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Item Open Access Understanding the mechanisms of robustness in intracellular protein signalling cascades and gene expression(2018) Paul, Debdas; Radde, Nicole (Prof. Dr. rer. nat.)We seek to understand the structural as well as the mechanistic basis of robustness in intracellular protein signalling cascades and in transcriptional regulation of gene expression. For protein signalling cascades, we employ a comparison based study involving a single, a double and a cascade of two double phosphorylation-dephosphorylation (PD) cycles. Using deterministic modelling approaches based on ordinary differential equations (ODE), we observe that the cascade of two double PD cycles exhibits robust output behaviour compared to that of a single and a double PD cycle upon constant as well as time- varying input perturbations. Furthermore, a system theoretic analysis reveals that the protein phosphorylation cascades act as an efficient low-pass filter that attenuates the noise mimicked as high-frequency input signals. Afterwards, we extend the study for a stochastic environment. Simulation results based on the stochastic simulation algorithm (SSA) reveal a novel phenomenon called dynamic sequestration that plays an ambivalent role as an intrinsic noise filter. Overall, the analysis indicates that complexity can be one of the basic principles of robust biological designs such as intracellular protein signalling cascades. A major function of intracellular signalling cascades is to transmit the extracellular signal to the nucleus to initiate the process of gene expression. Gene expression is an intrinsically stochastic process that results into cell-to-cell variability in protein and messenger RNA (mRNA) levels, often termed as the expression noise. In spite of such noise, how cells achieve robustness is therefore a fundamental biological problem. We conclude the thesis by introducing a rule-based modelling approach based on the Kappa (κ) platform with the goal to understand the underlying mechanisms that ensure robust cellular functioning during gene expression. In particular, we introduce a gene expression model that keeps the process of transcription and excludes the process of translation. Therefore, we quantify the expression noise using mRNA which is the end product of transcription. Besides, the motivation behind adopting a rule-based modelling approach is that unlike the ODE-based approach, the former subsumes the combinatorial complexity arises due to various binding configurations of transcription factors (TF) for regulation of gene expression and offers a compact graphical representation of the same. Afterwards, the representation is transformed into an equivalent set of executable κ rules that are simulated using the SSA to obtain distributions of mRNA copy numbers corresponding to different regulatory mechanisms.Item Open Access Sampling-based Bayesian approaches reveal the importance of quasi-bistable behavior in cellular decision processes on the example of the MAPK signaling pathway in PC-12 cell lines(2017) Jensch, Antje; Thomaseth, Caterina; Radde, NicolePositive and negative feedback loops are ubiquitous motifs in biochemical signaling pathways. The mitogen-activated protein kinase (MAPK) pathway module is part of many distinct signaling networks and comprises several of these motifs, whose functioning depends on the cell line at hand and on the particular context. The maintainance of specificity of the response of the MAPK module to distinct stimuli has become a key paradigm especially in PC-12 cells, where the same module leads to different cell fates, depending on the stimulating growth factor. This cell fate is regulated by differences in the ERK (MAPK) activation profile, which shows a transient response upon stimulation with EGF, while the response is sustained in case of NGF. This behavior was explained by different effective network topologies. It is widely believed that this sustained response requires a bistable system. In this study we present a sampling-based Bayesian model analysis on a dataset, in which PC-12 cells have been stimulated with different growth factors. This is combined with novel analysis methods to investigate the role of feedback interconnections to shape ERK response. Results strongly suggest that, besides bistability, an additional effect called quasi-bistability can contribute to explain the observed responses of the system to different stimuli. Quasi-bistability is the ability of a monostable system to maintain two distinct states over a long time period upon a transient signal, which is also related to positive feedback, but cannot be detected by standard steady state analysis methods.Item Open Access Die Phototaxis von Halobakterium salinarum - Mathematische Beschreibung stochastischer Prozesse(2006) Nutsch, Torsten; Gilles, Ernst Dieter (Prof. Dr.