This dissertation consists of two parts describing different mathematical and computational models developed for testing novel biological hypothesized mechanisms of Drosophila wing disc morphogenesis.

How a developing organ robustly coordinates the cellular mechanics and growth to reach a final size and shape remains poorly understood. Through iterations between experiments and model simulations that include a mechanistic description of interkinetic nuclear migration, in the first part, we show that the local curvature, height, and nuclear positioning of cells inthe Drosophila wing imaginal disc are defined by the concurrent patterning of actomyosin contractility, cell-ECM adhesion, ECM stiffness, and interfacial membrane tension. We show that increasing cell proliferation via different growth-promoting pathways results in two distinct phenotypes. Triggering proliferation through insulin signaling increases basal curvature, but an increase in growth through Dpp signaling and Myc causes tissue flattening. These distinct phenotypic outcomes arise from differences in how each growth pathway regulates the cellular cytoskeleton, including contractility and cell-ECM adhesion. The coupled regulation of proliferation and cytoskeletal regulators is a general strategy to meet the multiple context-dependent criteria defining tissue morphogenesis.

In the second part, we develop a 2D mathematical model of actomyosin network dynamics, intended to extend the simplified representation of actomyosin in the Subcellular Element (SCE) model presented in the first part. During Drosophila wing disc organogenesis, the actomyosin network gives rise to contractility, a key force-generating mechanism that regulates cell shape changes and interkinetic nuclear migration (IKNM). Although experimental studies have shown that actomyosin contractility is a key driver of IKNM, not enough work has been done to investigate the exact mechanism(s) of how actomyosin produces the contractile forces that constrict the basal membrane and in turn, facilitate the nuclear migration. Because of this, we developed an actomyosin network model that captures a detailed description of the actin-myosin interactions and the directionality of the contractile forces. Once coupled with the SCE model, it will allow us to explore the mechanism(s) behind the basal narrowing of cells that drive the apical migration of nuclei and mitotic rounding during cell division.