Cell Migration Boundary Motion in Drosophila Egg Chambers: A Combined Phase Field and Chemoattractant Model

Abstract

In the Drosophila melanogaster egg chamber, the collective migration of border cells toward the oocyte is guided by spatial gradients of chemoattractants. While cellular responses to these cues are well characterized, the spatial distribution of chemoattractant within the tissue remains difficult to measure experimentally due to imaging limitations and extracellular complexity. In this study, we develop a spatially resolved mathematical framework to model local chemoattractant concentrations during border cell migration. We use a phase-field approach to represent the egg chamber geometry and define a diffusion-reaction system with spatially heterogeneous diffusivity that accounts for confinement by cellular domains. This framework allows chemoattractant diffusion to be restricted to extracellular space while remaining excluded from the interiors of nurse cells, the border cell cluster, and the oocyte, similar to what we observe in vivo. We simulate secretion from the oocyte and degradation throughout the domain, showing how geometry shapes the distribution of signaling molecules. We further couple this chemical field to a mechanical model of cluster migration that includes a tangential interface migration (TIM) force, allowing the cluster to respond to both chemoattractant gradients and cell-cell contact. Our results show that signal localization and tissue geometry jointly influence directional persistence and the speed of migration. Notably, geometric bottlenecks and intersections can flatten local gradients and slow migration, consistent with experimental observations. This modeling framework offers a tool to investigate how biophysical constraints shape signaling environments and guide collective cell movement in vivo.

Figures (7)

• Figure 1: Architecture of Drosophila egg chamber. (A) Phase-field representation of the egg chamber structure, showing six nurse cells, the border cell cluster positioned at the anterior, and the oocyte at the posterior. (B) Spatial profile of the diffusion coefficient $D(\phi)$ (Eq. \ref{['eq pfm diff']}), illustrating how diffusivity is restricted within cellular regions and elevated in the extracellular space. The magenta arrow indicates the location of the oocyte in both panels. Parameter values used in the simulation are given in Table \ref{['table:1']}.
• Figure 2: Evolution of the chemoattractant concentration $c(x,t)$ (blue curve), the Allen--Cahn-based phase field variable $\phi(x-vt)$ (red, dashed curve), and the diffusion coefficient $D(\phi(x-vt))$ (green, dot-dashed curve) over time. Panel (A) shows the phase variable $\phi(x-vt)$ at an early stage of migration, while panel (B) shows its final position at the end of the simulation. The parameters used are $R=1$ and $\varepsilon=0.07$; all remaining parameter values are as in the 1D model and are listed in Table \ref{['table:1']} (see also \ref{['S1_Video']}).
• Figure 3: Live Distribution of Overexpressed PVF1-eGFP. (A) Representative egg chamber expressing PVF1-eGFP (green) under the control of mat$\alpha$-Gal4. Egg chamber was labeled with lipophilic FM4-64 dye (red) to label cell membranes and imaged live in a confocal microscope; maximum intensity projection is shown in A and the dotted line is shown in cross section in (A'). Bracket denotes the border cell cluster. (B) shows PVF-eGFP alone; note the that the majority of the signal is detected in the oocyte, but some is secreted and detectable along the border cell migration path.
• Figure 4: Chemoattractant concentration and diffusion profile prior to modeling border cell migration. (A) Two-dimensional steady-state distribution of chemoattractant concentration. The concentration is highest along the oocyte boundary (posterior) and decreases toward the anterior, with confinement by cells producing heterogeneous patterns. The magenta plane shows the cross sectional area at $Y=2.75$. (B) The cross section of the domain showing the chemoattractant concentration and the corresponding diffusion coefficient (green, dashed). The blue rectangular area indicates the position of the oocyte. Diffusion is restricted within the interiors of cells, resulting in sharp drops in effective diffusivity and localized peaks of chemoattractant in the extracellular space (See \ref{['S3_Video']}).
• Figure 5: Time evolution of the chemoattractant concentration field $c(x,y,t)$. Snapshots of the concentration field are shown $t= 115$ (A), $t=480$ (B), and $t=1000$ (C). The source of chemoattractant is localized to the posterior, corresponding to the oocyte boundary (right side), and diffusion occurs through the extracellular space while being excluded from the interiors of nurse cells and the oocyte. Over time, the distribution broadens and develops into a posterior–anterior gradient. By $t=1000$, the concentration field has stabilized into a steady-state profile, with the highest levels adjacent to the oocyte and progressively lower concentrations toward the anterior. The snapshots show how tissue geometry shapes anisotropic diffusion, producing heterogeneous gradients that provide directional cues for border cell migration (see \ref{['S4_Video']}).