Spatial regularity control of phyllotaxis pattern generated by the mutual interaction between auxin and PIN1

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.

A coherent feed-forward loop drives vascular regeneration in damaged aerial organs of plants growing in a normal developmental context

“…In that view, it is tantalising that the cellular defects associated with the malfunctioning of this circuit are the inability to redirect ground tissue cells to vascular identity and the inability to properly polarise PIN proteins. A regulatory feedback loop between auxin level, auxin flux and polarisation of auxin efflux carriers (PIN) has been proposed as a key regulatory mechanism of shoot branching, phyllotaxis and vascular tissue differentiation (Jönsson et al, 2006;Smith et al, 2006;Bayer et al, 2009;Schuetz et al, 2012;Mazur et al, 2016;Fujita and Kawaguchi, 2018). It is therefore conceivable that PLT-CUC2-dependent activation of YUC4 activates this feedback loop to drive vascular regeneration in damaged growing leaves (Fig.…”

Asynchrony of ovule primordia initiation in Arabidopsis

“…The auxin efflux carrier PIN1 is unevenly distributed at the cell i membrane, and its density in the membrane of cell i towards neighboring cell j is denoted by p i , j . The change in auxin concentration in cell i ( a i ) is described elsewhere ( Jönsson et al, 2006 ; Smith et al, 2006 ; Fujita and Kawaguchi, 2018 ). and where cell j is the neighbor of cell i , G a is the degradation rate, A is related to the synthesis rate, D a is the diffusion coefficient, E p is the efficiency of the PIN1 efflux carrier, and f i , j (= f j , i ) is the net flow of auxin by PIN1 from cell i to cell j , consisting of auxin efflux and influx.…”

“…, . The change in auxin concentration in cell ( ) is described elsewhere (Jönsson et al, 2006;Smith et al, 2006;Fujita and Kawaguchi, 2018).…”

A design principle for floral organ number and arrangement in flowers with bilateral symmetry

“…The first model included periodic initiation following Hofmeister's observations, while the second model relied on Snow and Snow's modification. The substance responsible for initiation inhibition has been suggested to be related to the polar transport of phytohormone auxin (Fujita and Kawaguchi, 2018;Jönsson et al, 2006;de Reuille et al, 2006;Smith et al, 2006), the mechanical properties of epidermal tissues (e.g. buckling wavelength) (Green, 1996) or the direction of microtubule alignment (Heisler et al, 2010).…”