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Plant development is a complex task, and many processes involve changes in the asymmetric subcellular distribution of cell components that strongly depend on cell polarity. Cell polarity regulates anisotropic growth and polar localization of membrane proteins and helps to identify the cell's position relative to its neighbors within an organ. Cell polarity is critical in a variety of plant developmental processes, including embryogenesis, cell division, and response to external stimuli. The most conspicuous downstream effect of cell polarity is the polar transport of the phytohormone auxin, which is the only known hormone transported in a polar fashion in and out of cells by specialized exporters and importers. The biological processes behind the establishment of cell polarity are still unknown, and researchers have proposed several models that have been tested using computer simulations. The evolution of computer models has progressed in tandem with scientific discoveries, which have highlighted the importance of genetic, chemical, and mechanical input in determining cell polarity and regulating polarity-dependent processes such as anisotropic growth, protein subcellular localization, and the development of organ shapes. The purpose of this review is to provide a comprehensive overview of the current understanding of computer models of cell polarity establishment in plants, focusing on the molecular and cellular mechanisms, the proteins involved, and the current state of the field., Competing Interests: Conflict of interest statement. None declared., (© The Author(s) 2023. Published by Oxford University Press on behalf of American Society of Plant Biologists.)

Plants develop new organs to adjust their bodies to dynamic changes in the environment. How independent organs achieve anisotropic shapes and polarities is poorly understood. To address this question, we constructed a mechano-biochemical model for Arabidopsis root meristem growth that integrates biologically plausible principles. Computer model simulations demonstrate how differential growth of neighboring tissues results in the initial symmetry-breaking leading to anisotropic root growth. Furthermore, the root growth feeds back on a polar transport network of the growth regulator auxin. Model, predictions are in close agreement with in vivo patterns of anisotropic growth, auxin distribution, and cell polarity, as well as several root phenotypes caused by chemical, mechanical, or genetic perturbations. Our study demonstrates that the combination of tissue mechanics and polar auxin transport organizes anisotropic root growth and cell polarities during organ outgrowth. Therefore, a mobile auxin signal transported through immobile cells drives polarity and growth mechanics to coordinate complex organ development., Competing Interests: MM, MG, EB, KW No competing interests declared, (© 2021, Marconi et al.)

Cell polarity reflected by asymmetric distribution of proteins at the plasma membrane is a fundamental feature of unicellular and multicellular organisms. It remains conceptually unclear how cell polarity is kept in cell wall-encapsulated plant cells. We have used super-resolution and semi-quantitative live-cell imaging in combination with pharmacological, genetic, and computational approaches to reveal insights into the mechanism of cell polarity maintenance in Arabidopsis thaliana. We show that polar-competent PIN transporters for the phytohormone auxin are delivered to the center of polar domains by super-polar recycling. Within the plasma membrane, PINs are recruited into non-mobile membrane clusters and their lateral diffusion is dramatically reduced, which ensures longer polar retention. At the circumventing edges of the polar domain, spatially defined internalization of escaped cargos occurs by clathrin-dependent endocytosis. Computer simulations confirm that the combination of these processes provides a robust mechanism for polarity maintenance in plant cells. Moreover, our study suggests that the regulation of lateral diffusion and spatially defined endocytosis, but not super-polar exocytosis have primary importance for PIN polarity maintenance.

Plant development is exceptionally flexible as manifested by its potential for organogenesis and regeneration, which are processes involving rearrangements of tissue polarities. Fundamental questions concern how individual cells can polarize in a coordinated manner to integrate into the multicellular context. In canalization models, the signaling molecule auxin acts as a polarizing cue, and feedback on the intercellular auxin flow is key for synchronized polarity rearrangements. We provide a novel mechanistic framework for canalization, based on up-to-date experimental data and minimal, biologically plausible assumptions. Our model combines the intracellular auxin signaling for expression of PINFORMED (PIN) auxin transporters and the theoretical postulation of extracellular auxin signaling for modulation of PIN subcellular dynamics. Computer simulations faithfully and robustly recapitulated the experimentally observed patterns of tissue polarity and asymmetric auxin distribution during formation and regeneration of vascular systems and during the competitive regulation of shoot branching by apical dominance. Additionally, our model generated new predictions that could be experimentally validated, highlighting a mechanistically conceivable explanation for the PIN polarization and canalization of the auxin flow in plants.