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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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Related in: MedlinePlus

(a) Configurations predicted with parameters appropriate for lily and Arabidopsis anthers as epidermal dehydration reduces turgor and hence . Arrows indicate  decreasing from 1.9 to 0.56. (b) The same configurations characterized instead by the y-coordinate at the tip of the anther wall as a function of . In the absence of the septum, the locules initially lie in a closed, tightly curled ‘case I’ configuration, which gradually uncurls as the epidermis dehydrates (green curves). For  ≍ 1.66, a snap-through transition to ‘case II’ occurs (red solid curves), at which point the anther wall is uncurled but the anther still remains closed. Case II solutions evolve until  ≍ 1.4, at which point a transition to ‘case III’ occurs and the anther opens (blue curves). In case III, anther walls are arcs of circles, which uncurl as  decreases. For these parameters, hysteresis occurs at the transition from case I to case II; the sequence of configurations attained by a dehydrating anther (illustrated by solid arrows in (b)) is slightly different from those seen during rehydration of an already open anther (dashed arrows in (b)). In panel (a), grey shapes represent mathematically viable case II solutions (solid, stable; dashed, unstable) that would not be attained by a dehydrating anther. Parameters used: α = 1000, β = 0.2,  = 1, Φ = 5,  = 0 x0 = 1/3, θ0 = 2π/3.
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fig02: (a) Configurations predicted with parameters appropriate for lily and Arabidopsis anthers as epidermal dehydration reduces turgor and hence . Arrows indicate decreasing from 1.9 to 0.56. (b) The same configurations characterized instead by the y-coordinate at the tip of the anther wall as a function of . In the absence of the septum, the locules initially lie in a closed, tightly curled ‘case I’ configuration, which gradually uncurls as the epidermis dehydrates (green curves). For ≍ 1.66, a snap-through transition to ‘case II’ occurs (red solid curves), at which point the anther wall is uncurled but the anther still remains closed. Case II solutions evolve until ≍ 1.4, at which point a transition to ‘case III’ occurs and the anther opens (blue curves). In case III, anther walls are arcs of circles, which uncurl as decreases. For these parameters, hysteresis occurs at the transition from case I to case II; the sequence of configurations attained by a dehydrating anther (illustrated by solid arrows in (b)) is slightly different from those seen during rehydration of an already open anther (dashed arrows in (b)). In panel (a), grey shapes represent mathematically viable case II solutions (solid, stable; dashed, unstable) that would not be attained by a dehydrating anther. Parameters used: α = 1000, β = 0.2, = 1, Φ = 5, = 0 x0 = 1/3, θ0 = 2π/3.

Mentions: Simulating the model using MATLAB, we can predict how changing the turgor pressure within the epidermis drives the dynamics of anther opening. Fig. 2 illustrates the configurations predicted by the model with different values of the epidermal turgor pressure (using the parameter values appropriate for the lily anther given in Table 2). Associated distributions of stress and strain are plotted in Fig. S4. As the epidermal cells dehydrate, their turgor reduces, and we predict that the anther wall progressively moves through this sequence of configurations. Initially, after septum breakage, the closed anther exhibits a case I configuration, with the free ends of the anther wall tightly curled at the point of contact between the locules (green curves, Fig. 2a). The model predicts that, as the epidermis dehydrates, the anther wall uncurls (remaining closed) until the tips of the locule walls are in contact. At this point a snap-through transition to case II occurs, the next configuration being that of a solid red curve in Fig. 2(a). To further clarify these dynamics, Fig. 2(b) shows the y-coordinate of the anther wall at the symmetry line as a function of the hydration parameter, (which decreases proportionately to the epidermal turgor pressure); the sequence of configurations attained by a dehydrating anther are shown by solid arrows. As the figure illustrates, for values of between c. 1.66 and 1.8 (equivalent to a range of epidermal hydration), there exist three possible solutions: a stable case I solution (solid green line) and two case II configurations, one unstable (dashed red line) and one stable (solid red line). During dehydration, at the transition from case I to case II, the anther adopts the only available stable configuration (which lies on the solid red curve in the figure). Continued epidermal dehydration reduces the contact force at the symmetry line to zero, at which point the anther opens (case III, blue curves). Further epidermal dehydration results in the anther opening progressively wider, recovering (at least approximately) the shapes illustrated in Fig. 1(d,e). Rehydration of a fully open anther is equivalent to traversing Fig. 2(b) from left to right, as marked by the dashed arrows. Close to the transition from case II to case I, the anther remains in a case II configuration for higher values of (when compared with the dehydrating configurations), jumping from the red curve back to the green curve for = 1.8.


