The concept of positional information is central to our understanding of how cells in a multicellular structure determine their developmental fates. Nevertheless, positional information has neither been defined mathematically nor quantified in a prin
cipled way. Here we provide an information-theoretic definition in the context of developmental gene expression patterns and examine which features of expression patterns increase or decrease positional information. We connect positional information with the concept of positional error and develop tools to directly measure information and error from experimental data. We illustrate our framework for the case of gap gene expression patterns in the early Drosophila embryo and show how information that is distributed among only four genes is sufficient to determine developmental fates with single cell resolution. Our approach can be generalized to a variety of different model systems; procedures and examples are discussed in detail.
Developmental processes in multicellular organisms occur far from equilibrium, yet produce complex patterns with astonishing reproducibility. We measure the precision and reproducibility of bilaterally symmetric fly wings across the natural range of
genetic and environmental conditions and find that wing patterns are specified with identical spatial precision and are reproducible to within a single cell width. The early fly embryo operates at a similar degree of reproducibility, suggesting that the overall spatial precision of morphogenesis in Drosophila performs at the single cell level, arguably the physical limit of what a biological system can achieve.
Cell fate decisions in multicellular organisms are precisely coordinated, leading to highly reproducible macroscopic outcomes of developmental processes. The origins of this reproducibility can be found at the molecular level during the earliest stag
es of development when spatial patterns of morphogen (form-generating) molecules emerge reproducibly. However, the initial conditions for these early stages are determined by the female during oogenesis, and it is unknown whether reproducibility is passed on to the zygote or whether it is reacquired by the zygote. Here we examine the earliest reproducible pattern in the Drosophila embryo, the Bicoid protein gradient. Using a unique combination of absolute molecule counting techniques, we show that it is generated from a highly controlled source of mRNA molecules that is reproducible from embryo to embryo to within ~8%. This occurs in a perfectly linear feed-forward process: changes in the females gene dosage lead to proportional changes in the mRNA and protein counts in the embryo. In this setup, noise is kept low in the transition from one molecular species to another, allowing the female to precisely deposit the same absolute number of mRNA molecules in each embryo and therefore confer reproducibility to the Bicoid pattern. Our results indicate that the reproducibility of the morphological structures that emerge in the embryo originates during oogenesis when all initial patterning signals are controlled with precision similar to what we observe for the Bicoid pattern.
