skip to main content


Title: Cell-Based Model of the Generation and Maintenance of the Shape and Structure of the Multilayered Shoot Apical Meristem of Arabidopsis thaliana
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, multilayeredSAMbased onWUSconcentration 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.  more » « less
Award ID(s):
1762063
NSF-PAR ID:
10096051
Author(s) / Creator(s):
; ; ; ; ; ;
Date Published:
Journal Name:
Bulletin of Mathematical Biology
ISSN:
0092-8240
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Nie, Qing (Ed.)
    Stem cell maintenance in multilayered shoot apical meristems (SAMs) of plants requires strict regulation of cell growth and division. Exactly how the complex milieu of chemical and mechanical signals interact in the central region of the SAM to regulate cell division plane orientation is not well understood. In this paper, simulations using a newly developed multiscale computational model are combined with experimental studies to suggest and test three hypothesized mechanisms for the regulation of cell division plane orientation and the direction of anisotropic cell expansion in the corpus. Simulations predict that in the Apical corpus, WUSCHEL and cytokinin regulate the direction of anisotropic cell expansion, and cells divide according to tensile stress on the cell wall. In the Basal corpus, model simulations suggest dual roles for WUSCHEL and cytokinin in regulating both the direction of anisotropic cell expansion and cell division plane orientation. Simulation results are followed by a detailed analysis of changes in cell characteristics upon manipulation of WUSCHEL and cytokinin in experiments that support model predictions. Moreover, simulations predict that this layer-specific mechanism maintains both the experimentally observed shape and structure of the SAM as well as the distribution of WUSCHEL in the tissue. This provides an additional link between the roles of WUSCHEL, cytokinin, and mechanical stress in regulating SAM growth and proper stem cell maintenance in the SAM. 
    more » « less
  2. Abstract Mechanical properties, size and geometry of cells, and internal turgor pressure greatly influence cell morphogenesis. Computational models of cell growth require values for wall elastic modulus and turgor pressure, but very few experiments have been designed to validate the results using measurements that deform the entire thickness of the cell wall. New wall material is synthesized at the inner surface of the cell such that full-thickness deformations are needed to quantify relevant changes associated with cell development. Here, we present an integrated, experimental–computational approach to analyze quantitatively the variation of elastic bending behavior in the primary cell wall of living Arabidopsis (Arabidopsis thaliana) pavement cells and to measure turgor pressure within cells under different osmotic conditions. This approach used laser scanning confocal microscopy to measure the 3D geometry of single pavement cells and indentation experiments to probe the local mechanical responses across the periclinal wall. The experimental results were matched iteratively using a finite element model of the experiment to determine the local mechanical properties and turgor pressure. The resulting modulus distribution along the periclinal wall was nonuniform across the leaf cells studied. These results were consistent with the characteristics of plant cell walls which have a heterogeneous organization. The results and model allowed the magnitude and orientation of cell wall stress to be predicted quantitatively. The methods also serve as a reference for future work to analyze the morphogenetic behaviors of plant cells in terms of the heterogeneity and anisotropy of cell walls. 
    more » « less
  3. null (Ed.)
    Abstract Plant cell deformations are driven by cell pressurization and mechanical constraints imposed by the nanoscale architecture of the cell wall, but how these factors are controlled at the genetic and molecular levels to achieve different types of cell deformation is unclear. Here, we used stomatal guard cells to investigate the influences of wall mechanics and turgor pressure on cell deformation and demonstrate that the expression of the pectin-modifying gene PECTATE LYASE LIKE12 (PLL12) is required for normal stomatal dynamics in Arabidopsis thaliana. Using nanoindentation and finite element modeling to simultaneously measure wall modulus and turgor pressure, we found that both values undergo dynamic changes during induced stomatal opening and closure. PLL12 is required for guard cells to maintain normal wall modulus and turgor pressure during stomatal responses to light and to tune the levels of calcium cross-linked pectin in guard cell walls. Guard cell-specific knockdown of PLL12 caused defects in stomatal responses and reduced leaf growth, which were associated with lower cell proliferation but normal cell expansion. Together, these results force us to revise our view of how wall-modifying genes modulate wall mechanics and cell pressurization to accomplish the dynamic cellular deformations that underlie stomatal function and tissue growth in plants. 
    more » « less
  4. Abstract Background

    Morphological properties of tissues and organs rely on cell growth. The growth of plant cells is determined by properties of a tough outer cell wall that deforms anisotropically in response to high turgor pressure. Cortical microtubules bias the mechanical anisotropy of a cell wall by affecting the trajectories of cellulose synthases in the wall that polymerize cellulose microfibrils. The microtubule cytoskeleton is often oriented in one direction at cellular length-scales to regulate growth direction, but the means by which cellular-scale microtubule patterns emerge has not been well understood. Correlations between the microtubule orientation and tensile forces in the cell wall have often been observed. However, the plausibility of stress as a determining factor for microtubule patterning has not been directly evaluated to date.

    Results

    Here, we simulated how different attributes of tensile forces in the cell wall can orient and pattern the microtubule array in the cortex. We implemented a discrete model with transient microtubule behaviors influenced by local mechanical stress in order to probe the mechanisms of stress-dependent patterning. Specifically, we varied the sensitivity of four types of dynamic behaviors observed on the plus end of microtubules – growth, shrinkage, catastrophe, and rescue – to local stress. Then, we evaluated the extent and rate of microtubule alignments in a two-dimensional computational domain that reflects the structural organization of the cortical array in plant cells.

    Conclusion

    Our modeling approaches reproduced microtubule patterns observed in simple cell types and demonstrated that a spatial variation in the magnitude and anisotropy of stress can mediate mechanical feedback between the wall and of the cortical microtubule array.

     
    more » « less
  5. Maini, Philip K (Ed.)
    Experiments on tumor spheroids have shown that compressive stress from their environment can reversibly decrease tumor expansion rates and final sizes. Stress release experiments show that nonuniform anisotropic elastic stresses can be distributed throughout. The elastic stresses are maintained by structural proteins and adhesive molecules, and can be actively relaxed by a variety of biophysical processes. In this paper, we present a new continuum model to investigate how the growth-induced elastic stresses and active stress relaxation, in conjunction with cell size control feedback machinery, regulate the cell density and stress distributions within growing tumors as well as the tumor sizes in the presence of external physical confinement and gradients of growth-promoting chemical fields. We introduce an adaptive reference map that relates the current position with the reference position but adapts to the current position in the Eulerian frame (lab coordinates) via relaxation. This type of stress relaxation is similar to but simpler than the classical Maxwell model of viscoelasticity in its formulation. By fitting the model to experimental data from two independent studies of tumor spheroid growth and their cell density distributions, treating the tumors as incompressible, neo-Hookean elastic materials, we find that the rates of stress relaxation of tumor tissues can be comparable to volumetric growth rates. Our study provides insight on how the biophysical properties of the tumor and host microenvironment, mechanical feedback control and diffusion-limited differential growth act in concert to regulate spatial patterns of stress and growth. When the tumor is stiffer than the host, our model predicts tumors are more able to change their size and mechanical state autonomously, which may help to explain why increased tumor stiffness is an established hallmark of malignant tumors. 
    more » « less