Fig 1.
Spatio-Temporal Progression of the Border Cell Cluster.
(A, C) Live imaging of border cell cluster migration in the Drosophila egg chamber. Time-lapse images showing the migration of the border cell cluster (green, Slbo-LifeAct-GFP) through the nurse cell complex toward the oocyte at the right. The cell membranes are labeled with Myr-tdTomato (magenta) expressed under the control of the mat promoter. The white arrowhead indicates the position of the border cell cluster at the time shown at the top right (hours:min). In (C), the border cells have reached the oocyte. (B) A cartoon of the egg chamber when border cells (indicated with black arrowhead) have migrated part of the way, with cell types labeled.
Fig 2.
Schematic representation of the phase-field model.
(Left column) The epithelial layer of the egg chamber is considered inside a rectangular region. The egg chamber is described by (blue). We consider the inside
and outside
with the transition region between them as effectively the epithelial layer. (Right column) The gray regions are indicated to nurse cells and oocyte and are considered as phase field
’s. Cross sectional line is taken through the egg chamber (green dashed). 1D phase-field representation of cells along the corresponding cross-section.
Fig 3.
Initial state of the model before border cell cluster migration in the egg chamber.
(a) The anterior region contains the border cell cluster (red arrow), while the posterior region contains the oocyte (white arrow), which is larger than the nurse cells. The model includes 6 nurse cells that are heterogeneous in size. Border cells, nurse cells, and the oocyte are shown in yellow. The blue surface represents the epithelial layer phase field, where inside the epithelium and
outside, defining the boundary of the extracellular space. (b) Visualization of the overlap term
, which highlights spatial regions where individual cells physically contact each other. This quantity is not the total energy; rather, it identifies zones of phase-field overlap that contribute to the interaction-energy component of the model. These regions correspond to interfaces where mechanical interactions— including those associated with TIM forces—are active during migration. The parameters are set as follow:
, size of spatial grid h = 0.05, the time step of
,
for nurse cells, oocyte, and border cell cluster, respectively. Also,
for all m,
,
for epithelial layer. The adhesion intensity
,
and
. The repulsion intensity
,
,
, and
(See Table A in S1 Text).
Fig 4.
Impact of traditional chemical force term (Fchem).
(a) 2D steady-state distribution of chemoattractant concentration c(x,y) in the egg chamber domain. (b) Receptor activation in response to the chemoattractant concentration increases along the anterior-posterior axis and saturates near the posterior at the oocyte. (See S1 Fig for chemoattractant distribution without impact of radial variation)(c)-(e) Time evolution of border cell cluster migration, simulated using the phase field model in Eq (9) with Fchem, Eq (12). The border cell cluster (green) initiates at the anterior end and migrates toward the posterior oocyte in response to a chemoattractant gradient. The green arrows in the cluster indicate () in Eq (12). Cell boundaries are represented by phase field contours (red for nurse cells, blue oocyte, and black epithelial layer) at the
level. The parameters are set as follows:
,
, s = 1, and
. The parameters used are consistent with those in Fig 3. (See S2 Fig for migration without impact of radial variation).
Fig 5.
Schematic representation of Tangential Interface Migration (TIM) force.
The border cell cluster (BC, green) is surrounded by nurse cells (NC, pink), the regions of contact between the border cell cluster and nurse cells are shown in orange representing the overlap of phases (border cell cluster phase variable and nurse cell phase variables
). The small gray arrows show the gradient of cluster phase
and large blue arrows show the tangential vectors corresponding to the vectors orthogonal to the gradient (
. Chemoattractant molecules (magenta dots) indicate that the presumed concentration at the front of cluster (posterior side) is more than at the back of the cluster (anterior side), which amplifies the movement of cluster from the anterior to the posterior.
Fig 6.
Comparison of Fchem and FTIM vector fields.
