  Morphogen profiles allow cells to determine their position within a
developing organism, but the mechanisms behind the formation of these profiles
are still not well agreed upon. Here we derive fundamental limits to the
precision of morphogen concentration sensing for two canonical models: the
diffusion of morphogen through extracellular space and the direct transport of
morphogen from source cell to target cell, e.g. via cytonemes. We find that
direct transport establishes a morphogen profile without adding extrinsic
noise. Despite this advantage, we find that for sufficiently large values of
population size and profile length, the diffusion mechanism is many times more
precise due to a higher refresh rate of morphogen molecules. Our predictions
are supported by data from a wide variety of morphogens in developing
organisms.
