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

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.

Prospects for Declarative Mathematical Modeling of Complex Biological Systems

“…(2005); see also Banwarth-Kuhn et al. (2018) in this issue] to the biomechanics. A similar mechanical/regulatory model with breakable springs for the stem cell niche of mouse olfactory receptor neurons was implemented in the Plenum prototype implementation of the dynamical grammars declarative modeling language (Yosiphon 2009).…”

A Sight on Single-Cell Transcriptomics in Plants Through the Prism of Cell-Based Computational Modeling Approaches: Benefits and Challenges for Data Analysis

“…The study combining experimental data on the organization of the extracellular matrix and numerical simulations demonstrated that auxin plays an essential role in altering cells' mechanical properties; this process involves the ABP1 and KATANIN 1 proteins (Sassi et al, 2014). Also, the advanced cell-based mathematical model describes the relationship between the concentration of morphogens and the cellular mechanistic properties in the developing apical shoot meristems (Banwarth-Kuhn et al, 2019).…”

“…Thus, the models of plant tissue morphogenesis put at the forefront three biological facts: (i) the dependence on intercellular hormonal signaling, (ii) the importance of the intracellular state and individual cellular characteristics, (iii) the relevance of mechanical stresses in intercellular interactions. Therefore, scRNA-seq technologies, microscopy, imaging techniques, and a range of complementary approaches to measuring cell mechanical properties (Banwarth-Kuhn et al, 2019;Bidhendi and Geitmann, 2019) can provide a complete picture of morphogenetic processes at the cellular level.…”

“…In center-based models, cells are represented as dots with mass, connected by mechanical elements (springs). Banwarth-Kuhn et al (2019) give an example of this formalism's application to the description of growth processes in the shoot apical meristem. Cellular Potts models are often used to describe the processes occurring in animal tissues and tumor formation processes; this formalism is implemented in CompuCell3D (Swat et al, 2012).…”

Smoothed particle hydrodynamics for root growth mechanics

“…A way to bring together these two aspects is to formulate a multi-scale approach, combining several levels of description and allowing them to interact. Several propositions exist and among them, gene-regulated network combined to growth [4,31,58,71,27], averaging approaches through analytical homogenisation [1,35,65,79,82], and the incorporation of a representation of individual cells in a continuous formulation of tissue deformation [5,13,42,48,53,99].…”