Arabidopsis leaves exhibit a large range of pavement cell sizes, similar to sepals

In sepals, giant cells are easily visible because they are highly elongated (S1A Fig). Similarly, we observe large and highly anisotropic cells in cauline leaves (S1B Fig). In rosette leaves, pavement cells of the epidermis are jigsaw puzzle-piece shaped with lobes and necks, such that cell size is not readily apparent by eye (S1C Fig); however, heterogeneity in pavement cell sizes has been previously observed [4,28]. Therefore, we wondered to what extent the distribution of cell sizes observed in sepals, ranging from giant cells to small cells, also occurs in rosette leaves. We imaged large sections of the blade (excluding midrib and margin cells) of leaf 1 or 2 from wild-type plants at 25 days postgermination (dpg) when the leaves are fully expanded and mature. Leaves 1 and 2 initiate simultaneously and are indistinguishable; therefore, we refer to them interchangeably as leaf 1 or 2. We measured the area of the epidermal cells of leaves 1 or 2 and sepals on the abaxial (bottom) side (Fig 2A and 2C). Throughout our analysis, we use the term size to mean cell area because area has been shown to be a more relevant measure of cell size than volume in highly vacuolated plant epidermal cells [4]. We observed that the abaxial cell-size distributions for both sepals and leaves are asymmetric, with long tails representing large cells (Fig 2E). Sepal giant cells are larger outliers in size and, consequently, the cell-size distribution in the sepal has a more extended tail than in the leaf (Fig 2E). Still, we observed that the cell-size range in the leaf and sepal are similar and the largest cells of the sepal are about the same size as the largest cells of the leaf (Fig 2A–2E). We conclude that Arabidopsis leaves have a diverse range of cell sizes characterized by a long-tailed distribution, similar to the abaxial side of sepals.

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Fig 2. Abaxial and adaxial cell-size distribution in the wild-type leaf and sepal epidermis; size correlates with DNA content.

(A–D) Cell area heat maps (in µm²) of (A) abaxial surface of wild-type sepal, (B) adaxial surface of wild-type sepal, (C) abaxial surface of 25-dpg wild-type leaf 1 or 2 (cell density: 234 cells mm⁻²) (D) adaxial surface of 25-dpg wild-type leaf 1 or 2 (cell density: 156 cells mm⁻²). Scale bars represent 100 µm. (E) Violin and strip plots of cell areas of abaxial and adaxial sides of 25-dpg wild-type leaves (two pooled replicates) and adult wild-type sepals (three pooled replicates). (F) Adaxial side (green) and abaxial side (purple) of 25-dpg leaf cell area vs. DNA content as measured by H2B-TFP total nuclear fluorescence, with R² = 0.85 for the abaxial side and R² = 0.82 for the adaxial side (one of two replicates). See S2 Fig for replicates. The underlying data for this figure can be found at Open Science Framework (osf.io), https://doi.org/10.17605/OSF.IO/RFCWS.

https://doi.org/10.1371/journal.pbio.3003469.g002

Large cells are formed on the adaxial side as well as the abaxial side of the leaf

In sepals, giant cells are restricted to the abaxial (outer) surface (Figs 2A, 2B, and S2A–S2D). We asked whether there was a difference in cell size between adaxial (top) and abaxial (bottom) surfaces of the leaf. Large cells of similar size are formed on both the adaxial and abaxial surfaces of the leaf, in contrast to the sepal (Figs 2A–2E and S2A–S2F). In addition, across the whole cell-size distribution, the cell density is lower and many cells are slightly more expanded on the adaxial side than the abaxial side (Figs 2C, 2D, S2E, and S2F). There are a greater number of stomata and stomatal lineage cells (very small cells) on the abaxial side compared with the adaxial side (Figs 2C–2E, S2E, and S2F). We also observed that the abaxial cells are more lobed than the adaxial cells (Figs 2C, 2D, S2E, and S2F). Despite slight differences, the cell-size distributions of the abaxial and adaxial sides of the leaf are quite similar, particularly in the tails, where both sides exhibit a similar range of larger cells, in contrast to the sepal, where only the abaxial side has very large cells.

