Mapping parameter spaces of biological switches
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).