Mathematical study for the mechanism of vascular and spot patterns by auxin and pin dynamics in plant development

Leaf morphogenesis: The multifaceted roles of mechanics

Plants produce a rich diversity of biological forms, and the diversity of leaves is especially notable. Mechanisms of leaf morphogenesis have been studied in the past two decades, with a growing focus on the interactive roles of mechanics in recent years. Growth of plant organs involves feedback by mechanical stress: growth induces stress, and stress affects growth and morphogenesis. Although much attention has been given to potential stress-sensing mechanisms and cellular responses, the mechanical principles guiding morphogenesis have not been well understood. Here we synthesize the overarching roles of mechanics and mechanical stress in multilevel and multiple stages of leaf morphogenesis, encompassing leaf primordium initiation, phyllotaxis and venation patterning, and the establishment of complex mature leaf shapes. Moreover, the roles of mechanics at multiscale levels, from subcellular cytoskeletal molecules to single cells to tissues at the organ scale, are articulated. By highlighting the role of mechanical buckling in the formation of three-dimensional leaf shapes, this review integrates the perspectives of mechanics and biology to provide broader insights into the mechanobiology of leaf morphogenesis.

Mathematical Modelling of Auxin Transport in Plant Tissues: Flux Meets Signalling and Growth

Plant hormone auxin has critical roles in plant growth, dependent on its heterogeneous distribution in plant tissues. Exactly how auxin transport and developmental processes such as growth coordinate to achieve the precise patterns of auxin observed experimentally is not well understood. Here we use mathematical modelling to examine the interplay between auxin dynamics and growth and their contribution to formation of patterns in auxin distribution in plant tissues. Mathematical models describing the auxin-related signalling pathway, PIN and AUX1 dynamics, auxin transport, and cell growth in plant tissues are derived. A key assumption of our models is the regulation of PIN proteins by the auxin-responsive ARF-Aux/IAA signalling pathway, with upregulation of PIN biosynthesis by ARFs. Models are analysed and solved numerically to examine the long-time behaviour and auxin distribution. Changes in auxin-related signalling processes are shown to be able to trigger transition between passage- and spot-type patterns in auxin distribution. The model was also shown to be able to generate isolated cells with oscillatory dynamics in levels of components of the auxin signalling pathway which could explain oscillations in levels of ARF targets that have been observed experimentally. Cell growth was shown to have influence on PIN polarisation and determination of auxin distribution patterns. Numerical simulation results indicate that auxin-related signalling processes can explain the different patterns in auxin distributions observed in plant tissues, whereas the interplay between auxin transport and growth can explain the ‘reverse-fountain’ pattern in auxin distribution observed at plant root tips.

Spatial development of transport structures in apple (Malus × domestica Borkh.) fruit

The void network and vascular system are important pathways for the transport of gases, water and solutes in apple fruit (Malus × domestica Borkh). Here we used X-ray micro-tomography at various spatial resolutions to investigate the growth of these transport structures in 3D during fruit development of "Jonagold" apple. The size of the void space and porosity in the cortex tissue increased considerably. In the core tissue, the porosity was consistently lower, and seemed to decrease toward the end of the maturation period. The voids in the core were more narrow and fragmented than the voids in the cortex. Both the void network in the core and in the cortex changed significantly in terms of void morphology. An automated segmentation protocol underestimated the total vasculature length by 9-12% in comparison to manually processed images. Vascular networks increased in length from a total of 5 m at 9 weeks after full bloom, to more than 20 m corresponding to 5 cm of vascular tissue per cubic centimeter of apple tissue. A high degree of branching in both the void network and vascular system and a complex three-dimensional pattern was observed across the whole fruit. The 3D visualizations of the transport structures may be useful for numerical modeling of organ growth and transport processes in fruit.