Figure 5

Contrasting the time-scales for morphogen pattern formation in the different mechanisms. Computer simulations were performed for the (A): source-decay; (B): unidirectional transport; and (C): reflux-loop mechanism. Simulations are done as described in Figure 3, for the parameter settings described therein that generate reasonable gradients, with one modification, which is using for the source-decay model with fast decay an equally increased production rate. At t=0 the tissue is free of morphogen/auxin. Graphs show morphogen profiles along a longitudinal cross-section through a vascular cell file at different time points, indicated by the colours. (A1) With high decay rates, the source-decay mechanism quickly reaches the exponential steady state. The required high influx rate needed for this system to acquire similar morphogen concentrations as the other models ensures the formation of the maximum after already 5 s. Within 5 min the steady state is reached. (A2) With slow morphogen diffusion, the source-decay mechanism presents an extremely slow progression towards the steady state pattern. Even after 4 days the maximum is still building up, and the tail of the distribution fails to span a larger tissue region. (B) The unidirectional transport mechanism initially develops an inverted gradient, only after 1 h concentrations at the tip become higher than elsewhere. Thereafter, the pattern remains relatively similar, while concentrations slowly rise over the whole tissue. (C) The reflux-loop mechanism quickly establishes an exponential profile with a characteristic slope, forming an ‘elbow’ with the proximal, flat influx-driven gradient. As time progresses, the slope of the exponential profile is conserved, while the overall absolute values increase, but only in the distal region, allowing the ‘elbow’ to shift proximally. The formation of the gradient (maximum and slope establishment) occurs on very fast time-scales, while the ‘shift’ in the slope along the tissue occurs on a much slower time-scale.