Fig. 2: A theoretical model of germ cell and rachis fluxes reveals a hydraulic instability.

a, Schematic of a 1D hydrodynamic model for pressures, material fluxes and volume exchange in the C. elegans gonad. P_c and P_r denote the pressure field in germ cells and rachis, respectively; S, profile of material uptake from the outside; J, germ-cell-to-rachis current associated with flows through the rachis bridges; Q_r, rachis flux; and v_c, germ cell velocities. b, Green open circles, estimated germ-cell-to-rachis current J along the gonad length; vertical dashed line and grey bar denote the region of transition between the growth modes of germ cells (Fig. 1b). Solid line, best parameter theory fit given the profile of material uptake S shown in Fig. 1d. c, Schematic of a germ cell doublet and two connected balloons depicting how a difference in volumes leads to difference in pressures. d, Evolution of small volume differences between coupled germ cells with time. The symmetric state (ν = 0) of equal germ cell volumes is unstable when the pressure in the rachis is higher than in germ cells (right). Here the initially larger cell grows at the expense of the smaller one. e, Relative volume difference ν in a cell doublet bifurcates around 60% germline length where material uptake S vanishes and pressure difference P_c – P_r changes sign. Insets illustrate cell configurations and corresponding effective potentials W as a function of ν normalized by its value at ν = 0 (Supplementary Information). Error bars indicate the error of the mean at 95% confidence.