Fig. 1. Modeling seed growth using a mechanosensitive incoherent feedforward loop.

a Representative WT seeds (Col-0 ecotype) at different days post-anthesis (DPA). The seed compartments are highlighted using false colors. Scale bars = 100 µm. b Relative seed radius as a function of time (DPA). Gray violin plots and black points correspond to the biological data (Col-0, pool of 6 independent experiments, 0DPA: n = 428, 1DPA: n = 485, 2DPA: n = 529, 3 DPA n = 483, 4 DPA: n = 510, 5 DPA: n = 511, 6 DPA: n = 505; 7 DPA: n = 493, 8 DPA: n = 501, 9 DPA: n = 446, 10 DPA: n = 447). The yellow line and yellow band depict the dynamics of the 100 simulations that fit best the experimental data, while the red line represents the simulation that best fits the data. c, d Modeling seed growth with an incoherent feedforward loop (IFFL). e Example of a representative stream map showing the evolution of the system over time within the relative radius/rigidity state space. All trajectories start from different sets of initial values of rigidity K₀ and radius r₀ and evolve according to the same set of parameter values (α = 1, γ = 5, η = 5, ρ = 8). The area in pink corresponds to the zone of no growth, while the black dotted sigmoid curve marks the arrest of stiffening. The trajectories hitting the yellow part of this sigmoid curve (such as the one depicted in dark blue) correspond to simulations converging toward a steady state for both growth and stiffening. The trajectories oriented toward the right side of the graph (such as that depicted in red) correspond to diverging simulations that will not reach any steady state. f Fitting score of the simulations to the biological data (Col-0) as a function of four parameters characterizing stress-dependent shell stiffening: (α) amplitude of stiffening, (ρ) ratio between stiffening and growth thresholds, (η) steepness of the stiffening mechanism (Hill function exponent), (γ) characteristic time ratio between growth and stiffening.