A New Scaling Measure Quantifies the Conservation of Proportions of Gene Expression Profiles in Developing Organic Shapes

Most organisms and organs go through a developmental phase before they reach their adult size and proportions. We studied the scaling properties of the fruit fly embryo and its wing. Even in batches of genetically identical embryos their length fluctuates about 10% around its mean value of 0.5mm. Yet, expression domains of certain genes that define the adult body plan of the fly extend over areas proportional to embryo length. This kind of scaling property makes sure that while flies may have different sizes, the proportionality of their respective body parts are extremely well conserved, thus ensuring their functionality. A similar phenomenon is observed for the wing, which evolves from a growing tissue known as the imaginal wing disk. Again expression patterns of many genes responsible for the later cell differentiation scale with the growing total size of the wing disk. Here we focus on how scaling of graded expression profiles can be quantified properly in growing tissues. This extends our previous work for the quantification of scaling of discrete expression domains (Mol. Syst. Biol.: 2010, 6;351).