Mathematical Modeling of Border Cell Cluster Migration in Drosophila melanogaster

Abstract

Cell migration plays a key role in development, wound healing, immune response, and cancer metastasis. This dissertation presents mathematical models of border cell cluster migration in Drosophila melanogaster, focusing on tissue geometry and chemoattractant diffusion. We first develop a 1D hybrid model to study how extracellular egg chamber structures shape chemoattractant gradients and border cell movement. Simulations show that narrow regions enhance directional cues and migration speed, while broader regions reduce gradients. High chemoattractant concentrations can impair movement due to receptor saturation, revealing a non-monotonic link between signal strength and motility. A key contribution of this work is the development of a predictive compu-tational model that integrates chemoattractant diffusion, receptor dynamics, and force-based migration mechanics. We establish a framework capturing the interplay between signaling and physical constraints. Sensitivity analyses further reveal that alterations in tissue structure, such as genetic mutations affecting egg chamber morphology, lead to predictable shifts in migration dynamics. Next, we develop a phase field modeling framework (system of coupled partial differential equations) for multicellular cluster migration within the 2D egg chamber geometry. A key innovation is the development of a novel Tangential Interface Migration (TIM) term, representing the climbing behavior of border cells as they navigate through the nurse cell environment. This term replaces the standard chemical gradient response with a more biophysically appropriate mechanism. Importantly, with the TIM force, cluster migration depends on the presence and alignment of neighboring cells, consistent with experimental observations that collective proximity is required for successful migration. This study introduces phase field modeling as a novel approach to investigating border cell cluster migration, offering a significant alternative over traditional agent-based and continuum models. Unlike models that track individual cells or oversimplify the extracellular space, the phase field method provides a continuous representation of the migrating cluster, naturally capturing dynamic shape changes, cell-cell adhesion, and interactions with tissue structure. By incorporating chemoattractant diffusion and receptor dynamics into this framework, we create a powerful and flexible tool that enables a more precise study of collective migration in structured environments. In conclusion, this research advances our understanding of collective migration by integrating experimental observations with novel mathematical modeling. These insights support future research in development and disease modeling.