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Despite unavoidable fluctuations in egg or embryo size, the gene expression pattern and hence the embryonic structure formed through development often scale with body size, known as the scaling or scale-invariance phenomena. Scale-invariant patterning of gene expression is a common feature in development and regeneration, and has attracted biologists' attention since nearly 100 years ago.
In some cases, like the Drosophila wing imaginal disk, scale invariance is derived from a scale-invariant morphogen gradient. Downstream genes read the morphogen concentration threshold faithfully, thereby achieving scale-invariant expression patterns. In other examples, such as somitogenesis in vertebrates, the scale-invariant number of somites could stem from the coupling between dynamic oscillation and tissue growth.
Different from these scaling mechanisms, segmentation in Drosophila embryogenisis represents another type of scale-invariant patterning – scaling downstream gene expression patterns are formed by interpreting multiple static and non-scaling morphogen gradients. Drosophila segmentation is a classic example in textbooks. Its scale-invariant nature is an important issue that has been widely studied over the past two decades, both experimentally and theoretically. Scale-invariant is at the heart of a quantitative understanding of this classic developmental gene regulation system.
Based on a carfully performed review on the existing experiments and models, this thesis developed a comprehensive theoretical framework for scale-invariant patterning in Drosophila segmentation, and supported it with a large number of (previously published) experimental evidences. These results provide a unified mechanistic explanation for three important aspects of quantitative study on Drosophila segmentation – scale invariance, mutant phenotype, and the underlying gene regulation network. The problem of scaling in Drosophila segmentation is, therefore, largely solved.
