Precision in Models of Epithelial Growth

One of the key questions in the study of the control of tissue growth is the question of precision. What mechanisms do growing tissues have at their disposal to ensure that they grow to the correct size? How reliable are these different strategies? We present a study of possible mechanisms for the arrest of growth in the Drosophila wing disc epithelium, which appears to robustly arrive at a unique final size. In particular we investigate different methods by which mechanical feedback by stresses induced by nonuniform growth could halt growth. We introduce an analytic framework for comparing different feedback structures. This allows us to make precise claims about the fixed point structures of the growth models induced by these feedback structures. From this we can understand to what extent each model predicts precision in the growing disk as well as how stable these final sizes are.