Figure 1.

Coding problem of positional information. (Left panels) (Blue, red, and green lines) Morphogen gradients (contours of concentrations). (Black images, represented by T) The regions that need to differentiate from the rest of tissue based on the morphogen concentrations. The spatial profiles of the morphogens determine the way the shape T in real space is mapped into T′ in chemical space where the coordinates are given by the morphogen concentrations (middle panels). In the presence of noise in the morphogen concentrations, the reproducibility of differentiation (right panels) depends on the spatial profiles of the morphogens, suggesting that the spatial profile determines the reliability of positional information. In this example, profile A provides more precise information than profile B, even though the noise has the same magnitude in both cases. Finding the best spatial profile for achieving maximal reliability is thus a coding problem (specifically, encoding problem). (See Model in the main text, and see subsection SA in the Supporting Material for additional details.)