The active transport of the plant hormone auxin plays a major role in the initiation of organs at the shoot apex. Polar localized membrane proteins of the PIN1 family facilitate this transport, and recent observations suggest that auxin maxima created by these proteins are at the basis of organ initiation. This hypothesis is based on the visual, qualitative characterization of the complex distribution patterns of the PIN1 protein in Arabidopsis. To take these analyses further, we investigated the properties of the patterns using computational modeling. The simulations reveal previously undescribed properties of PIN1 distribution. In particular, they suggest an important role for the meristem summit in the distribution of auxin. We confirm these predictions by further experimentation and propose a detailed model for the dynamics of auxin fluxes at the shoot apex.