Fig 1.
Changes in pollen ploidy and size correlate with changes in aperture number.
(A-A’) Haploid pollen of wild-type Arabidopsis (Landsberg erecta ecotype) have three apertures (arrowheads). Front and back views of the auramine O-stained pollen grains are shown here and in other images as indicated. (B-B’) Diploid Landsberg pollen grains from tetraploid plants are larger than haploid pollen grains and have primarily four apertures (arrowheads). (C-D’) Diploid pollen grains from a diploid osd1 mutant usually have either four (C-C’) or six (D-D’) apertures (arrowheads). (E-F’) Irregular aperture patterns, often adopting a ring-shaped morphology, are common among tetraploid pollen grains from the tetraploid osd1 mutants. (G) A diagram of pollen development and aperture formation in the wild-type Arabidopsis and in several mutants with abnormal pollen ploidy. The ploidy of microspore mother cells (MMC), which divide meiotically to generate microspores, is the same as in the plants producing these MMCs. In the wild-type (WT) Arabidopsis, the 2n MMC undergoes two rounds of nuclear division (MI and MII), followed by cytokinesis (CK), and produces a tetrad of 1n microspores arranged in the tetrahedral conformation. The grey areas around the MMCs and the postmeiotic microspore arrangements represent the callose walls. First signs of apertures become apparent in postmeiotic microspores held together by the callose wall. After the callose wall dissolution, each microspore develops into a mature pollen grain, which, depending on its ploidy, exhibits a characteristic number of apertures. In the osd1 mutant, the second nuclear division (MII) is skipped, resulting in the formation of a dyad of microspores whose ploidy is identical to that of their MMC precursor. Scale bars = 10 μm.
Fig 2.
Morphogen interaction diagram.
The activator (A) self-activates and activates the inhibitor. The inhibitor (H) inhibits the activator.
Fig 3.
Examples of patterns observed on the 1D domain.
The 1D domain representing the pollen equator is shown in blue, the concentration of the activator is in red, and the concentration of the inhibitor is in green. We could commonly observe a three-spike pattern (A), a four-spike pattern (B), and a two-spike pattern (C). The concentration of the activator fluctuates between zero and its maximum, while the concentration of the inhibitor never gets reduced to zero, even between the spikes. The results were obtained running Eqs 1 and 2 with parameter values given in Table 1.
Table 1.
Parameter values used in the model to reproduce wild-type patterning.
Fig 4.
Increase in the domain size can lead to an increase in spike number.
The distribution of patterns produced using domains corresponding to surface areas ranging from 250 μm2 to 1450 μm2 in 1D (left) and 3D (right). As the surface area increased, patterns with more spikes were produced. Arrows mark the wild-type domain and circles mark the larger-sized domain. In this and all subsequent figures, unless stated otherwise, the results were obtained by running Eqs 1 and 2 with parameter values given in Table 1.
Fig 5.
Increase in the diffusion rate leads to a decrease in spike number.
In all domains, an increase in diffusion of either the activator (DA, top two rows) or the inhibitor (DH, bottom two rows) leads to a decrease in the number of spikes. The ring-like pattern had increased morphogen concentration along a great circle. The values of the diffusion parameters were varied from 20% to 300% of their original values from Table 1.
Fig 6.
Increase in the morphogen decay leads to an increase in spike number.
In both domains, an increase in decay of either the activator (μA, top rows) or the inhibitor (μH, bottom rows) led to an increase in the number of spikes. “Ring” represents increased morphogen concentration along a great circle, “1 and Ring” represents a single spike located at a pole of the sphere combined with a ring located on the opposite side of the sphere, and “Elong.” represents six elongated spikes located on the edges of a tetrahedron. The values of the decay parameters were varied from 20% to 300% of their original values from Table 1.
Fig 7.
Examples of the different patterns the model simulated on a sphere was able to produce when varying the kinetics.
In 3D, the following patterns were commonly observed: (A) two spikes on opposite poles, (B) three spikes equally spaced along a great circle, (C) four spikes located on the corners of a tetrahedron, (D) five spikes, (E) six spikes, with four spikes equally spaced along a great circle and the remaining two spikes on the poles, (F) a ring-like pattern with increased morphogen concentration along a great circle, (G) a single spike and a ring-like pattern, and (H,H’) six elongated spikes located on the edges of a tetrahedron. In the 3D plots, the activator concentration is represented by the height from the initial surface of the sphere (dark blue), color-coded from blue (almost no activator) to yellow (the highest amount of activator).
