for model simplification in order to approximately quantify cellular noise can thus lead to poor estimates. This is, for example, the case with the classical linear noise approximation (LNA). Due to that, a novel method called hybrid LNA (hLNA) was developed for the evaluation of noise. This method is able to predict the variance of mRNA and protein fluctuations, based on the kinetic parameters of the underlying regulatory system, with significantly increased accuracy. Using this method, every stable expression state can be analyzed separately, so that multistable systems can be characterized as well. Moreover, new definitions for the average protein burst size and frequency were derived, which are again suitable for the characterization of multistable systems. Based on those measures, the temporal structure of fluctuations can be investigated. Additionally, a model reduction method was proposed based on the burst characteristics, which enables an a priori estimation of the location of modes in a protein distribution. The quality of all newly developed methods was verified through simulation studies. This framework of novel methods was subsequently used to comprehensively characterize noise in two bistable motifs, namely in an autoregulatory gene expression system and in the genetic toggle switch. It was systematically evaluated how the strength and structure of mRNA and protein fluctuations may be manipulated using specific genetic modifications of the regulatory system. That way, the robustness of single expression states could be changed, which led to various, partially complex heterogeneous patterns of population behavior. All in all, this work demonstrated the significance of intrinsic noise in gene expression systems, regarding the choice and reliability of mathematical modeling approaches as well as the biological functionality of a system. The presented methods are not only suited to incorporate the effects of cellular noise into the study of natural systems, but also to support the creation of robust synthetic constructs, for example for applications in biotechnology. vii Zusammenfassung In biologischen Zellen verursacht die Stochastizit¨atbiochemischer Reaktionen zwangsl¨aufigso- genanntes zellul¨ares Rauschen. Dieses ¨außertsich u. a. in fluktuierenden Kopienzahlen von mRNA- und Proteinspezies. In multistabilen Genexpressionssystemen kann starkes Rauschen zu zufallsgetriebenen Uberg¨angenzwischen¨ verschiedenen Zellzust¨anden und damit zu hetero- genem Populationsverhalten f¨uhren. Das Ziel der Arbeit bestand darin, mit Hilfe mathemati- scher Methoden die St¨arke und die Auswirkungen von Genexpressions-Rauschen vorhersagbar und besser kontrollierbar zu machen. Als Voruntersuchung wurde ein analytischer Vergleich deterministischer und stochastischer Modellbeschreibungen vollzogen und gezeigt, dass die Aussagekraft deterministischer Modelle im Kontext der Genexpression eingeschr¨anktist: Unter ¨ublichen Bedingungen bildeten sie weder das durchschnittliche Zellverhalten, noch bevorzugte Zellzust¨andekorrekt ab. Insbesondere war deterministische Bistabilit¨atnicht immer mit stochastischer Bimodalit¨at(und damit mit ph¨ano- typischer Heterogenit¨at)assoziiert. Kriterien f¨urdas Auftreten solcher Diskrepanzen konnten durch eine systematische graphische Modellanalyse identifiziert und veranschaulicht werden. Unter diesen Kriterien sind vor allem große Protein-Bursts, kombiniert mit nichtlinearen Reak- tionskinetiken, zu nennen. Werden demnach deterministische Ans¨atzezur Modelleinfachung genutzt, um zellul¨aresRauschen approximativ zu quantifizieren, kann dies zu gravierenden Fehleinsch¨atzungenf¨uhren. Dies ist beispielsweise bei der klassischen Linear Noise Approxi- mation (LNA) der Fall. Daher wurde zur Quantifizierung des Rauschens eine neue Methode, die Hybrid-LNA (hLNA) entwickelt. Diese kann, basierend auf den kinetischen Parametern des betrachteten Regula- tionssystems, die sich ergebende Varianz der mRNA- und Proteinfluktuationen mit deutlich gesteigerter Genauigkeit vorhersagen. Dabei kann jeder stabile Expressionszustand getrennt untersucht werden, so dass auch multistabile Systeme charakterisiert werden k¨onnen. Deswei- teren wurden neue Definitionen f¨urdie durchschnittliche Protein-Burst-Gr¨oßeund {Frequenz hergeleitet, die ebenfalls f¨urdie Charakterisierung multistabiler Systeme geeignet sind. Damit kann auch die zeitliche Struktur von Fluktuationen untersucht werden. Dar¨uberhinaus wurde basierend auf den Burst-Charakteristiken eine Methode zur Modellreduktion vorgeschlagen, mit deren Hilfe eine a-priori-Absch¨atzungder Lage der Modalwerte einer Proteinverteilung m¨oglich ist. Die Qualit¨atder neu entwickelten Methoden wurde durch Simulationsstudien verifiziert. Das erarbeitete Methodenspektrum wurde anschließend zur umfassenden Charakterisierung des Rauschens in zwei bistabilen Motiven verwendet, n¨amlich in einem autoregulatorischen Gen- expressionssystem
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