< Back to Article

Polarization and migration in the zebrafish posterior lateral line system

Fig 4

Analysis of mutual inhibition dynamics leads to model insights.

The scaled mutual inhibition Eq (7) can have one of four possible behaviours represented by nullclines in the WR FR phase plane. (FR nullcline in black, WR nullcline in red.) (a) Bistability, in which either a high Wnt receptor (WR) or high FGF (FR) receptor expressing state can result, depending on initial conditions. (b) A Wnt-receptor expressing state always result, (c) a coexistence-state, with both Wnt and FGF receptors expressed, and (d) an FGF only receptor expression state exists. When the Hill coefficients n, m are large, the steady states (appropriately scaled) occur approximately at a subset of the points {(1, 0), (1, 1), (0, 1)} and transitions between the four qualitative outcomes displayed in this figure can be summarized by simple inequalities in terms of aggregate quantities ϕ and ω, see Eq (7c).

Fig 4