Fig 8.
Pollen aperture phenotypes and INP1-YFP localization in the mcr and dnt mutants.
(A-A’) mcr pollen has a single ring-like aperture (arrowheads) that runs around the pollen circumference (front and back views of the same pollen grain are shown). See also S2 Video. (B-B’) dnt pollen usually has two round apertures (arrowheads) located at diametrically opposite positions (front and back views of the same pollen grain are shown). See also S3 Video. Scale bars = 10 μm. (C) A 3D reconstruction of a tetrad of mcr microspores with early exine (blue) and single ring-like apertures (arrowhead) visible. Each aperture runs through the poles of microspores. (D-F) INP1-YFP localization changes in the mcr and dnt mutants. (D) INP1-YFP forms a single punctate line in mcr microspores, passing through the microspore poles and underlying the position of the future single ring-like aperture. See also S4 Video. (E) INP1-YFP localization to two sites close to each microspore equator indicates that the round apertures in mcr start their development as two apertures that eventually fuse at the poles. See also S5 Video. (F) In the dnt mutant tetrads, INP1-YFP forms punctate circles at the proximal and distal poles of each microspore. See also S6 Video.
Fig 9.
Effects of changes in pollen ploidy/size on pollen aperture patterns in the mcr and dnt mutants.
(A-B’) Diploid mcr pollen forms three apertures (arrowheads), independently of the meiotic product arrangement. (A-A’) Front and back views of the 2n mcr pollen produced by a 4n plant through a tetrad formation. (B-B’) Front and back views of the 2n mcr osd1 pollen produced through a dyad formation. (C-C’) Diploid pollen of dnt osd1, similar to the haploid dnt pollen, usually has two round apertures (arrowheads). See also S7 Video. (D) INP1-YFP forms three longitudinal lines (arrowheads) in diploid mcr osd1 dyads. A 3D reconstruction of a mcr osd1 INP1-YFP dyad is shown. See also S8 Video. (E) INP1-YFP forms puncta at the proximal and distal poles of microspores in diploid dnt osd1 dyads. A 3D reconstruction of a dnt osd1 INP1-YFP dyad is shown. See also S9 Video. (F-F’) Increase of pollen ploidy in mcr osd1 to 4n most commonly leads to the formation of a ring-like aperture on one side of the pollen grain (F, arrowhead) and one or several hole-like apertures (F’, arrowhead) on the other side. (G-G’) Increase of pollen ploidy in dnt osd1 to 4n usually increases the number of round apertures to more than two. (H-H”’) The ring-like apertures (arrowheads) in the 4n mcr osd1 dyads are located on the distal end of each microspore, thus placing the hole-like apertures at the proximal end, near the intersporal callose wall (black arrows). Shown are different views of a 3D reconstruction of a late-stage dyad (H-H”) and a maximum intensity projection of a confocal z-stack of the same dyad (H”’) See also S10 Video. Scale bars = 10 μm.
Fig 10.
Adding a transient or continuous stimulus to the 3D domain.
The type of pattern produced depends on the stimulus pattern, its amplitude, and whether it is transient (A) or continuous (B). Stimuli with larger amplitudes or with three or four spikes were able to better specify the final pattern produced. Left bars show the results for simulations performed on the WT domain; right bars show the results for simulations performed on the larger-size domain. “4 E” represents four spikes on the equator; “4 T” represents four spikes at the corners of a tetrahedron. Some ranges of stimulus amplitudes produced patterns that were not consistently the same; these ranges are marked as “transition”. The ring-patterned transient stimulus caused the PDE solver to fail when the amplitude was too large; these are marked as “Failed”. “No Effect” marks the situations when the produced pattern did not correspond to any positions of the applied stimulus. When a stimulus had an effect on a pattern, we observed at least one of the resulting spikes in all simulations to form at a position where the stimulus was applied. The results in panel A were obtained running Eqs 1 and 2. Panel B was produced using Eqs 2 and 4.