Extension of Generalized Modeling and Application to Problems from Cell Biology

Mathematical modeling is an important tool in improving the understanding of complex biological processes. However, mathematical models are often faced with challenges that arise due to the limited knowledge of the underlying biological processes and the high number of parameters for which exact values are unknown. The method of generalized modeling is an alternative modeling approach that aims to address these challenges by extracting information about stability and bifurcations of classes of models while making only minimal assumptions on the specific functional forms of the model. This is achieved by a direct parameterization of the Jacobian in the steady state, introducing a set of generalized parameters which have a biological interpretation. In this thesis, the method of generalized modeling is extended and applied to different problems from cell biology. In the first part, we extend the method to include also the higher derivatives at the steady state. This allows an analysis of the normal form of bifurcations and thereby a more specific description of the nearby dynamics. In models of gene-regulatory networks, it is shown that the extended method can be applied to better characterize oscillatory systems and to detect bistable dynamics. In the second part, we investigate mathematical models of bone remodeling, a process that renews the human skeleton constantly. We investigate the connection between structural properties of mathematical models and the stability of steady states in different models. We find that the dynamical system operates from a stable steady state that is situated in the vicinity of bifurcations where stability can be lost, potentially leading to diseases of bone. In the third part of this thesis, models of the MAPK signal transduction pathway are analyzed. Since mathematical models for this system include a high number of parameters, statistical methods are employed to analyze stability and bifurcations. Thereby, the parameters with a strong influence on the stability of steady states are identified. By an analysis of the bifurcation structure of the MAPK cascade, it is found that a combination of multiple layers in a cascade-like way allows for additional types of dynamic behavior such as oscillations and chaos. In summary, this thesis shows that generalized modeling is a fruitful alternative modeling approach for various types of systems in cell biology.Mathematische Modelle stellen ein wichtiges Hilfmittel zur Verbesserung des Verständnisses komplexer biologischer Prozesse dar. Sie stehen jedoch vor Schwierigkeiten, wenn wenig über die zugrundeliegende biologischen Vorgänge bekannt ist und es eine große Anzahl von Parametern gibt, deren exakten Werte unbekannt sind. Die Methode des Verallgemeinerten Modellierens ist ein alternativer Modellierungsansatz mit dem Ziel, diese Schwierigkeiten dadurch anzugehen, dass dynamische Informationen über Stabilität und Bifurkationen aus Klassen von Modellen extrahiert werden, wobei nur minimale Annahmen über die spezifischen funktionalen Formen getätigt werden. Dies wird erreicht durch eine direkte Parametrisierung der Jacobimatrix im Gleichgewichtszustand, bei der neue, verallgemeinerte Parameter eingeführt werden, die eine biologische Interpretation besitzen. In dieser Arbeit wird die Methode des Verallgemeinerten Modellierens erweitert und auf verschiedene zellbiologische Probleme angewandt. Im ersten Teil wird eine Erweiterung der Methode vorgestellt, bei der die Analyse höherer Ableitungen im Gleichgewichtszustand integriert wird. Dies erlaubt die Bestimmung der Normalform von Bifurkationen und hierdurch eine spezifischere Beschreibung der Dynamik in deren Umgebung. In Modellen für genregulatorische Netzwerke wird gezeigt, dass die so erweiterte Methode zu einer besseren Charakterisierung oszillierender Systeme sowie zur Erkennung von Bistabilität verwendet werden kann. Im zweiten Teil werden mathematische Modelle zur Knochenremodellierung untersucht, einem Prozess der das menschliche Skelett kontinuierlich erneuert. Wir untersuchen den Zusammenhang zwischen strukturellen Eigenschaften verschiedener Modelle und der Stabilität von Gleichgewichtszuständen. Wir finden, dass das dynamische System von einem stabilen Zustand operiert, in dessen Nähe Bifurkationen existieren, welche das System destabilisieren und so potentiell Knochenkranheiten verursachen können. Im dritten Teil werden Modelle für den MAPK Signaltransduktionsweg analysiert. Da mathematische Modelle für dieses System eine hohe Anzahl von Parametern beinhalten, werden statistische Methoden angewandt zur Analyse von Stabilität und Bifurkationen. Zunächst werden Parameter mit einem starken Einfluss auf die Stabilität von Gleichgewichtszuständen identifizert. Durch eine Analyse der Bifurkationsstruktur wird gezeigt, dass eine kaskadenartige Kombination mehrerer Ebenen zu zusätzliche Typen von Dynamik wie Oszillationen und Chaos führt. Zusammengefasst zeigt diese Arbeit, dass Verallgemeinertes Modellieren ein fruchtbarer alternativer Modellierungsansatz für verschiedene zellbiologische Probleme ist

