AbstractDespite variability in embryo size, the tissue, organ and body plan developin proportionwith embryo size, known as the scaling phenomenon. Scale-invariant patterning of gene expression is a common feature in development and regeneration, and can be generated by mechanisms such as scaling morphogen gradient and dynamic oscillation. However, whether and how static non-scaling morphogens (input) can induce a scaling gene expression (output) across the entire embryo is not clear. Here we show that scaling requirement sets severe constraints on the geometric structure of the input-output relation (the decoder), from which information about the regulation and mutants’ behavior can be deduced without going into any molecular details. We demonstrate that theDrosophilagap gene system achieves scaling in the way that is entirely consistent with our theory. Remarkably, following the geometry dictated by scaling, a parameter-free decoder correctly and quantitatively accounts for the gap gene expression patterns in nearly all morphogen mutants. Furthermore, the regulation logic and the coding/decoding strategy of the gap gene system can also be revealed from the decoder geometry. Our work provides a general theoretical framework on a large class of problems where scaling output is induced by non-scaling input, as well as a unified understanding of scaling, mutants’ behavior and regulation in theDrosophilagap gene and related systems.Significance StatementWithin a given species, fluctuation in egg or embryo size is unavoidable. Despite this, the gene expression pattern and hence the embryonic structure often scale in proportion with the body length. Thisscalingphenomenon is very common in development and regeneration, and has long fascinated scientists. In this paper, the authors address the question of whether and how a scaling gene expression pattern can originate from non-scaling signals (morphogens). They found that scaling has profound implications in the developmental programming -- properties and behaviors of the underlying gene network can be deduced from the scaling requirement. They demonstrated that the scaling in fruit fly embryogenesis indeed works in this way. Thus, although biological regulatory systems are very complex in general, it can be forced to exhibit simple macroscopic behaviors due to selection pressure, as demonstrated in this study.
Decoding temporal interpretation of the morphogen Bicoid in the early Drosophila embryo