Abstract
Phyllotaxis, the arrangement of leaves on a plant stem, is well known because of its beautiful geometric configuration, which is derived from the constant spacing between leaf primordia. This phyllotaxis is established by mutual interaction between a diffusible plant hormone auxin and its efflux carrier PIN1, which cooperatively generate a regular pattern of auxin maxima, small regions with high auxin concentrations, leading to leaf primordia. However, the molecular mechanism of the regular pattern of auxin maxima is still largely unknown. To better understand how the phyllotaxis pattern is controlled, we investigated mathematical models based on the auxin–PIN1 interaction through linear stability analysis and numerical simulations, focusing on the spatial regularity control of auxin maxima. As in previous reports, we first confirmed that this spatial regularity can be reproduced by a highly simplified and abstract model. However, this model lacks the extracellular region and is not appropriate for considering the molecular mechanism. Thus, we investigated how auxin maxima patterns are affected under more realistic conditions. We found that the spatial regularity is eliminated by introducing the extracellular region, even in the presence of direct diffusion between cells or between extracellular spaces, and this strongly suggests the existence of an unknown molecular mechanism. To unravel this mechanism, we assumed a diffusible molecule to verify various feedback interactions with auxin–PIN1 dynamics. We revealed that regular patterns can be restored by a diffusible molecule that mediates the signaling from auxin to PIN1 polarization. Furthermore, as in the one-dimensional case, similar results are observed in the two-dimensional space. These results provide a great insight into the theoretical and molecular basis for understanding the phyllotaxis pattern. Our theoretical analysis strongly predicts a diffusible molecule that is pivotal for the phyllotaxis pattern but is yet to be determined experimentally.
Highlights
Living organisms often form periodic patterns with spatial regularity in a self-organizing manner [1, 2]
Spatial regularity control of phyllotaxis pattern shows diverse patterns depending on plant species, which attracts many people because of its beautiful geometric configuration
The phyllotaxis pattern is established by the mutual interaction between a diffusible plant hormone auxin and its efflux carrier PIN1, but its molecular mechanism is still largely unknown
Summary
Living organisms often form periodic patterns with spatial regularity in a self-organizing manner [1, 2]. One such well-known example is phyllotaxis, the arrangement of leaves on a plant stem. Phyllotaxis is originated at the shoot meristem, in which leaf primordia are periodically formed by maintaining a constant distance from each other [4,5,6,7] This spatial regularity is established by the mutual interaction between a mobile plant hormone auxin and its efflux carrier membrane protein PIN1, which cooperatively generate small regions with high auxin concentrations called auxin maxima that are involved in leaf primordia. According to this experimental observation, the auxin maxima pattern is often explained by the concept of “up-the-gradient” in which auxin is transported by PIN1 against its own gradient while PIN1 is polarized toward higher auxin [11,12,13]
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