Cell area correlates with DNA content

Cell area and ploidy are positively correlated in leaf epidermal cells [4]. A recent study showed that fluorescence levels of histone fluorescence reporters measured from microscopy images are a good proxy to infer nuclear ploidy in Arabidopsis cotyledons [29]. Hence, to validate whether cell area and ploidy were correlated in our leaves, we measured DNA content by quantifying total fluorescence of Histone 2B-TFP (pUBQ10::H2B-TFP) within each cell nucleus of the 25-dpg leaf images. For this reporter, the H2B-TFP signal distribution is noisy and continuous, not divided into four discrete peaks, providing an approximation of ploidy, not exact DNA content. As expected, a strong linear correlation between H2B-TFP fluorescence and cell area was observed for both the abaxial pavement cells (R² = 0.85 and 0.91; n = 2) and the adaxial pavement cells (R² = 0.79 and 0.82; n = 2) (Figs 2F and S2G). Therefore, we focus on analyzing cell size, and infer that large cell size indicates high ploidy.

We wondered whether cells of similar size on the abaxial and adaxial side of the same leaf also have a similar DNA content. We found that cells of similar DNA content are larger on the adaxial side than on the abaxial side (Figs 2F and S2G), suggesting that adaxial cells have expanded more than abaxial cells, as noted above. Because the largest sepal cells and the largest leaf cells had approximately the same areas, we asked whether the DNA content of these cells was also similar. We found that the total H2B-TFP fluorescence values of the largest cells were very similar between sepal and leaf, suggesting that these largest cells are similar in ploidy (S2H Fig).

Cell-size patterning emerges at the tip and progresses basipetally as the leaf differentiates

To determine how the cell-size pattern emerges in the leaf during development, we imaged both the adaxial and abaxial surfaces of each leaf at different stages of development. From 5 to 9 dpg, cell size increases greatly (S3 Fig), as expected. At day 5, cells throughout the blade are fairly homogeneous in size, with a few cells starting to expand near the distal tip, and the large cells of the margin and overlying midrib already apparent (Fig 3A). We focus on pavement cells in the blade and exclude margin and midrib cells from further analysis. The cell-size pattern consisting of large cells interspersed between small cells progressively develops basipetally from the tip (Fig 3A–3A), whereas at the base the cells remain uniformly small. The progression of cell-size patterning down the leaf is consistent with the well-established basipetal wavefront of differentiation and cessation of cell division [30]. The cell area distributions showed that more large cells appear throughout development and the maximal cell size increases (Fig 3A, 3B, and 3D). By 9 dpg, cell size has been patterned almost to the base of the leaf (Fig 3A and 3B).

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Fig 3. Cell-size patterning occurs as a basipetal wave simultaneously on the adaxial and abaxial sides of the leaf.

(A–B) Cell area heat maps in µm² of leaf 1 or 2 at different stages of development on (A) the abaxial side and on (B) the adaxial side of the same leaf at 5, 6, 7, 8, and 9 dpg (half leaf). Unsegmented regions on adaxial leaves correspond to trichomes, which were not considered in this analysis. Each stage is associated with a distinct heat map color range. Scale bars represent 50 µm at 5 and 6 dpg, and 100 µm at 7, 8, and 9 dpg. (C) Spatial positions of the largest cells (those above an area threshold, see below) on the abaxial (purple points) and adaxial (green points) sides of the same leaf at 6, 7, 8, and 9 dpg. Area thresholds for each leaf were determined from the 98th percentile cell area of the abaxial side. (Note that the midrib and margin cells are included in these overlays of large cell positions.) (D) Violin plots of cell areas (in µm²) of the largest cells (as defined in (C) and excluding margin and midrib cells) on abaxial and adaxial sides of leaves at different developmental stages. Abaxial and adaxial sides are from the same leaf. See also S3 Fig for the leaves shown to scale. The underlying data for this figure can be found at Open Science Framework (osf.io), https://doi.org/10.17605/OSF.IO/RFCWS.

https://doi.org/10.1371/journal.pbio.3003469.g003

We next asked whether the wavefront of cell-size patterning progresses basipetally at the same rate on the abaxial and adaxial sides of the leaf. Using images of both the abaxial and adaxial sides of the same leaf, we plotted the positions of the centers of the largest cells on both sides (including margin and midrib cells for landmarks) (Fig 3C). Large pavement cells are observed in the same proximal–distal region on abaxial and adaxial sides during development (Fig 3C). The region expands in the proximal direction as development progresses. This suggests that the wavefront of patterning and differentiation is coordinated across the abaxial/adaxial axis of the leaf.

