FIGURE 1 

Dynamics and steady state of morphogen gradients. (A) Morphogen gradients specify a pattern in a field of cells. (Left) All cells (yellow big circles) are equivalent and a morphogen gradient is set (small green circles). Over time (blue arrow), cells respond directly to the graded concentration of a secreted molecule and a pattern (right) is specified. (Right) Depending on the amount of graded signal, distinct genes become expressed within cells (represented by different colours inside cells) and different cellular behaviours are elicited (represented by different shapes of cells). (B) Bicoid, Dpp and Wingless gradients are represented by exponential profiles with their corresponding characteristic length (L). M stands for the morphogen level and x for the spatial position. (C) Transient (T) and steady-state (ST) gradients for two different molecules (simulating Dpp in red and a molecule X in green) that have different diffusion and degradation rates but the same characteristic length in the steady-state profile (L=20 m). Transient gradients are computed at the same time point but, as shown, are distinct. Red curves were obtained by using the diffusion and degradation rates of Dpp. Green curves were computed by setting the molecular half-life eight times shorter than that of Dpp and the diffusion rate eight times larger. (D) Shape of the gradient profile at a transient time (T) and at the steady state (ST) in logarithmic spatial scale for parameter values of Dpp. The features of the gradients at the two time points are very distinct. In panels B and C, the morphogen level has been scaled such that the steady state has a morphogen level of 1 at the source (x=0). Profiles in panels C and D have been computed numerically according to M(x,t)/t=(x)+D²M/x²-M with an impermeable wall at x=0.