Geometric and mechanical guidance: Role of stigmatic epidermis in early pollen tube pathfinding in arabidopsis
Fig 5
Model for pollen tube growth guidance assuming a rigidity contrast between the two-dimensional isotropic elastic leaflets of the papilla wall.
(A) The orientation of pollen tube growth (longitudinal vs. circumferential) influences the strain experienced by the papilla cell wall. To facilitate the visualisation of the deformation generated by the pollen tube growth, the papilla surface is represented using a grid of circumferential and longitudinal lines. In contrast to the papilla without tube growth, where the grid is made of squares (square, insert a), longitudinal growth generates a deformation causing expansion of the grid in one direction (grey arrows, insert b, and dashed square for non-deformed state). Circumferential growth results in deformation causing the grid to expand in two directions (grey arrows, insert c, dashed square for non-deformed state) The colours represent schematically the local strain energy in the papilla cell wall, flg and fci, for longitudinal and circumferential growth, respectively. (B,C) Mechanical model of pollen tube growth within the WT (B) or the ktn1-5 (C) papilla cell wall. The pollen tube separates and deforms the cell wall bilayer with an outer (inner) Young’s modulus Yout (Yin) and exerts volume work against the papilla pressure p. The shape of the deformation cross-section is approximated by two half-ellipses with the indentation ratio corresponding to the ratio between the external (rout) and internal (rin) papilla deformation.
for pollen tube growing within the WT papilla cell wall and
for pollen tube growing within ktn1-5 papilla cell wall. (D) Relation between inner and outer cell wall rigidities for a given value of
(WT) and
(ktn1-5) for growth in the circumferential (circ.) direction compared to the longitudinal (long.) direction. In the shaded region, the rigidity of the outer cell wall layer Yout is lower than the rigidity of the inner cell wall layer Yin which corresponds to a negative rigidity contrast
, otherwise the rigidity contrast is positive
. Note that both tube growth directions require a similar rigidity contrast and differences in the indentation ratio
are experimentally probably not detectable. For further details see S1 Text. (E) Adimensional alignment strength
for WT (
) and ktn1-5 (
) papilla cells depending on the effective cell wall stiffness
. The label ktn1 in (D) refers to the ktn1-5 mutant.