Fig 1.
Pollen-stigma interactions in A. thaliana and characterisation of papilla shape.
(A) A mature A. thaliana flower. The pistil at the center of the flower is surrounded by six anthers containing the male gametophytes (yellow pollen grains). Scale bar = 500 m. (B) View of the top part of the pistil, the stigmatic epidermis, imaged by scanning electron microscopy (SEMi), and composed of hundreds of elongated papillae (p). Scale bar = 100
m. (C) Schematic representation of the pollen tube journey within the pistil tissue. A pollen grain (pg) released from the anthers lands on a papilla and germinates a pollen tube (pt) which transport the male gametes through the stigma, style and ovary, towards the ovules for fertilization. (D,E) Transversal section of a WT (D) and ktn1-5 (E) papilla pollinated with WT pollen and observed by transmission electron microscopy. The cuticle appears as an electron-dense black layer. The pollen tube progresses within the stigmatic cell wall, between its internal (iCW) and external (eCW) layers. For better visualisation, stigmatic (iCW + eCW) and pollen tube (ptCW) cell walls are highlighted with a green and orange dashed line, respectively. The original information was previously published in [6]. Images displayed here differ from the ones in [6]. Scale bar = 1
m. (F, G) SEMi images of WT (F) and ktn1-5 (G) papillae pollinated with WT pollen grains. Most of the pollen tubes go straight towards the base of the WT stigma (F) whereas pollen tubes make loops in the ktn1-5 papillae (G). The original information was previously published in [6]. Images displayed here differ from the ones in [6]. Scale bar = 10
m. (H,I) Light microscopy images of WT (H) and ktn1-5 papillae (I) with relevant shape descriptors
,
,
and
. Scale bar = 10
m. (J) Box plots of the shape descriptor dimensions measured on 30 papillae from 3 WT or 6 ktn1-5 stigmas. The horizontal bar in the boxes corresponds to the mean value. Statistical analysis was based on a non-parametric Wilcoxon Rank Sum test. *** indicates a p-value <0.001. The label ktn1 refers to the ktn1-5 mutant. (K) Means of the shape descriptor dimensions +/- standard error of the mean. Measurements are provided in S2 Table. n denotes number of papillae analysed.
Fig 2.
Theoretical geodesic trajectories on pin-like surfaces of varying shapes.
This sequence displays pin-like structures, characterized, from left to right by a gradual decrease in neck mid-height diameter (D) while maintaining a constant height (H). The top row features 3D surface rendering of the shape. Bottom row: wire-frame rendering where the whole geodesic trajectory is visible (yellow curve). All the geodesics start at the same position (green dot) at point P0 with azimuth = 0 and altitude = -0.1 with respect to the pole of the pin structure, and with an initial inclination angle of downward with respect to the circumferential direction. D is given in arbitrary units (a.u.) and H=2.0 a.u. Note that the curve can cross itself (rightmost two situations).
Fig 3.
Papilla prototypes and pollen tube trajectories without guidance on WT and ktn1-5 papillae.
(A) Three dimensional shapes of WT and ktn1-5 papillae. The papilla long axis is oriented along the z axis. z = 0 corresponds to the papilla pole. Scale bar = 10 m. (B) Three-dimensional view of the top region of a ktn1-5 papilla showing the initial position of the pollen grain (z0, red dot) and the initial direction of the pollen tube upon emergence from the grain (
, red arrow). The vector
represents a papilla surface tangent vector pointing in the longitudinal direction.
(
) indicates an initial tube direction towards the papilla base (pole). Scale bar = 10
m. (C) Examples of simulated pollen tube trajectories on ktn1-5 papilla surfaces, varying in initial positions z0 of the pollen grain and initial directions
of the emerging pollen tube (indicated by black arrows). The numbers in brackets denote the normalized initial positions (
) and the initial directions (
) for each trajectory. T (below each papilla) represents the number of turns the pollen tube makes to reach the papilla base . Each configuration is labelled from a to h. Trajectories on WT stigma with identical initial conditions are shown in S2 Fig. (D) Morphological phase diagrams of the pollen tube turn number T depending on the initial pollen grain position z0 (normalised to the papilla distance head length
) and the initial pollen tube direction (
) on WT and ktn1-5 papillae.
