The Impact of Microfibril Orientations on the Biomechanics of Plant Cell Walls and Tissues

Ptashnyk, Mariya; Seguin, Brian

doi:10.1007/s11538-016-0207-8

Cited by 10 publications

(4 citation statements)

References 39 publications

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“…This hypothesis has been previously put forward [ 19 ]. Cellulose reorientation reducing axial growth has been previously reported in other mathematical models [ 53 , 54 ].…”

Section: Resultsmentioning

confidence: 79%

A continuum mechanics model of the plant cell wall reveals interplay between enzyme action and cell wall structure

Smithers,

Luo,

Dyson

2024

Eur. Phys. J. E

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Plant cell growth is regulated through manipulation of the cell wall network, which consists of oriented cellulose microfibrils embedded within a ground matrix incorporating pectin and hemicellulose components. There remain many unknowns as to how this manipulation occurs. Experiments have shown that cellulose reorients in cell walls as the cell expands, while recent data suggest that growth is controlled by distinct collections of hemicellulose called biomechanical hotspots, which join the cellulose molecule together. The enzymes expansin and Cel12A have both been shown to induce growth of the cell wall; however, while Cel12A’s wall-loosening action leads to a reduction in the cell wall strength, expansin’s has been shown to increase the strength of the cell wall. In contrast, members of the XTH enzyme family hydrolyse hemicellulose but do not appear to cause wall creep. This experimentally observed behaviour still awaits a full explanation. We derive and analyse a mathematical model for the effective mechanical properties of the evolving cell wall network, incorporating cellulose microfibrils, which reorient with cell growth and are linked via biomechanical hotspots made up of regions of crosslinking hemicellulose. Assuming a visco-elastic response for the cell wall and using a continuum approach, we calculate the total stress resultant of the cell wall for a given overall growth rate. By changing appropriate parameters affecting breakage rate and viscous properties, we provide evidence for the biomechanical hotspot hypothesis and develop mechanistic understanding of the growth-inducing enzymes. Graphic Abstract

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“…This hypothesis has been previously put forward [ 19 ]. Cellulose reorientation reducing axial growth has been previously reported in other mathematical models [ 53 , 54 ].…”

Section: Resultsmentioning

confidence: 79%

A continuum mechanics model of the plant cell wall reveals interplay between enzyme action and cell wall structure

Smithers,

Luo,

Dyson

2024

Eur. Phys. J. E

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“…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].…”

Section: Eect Of Dierential Growthmentioning

confidence: 99%

Smoothed particle hydrodynamics for root growth mechanics

Mimault

Ptashnyk

Bassel

et al. 2019

Engineering Analysis with Boundary Elements

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A major challenge of plant developmental biology is to understand how cells grow during the formation of an organ. To date, it has proved dicult to develop computational models of entire organs at cellular resolution and, as a result, the testing of hypotheses on the biophysics of self-organisation is currently limited. Here, we formulate a model for plant tissue growth in an SPH framework. The framework identies the SPH particle with individual cells in a tissue, but the tissue growth is performed at the macroscopic level using SPH approximations. Plant tissue is represented as an anisotropic poro-elastic material where turgor pressure deforms the cell walls and biosynthesis and cell division control the density of the tissue. The performance of the model is evaluated through a series of tests and benchmarks. Results demonstrate good stability and convergence of simulations as well as readiness of the technique for more complex biological problems.

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“…Many results can be found for multiscale modelling and analysis of the periodic microstructure of wood [26,46,60]. Multiscale modelling and analysis of the impact of the microscopic structure of plant cell walls, especially orientation and distribution of micro brils, on mechanical properties of cell walls were conducted in [58]. A vertex-element model and hybrid vertex-midline model for plant tissue deformation and growth, coupled with the cell-scale transport of plant hormone, were considered in [30,31].…”

Section: Introductionmentioning

confidence: 99%

Homogenization of biomechanical models of plant tissues with randomly distributed cells

Piatnitski

Ptashnyk

2020

Nonlinearity

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In this paper homogenization of a mathematical model for biomechanics of a plant tissue with randomly distributed cells is considered. Mechanical properties of a plant tissue are modelled by a strongly coupled system of reaction-diffusion-convection equations for chemical processes in plant cells and cell walls, the equations of poroelasticity for elastic deformations of plant cell walls and middle lamella, and the Stokes equations for fluid flow inside the cells. The nonlinear coupling between the mechanics and chemistry is given by the dependence of elastic properties of plant tissue on densities of chemical substances as well as by the dependence of chemical reactions on mechanical stresses present in a tissue. Using techniques of stochastic homogenization we derive rigorously macroscopic model for plant tissue biomechanics with random distribution of cells. Strong stochastic two-scale convergence is shown to pass to the limit in the non-linear reaction terms. Appropriate meaning of the boundary terms is introduced to define the macroscopic equations with flux boundary conditions and transmission conditions on the microscopic scale.

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The Impact of Microfibril Orientations on the Biomechanics of Plant Cell Walls and Tissues

Cited by 10 publications

References 39 publications

A continuum mechanics model of the plant cell wall reveals interplay between enzyme action and cell wall structure

A continuum mechanics model of the plant cell wall reveals interplay between enzyme action and cell wall structure

Smoothed particle hydrodynamics for root growth mechanics

Homogenization of biomechanical models of plant tissues with randomly distributed cells

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