FIG. 4.
Regrowing a morphogen gradient with τgd ≈ τspread. This shows the rate of generation/decay being well balanced with that of electrodiffusion. The graph shows [M] vs time; each of the five worm cells is a separate curve in the graph. (a) A fragment from near the tail of a 5-cell worm has all 5 cells starting with very low [M]. Generation/decay raises them all toward [M]ss (which is 1.0 in this example). As all cells rise toward [M]ss, they barely maintain their very small Δ[M]. As they all approach [M] = kM (0.8 in this example; the knee of the Hill model), the loop gain rises sharply and a substantial gradient quickly forms. (b) Exactly like (a), but now a fragment from near the head of a 5-cell worm; it starts with all cells having a high [M] (but with a small Δ[M] still existing). As generation/decay lowers them all toward [M]ss, they eventually approach the knee of the Hill-model curve and generate a substantial gradient. If generation/decay is too slow, this process does not occur in time to affect cellular differentiation. If generation/decay is too fast, the small initial Δ[M] collapses before we reach the knee.