-Ing. Dr. h.c. mult.)Die Phototaxis von Halobacterium salinarum ist ein elegantes Beispielsystem für Signaltransduktion in Prokaryoten. Die Zellen verfügen über zwei verschiedene Typen von Photorezeptoren SRI und SRII, die für Licht verschiedener Wellenlängen empfindlich sind. An den Rezeptoren schließt sich ein molekulares Signaltransduktionsnetzwerk an, das das Schwimmverhalten der Zellen je nach äußerem Reiz beeinflusst. Ohne Stimulation wechseln die Zellen immer wieder zufällig zwischen der vorwärts- und rückwärts gerichteten Schwimmbewegung hin und her. Im Mittel geschieht das alle 12 Sekunden. Nach einer Schreckstimulation wird der Wechsel der Schwimmrichtung deutlich schneller eingeleitet, während die Zellen bei einer Lockstimulation die Dauer der aktuellen Schwimmrichtung noch länger ausdehnen. Beide Schwimmphasen verhalten sich sowohl im unstimulierten als auch im stimulierten Fall symmetrisch zueinander. Im Gegensatz zu den gängigen Motormodellen von E. coli befindet sich der Schaltprozess von Halobacterium salinarum nicht im thermischen Gleichgewicht. Vielmehr handelt es sich hier um einen energieverbrauchenden Kreisprozess, der nacheinander unterschiedliche Phasen in einer bestimmten Vorzugsrichtung durchläuft. In einem ersten Schritt konnten mittels Analyse von experimentellen Ergebnissen 8 verschiedene Funktionszustände (Phasen) des halobakteriellen Schaltprozesses identifiziert werden (4 Phasen pro Schwimmrichtung). Die Stopp-Phase ist leicht durch Beobachten der Schwimmbewegung zu erkennen. Sie dauert sowohl im stimulierten als auch im unstimulierten Fall im Mittel 0,43 Sekunden. Nach dieser Phase schwimmt die Zelle in der entgegengesetzten Richtung weiter. In den ersten 1-2 Sekunden nach dieser Richtungsumkehr reagiert sie allerdings verzögert (refraktär) auf einen Schreckreiz. Dieses Verhalten wird der Refraktär-Phase zugeordnet, deren Dauer durch einen Schreckreiz deutlich verlängert wird. Anschließend befindet sich der Schaltkomplex in der Kompetent-Phase. Hier ist der Motor 'kompetent', die Richtungsumkehr bei einem Schreckreiz zu aktivieren. Diese Aktivierung geschieht schließlich in der letzten Phase, der Aktiv-Phase. Danach stoppt der Motor, bevor die Funktionszustände in analoger Art und Weise in der entgegengesetzten Schwimmrichtung durchlaufen werden. In einem zweiten Schritt wurde die Kinetik der einzelnen Phasen aufgrund von gemessenen Häufigkeitsverteilungen von Prozessdauern bestimmt. Darauf hin konnte schließlich ein detailliertes Modell aufgestellt werden, das die einzelnen Phasen sowie die Kinetik ihrer Übergänge miteinander vereint. Es besteht aus 44 Untereinheiten, die sich synchron in einem der oben genannten Funktionszustände befinden. Mit Hilfe des aufgestellten Gesamtmodells, bestehend aus dem einfachen Modell der Signaltransduktion und dem detaillierten Modell des Schaltverhaltens, war es möglich die verschiedensten Experimente zu simulieren. Alle Simulationen zeigten eine recht gute, viele sogar eine sehr gute Übereinstimmung mit den experimentellen Ergebnissen. So kann das Modell z.B. die Häufigkeitsverteilung der Länge einer Schwimmphase sowohl im spontanen als auch im lichtinduzierten Fall bei Stimulation mit einem Schreck- oder Locksignal korrekt wiedergeben. Ebenso beschreibt es die mittlere Reaktionszeit der Zellen auf Einzel- und Doppelpulse aus blauem Licht. Diese Reaktionszeit ist proportional zum Kehrwert der applizierten Lichtmenge sowie proportional zur Dunkelpause zwischen beiden Pulsen und ihrem Tastverhältnis. Weiterhin ist das Gesamtmodell in der Lage, Experimente zu beschreiben, für die bisher keine Erklärung bekannt war. Dies ist z.B. bei der inversen Antwort auf einen Lockreiz der Fall. Eine Stimulation mit einem Orangelicht-Puls hat normalerweise eine Verringerung der Schalthäufigkeit der Zellen zur Folge. Wird ein solcher Puls allerdings bis zu 8 Sekunden nach einem Schreckreiz gegeben, hat er die entgegengesetzte Wirkung und lässt die Zellen erneut die Schwimmrichtung umkehren. Das Modell zeigt dasselbe Verhalten. Grund dafür ist die Refraktär-Phase, in der die Zellen nach dem Schreckreiz durch die erhöhte Konzentration des Schaltsignals 'festgehalten' werden. Der Orangelicht-Puls 'befreit' die Zellen wieder aus der Refraktär-Phase, indem er kurzzeitig die Schaltsignalkonzentration absenkt. Nach diesem Puls erhöht sich diese Konzentration wieder, weil die Adaptation an den noch andauernden Schreckreiz noch nicht abgeschlossen ist. Nun reagieren die Zellen aber mit einer erneuten Richtungsumkehr, da sie sich jetzt in der Kompetent-Phase befinden. Dadurch hat der Orangelicht-Puls, der normalerweise die Schalthäufigkeit verringert, eine inverse Wirkung.Item Open Access Modeling and parameter estimation for heterogeneous cell populations(2013) Hasenauer, Jan; Allgöwer, Frank (Prof. Dr.