Fig 3. Read-out of morphogen gradients with increasing amplitude C ₀ on a growing domain.

Gradient read-out for a gradient with an increasing amplitude, c ₀ ∼ L(t)^2β with β = 0.6, in case of (left column) perfect scaling with λ = k ₁ ⋅ L(t); k ₁ = 0.11 (ref [10]), (center column) absence of scaling with λ = 20.2 μm (ref [9]), and (right column) imperfect scaling with $\lambda =\sqrt{\frac{D}{2v_g}L(t)-\frac{D}{2v_g}{L}_0}$; $\frac{D}{2v_g}=3\mu m$ and L ₀ = 46 μm (ref [20]). (a-c) A morphogen gradient at three timepoints L(t) = 100 μm (light grey), L(t) = 200 μm (dark grey), L(t) = 300 μm (black)) on a rescaled domain. Differently colored lines represent different concentration thresholds. (d-f) Trajectories of the positions, ζ _θ, where the different threshold concentration, shown in panels a-c, are attained. The dashed horizontal lines mark the time interval that is further analysed in panels m-o. (g-i) The derivative of the relative read-out position with respect to the domain length, $\frac{d{\zeta }_{\theta }}{dL}$. (j-l) The derivative $\frac{d{\zeta }_{\theta }}{dL}$ not only depends on the relative position ζ _θ (red lines), but also on the gradient amplitude, β (blue lines); see Methods section. (m-o) The maximal deviation of the relative read-out positions, Δζ, in the interval from 125 μm to 300 μm (marked by dashed horizontal lines in panels d-f) for different final read-out positions. The colored dots indicate the final read-out position of the thresholds shown in panels a-c.