Morphogen Gradients Stable During Growth? an example in plant development

In plant development, the phytohormone auxin plays a key-role, controlling cell identity, cell division and cell expansion. Interestingly, in both distal regions of plant roots and shoots, characteristic auxin maxima have been found which correlate with these developmental outputs. It is also known that auxin export facilitators (PINs) are associated with auxin maxima. Combining such empirical knowledge, we present a multilevel model for the Arabidopsis root that spans molecular and cellular levels describing diffusion and PIN-mediated transport in and across cells within a structured tissue layout. The modelling study allows us to pinpoint the necessary elements for the formation and maintenance of an auxin-maximum. It also permits us to draw connections between PIN-topology and macroscopic properties such as auxin-capacitance, auxin gradient properties and timescales. We explain how pattern formation and morphogenesis at timescales varying from seconds to days/weeks can be understood, and thus, how such morphogen gradients should be treated as out-of-equilibrium processes.