TY - THES AB - Hybrid automata combine finite automata and dynamical systems, and model the interaction of digital with physical systems. Formal analysis that can guarantee the safety of all behaviors or rigorously witness failures, while unsolvable in general, has been tackled algorithmically using, e.g., abstraction, bounded model-checking, assisted theorem proving. Nevertheless, very few methods have addressed the time-unbounded reachability analysis of hybrid automata and, for current sound and automatic tools, scalability remains critical. We develop methods for the polyhedral abstraction of hybrid automata, which construct coarse overapproximations and tightens them incrementally, in a CEGAR fashion. We use template polyhedra, i.e., polyhedra whose facets are normal to a given set of directions. While, previously, directions were given by the user, we introduce (1) the first method for computing template directions from spurious counterexamples, so as to generalize and eliminate them. The method applies naturally to convex hybrid automata, i.e., hybrid automata with (possibly non-linear) convex constraints on derivatives only, while for linear ODE requires further abstraction. Specifically, we introduce (2) the conic abstractions, which, partitioning the state space into appropriate (possibly non-uniform) cones, divide curvy trajectories into relatively straight sections, suitable for polyhedral abstractions. Finally, we introduce (3) space-time interpolation, which, combining interval arithmetic and template refinement, computes appropriate (possibly non-uniform) time partitioning and template directions along spurious trajectories, so as to eliminate them. We obtain sound and automatic methods for the reachability analysis over dense and unbounded time of convex hybrid automata and hybrid automata with linear ODE. We build prototype tools and compare—favorably—our methods against the respective state-of-the-art tools, on several benchmarks. AU - Giacobbe, Mirco ID - 6894 TI - Automatic time-unbounded reachability analysis of hybrid systems ER - TY - THES AB - The development and growth of Arabidopsis thaliana is regulated by a combination of genetic programing and also by the environmental influences. An important role in these processes play the phytohormones and among them, auxin is crucial as it controls many important functions. It is transported through the whole plant body by creating local and temporal concentration maxima and minima, which have an impact on the cell status, tissue and organ identity. Auxin has the property to undergo a directional and finely regulated cell-to-cell transport, which is enabled by the transport proteins, localized on the plasma membrane. An important role in this process have the PIN auxin efflux proteins, which have an asymmetric/polar subcellular localization and determine the directionality of the auxin transport. During the last years, there were significant advances in understanding how the trafficking molecular machineries function, including studies on molecular interactions, function, subcellular localization and intracellular distribution. However, there is still a lack of detailed characterization on the steps of endocytosis, exocytosis, endocytic recycling and degradation. Due to this fact, I focused on the identification of novel trafficking factors and better characterization of the intracellular trafficking pathways. My PhD thesis consists of an introductory chapter, three experimental chapters, a chapter containing general discussion, conclusions and perspectives and also an appendix chapter with published collaborative papers. The first chapter is separated in two different parts: I start by a general introduction to auxin biology and then I introduce the trafficking pathways in the model plant Arabidopsis thaliana. Then, I explain also the phosphorylation-signals for polar targeting and also the roles of the phytohormone strigolactone. The second chapter includes the characterization of bar1/sacsin mutant, which was identified in a forward genetic screen for novel trafficking components in Arabidopsis thaliana, where by the implementation of an EMS-treated pPIN1::PIN1-GFP marker line and by using the established inhibitor of ARF-GEFs, Brefeldin A (BFA) as a tool to study trafficking processes, we identified a novel factor, which is mediating the adaptation of the plant cell to ARF-GEF inhibition. The mutation is in a previously uncharacterized gene, encoding a very big protein that we, based on its homologies, called SACSIN with domains suggesting roles as a molecular chaperon or as a component of the ubiquitin-proteasome system. Our physiology and imaging studies revealed that SACSIN is a crucial plant cell component of the adaptation to the ARF-GEF inhibition. The third chapter includes six subchapters, where I focus on the role of the phytohormone strigolactone, which interferes with auxin feedback on PIN internalization. Strigolactone moderates the polar auxin transport by increasing the internalization of the PIN auxin efflux carriers, which reduces the canalization related growth responses. In addition, I also studied the role of phosphorylation in the strigolactone regulation of auxin feedback on PIN internalization. In this chapter I also present my results on the MAX2-dependence of strigolactone-mediated root growth inhibition and I also share my results on the auxin metabolomics profiling after application of GR24. In the fourth chapter I studied the effect of two small molecules ES-9 and ES9-17, which were identified from a collection of small molecules with the property to impair the clathrin-mediated endocytosis. In the fifth chapter, I discuss all my observations and experimental findings and suggest alternative hypothesis to interpret my results. In the appendix there are three collaborative published projects. In the first, I participated in the characterization of the role of ES9 as a small molecule, which is inhibitor of clathrin- mediated endocytosis in different model organisms. In the second paper, I contributed to the characterization of another small molecule ES9-17, which is a non-protonophoric analog of ES9 and also impairs the clathrin-mediated endocytosis not only in plant cells, but also in mammalian HeLa cells. Last but not least, I also attach another paper, where I tried to establish