Positional information, positional error, and read-out precision in morphogenesis: a mathematical framework

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 principled 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

Fly wing vein patterns have spatial reproducibility of a single cell

Developmental processes in multicellular organisms occur in fluctuating environments and are prone to noise, yet they produce complex patterns with astonishing reproducibility. We measure the left-right and inter-individual precision of bilaterally symmetric fly wings across the natural range of genetic and environmental conditions and find that wing vein 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. Could development be operating at the physical limit of what a biological system can achieve

Maternal Origins of Developmental Reproducibility

Cell fate decisions during multicellular development are precisely coordinated, leading to highly reproducible macroscopic structural outcomes [1-3]. The origins of this reproducibility are found at the molecular level during the earliest stages of development when patterns of morphogen molecules emerge reproducibly [4, 5]. However, although the initial conditions for these early stages are determined by the female during oogenesis, it is unknown whether reproducibility is perpetuated from oogenesis or reacquired by the zygote. To address this issue in the early Drosophila embryo, we sought to count individual maternally deposited bicoid mRNA molecules and compare variability between embryos with previously observed fluctuations in the Bicoid protein gradient [6, 7]. Here, we develop independent methods to quantify total amounts of mRNA in individual embryos and show that mRNA counts are highly reproducible between embryos to within similar to 9%, matching the reproducibility of the protein gradient. Reproducibility emerges from perfectly linear feedforward processes: changing the genetic dosage in the female leads to proportional changes in both mRNA and protein numbers in the embryo. Our results indicate that the reproducibility of the morphological structures of embryos originates during oogenesis, which is when the expression of maternally provided patterning factors is precisely controlled

Optimal decoding of cellular identities in a genetic network

In developing organisms, spatially prescribed cell identities are thought to be determined by the expression levels of multiple genes. Quantitative tests of this idea, however, require a theoretical framework capable of exposing the rules and precision of cell specification over developmental time. We use the gap gene network in the early fly embryo as an example to show how expression levels of the four gap genes can be jointly decoded into an optimal specification of position with 1% accuracy. The decoder correctly predicts, with no free parameters, the dynamics of pair-rule expression patterns at different developmental time points and in various mutant backgrounds. Precise cellular identities are thus available at the earliest stages of development, contrasting the prevailing view of positional information being slowly refined across successive layers of the patterning network. Our results suggest that developmental enhancers closely approximate a mathematically optimal decoding strategy