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Mathematical Model for Studying Combined Effect of Individual Cell Behavior on Developing Tissue Shape in Plants


The development of an organ or organism is a complex process that includes many interact- ing components. Scientific inquiries in developmental biology have motivated the creation of novel mathematical tools to better understand how distributions of cellular identities and phenotypes are attained through spatiotemporal regulation of cell behaviors and gene regulation. One of the central problems in animal and plant developmental biology is de- ciphering how chemical and mechanical signals interact within a tissue to produce organs of defined size, shape, and function. Plant development is much different from animals since the majority of organs are continually produced throughout the life of the plant and the presence of the cell wall imposes a unique constraint on cell behaviors. How exactly cell wall mechanical properties influence cell behaviors that lead to stem cell maintenance and correct organ formation is still largely unknown. To address this problem, a novel, subcellular element computational model of growth of stem cells within the multilayered shoot apical meristem (SAM) of Arabidopsis thaliana is developed and calibrated using experimental data. Novel features of the model include separate, detailed descriptions of cell wall extensibility and mechanical stiffness, deformation of the middle lamella, and in- crease in cytoplasmic pressure generating internal turgor pressure. The model is used to test novel hypothesized mechanisms of formation of the shape and structure of the growing, multilayered SAM based on WUS concentration of individual cells controlling cell growth rates and layer-dependent anisotropic mechanical properties of subcellular components of individual cells determining anisotropic cell expansion directions. Model simulations also provide a detailed prediction of distribution of stresses in the growing tissue which can be tested in future experiments.

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