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

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. </p

Using mathematical modelling to understand how plant cell growth is controlled

Understanding plant growth is essential for a future sustainable world and to ensure food security. With a growing population there will be an increasing need for higher crop yields as well as plants that can cope with the problems that climate change will bring. Plants are also fascinatingly complex, which have many intertwining mechanical and chemical processes, with many pathways yet to be fully unravelled. To investigate cell growth control, first on the microscale, we derive and analyse a simple mathematical model for the effective mechanical properties of the evolving cell wall network, incorporating cellulose microfibres, which reorient with cell growth and are linked via biological hotspots made up of regions of crosslinking hemicellulose. Assuming a viscoelastic 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 effecting the breakage rate and viscous properties, we provide evidence for this biological hotspot hypothesis and develop a mechanistic understanding of how these enzymes work. Next, to investigate pavement cell development, a joint experimental and theoretical approach is taken. Using GFP transgenic and Atomic force microscopy, signs of chemical initiation were observed, with actin cytoskeleton observations contracting some previous studies. We combine a stochastic microtubule model, a reaction-diffusion model for the signalling processes, and a vertex-element mechanical growth model to form a novel hybrid model for pavement cell development incorporating effects at multiple spatial and time scales. Model simulations demonstrate that the currently hypothesised signalling network can reinforce but not initiate lobe formation. Lobe initiation could be generated through spatial variations in mechanical properties, differential growth rates between neighbouring cells or a buckling mechanism when growth is restricted. We conclude by discussing these results in the context of current biological research

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

Plant cell growth is regulated through manipulation of the cell wall net- work, 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 dis- tinct 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 whilst 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 experimen- tally 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

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

Acknowledgements: We would like to thank Cara Neal and Alexander Brune for their helpful inputs and the reviewers. RJD and ETS thank EPSRC for funding via grants EP/M00015X/1 and EP/N509590/1, respectively.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

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

Acknowledgements: We would like to thank Cara Neal and Alexander Brune for their helpful inputs and the reviewers. RJD and ETS thank EPSRC for funding via grants EP/M00015X/1 and EP/N509590/1, respectively.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

Stiffness transitions in new walls post-cell division differ between Marchantia polymorpha gemmae and Arabidopsis thaliana leaves

Plant morphogenesis is governed by the mechanics of the cell wall-a stiff and thin polymeric box that encloses the cells. The cell wall is a highly dynamic composite material. New cell walls are added during cell division. As the cells continue to grow, the properties of cell walls are modulated to undergo significant changes in shape and size without breakage. Spatial and temporal variations in cell wall mechanical properties have been observed. However, how they relate to cell division remains an outstanding question. Here, we combine time-lapse imaging with local mechanical measurements via atomic force microscopy to systematically map the cell wall's age and growth, with their stiffness. We make use of two systems, Marchantia polymorpha gemmae, and Arabidopsis thaliana leaves. We first characterize the growth and cell division of M. polymorpha gemmae. We then demonstrate that cell division in M. polymorpha gemmae results in the generation of a temporary stiffer and slower-growing new wall. In contrast, this transient phenomenon is absent in A. thaliana leaves. We provide evidence that this different temporal behavior has a direct impact on the local cell geometry via changes in the junction angle. These results are expected to pave the way for developing more realistic plant morphogenetic models and to advance the study into the impact of cell division on tissue growth