denotes the papilla pole,
the frontier between the head and cylindrical shaft, and
the pollen grain landing limit. The colour code indicates the number of turns the trajectories undergoes before it reaches the papilla base. In the white region (caged), the tube path is trapped by its own trajectory, preventing it from reaching the papilla base; such trajectories were categorised as having T>2.5. The letters a to h correspond to the example configurations depicted in (C). (E) Comparison of simulated (solid lines) and experimental (squares) cumulative distributions of pollen tube turn numbers. To calculate the cumulative fraction for experimental data, we utilized data from Ref [6], where we examined 251 WT and 327 ktn1-5 pollinated papillae; error bars represent the standard error of the mean. The label ktn1 refers to the ktn1-5 mutant.
Fig 4.
Effect of longitudinal growth guidance on pollen tube trajectories.
(A) Two-dimensional representation of the papilla, indicating where the alignment forces act (yellow region). (B) Example of pollen tube trajectories on WT papilla surfaces under various initial conditions, the initial pollen grain position z0 and initial pollen tube direction (indicated by black arrows), simulated without growth guidance (upper panel) and with growth guidance (adimensional guidance strength
, lower panel). The numbers in brackets denote the normalized initial position (
) and the initial directions (
) for each trajectory. T represents the number of turns the pollen tube makes to reach the papilla base. Each configuration is labelled from a to f. (C) Morphological phase diagram of the pollen tube turn number T depending on the initial pollen grain position z0 (normalised to the papilla head length
) and the initial pollen tube direction (
) on WT papillae.
denotes the papilla pole,
the frontier between the head and cylindrical shaft, and
the pollen grain landing limit. The colour code indicates the number of turns the trajectories undergoes before it reaches the papilla base. The letters d, e, f correspond to the example configurations depicted in (B). Trajectories of pollen tubes on ktn1-5 papilla with identical initial conditions and the corresponding morphological phase diagram are shown in S3 Fig. (D) Comparison of simulated (solid lines) and experimental (squares) cumulative distributions of pollen tube turn numbers. Simulated cumulative distributions for turn numbers on WT papillae are calculated with a growth guidance of
(dashed orange curve). Simulated cumulative distributions for turn numbers on ktn1-5 papillae are calculated without guidance (blue curve, reproduced from Fig 3E). To calculate the cumulative fraction for experimental data, we utilized data from Ref [6], where we examined 251 WT and 327 ktn1-5 pollinated papillae; error bars represent the standard error of the mean. The label ktn1 refers to the ktn1-5 mutant.
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.
Fig 6.
Role of cell wall mechanical anisotropy in pollen tube guidance.
(A) Schematic representation of the papilla cell wall anisotropy and alignment strength factor
. Ylg (Yci) stands for the effective stiffness in the longitudinal (circumferential) direction within the papilla wall. Note that we considered Yci (Ylg) to be the same in the inner and outer papilla wall leaflets. When
,
is negative, the longitudinal direction is softer (narrow blue arrow) compared to the circumferential one (large blue arrow). When
,
is positive, the circumferential direction is softer compared to the longitudinal one. A positive value of the alignment strength factor
favours a circumferential pollen tube growth whereas a negative value of
favours a longitudinal growth. We explored how the anisotropy
can influence the alignment strength factor
and hence the pollen tube growth direction (question mark). (B,C) Indentation ratio
(upper panels) and alignment strength factor
(lower panels) for circumferential (circ, solid line) and longitudinal (long, dashed line) tube growth depending on the papilla wall mechanical anisotropy
and the effective rigidity of the papilla wall (
, B:
, C). The calculations were done using the ratio
for ktn1-5 geometry (
m/
m, depicted in blue, B) or for WT geometry (
m/
m, depicted in orange, C). The grey lines correspond to the experimentally measured indentation ratios
on ktn1-5 and
on WT papillae. Additional calculations for ktn1 geometry with rigid cell wall, WT geometry with soft cell wall and intermediate wall rigidity (
) are provided in S1 Text. The dashed red line highlights the isotropic case (
).
Fig 7.
Papilla geometry and cell wall mechanics act synergistically to orient the advancing pollen tube along the longitudinal papilla axis.