Final answer:
Experimental studies and mathematical modeling both contribute to the understanding of the optimal shape of Drosophila epithelial cells. The influence of physical forces on cell shape is supported by empirical evidence, as well as theoretical frameworks from soft matter physics.
Step-by-step explanation:
The optimal shape of epithelial cells in Drosophila tissue and the mechanics of cell packing are complex topics that involve both empirical evidence and theoretical modeling to understand. While mathematical calculations of cellular packing and neighbors play a role, experimental evidence also supports the understanding of cell shapes. Concepts borrowed from soft matter physics, such as cellular tension and elasticity, help explain the cellular dynamics and structures observed, including the hexagonal packing in epithelial tissue.
This is seen in Drosophila, where vertex models accommodate the fact that cell walls are contractile, influencing cell shape and interactions. These scientific endeavors have also been supported by studies in organogenesis in fruit flies (Drosophila) which aided in understanding the role of genes in the formation of cellular structures. Moreover, micro-contact printing of adhesive patterns has been used experimentally to show how cells are constrained into predefined shapes and the subsequent effects on cell function.