TY - JOUR AB - A crucial step in the early development of multicellular organisms involves the establishment of spatial patterns of gene expression which later direct proliferating cells to take on different cell fates. These patterns enable the cells to infer their global position within a tissue or an organism by reading out local gene expression levels. The patterning system is thus said to encode positional information, a concept that was formalized recently in the framework of information theory. Here we introduce a toy model of patterning in one spatial dimension, which can be seen as an extension of Wolpert's paradigmatic "French Flag" model, to patterning by several interacting, spatially coupled genes subject to intrinsic and extrinsic noise. Our model, a variant of an Ising spin system, allows us to systematically explore expression patterns that optimally encode positional information. We find that optimal patterning systems use positional cues, as in the French Flag model, together with gene-gene interactions to generate combinatorial codes for position which we call "Counter" patterns. Counter patterns can also be stabilized against noise and variations in system size or morphogen dosage by longer-range spatial interactions of the type invoked in the Turing model. The simple setup proposed here qualitatively captures many of the experimentally observed properties of biological patterning systems and allows them to be studied in a single, theoretically consistent framework. AU - Hillenbrand, Patrick AU - Gerland, Ulrich AU - Tkacik, Gasper ID - 1270 IS - 9 JF - PLoS One TI - Beyond the French flag model: Exploiting spatial and gene regulatory interactions for positional information VL - 11 ER - TY - GEN AB - The effect of noise in the input field on an Ising model is approximated. Furthermore, methods to compute positional information in an Ising model by transfer matrices and Monte Carlo sampling are outlined. AU - Hillenbrand, Patrick AU - Gerland, Ulrich AU - Tkačik, Gašper ID - 9870 TI - Computation of positional information in an Ising model ER - TY - GEN AB - A lower bound on the error of a positional estimator with limited positional information is derived. AU - Hillenbrand, Patrick AU - Gerland, Ulrich AU - Tkačik, Gašper ID - 9869 TI - Error bound on an estimator of position ER - TY - GEN AB - The positional information in a discrete morphogen field with Gaussian noise is computed. AU - Hillenbrand, Patrick AU - Gerland, Ulrich AU - Tkačik, Gašper ID - 9871 TI - Computation of positional information in a discrete morphogen field ER - TY - THES AB - The process of gene expression is central to the modern understanding of how cellular systems function. In this process, a special kind of regulatory proteins, called transcription factors, are important to determine how much protein is produced from a given gene. As biological information is transmitted from transcription factor concentration to mRNA levels to amounts of protein, various sources of noise arise and pose limits to the fidelity of intracellular signaling. This thesis concerns itself with several aspects of stochastic gene expression: (i) the mathematical description of complex promoters responsible for the stochastic production of biomolecules, (ii) fundamental limits to information processing the cell faces due to the interference from multiple fluctuating signals, (iii) how the presence of gene expression noise influences the evolution of regulatory sequences, (iv) and tools for the experimental study of origins and consequences of cell-cell heterogeneity, including an application to bacterial stress response systems. AU - Rieckh, Georg ID - 1128 SN - 2663-337X TI - Studying the complexities of transcriptional regulation ER -