the grafting method as a technique in our lab to study canalization related processes. AU - Vasileva, Mina K ID - 7172 TI - Molecular mechanisms of endomembrane trafficking in Arabidopsis thaliana ER - TY - THES AB - Single cells are constantly interacting with their environment and each other, more importantly, the accurate perception of environmental cues is crucial for growth, survival, and reproduction. This communication between cells and their environment can be formalized in mathematical terms and be quantified as the information flow between them, as prescribed by information theory. The recent availability of real–time dynamical patterns of signaling molecules in single cells has allowed us to identify encoding about the identity of the environment in the time–series. However, efficient estimation of the information transmitted by these signals has been a data–analysis challenge due to the high dimensionality of the trajectories and the limited number of samples. In the first part of this thesis, we develop and evaluate decoding–based estimation methods to lower bound the mutual information and derive model–based precise information estimates for biological reaction networks governed by the chemical master equation. This is followed by applying the decoding-based methods to study the intracellular representation of extracellular changes in budding yeast, by observing the transient dynamics of nuclear translocation of 10 transcription factors in response to 3 stress conditions. Additionally, we apply these estimators to previously published data on ERK and Ca2+ signaling and yeast stress response. We argue that this single cell decoding-based measure of information provides an unbiased, quantitative and interpretable measure for the fidelity of biological signaling processes. Finally, in the last section, we deal with gene regulation which is primarily controlled by transcription factors (TFs) that bind to the DNA to activate gene expression. The possibility that non-cognate TFs activate transcription diminishes the accuracy of regulation with potentially disastrous effects for the cell. This ’crosstalk’ acts as a previously unexplored source of noise in biochemical networks and puts a strong constraint on their performance. To mitigate erroneous initiation we propose an out of equilibrium scheme that implements kinetic proofreading. We show that such architectures are favored over their equilibrium counterparts for complex organisms despite introducing noise in gene expression. AU - Cepeda Humerez, Sarah A ID - 6473 KW - Information estimation KW - Time-series KW - data analysis SN - 2663-337X TI - Estimating information flow in single cells ER - TY - THES AB - Transcription factors, by binding to specific sequences on the DNA, control the precise spatio-temporal expression of genes inside a cell. However, this specificity is limited, leading to frequent incorrect binding of transcription factors that might have deleterious consequences on the cell. By constructing a biophysical model of TF-DNA binding in the context of gene regulation, I will first explore how regulatory constraints can strongly shape the distribution of a population in sequence space. Then, by directly linking this to a picture of multiple types of transcription factors performing their functions simultaneously inside the cell, I will explore the extent of regulatory crosstalk -- incorrect binding interactions between transcription factors and binding sites that lead to erroneous regulatory states -- and understand the constraints this places on the design of regulatory systems. I will then develop a generic theoretical framework to investigate the coevolution of multiple transcription factors and multiple binding sites, in the context of a gene regulatory network that performs a certain function. As a particular tractable version of this problem, I will consider the evolution of two transcription factors when they transmit upstream signals to downstream target genes. Specifically, I will describe the evolutionary steady states and the evolutionary pathways involved, along with their timescales, of a system that initially undergoes a transcription factor duplication event. To connect this important theoretical model to the prominent biological event of transcription factor duplication giving rise to paralogous families, I will then describe a bioinformatics analysis of C2H2 Zn-finger transcription factors, a major family in humans, and focus on the patterns of evolution that paralogs have undergone in their various protein domains in the recent past. AU - Prizak, Roshan ID - 6071 SN - 2663-337X TI - Coevolution of transcription factors and their binding sites in sequence space ER - TY - THES AB - In the first part of this thesis we consider large random matrices with arbitrary expectation and a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent in the bulk and edge regime. The main novel tool is a systematic diagrammatic control of a multivariate cumulant expansion. In the second part we consider Wigner-type matrices and show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue statistics are uni- versal and form a Pearcey process. Since the density of states typically exhibits only square root or cubic root cusp singularities, our work complements previous results on the bulk and edge universality and it thus completes the resolution of the Wigner- Dyson-Mehta universality conjecture for the last remaining universality type. Our analysis holds not only for exact cusps, but approximate cusps as well, where an ex- tended Pearcey process emerges. As a main technical ingredient we prove an optimal local law at the cusp, and extend the fast relaxation to equilibrium of the Dyson Brow- nian motion to the cusp regime. In the third and final part we explore the entrywise linear statistics of Wigner ma- trices and identify the fluctuations for a large class of test functions with little regularity. This enables us to study the rectangular Young diagram obtained from the interlacing eigenvalues of the random matrix and its minor, and we find that, despite having the same limit, the fluctuations differ from those of the algebraic Young tableaux equipped with the Plancharel measure. AU - Schröder, Dominik J ID - 6179 SN - 2663-337X TI - From Dyson to Pearcey: Universal statistics in random matrix theory ER -