Quantifying positional information during early embryonic development

Abstract

During the development of multicellular organisms, cells acquire information about their position in the embryo in response to morphogens whose concentrations vary along the anteroposterior axis. In this thesis, we provide an information-theoretic definition of positional information and demonstrate how it can be quantified from experimental data. We start by setting up the mathematical framework and qualitatively discuss which features of expression patterns can contribute to positional information. Then, using the four major gap genes of Drosophila (Hunchback, Krüppel, Giant, and Knirps) as an example, we focus on the experimental standards that need to be met to accurately compute positional information from imunofluorescence stainings. We show that imunofluorescence makes it possible to extract not only very accurate mean profiles but also statistical noise and noise correlations from gene expression profile distributions. We use this analysis to extract gap gene profile dynamics with 1-2 min precision and to quantify their profile reproducibility. Finally, we describe how to quantify positional information, in bits, from the experimental gap gene profiles previously generated. Our results show that any individual gene carries nearly two bits of information and that, taken together, these four gap genes carry enough information to define a cell's location along the anteroposterior axis of the embryo with an error bar of half the intercellular distance. This precision is nearly constant along the length of the embryo and nearly enough for each cell to have a unique identity. We argue that this constancy is a signature of optimality in the transmission of information from primary morphogen inputs to the output of the gap gene network.