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Cell-Based Model of the Generation and Maintenance of the Shape and Structure of the Multilayered Shoot Apical Meristem of Arabidopsis thaliana

  • Special Issue: Multi-scale Modeling of Tissue Growth and Shape
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Abstract

One of the central problems in animal and plant developmental biology is deciphering how chemical and mechanical signals interact within a tissue to produce organs of defined size, shape, and function. Cell walls in plants impose a unique constraint on cell expansion since cells are under turgor pressure and do not move relative to one another. Cell wall extensibility and constantly changing distribution of stress on the wall are mechanical properties that vary between individual cells and contribute to rates of expansion and orientation of cell division. How exactly cell wall mechanical properties influence cell behavior 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 increase 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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Acknowledgements

The authors acknowledge partial support from the National Science Foundation Grant DMS-1762063 through the joint NSF DMS/NIH NIGMS Initiative to Support Research at the Interface of the Biological and Mathematical Sciences. G.V.R. was also partially supported by the National Science Foundation Grant IOS-1456725 and RSAP-AES mission funding to GVR. CGR acknowledges funding from National Science Foundation Grant MCB-1716972. The authors thank Andrew Whitaker for his invaluable help with transferring computational code to C++ language and code optimization. The authors thank Dr. Weitao Chen for her invaluable help with many computational problems as well as insightful discussions about model development.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Riverside, USA

    Mikahl Banwarth-Kuhn, Ali Nematbakhsh & Mark Alber

  2. Center for Quantitative Modeling in Biology, University of California, Riverside, USA

    Mikahl Banwarth-Kuhn, Ali Nematbakhsh & Mark Alber

  3. Department of Botany and Plant Sciences, Center for Plant Cell Biology (CEPCEB), University of California, Riverside, USA

    Kevin W. Rodriguez, Stephen Snipes, Carolyn G. Rasmussen & G. Venugopala Reddy

  4. Institute of Integrative Genome Biology, University of California, Riverside, USA

    Kevin W. Rodriguez, Stephen Snipes & G. Venugopala Reddy

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  1. Mikahl Banwarth-Kuhn
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  2. Ali Nematbakhsh
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Banwarth-Kuhn, M., Nematbakhsh, A., Rodriguez, K.W. et al. Cell-Based Model of the Generation and Maintenance of the Shape and Structure of the Multilayered Shoot Apical Meristem of Arabidopsis thaliana. Bull Math Biol 81, 3245–3281 (2019). https://doi.org/10.1007/s11538-018-00547-z

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