The sepal giant cell specification pathway also patterns giant cells in leaves

Because the cell-size distributions have similarities in leaves and sepals, we tested whether the giant cell specification pathway in sepals (Fig 1H) also functions in the leaf to pattern cell size. We imaged leaf 1 or 2 at both 9 and 25 dpg from wild-type and giant cell pathway mutants. At 9 dpg, patterning has just extended to the base of the leaf, and the leaf is still small enough that we could image the whole upper abaxial quadrant to determine the pattern over a large fraction of the leaf blade (Figs 4A, S4, and S5). At 25 dpg, the leaf is fully differentiated, fully expanded, and the pattern is established (Figs 4B, S6, and S7). We found that cell-size patterning in the leaf is similarly affected in the mutants at both 9 and 25 dpg as in the mature sepal (Figs 4, S8A, and S8B). Notably, the largest cells show similar variations in their numbers across genotypes. Similar to the sepal, the size of the largest cells is moderately reduced in acr4-2 mutants (Figs 1B and 4A–4D), and more greatly reduced in atml1-3 mutants (Figs 1C and 4A–4D). The reduction in large cells is drastic in dek1-4 and lgo-2 mutant sepals and leaves, resulting in the absence of a long tail in the cell-size distribution (Figs 1D–1E, 4C, and 4D). For these genotypes, the number of medium-sized cells is also substantially decreased (Figs 1D, 1E, 4C, and 4D). Conversely, the overexpression of ATML1 (ATML1-OX) or LGO (LGO-OX) leads to an increase in the size of large cells and in fewer small cells compared to wild type, as in the sepal (Figs 1F, 1G, and 4A–4D).

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Fig 4. The sepal giant cell specification pathway also patterns cell size in leaves.

(A, B) Cell area heat maps (in µm²) of the upper abaxial quadrant of leaf 1 or 2 at 9 dpg (A) and of a section on the abaxial side of leaf 1 or 2 at 25 dpg (B) for the following genotypes: wild type, acr4-2, atml1-3, dek1-4, lgo-2, LGO-OX (pATML1::LGO), and ATML1-OX (pPDF1::FLAG-ATML1). Scale bars represent 100 µm. Cell area heat maps of other replicates are shown in S4–S7 Figs. (C, D) Violin plots of cell area distributions on a log₁₀ scale for 9-dpg replicates (C) and for 25-dpg replicates (D). Stomata were classified and removed in (C, D). Violin plots of individual replicates are shown in S8A and S8B Fig. (E) Wasserstein distance plot of normalized cell-size distributions (see Materials and methods) for all 9- and 25-dpg replicates displayed as Euclidean distances embedded in 2D. The 25-dpg replicates are indicated by circular dots and 9-dpg replicates by triangular dots. The Wasserstein distance plot for 9- and 25-dpg and Wasserstein statistical tests among replicates are shown in S4 and S6 Figs. Associated with S4–S8 Figs. The underlying data for this figure can be found at Open Science Framework (osf.io), https://doi.org/10.17605/OSF.IO/RFCWS.

https://doi.org/10.1371/journal.pbio.3003469.g004

To quantify the variations in the number of large cells precisely, we quantitatively defined leaf giant cells on the basis of a cell area threshold. Specifically, we first classified pavement cells and stomata using a Support Vector Machine classifier based on features of cell shape (see Materials and methods, S9 Fig). Next, a cell-size threshold was established in the mature sepal and in the leaf, at both 9 and 25 dpg, using the atml1-3 mutants, which are known to have very few giant cells in sepals (see Materials and methods, Figs 1C and S9). Those cells in the 9- and 25-dpg leaves as well as in the sepal that exceeded their associated threshold were categorized as giant cells (see cell-type classification outcomes in S10 and S11 Figs). On the basis of this definition, we performed a quantitative comparison and statistically compared the number of giant cells per unit area among genotypes in leaves. Two-sample, two-tailed t tests showed that in the 9-dpg leaf and the mature leaf, wild type had significantly more giant cells than lgo-2 (9 dpg: p = 0.002, 25 dpg: p = 0.003), dek1-4 (9 dpg: p = 0.002, 25 dpg: p = 0.002), atml1-3 (9 dpg: p = 0.002, 25 dpg: p = 0.005), and acr4-2 (9 dpg: p = 0.010, 25 dpg: p = 0.044). Conversely, LGO-OX had significantly more giant cells than wild type (9 dpg: p = 0.001, 25 dpg: p = 0.003). However, no statistically significant difference in the number of giant cells per unit area was observed between wild type and ATML1-OX (9 dpg: p = 0.213, 25 dpg: p = 0.75). Because the giant cells in ATML1-OX are so much bigger than wild-type giant cells, each of the giant cells in a given area of ATML1-OX leaf takes up a large amount of space, resulting in few giant cells per unit area despite the fact that most of the unit area is occupied by giant cells. We sought to quantify what was apparent visually by comparing the fractional area occupied by giant cells between ATML1-OX and wild type and found that the fractional area occupied by giant cells was significantly higher in ATML1-OX (9 dpg: p < 0.005, 25 dpg: p < 0.005). Thus, in ATML1-OX the number of giant cells is not changed, but the fractional area covered by giant cells is increased.