Vector fields prior to taking the divergences in each of the chemotactic forms. (a) Visualization of the chemotactic force vector field (Fchem), which directs the cluster toward regions of higher chemoattractant concentration. The magnitude and orientation of the force vectors vary in response to spatial changes in the chemoattractant. (b) Visualization of the tangential interface migration force (FTIM), which is generated by interfacial interactions between the cluster and adjacent nurse cells. The enlarged panel shows tangentially oriented vectors along the cluster boundary, capturing contact-mediated propulsion. In both panels migration is shown at the same time t = 340; nurse cell boundaries are denoted by red; black outlines the epithelial layer of the egg chamber; the blue contour marks the oocyte; and the green region represents the border cell cluster.
Fig 7.
Impact of Tangential Interface Migration force (FTIM).
Snapshots of the cell configuration and TIM force vector field at three time points (a) t = 0: The cluster is initially positioned near the anterior of the egg chamber and begins contact-mediated migration along adjacent nurse cell interfaces. Forward movement is initiated as the leading edge of the cluster experiences higher chemoattractant concentration, as indicated by the purple arrow at the front. (b) t = 340: The cluster is midway through its migration path, exhibiting tangential traction along adjacent nurse cell boundaries. Vectors indicate directed force aligned with the interfaces. (c) t = 800: The cluster approaches the oocyte boundary. At this stage, the front of the cluster senses reduced chemoattractant signaling due to receptor saturation, leading to a gradual decrease in migration speed and eventual attachment to the oocyte.
Fig 8.
Comparison of border cell cluster migration under Fchem and FTIM.
(a) Temporal evolution of the center of cluster’s position along the anterior-posterior axis. (b) Speed of the border cell cluster during migration along the anterior–posterior (A–P) axis.
Fig 9.
The short‑range Gurken cue drives the dorsal turn of the border‑cell cluster: comparison of live imaging and phase‑field simulation.
Top row: Time-lapse images of the egg chamber expressing a membrane localized GFP marker (green), which shows the border cell cluster and outlines the oocyte. The border‑cell cluster (bright spot) migrates toward the right (A), and as it nears the surface of the oocyte, reorients dorsally toward the germinal vesicle (B) and continues along the anterior side of the oocyte towards the dorsal side of the egg chamber (top) (C). Bottom row: Corresponding snapshots from the phase‑field model at the indicated simulation times (T = 258, 426, 1311). The arrows depict the TIM force, which is proportional to the local chemoattractant gradient c(x,y). The shallow dorsal component of c becomes appreciable once the cluster contacts the oocyte, redirecting TIM stresses upward and reproducing the experimentally-observed dorsal migration without additional parameter tuning.
Fig 10.
Comparison of chemotactic and tangential interface migration (TIM) forces under weak chemoattractant gradients.
(a–c) Time evolution of border cell cluster migration driven by the classical chemotactic force Fchem under a shallow chemoattractant gradient, shown at t = 0, t = 340, and t = 800. As the cluster enters regions where the gradient magnitude is reduced, the chemotactic force weakens and the cluster stalls midway through the egg chamber, failing to reach the oocyte. (d–f) Corresponding snapshots for migration driven by the tangential interface migration (TIM) force FTIM under the same shallow-gradient conditions and at the same time points. Despite the shallow chemoattractant profile, the cluster maintains directed motion and successfully completes migration to the oocyte. TIM-generated traction is localized to border cell–nurse cell interfaces and depends on receptor activation and interfacial contact rather than on the magnitude of the gradient, allowing migration to proceed when classical chemotaxis fails.
Fig 11.
Effects of reduced chemoattractant secretion on gradient profile and migration outcome.
(a) Comparison of the original chemoattractant concentration profile and a shallower profile generated by reduced secretion from the oocyte. The shallow profile preserves anterior–posterior asymmetry but exhibits a substantially reduced spatial gradient. (b) Cluster position over time under the shallow gradient. Migration driven by the chemotactic force stalls prematurely (green), whereas migration driven by the TIM force successfully completes migration to the oocyte (purple).