Limitations on Tissue Shape Control by Mechanical Feedback

How size and shape of living tissues are controlled is a fundamental question of developmental biology. What are the mechanisms that can produce correct sizes? How does size control relate to shape control? We investigate how size and shape control interact in a model of growth control in the Drosophila wing disc epithelium, which appears to achieve a robust final size. In particular, we study the capacity of mechanical feedback models to control not only tissue size, but tissue shape. We develop an analytic model capable of integrating mechanical feedback on tissue growth into an elastic theory. This allows us to make precise claims about the limitations of shape control by mechanical feedback, and demonstrate how these limitations derive from underlying elastic principles.