Complex and Adaptive Dynamical Systems: A Primer

An thorough introduction is given at an introductory level to the field of quantitative complex system science, with special emphasis on emergence in dynamical systems based on network topologies. Subjects treated include graph theory and small-world networks, a generic introduction to the concepts of dynamical system theory, random Boolean networks, cellular automata and self-organized criticality, the statistical modeling of Darwinian evolution, synchronization phenomena and an introduction to the theory of cognitive systems. It inludes chapter on Graph Theory and Small-World Networks, Chaos, Bifurcations and Diffusion, Complexity and Information Theory, Random Boolean Networks, Cellular Automata and Self-Organized Criticality, Darwinian evolution, Hypercycles and Game Theory, Synchronization Phenomena and Elements of Cognitive System Theory.Comment: unformatted version of the textbook; published in Springer, Complexity Series (2008, second edition 2010

A dynamical model of the distributed interaction of intracellular signals

A major goal of modern cell biology is to understand the regulation of cell behavior in the reductive terms of all the molecular interactions. This aim is made explicit by the assertion that understanding a cell\u27s response to stimuli requires a full inventory of details. Currently, no satisfactory explanation exists to explain why cells exhibit only a relatively small number of different behavioral modes. In this thesis, a discrete dynamical model is developed to study interactions between certain types of signaling proteins. The model is generic and connectionist in nature and incorporates important concepts from the biology. The emphasis is on examining dynamic properties that occur on short-term time scales and are independent of gene expression. A number of modeling assumptions are made. However, the framework is flexible enough to be extended in future studies. The dynamical states of the system are explored both computationally and analytically. Monte Carlo methods are used to study the state space of simulated networks over selected parameter regimes. Networks show a tendency to settle into fixed points or oscillations over a wide range of initial conditions. A genetic algorithm (GA) is also designed to explore properties of networks. It evolves a population of modeled cells, selecting and ranking them according to a fitness function, which is designed to mimic features of real biological evolution. An analogue of protein domain shuffling is used as the crossover operator and cells are reproduced asexually. The effects of changing the parameters of the GA are explored. A clustering algorithm is developed to test the effectiveness of the GA search at generating cells, which display a limited number of different behavioral modes. Stability properties of equilibrium states in small networks are analyzed. The ability to generalize these techniques to larger networks is discussed. Topological properties of networks generated by the GA are examined. Structural properties of networks are used to provide insight into their dynamic properties. The dynamic attractors exhibited by such signaling networks may provide a framework for understanding why cells persist in only a small number of stable behavioral modes

Complex Systems: Nonlinearity and Structural Complexity in spatially extended and discrete systems

Resumen Esta Tesis doctoral aborda el estudio de sistemas de muchos elementos (sistemas discretos) interactuantes. La fenomenología presente en estos sistemas esta dada por la presencia de dos ingredientes fundamentales: (i) Complejidad dinámica: Las ecuaciones del movimiento que rigen la evolución de los constituyentes son no lineales de manera que raramente podremos encontrar soluciones analíticas. En el espacio de fases de estos sistemas pueden coexistir diferentes tipos de trayectorias dinámicas (multiestabilidad) y su topología puede variar enormemente dependiendo de dos parámetros usados en las ecuaciones. La conjunción de dinámica no lineal y sistemas de muchos grados de libertad (como los que aquí se estudian) da lugar a propiedades emergentes como la existencia de soluciones localizadas en el espacio, sincronización, caos espacio-temporal, formación de patrones, etc... (ii) Complejidad estructural: Se refiere a la existencia de un alto grado de aleatoriedad en el patrón de las interacciones entre los componentes. En la mayoría de los sistemas estudiados esta aleatoriedad se presenta de forma que la descripción de la influencia del entorno sobre un único elemento del sistema no puede describirse mediante una aproximación de campo medio. El estudio de estos dos ingredientes en sistemas extendidos se realizará de forma separada (Partes I y II de esta Tesis) y conjunta (Parte III). Si bien en los dos primeros casos la fenomenología introducida por cada fuente de complejidad viene siendo objeto de amplios estudios independientes a lo largo de los últimos años, la conjunción de ambas da lugar a un campo abierto y enormemente prometedor, donde la interdisciplinariedad concerniente a los campos de aplicación implica un amplio esfuerzo de diversas comunidades científicas. En particular, este es el caso del estudio de la dinámica en sistemas biológicos cuyo análisis es difícil de abordar con técnicas exclusivas de la Bioquímica, la Física Estadística o la Física Matemática. En definitiva, el objetivo marcado en esta Tesis es estudiar por separado dos fuentes de complejidad inherentes a muchos sistemas de interés para, finalmente, estar en disposición de atacar con nuevas perspectivas problemas relevantes para la Física de procesos celulares, la Neurociencia, Dinámica Evolutiva, etc..

