Gene expression levels carry information about signals that have functional significance for the organism. Using the gap gene network in the fruit fly embryo as an example, we show how this information can be decoded, building a dictionary that translates expression levels into a map of implied positions. The optimal decoder makes use of graded variations in absolute expression level, resulting in positional estimates that are precise to ∼ 1% of the embryo's length. We test this optimal decoder by analyzing gap gene expression in embryos lacking some of the primary maternal inputs to the network. The resulting maps are distorted, and these distortions predict, with no free parameters, the positions of expression stripes for the pair-rule genes in the mutant embryos.

The concept of positional information is central to our understanding of how cells determine their location in a multicellular structure and thereby 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 the features of expression patterns that affect positional information quantitatively. 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 nearly single-cell resolution. Our approach can be generalized to a variety of different model systems; procedures and examples are discussed in detail.

Summary 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, while 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 ~9%, matching the reproducibility of the protein gradient. Reproducibility emerges from perfectly linear feed-forward processes: changing the genetic dosage in the female leads to proportional changes in the mRNA and protein numbers in the embryo. Our results indicate that the reproducibility of the morphological structures of embryos originates during oogenesis when initial patterning signals are precisely controlled.

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?