Collectively, the similarities in the variation between the number of giant cells in the leaf and the sepal indicates that the sepal giant cell specification pathway also regulates the formation of giant cells in leaves.

Giant cell mutants affect the entire cell-size distribution

We observed that not only are giant cells affected in these mutants, but other aspects of the cell-size distribution are also affected. For example, the number of medium-sized cells in lgo-2 and dek1-4 is reduced in addition to the number of giant cells (Fig 4A–4D) and, correspondingly, the number of small cells is increased in these mutants. To statistically analyze the difference in cell-size distributions, we conducted a principal coordinate analysis based on the Wasserstein distances between cell-size distributions (termed Wasserstein distance plot), which showed the difference between leaf samples according to their cell-size distributions on a 2-dimensional plane (S4H, S6H, and S8C–S8F Figs, see Materials and methods). Samples clustered according to genotype, indicating that genotype controls the cell-size distribution. We observed a progressive increase in the number of giant cells along the first principal coordinate V1 from lgo-2 mutants to ATML1-OX and LGO-OX (S4H and S6H Figs). ATML1-OX and LGO-OX were distant from each other in this plot, which might partly reflect the fact that LGO-OX has more giant cells, whereas ATML1-OX has fewer but larger giant cells. When we created the combined Wasserstein distance plot using normalized cell-size distributions from both 9- and 25-dpg leaves (see Materials and methods), the samples continued to group according to genotype rather than developmental stage, further supporting the idea that these genes have affected the cell-size distribution by 9 dpg (Fig 4E). Thus, we conclude that these genes affect the entire cell-size distribution.

However, some differences in the cell-size distribution are apparent between 9-dpg and mature 25-dpg leaves. Firstly, at 9 dpg, dek1-4, and lgo-2 mutants are very similar; however, in the fully mature 25-dpg leaves, the lgo-2 cell-size range is notably smaller than that in the dek1-4 mutant (Fig 4A–4D), suggesting that lgo-2 cells continue to divide after 9 dpg. In addition, the small cells in lgo-2 mutants were more uniform in size than all of the other genotypes because the typical small stomatal lineage cells that encircle the stomata in mature leaves were fewer in lgo-2 (Fig 4A–4D). This altered cell-size distribution relates to the previous finding that LGO affects pavement cell differentiation in these stomatal lineage ground cells and that cells undergo division for a longer time in the absence of LGO [19]. Secondly, although at 9 dpg the LGO-OX giant cells were slightly smaller than the ATML1-OX giant cells, at 25 dpg, the LGO-OX giant cells were nearly equivalent in size to ATML1-OX giant cells (Fig 4A–4D). In addition, we observed that more pavement cells were larger in LGO-OX, whereas only a few cells became giant in ATML1-OX (Fig 4A–4D). ATML1-OX leaves had a few connected giant cells separating large islands of small cells, whereas LGO-OX leaves showed more giant cells interspersed among smaller clusters of small cells (Fig 4A and 4B). These phenotypic differences might reflect either inherent differences in ATML1 and LGO activities or the fact that ATML1 and LGO overexpression transgenes are under the control of different promoters that might have differences in activity at different developmental stages.

Relationship between the size and shape of cells and organs

In plants, compensation is the process by which organ size is maintained when cell number is altered by an accompanying change in cell size [31]. We observed compensation in our leaf giant cell mutants (S12 Fig). Mature leaves of the mutants acr4-2, atml1-3, dek1-4, and lgo-2 are similar in size to wild-type leaves. Having fewer giant cells is compensated by having more small pavement cells (Fig 4). However, ATML1-OX and LGO-OX mature leaves, which have much larger cells (see, e.g., Fig 4B and 4D), are smaller than wild-type (S12N–S12P Fig). Therefore, only partial compensation for having fewer cells by having larger cells is observed in ATML1-OX and LGO-OX plants.