Reconstruction And Analysis Of The Molecular Programs Involved In Deciding Mammalian Cell Fate

Cellular function hinges on the ability to process information from the outside environment into specific decisions. Ultimately these processes decide cell fate, whether it be to undergo proliferation, apoptosis, differentiation, migration and other cellular functions. These processes can be thought of as finely tuned programs evolved to maintain robust function in spite of environmental perturbations. Malfunctions in these programs can lead to improper cellular function and various disease states. To develop more effective, personalized and even preventative therapeutics we must attain a better, more detailed, understanding of the programs involved. To this end we have employed mechanistic mathematical modeling to a variety of complex cellular programs. In Chapter 1, we review a variety of computational methods have have been used successfully in different areas of biotechnology. In Chapter 2, we present the software platform UNIVERSAL, which was developed in our lab. UNIVERSAL is an extensible code generation framework for Mac OS X which produces editable, fully commented platform-independent physiochemical model code in several common programming languages from a variety of inputs. UNIVERSAL generates mass-action ODE models of intracellular signal transduction processes and model analysis code, such as adjoint sensitivity balances. We employed the mass-action ODE framework, as generated by UNIVERSAL, commonly throughout the studies presented here. In Chapter 3, we introduce a variety of modeling strategies in the context of EGF-induced Eukaryotic transcription. We demon- strated the ability to make meaningful and statistically consistent model predictions despite considerable parametric uncertainty. In Chapter 4, we constructed a mathematical model to study a mechanism for androgen independent proliferation in prostate cancer. Analysis of the model provided insight into the importance of network components as a function of androgen dependence. Translation became progressively more important in androgen independent cells. Moreover, the analysis suggested that direct targeting of the translational machinery, specifically eIF4E, could be efficacious in androgen independent prostate cancers. In Chapter 5, A mathematical model of RA-induced cell-cycle arrest and differentiation was formulated and tested against BLR1 wild-type (wt) knock-out and knock-in HL-60 cell lines with and without RA. The ensemble of HL-60 models recapitulated the positive feedback between BLR1 and MAPK signaling. We investigated the robustness of the HL-60 network architecture to structural perturbations and generated experimentally testable hypotheses for future study. In Chapter 6, we carried out experimental studies to reduce the structural uncertainty of the HL60 model. Result from the HL-60 model cRaf as the most critical component of the MAPK cascade. To investigate the role of cRaf in RA-induced differentiation we observed the effect of cRaf kinase inhibition. Furthermore, we interrogated a panel of proteins to identify RA responsive cRaf binding partner. We found that cRaf kinase activity was necessary for functional ROS response, but not for RA-induced growth arrest. Based on our findings, we proposed a simplified ontrol architecture for sustained MAPK activation. Computational modeling identified a bistability suggesting that the MAPK activation was self-sustaining. This result was experimentally validated, and could explain previously observed cellular memory effects. Taken together, the results of these studies demonstrated that computational modeling can identify therapeutically relevant targets for human disease such as cancer. Furthermore, we demonstrated the ability of an iterative strategy between computational and experimental analysis to provide insight on key regulator circuits for complex programs involved in deciding cell fate

Deep Neural Networks and Data for Automated Driving

This open access book brings together the latest developments from industry and research on automated driving and artificial intelligence. Environment perception for highly automated driving heavily employs deep neural networks, facing many challenges. How much data do we need for training and testing? How to use synthetic data to save labeling costs for training? How do we increase robustness and decrease memory usage? For inevitably poor conditions: How do we know that the network is uncertain about its decisions? Can we understand a bit more about what actually happens inside neural networks? This leads to a very practical problem particularly for DNNs employed in automated driving: What are useful validation techniques and how about safety? This book unites the views from both academia and industry, where computer vision and machine learning meet environment perception for highly automated driving. Naturally, aspects of data, robustness, uncertainty quantification, and, last but not least, safety are at the core of it. This book is unique: In its first part, an extended survey of all the relevant aspects is provided. The second part contains the detailed technical elaboration of the various questions mentioned above

Dynamics of Macrosystems; Proceedings of a Workshop, September 3-7, 1984

There is an increasing awareness of the important and persuasive role that instability and random, chaotic motion play in the dynamics of macrosystems. Further research in the field should aim at providing useful tools, and therefore the motivation should come from important questions arising in specific macrosystems. Such systems include biochemical networks, genetic mechanisms, biological communities, neutral networks, cognitive processes and economic structures. This list may seem heterogeneous, but there are similarities between evolution in the different fields. It is not surprising that mathematical methods devised in one field can also be used to describe the dynamics of another. IIASA is attempting to make progress in this direction. With this aim in view this workshop was held at Laxenburg over the period 3-7 September 1984. These Proceedings cover a broad canvas, ranging from specific biological and economic problems to general aspects of dynamical systems and evolutionary theory