Contrasting the steady-state morphogen gradients. (A): Source-decay mechanism. (A1) Mathematical solutions. Default parameters for auxin (a high diffusion coefficient and a slow decay rate) result in a very shallow gradient (black). Either very fast decay (red) or slow diffusion (blue) is required to obtain a gradient with a reasonable slope and characteristic length. (A2) Simulations using a realistic tissue layout confirm the mathematically derived profiles: using the default parameters, the gradient is very flat (black line and inset). Only high decay (red) or low diffusion (blue) result in a reasonable gradient; while the slope is the same, the amplitude is very different. (B): Unidirectional transport mechanism. (B1) Mathematical solutions. For biophysically reasonable permeability values, an extremely steep gradient forms (black). To obtain a reasonable characteristic length, the contribution of PINs to the auxin efflux permeability has to be greatly reduced (red). (B2) Computer simulations on the vascular tissue layout yield similar results as the mathematically derived ones. (C): Reflux-loop mechanism. When using the full root layout, a reasonable gradient forms at biophysically realistic parameters. Black and green lines represent longitudinal cross-sections through a vascular and epidermal cell file, respectively. Default parameters are defined in Figure 1.