A dynamical model of growth and maturation in Drosophila

The decision to stop growing and mature into an adult is a critical point in development that determines adult body size, impacting multiple aspects of an adult’s biology. In many animals, growth-cessation is a consequence of hormone release that appears to be tied to attainment of particular body size or condition. Nevertheless, the size-sensing mechanism animals use to initiate hormone synthesis is poorly understood. Here we develop a simple mathematical model of growth cessation in Drosophila melanogaster, which is ostensibly triggered by attainment of a critical weight early in the last instar. Attainment of critical weight is correlated with synthesis of the steroid hormone ecdysone, which causes a larva to stop growing, pupate and metamorphose into the adult form. Our model suggests that, contrary to expectation, the size-sensing mechanism that initiates metamorphosis occurs before the larva reaches critical weight; that is, the critical-weight phenomenon is a downstream consequence of an earlier size-dependent developmental decision, not a decision point itself. Further, this size-sensing mechanism does not require a direct assessment of body size, but emerges from the interactions between body size, ecdysone and nutritional signaling. Because many aspects of our model are evolutionarily conserved among all animals, the model may provide a general framework for understanding how animals commit to maturing from their juvenile to adult form.

Methods
The experimental data were collected as detailed in B. C. Stieper, M. Kupershtok, M. V. Driscoll, A. W. Shingleton, Imaginal discs regulate developmental timing in Drosophila melanogaster. Dev Biol 321, 18 26 (2008). The simulated data were generated using the deposited XPP-Auto and Simulink/Matlab scripts.