-Ing.)Most of the modeling performed in biology aims at achieving a quantitative description and understanding of the intracellular signaling pathways within a “typical cell”. However, in many biologically important situations even genetically identical cell populations show a heterogeneous response. This means that individual members of the cell population behave differently. Such situations require the study of cell-to-cell variability and the development of models for heterogeneous cell populations. The main contribution of this thesis is the development of unifying modeling frameworks for signal transduction and proliferation processes in heterogeneous cell populations. These modeling frameworks allow for the detailed description of individual cells as well as differences between them. In contrast to many existing modeling approaches, the proposed frameworks allow for a direct comparison of model predictions with available data. Beyond this, the proposed population models can be simulated efficiently and, by exploiting the model structures, we are able to develop model-tailored Bayesian parameter estimation methods. These methods enable the calculation of the optimal parameter estimates, as well as the evaluation of the parameter and prediction uncertainties. The proposed tools allow for novel insights in population dynamics, in particular the model-based characterization of population heterogeneity and cellular subgroups. This is illustrated for two different application examples: pro- and anti-apoptotic signaling, which is interesting in the context of cancer therapy, and immune cell proliferation.Item Open Access A statistical and mechanistic, model-based analysis of spindle assembly checkpoint signalling(2017) Geissen, Eva-Maria; Radde, Nicole (Prof. Dr. rer. nat.)The mechanisms that ascertain whether a phase of the cell cycle has been successfully completed and the conditions to proceed to the next phase are fulfilled are called checkpoints. One of them is the spindle assembly checkpoint (SAC), which clears for completion of cell division only if the conditions for a proper partitioning of the genetic material are fulfilled. Despite complete knowledge of its function for decades, the underlying mechanism on themolecular level is still not completely elucidated. We have data at hand that show how persistent the SAC is in individual yeast cells, when the amounts of its signalling components are altered. Since these manipulations are done on the genetic level, the effcacy is the same for each cell of a strain. Therefore, one would expect the SAC to show a homogeneous response in such a clonal population of cells. However, the data reveal that SAC persistence, measured as duration of cell cycle arrest in prometaphase, is highly variable between cells of the same strain. In this thesis we use statistical modelling to quantify the observed cell-to-cell variability and analyse subpopulation structures in clonal populations of yeast cells. The sophisticated statistical analysis is complemented by mechanistic modelling of the molecular mechanism of the SAC on the population level. The statistical analysis of the data is hampered by the fact that the data are censored, i.e. that prometaphase length as the variable of interest is not completely observable in many cells. To account for this in the analysis and to exploit the information which is only accessible by simultaneously analysing the data from multiple stains, we propose a general framework for multi-experiment mixture modelling, named MEMO. Employing this framework, we show that reduction of the amount of individual SAC proteins results in a split of the clonal population of cells into subpopulations with opposing SAC phenotypes. While one subpopulation retains a completely functional SAC, a second subpopulation with an impaired SAC emerges and increases. We quantify the sensitivity of this effect as a function of type and amount of the manipulated protein. Such a quantification allows for the prediction of the subpopulation structure of yet unobserved protein manipulations. The striking observation of phenotypically different subpopulations in a population of genetically identical cells is underscored by the fact that noise in the protein abundances is small. We complement the statistical analysis of the data with mechanistic models of the molecular mechanism of SAC signalling. By exploiting the information contained in the population split, we identify ultrasensitivity and potential bistability to be a property of the dynamical system that forms the SAC. This implies high sensitivity with respect to noise in the abundance of signalling and targeted proteins. Furthermore, we assess the contribution of different SAC components to the observed cell-to-cell variability. While the statistical modelling framework proposed in this thesis can help to prevent misinterpretation of data in the presence of censoring, also in other single-cell data settings, our findings on the properties of the SAC signalling system provide novel insights into this intricate molecular mechanism.Item Open Access Probabilistic modelling of population variability(2025) Wagner, Vincent; Radde, Nicole (Prof. Dr. rer. nat.)Vincent Wagner's dissertation summarises progress in the probabilistic modelling of population variability. It comprises two chapters with complementary approaches to this challenging and broad topic. The first chapter deals with the Method of Moments for the Chemical Master Equation, while the second chapter uses random variable transformations to estimate distributed simulation model parameters.