Multiscale modeling of diffusion in the early Drosophila embryo.

We developed a multiscale approach for the computationally efficient modeling of morphogen gradients in the syncytial Drosophila embryo, a single cell with multiple dividing nuclei. By using a homogenization technique, we derived a coarse-grained model with parameters that are explicitly related to the geometry of the syncytium and kinetics of nucleocytoplasmic shuttling. One of our main results is an accurate analytical approximation for the effective diffusivity of a morphogen molecule as a function of the nuclear density. We used this expression to explore the dynamics of the Bicoid morphogen gradient, a signal that patterns the anterior-posterior axis of the embryo. A similar approach can be used to analyze the dynamics of all three maternal morphogen gradients in Drosophila.