Egg
development in the fruit fly
Drosophila melanogaste
r has been used for decades
as a model system in developmental biology. Studies of this system provided
invaluable insights into the general mechanisms that guide the formation of
robust multicellular structures. As a rule, the proposed mechanisms rely on multiscale
interactions of multiple components, only some of which can be monitored directly.
At this level of complexity, mathematical models can play a key role in the rigorous
evaluation of candidate mechanisms and design of future experiments. I will present
our work on the formulation and analysis of such models. The first model
describes how a sheet of identical cells is patterned by a chemical signal. The
second model explains how the patterned sheet may be transformed in a
glove-like structure. The third model is purely geometrical and is used to
describe packing of small cell clusters. For each of these models, I will
discuss the key aspects of model formulation, computational analysis, and experimental
validation.