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A biomechanical model of anther opening reveals the roles of dehydration and secondary thickening.

Nelson MR, Band LR, Dyson RJ, Lessinnes T, Wells DM, Yang C, Everitt NM, Jensen OE, Wilson ZA - New Phytol. (2012)

Bottom Line: Our mathematical model describing the biomechanics of anther opening incorporates the bilayer structure of the mature anther wall, which comprises the outer epidermal cell layer, whose turgor pressure is related to its hydration, and the endothecial layer, whose walls contain helical secondary thickening, which resists stretching and bending.The model demonstrates that epidermal dehydration can drive anther opening, and suggests why endothecial secondary thickening is essential for this process (explaining the phenotypes presented in the myb26 and nst1nst2 mutants).The research hypothesizes and demonstrates a biomechanical mechanism for anther opening, which appears to be conserved in many other biological situations where tissue movement occurs.

View Article: PubMed Central - PubMed

Affiliation: School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK. martin.nelson@nottingham.ac.uk

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configurations attained for mutants with a stiffened epidermis or reduced endothecial secondary thickening (coloured curve), compared with those of a wildtype anther given in Fig. 2(shown in grey). The dominant parameter controlling the transition from closed to open states is Φ; for larger Φ, the solution curve is squashed horizontally towards  = 1, requiring stronger dehydration for the anther to open. Also illustrated is a speculated normal range of hydration. Parameter changes that push the transition from case II to case III outside the biologically feasible range correspond to anthers that fail to open. Parameters used for mutants: β = 0.4, Φ = 10, and all other parameters as in Fig. 2.
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fig03: configurations attained for mutants with a stiffened epidermis or reduced endothecial secondary thickening (coloured curve), compared with those of a wildtype anther given in Fig. 2(shown in grey). The dominant parameter controlling the transition from closed to open states is Φ; for larger Φ, the solution curve is squashed horizontally towards = 1, requiring stronger dehydration for the anther to open. Also illustrated is a speculated normal range of hydration. Parameter changes that push the transition from case II to case III outside the biologically feasible range correspond to anthers that fail to open. Parameters used for mutants: β = 0.4, Φ = 10, and all other parameters as in Fig. 2.

Mentions: We now consider the extent to which biomechanical changes impact the anther's ability to open. Anther dehiscence has been observed to be hindered by both reduced endothecial secondary thickening, such as that observed in the myb26 and nst1nst2 mutants (Dawson et al., 1999; Mitsuda et al., 2005), and stiffening of the epidermis through, for example, ectopic deposition of secondary thickening (Yang et al., 2007). In the former case, the endothecial extensional and bending stiffnesses are reduced by the same factor, whereas in the latter case the epidermal extensional stiffness is increased. Thus, considering the dimensionless parameter groupings in Table 2, both cases cause an increase in the parameter β and an associated proportional increase in the parameter Φ. Since α ≫ 1 and β ≪ 1, we find (see Notes S1: Reduced model in the inextensible limit) that the behaviour of the anther is dominated by the parameter Φ, such that an increase in Φ simply shrinks solution curves in Fig. 2(b) with respect to the horizontal axis about the point = 1. Fig. 3 illustrates the solution branches obtained for β = 0.4 and Φ = 10 (double the values used in Fig. 2), with all other parameters as in Fig. 2. (The predicted wildtype behaviour is marked in grey for comparison.) The increase in Φ results in solution curves being pushed towards = 1 in Fig. 3, with anther opening (the transition from red to blue curves) now requiring greater epidermal dehydration (smaller ). Also illustrated in Fig. 3 is a speculated ‘normal range’ of (equivalent to epidermal turgor) in a healthy anther. Changes in Φ that result in the transition from case II to case III (red to blue) falling outside this healthy range correspond to anthers which would fail to open under normal conditions.


A biomechanical model of anther opening reveals the roles of dehydration and secondary thickening.

Nelson MR, Band LR, Dyson RJ, Lessinnes T, Wells DM, Yang C, Everitt NM, Jensen OE, Wilson ZA - New Phytol. (2012)

configurations attained for mutants with a stiffened epidermis or reduced endothecial secondary thickening (coloured curve), compared with those of a wildtype anther given in Fig. 2(shown in grey). The dominant parameter controlling the transition from closed to open states is Φ; for larger Φ, the solution curve is squashed horizontally towards  = 1, requiring stronger dehydration for the anther to open. Also illustrated is a speculated normal range of hydration. Parameter changes that push the transition from case II to case III outside the biologically feasible range correspond to anthers that fail to open. Parameters used for mutants: β = 0.4, Φ = 10, and all other parameters as in Fig. 2.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3569878&req=5

fig03: configurations attained for mutants with a stiffened epidermis or reduced endothecial secondary thickening (coloured curve), compared with those of a wildtype anther given in Fig. 2(shown in grey). The dominant parameter controlling the transition from closed to open states is Φ; for larger Φ, the solution curve is squashed horizontally towards = 1, requiring stronger dehydration for the anther to open. Also illustrated is a speculated normal range of hydration. Parameter changes that push the transition from case II to case III outside the biologically feasible range correspond to anthers that fail to open. Parameters used for mutants: β = 0.4, Φ = 10, and all other parameters as in Fig. 2.
Mentions: We now consider the extent to which biomechanical changes impact the anther's ability to open. Anther dehiscence has been observed to be hindered by both reduced endothecial secondary thickening, such as that observed in the myb26 and nst1nst2 mutants (Dawson et al., 1999; Mitsuda et al., 2005), and stiffening of the epidermis through, for example, ectopic deposition of secondary thickening (Yang et al., 2007). In the former case, the endothecial extensional and bending stiffnesses are reduced by the same factor, whereas in the latter case the epidermal extensional stiffness is increased. Thus, considering the dimensionless parameter groupings in Table 2, both cases cause an increase in the parameter β and an associated proportional increase in the parameter Φ. Since α ≫ 1 and β ≪ 1, we find (see Notes S1: Reduced model in the inextensible limit) that the behaviour of the anther is dominated by the parameter Φ, such that an increase in Φ simply shrinks solution curves in Fig. 2(b) with respect to the horizontal axis about the point = 1. Fig. 3 illustrates the solution branches obtained for β = 0.4 and Φ = 10 (double the values used in Fig. 2), with all other parameters as in Fig. 2. (The predicted wildtype behaviour is marked in grey for comparison.) The increase in Φ results in solution curves being pushed towards = 1 in Fig. 3, with anther opening (the transition from red to blue curves) now requiring greater epidermal dehydration (smaller ). Also illustrated in Fig. 3 is a speculated ‘normal range’ of (equivalent to epidermal turgor) in a healthy anther. Changes in Φ that result in the transition from case II to case III (red to blue) falling outside this healthy range correspond to anthers which would fail to open under normal conditions.

Bottom Line: Our mathematical model describing the biomechanics of anther opening incorporates the bilayer structure of the mature anther wall, which comprises the outer epidermal cell layer, whose turgor pressure is related to its hydration, and the endothecial layer, whose walls contain helical secondary thickening, which resists stretching and bending.The model demonstrates that epidermal dehydration can drive anther opening, and suggests why endothecial secondary thickening is essential for this process (explaining the phenotypes presented in the myb26 and nst1nst2 mutants).The research hypothesizes and demonstrates a biomechanical mechanism for anther opening, which appears to be conserved in many other biological situations where tissue movement occurs.

View Article: PubMed Central - PubMed

Affiliation: School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK. martin.nelson@nottingham.ac.uk

Show MeSH
Related in: MedlinePlus