Diffusion vs. direct transport in the precision of morphogen readout

Morphogen profiles allow cells to determine their position within a developing organism, but there are multiple mechanisms by which these profiles form, and in some cases the mechanism is still not agreed upon. Here we derive fundamental limits to the precision of morphogen concentration sensing for two canonical mechanisms: 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. We compare our predictions with data from a wide variety of morphogens in developing organisms.