  Morphogen profiles play a vital role in biology by specifying position in
embryonic development. However, the factors that influence the shape of a
morphogen profile remain poorly understood. Since morphogens should provide
precise positional information, one significant factor is the robustness of the
profile to noise. We compare three classes of morphogen profiles (linear,
exponential, algebraic) to see which is most precise when subject to both
external embryo-to-embryo fluctuations and internal fluctuations due to
intrinsically random processes such as diffusion. We find that both the kinetic
parameters and the overall gradient shape (e.g. exponential versus algebraic)
can be optimised to generate maximally precise positional information.
