Fig 1.
Dynamics of oocyte determination.
(A) During the cyst’s progression through the germarium, the oocyte-specifying factor Orb is initially produced in all cells, but then localizes to the two central cells, and finally to a single cell, the future oocyte. Throughout this process, the fusome (green) forms a backbone within the cyst, leading to the formation of polarized microtubules terminating in the oocyte. (B) Confocal images of the fusome (α-Spectrin, green) and ring (Pavarotti, red) backbone that lies within the network of cells, and corresponding 16-cell schematic denoting the progression of orb mRNA (gray), from a uniform distribution throughout all cells, to localization within the two central cells, and finally to the oocyte (scale bar = 5 μm).
Fig 2.
(A) Overview of species in the model. orb mRNA that has been bound (b) to fusome does not exchange between cells, unbound orb mRNA (u) and Orb protein (p) are not restricted in their movement. (B) Schematic of unbound orb mRNA (u1,2), bound orb mRNA (b1,2), and Orb protein (p1,2) interactions between the two most central cells. (C) Regulatory interactions in the reduced model.
Table 1.
Model parameters.
Table 2.
Dimensionless parameters.
Fig 3.
(A) Single-variable model. (B) Division of X into 2 regions based on the value of θ. (C) All distributions of steady states in the sharp switch limit. (D) Adjacency relations of parameter regions defined in (C). (E) Visualization of parameter space projected onto (θ, γ) space for some fixed b. Here, we can explicitly see how parameter space has been divided based on the parametrically-derived steady state configurations.
Table 3.
Proportion of parameter sets that remain in the same region under finite Hill dynamics.
Fig 4.
Model decomposition for oocyte selection.
(A) Division of P1, P2 space into 9 regions based on the values of θ1 and θ2. For the Heaviside case, each of the 9 regions defines a distinct set of 4 linear ODEs that can be solved at steady state, yielding a fixed point which may or may not lie within the region. (B) Schematic of desired phase plane dynamics on P1 and P2 for the system given by Eqs (11)–(14), where asymmetric steady states (shown in red) will result in the selection of one cell as the oocyte. (C) Example of dynamics that yields only asymmetric steady states over a range of initial conditions. For (θ1, θ2, μ, γ, η, κ, π, ϵ) = (1.4, 0.9, 0.8, 0.2, 2.3, 2.5, 1.2, 0.1) with finite Hill exponents n = ν = 10, a number of initial conditions relax to select cell 1 as the oocyte (red trajectories), while the rest will select cell 2 (shown in blue).
Fig 5.
Distribution of stable steady states in the sharp switch limit.
Each distinct parameter region is defined by its distribution of attractors within the 9 regions of P1, P2 space (from Fig 4), with symmetric steady states denoted by hollow dots and asymmetric steady states denoted as filled dots. The color represents the number of disjoint connected components that exist throughout parameter space that contain the same steady state configuration. For the corresponding distribution in the case θ1 < θ2, see Figure B in S1 Text.
Fig 6.
Graph adjacency and topology of parameter space.
Adjacency of all regions identified through the division of the entire parameter space under the sharp switch limit. Each node is colored based on how many distinct components exist for each defined region. Top right: inset for adjacency graph between the two components of region 27, along with steady state configurations of each adjacent region. Bottom: inset showing an example path for the diameter of the adjacency graph, along with the steady state configurations of each region along the path. Left: inset for adjacency graph for the singly-defined component of region 16, along with steady state configurations of each adjacent region. Top left: histogram of number of regions separating any pair of nodes in the graph. To see the individual labels for each region, see Figure A in S1 Text. For the corresponding parameter space graph in the case θ1 < θ2, see Figure C in S1 Text.