Abstract
The morphogenesis of organs necessarily involves mechanical interactions and changes in mechanical properties of a tissue. A long standing question is how such changes are directed on a cellular scale while being coordinated at a tissular scale. Growing evidence suggests that mechanical cues are participating in the control of growth and morphogenesis during development. We introduce a mechanical model that represents the deposition of cellulose fibers in primary plant walls. In the model both the degree of material anisotropy and the anisotropy direction are regulated by stress anisotropy. We show that the finite element shell model and the simpler triangular biquadratic springs approach provide equally adequate descriptions of cell mechanics in tissue pressure simulations of the epidermis. In a growing organ, where circumferentially organized fibers act as a main controller of longitudinal growth, we show that the fiber direction can be correlated with both the maximal stress direction and the direction orthogonal to the maximal strain direction. However, when dynamic updates of the fiber direction are introduced, the mechanical stress provides a robust directional cue for the circumferential organization of the fibers, whereas the orthogonal to maximal strain model leads to an unstable situation where the fibers reorient longitudinally. Our investigation of the more complex shape and growth patterns in the shoot apical meristem where new organs are initiated shows that a stress based feedback on fiber directions is capable of reproducing the main features of in vivo cellulose fiber directions, deformations and material properties in different regions of the shoot. In particular, we show that this purely mechanical model can create radially distinct regions such that cells expand slowly and isotropically in the central zone while cells at the periphery expand more quickly and in the radial direction, which is a well established growth pattern in the meristem.
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Claims 6
Claim · model-written summary
Fibre direction in a growing organ can be correlated with the maximal stress direction and with the direction orthogonal to the maximal strain direction.
Not reportedDirection
Verbatim
e1“We introduce a mechanical model that represents the deposition of cellulose fibers in primary plant walls”
e2“we show that the fiber direction can be correlated with both the maximal stress direction and the direction orthogonal to the maximal strain direction”
Claim · model-written summary
With dynamic updates, mechanical stress gave a robust directional cue for circumferential fibre organization.
Verbatim
e3“when dynamic updates of the fiber direction are introduced, the mechanical stress provides a robust directional cue for the circumferential organization of the fibers, whereas the orthogonal to maximal strain model leads to an unstable situation where the fibers reorient longitudinally”
Claim · model-written summary
The orthogonal-to-maximal-strain model led to an unstable situation where fibres reorient longitudinally.
Verbatim
e3“when dynamic updates of the fiber direction are introduced, the mechanical stress provides a robust directional cue for the circumferential organization of the fibers, whereas the orthogonal to maximal strain model leads to an unstable situation where the fibers reorient longitudinally”
Claim · model-written summary
A stress-based feedback on fibre directions reproduced the main features of in vivo cellulose fibre directions, deformations and material properties in the shoot.
Verbatim
e4“a stress based feedback on fiber directions is capable of reproducing the main features of in vivo cellulose fiber directions, deformations and material properties in different regions of the shoot”
Claim · model-written summary
The finite element shell model and the simpler triangular biquadratic springs approach gave equally adequate descriptions of epidermal cell mechanics.
Verbatim
e5“the finite element shell model and the simpler triangular biquadratic springs approach provide equally adequate descriptions of cell mechanics in tissue pressure simulations of the epidermis”
Claim · model-written summary
The model created radially distinct regions in the shoot, with slow isotropic expansion in the central zone and faster radial expansion at the periphery.
Verbatim
e1“We introduce a mechanical model that represents the deposition of cellulose fibers in primary plant walls”
e6“this purely mechanical model can create radially distinct regions such that cells expand slowly and isotropically in the central zone while cells at the periphery expand more quickly and in the radial direction”