Scale invariance in early embryonic development

Abstract

The expression of a few key genes determines the body plan of the fruit fly. We show that the spatial expression patterns for several of these genes scale precisely with embryo size. Discrete positional markers such as the peaks in striped patterns or the boundaries of expression domains have positions along the embryo’s major axis proportional to embryo length, accurate to within 1%. Further, the information (in bits) that graded patterns of expression provide about a cell’s position can be decomposed into information about fractional or scaled position and information about absolute position or embryo length; all information available is about scaled position, with < 2% error. These findings imply that the underlying genetic network’s behavior exhibits scale invariance in a more precise mathematical sense. We argue that models that can explain this scale invariance also have a “zero mode” in the dynamics of gene expression, and this connects to observations on the spatial correlation of fluctuations in expression levels.