Fig. 2: Parameter description of the model and time evolution of the reference simulation.

A–C Lockhart-Ortega elongating single-cell model. A Cell pressure and wall tension equilibrate: pressure \({{\boldsymbol{P}}}\) is proportional to elastic modulus \({{\boldsymbol{E}}}\) and elastic deformation \({{{\boldsymbol{\varepsilon }}}}_{{{\boldsymbol{e}}}}\). B Volume variation and water fluxes over surface \({{\boldsymbol{A}}}\) of permeability \({{\boldsymbol{L}}}\) depend on the difference between cell (\({{\boldsymbol{\Psi }}}\)) and external (\({{{\boldsymbol{\Psi }}}}_{{{\boldsymbol{ext}}}}\)) water potentials. C Wall mechanical response decomposes into elastic (1^st term on the left-hand side) and plastic (2^nd term) responses; the plastic response corresponds to irreversible growth characterized by extensibility \({{{\boldsymbol{\phi }}}}^{{{\boldsymbol{w}}}}\) and is triggered when the elastic deformation is above the threshold \({{{\boldsymbol{\varepsilon }}}}^{{{\boldsymbol{Y}}}}\). The driving force is a large enough value of osmotic pressure \({{\boldsymbol{\pi }}}\) that induces water flux into the cell, which triggers simultaneously volume increase, wall deformation, pressure, and growth. D Scenario presented in the main text: initiation with a zero elastic deformation with regions defined by heterogeneous parameters (variables description in Supplementary Table 1); initial pressurization of the tissue; initiation of the primordium at \({{\boldsymbol{t}}}={{\boldsymbol{0}}}\); growth of the primordium. E Regions where the time evolution is monitored: mean values over primordium cells (P) and central zone (CZ), individual cell values for the boundary cells (B1, B2 and B3). F–H Time evolution of cell volume (F), volume relative growth rate (G), and hydrostatic pressure (H). I Time evolution of boundary cell B3 (indicated in E) showing dynamics of sphericity change vs. volume. J Time evolution of selected cells (indicated in E) showing dynamics of volume relative growth rate vs. sphericity change. Time \({{\boldsymbol{t}}}={{\boldsymbol{0}}}\) indicates the initiation of the primordium with a reduction of the elastic modulus.