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)

(a) Configurations predicted with parameters appropriate for lily and Arabidopsis anthers as epidermal dehydration reduces turgor and hence . Arrows indicate  decreasing from 1.9 to 0.56. (b) The same configurations characterized instead by the y-coordinate at the tip of the anther wall as a function of . In the absence of the septum, the locules initially lie in a closed, tightly curled ‘case I’ configuration, which gradually uncurls as the epidermis dehydrates (green curves). For  ≍ 1.66, a snap-through transition to ‘case II’ occurs (red solid curves), at which point the anther wall is uncurled but the anther still remains closed. Case II solutions evolve until  ≍ 1.4, at which point a transition to ‘case III’ occurs and the anther opens (blue curves). In case III, anther walls are arcs of circles, which uncurl as  decreases. For these parameters, hysteresis occurs at the transition from case I to case II; the sequence of configurations attained by a dehydrating anther (illustrated by solid arrows in (b)) is slightly different from those seen during rehydration of an already open anther (dashed arrows in (b)). In panel (a), grey shapes represent mathematically viable case II solutions (solid, stable; dashed, unstable) that would not be attained by a dehydrating anther. Parameters used: α = 1000, β = 0.2,  = 1, Φ = 5,  = 0 x0 = 1/3, θ0 = 2π/3.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig02: (a) Configurations predicted with parameters appropriate for lily and Arabidopsis anthers as epidermal dehydration reduces turgor and hence . Arrows indicate decreasing from 1.9 to 0.56. (b) The same configurations characterized instead by the y-coordinate at the tip of the anther wall as a function of . In the absence of the septum, the locules initially lie in a closed, tightly curled ‘case I’ configuration, which gradually uncurls as the epidermis dehydrates (green curves). For ≍ 1.66, a snap-through transition to ‘case II’ occurs (red solid curves), at which point the anther wall is uncurled but the anther still remains closed. Case II solutions evolve until ≍ 1.4, at which point a transition to ‘case III’ occurs and the anther opens (blue curves). In case III, anther walls are arcs of circles, which uncurl as decreases. For these parameters, hysteresis occurs at the transition from case I to case II; the sequence of configurations attained by a dehydrating anther (illustrated by solid arrows in (b)) is slightly different from those seen during rehydration of an already open anther (dashed arrows in (b)). In panel (a), grey shapes represent mathematically viable case II solutions (solid, stable; dashed, unstable) that would not be attained by a dehydrating anther. Parameters used: α = 1000, β = 0.2, = 1, Φ = 5, = 0 x0 = 1/3, θ0 = 2π/3.
Mentions: Simulating the model using MATLAB, we can predict how changing the turgor pressure within the epidermis drives the dynamics of anther opening. Fig. 2 illustrates the configurations predicted by the model with different values of the epidermal turgor pressure (using the parameter values appropriate for the lily anther given in Table 2). Associated distributions of stress and strain are plotted in Fig. S4. As the epidermal cells dehydrate, their turgor reduces, and we predict that the anther wall progressively moves through this sequence of configurations. Initially, after septum breakage, the closed anther exhibits a case I configuration, with the free ends of the anther wall tightly curled at the point of contact between the locules (green curves, Fig. 2a). The model predicts that, as the epidermis dehydrates, the anther wall uncurls (remaining closed) until the tips of the locule walls are in contact. At this point a snap-through transition to case II occurs, the next configuration being that of a solid red curve in Fig. 2(a). To further clarify these dynamics, Fig. 2(b) shows the y-coordinate of the anther wall at the symmetry line as a function of the hydration parameter, (which decreases proportionately to the epidermal turgor pressure); the sequence of configurations attained by a dehydrating anther are shown by solid arrows. As the figure illustrates, for values of between c. 1.66 and 1.8 (equivalent to a range of epidermal hydration), there exist three possible solutions: a stable case I solution (solid green line) and two case II configurations, one unstable (dashed red line) and one stable (solid red line). During dehydration, at the transition from case I to case II, the anther adopts the only available stable configuration (which lies on the solid red curve in the figure). Continued epidermal dehydration reduces the contact force at the symmetry line to zero, at which point the anther opens (case III, blue curves). Further epidermal dehydration results in the anther opening progressively wider, recovering (at least approximately) the shapes illustrated in Fig. 1(d,e). Rehydration of a fully open anther is equivalent to traversing Fig. 2(b) from left to right, as marked by the dashed arrows. Close to the transition from case II to case I, the anther remains in a case II configuration for higher values of (when compared with the dehydrating configurations), jumping from the red curve back to the green curve for = 1.8.

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