Additionally, ATML1-OX leaves are narrower than those of wild type and LGO-OX (S12A, S12F, S12G, S12I, S12N, and S12O Fig). We also observed that giant cells are more directionally elongated in ATML1-OX than in other genotypes (Figs 4A, 4B, S4F, 4G, S5F, S5G, S6F, 6G, S7G and 7H), reflecting the elongated shape of the leaf. This suggests the existence of a relationship between giant cell shape and leaf morphology. Likewise, wild-type cauline leaves are both narrower and more elongated than wild-type rosette leaves, and also have more anisotropic elongated giant cells than in rosette leaves (S1 Fig). This observation supports the idea that cell shape reflects the anisotropy of the growing tissue [32].

Spatial patterning of giant cells within the leaf blade

In wild-type plants, giant cells vary in position from sepal to sepal and from leaf to leaf [10–12]. An open question has been whether the spatial organization of giant cells is random, or whether there is an underlying order. Classically, many specialized cell types such as stomata and trichomes are spaced such that they are not in direct contact to one another [23,33]. Giant cells are frequently adjacent to each other and, therefore, it is clear that there is not a strong lateral inhibition between them. We set out to determine firstly whether giant cell position is correlated with underlying vasculature and secondly, how giant cells are spatially positioned relative to one another.

Giant cells are not preferentially positioned overlying the vasculature

We wondered whether giant cell positioning was correlated with the position of leaf vasculature for two reasons. Firstly, we observed that large, highly endoreduplicated cells overlie the midrib of the leaf, extending all the way to the leaf tip (S13A Fig). We wondered whether giant cells might be similarly preferentially located over the other veins. Secondly, we observed that large, highly endoreduplicated cells often appear to “peel” away from the midrib, as if following vascular branches (S13A Fig). This phenomenon is most common in ATML1-OX leaves (S13C–S13F Fig). To investigate whether giant cells overlie veins, we traced the veins from the original confocal image onto the heat map of cell area for a 9-dpg wild-type half leaf and four ATML1-OX half leaves. We found that many giant cells did not overlie the vasculature (S13B–S13F Fig). Specifically, we noted that the points where giant cells peel off the midrib often do not align with where veins extend from the midvein. Furthermore, the orientation of giant cells do not follow the direction of the veins (S13B–S13F Fig). Instead, veins in ATML1-OX plants frequently pass through patches of small cells (S13C–S13F Fig). We conclude that vascular and giant cell patterns are not obviously correlated.

Giant cells are clustered more often than expected by chance

A cell-autonomous and stochastic mechanism has been proposed to explain giant cell formation in the sepal [12]. However, it remains unknown whether giant cells are randomly arranged within the tissue. To statistically assess the randomness of the pattern, we needed a random reference (or null model) to compare with our experimental replicates. Previous studies addressing this problem considered cells as points [26,34], or used a regular hexagonal grid to build a null model [35]. In our case, these assumptions are not applicable due to the complexity of giant cell shapes and the heterogeneity of cell shapes and sizes that affect cellular arrangements [36]. Therefore, we used the dmSET image-based method [36,37] to generate randomized tissues from the real segmented images (Figs 5A and S14), allowing to randomly shuffle cell positions by preserving cell sizes and shapes of the original tissues (S15 Fig, see Materials and methods). We generated 400 randomized tissues for each biological replicate for both the wild-type sepal and 25-dpg leaf.

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Fig 5. Giant cells are more clustered than expected in a randomized null model both in the wild-type leaf and sepal.

(A) Scheme summarizing the method used to assess the randomness of the cellular patterns. Each segmentation is computationally randomized using the dmSET method into 400 randomized tissues where cell positions (and orientation in the case of the leaf) have been randomly shuffled (left; see Materials and methods). To statistically assess the extent to which the segmented image shows a random giant cell pattern, a quantitative observable (middle) extracted from the segmentation is compared with the same observable computed in all randomized tissues, forming the estimated ‘null distribution’ (right). (B) Example of a representative segmentation of a wild-type leaf 25 dpg (top left) and a wild-type sepal (bottom left) and one of their randomized tissue (randomization) images (right). (C) Mean number of giant cell neighbors (also referred to as giant neighbors) per giant cell (also referred to as giant) in leaves (top) and sepals (bottom). The value extracted from the segmentations (in red) was statistically tested against all the values extracted from the 400 pooled randomizations (in gray). The mean number of giant cell neighbors per giant cell is higher than expected in a randomized null model, and the null hypothesis can be rejected (p-value <0.05), indicating that giant cells are clustered. (D) Distributions of the number of giant cell neighbors for all giant cells found in all replicates of segmentations (in red) and randomizations (in gray) in leaves (top) and sepals (bottom). Total number of giant cells counted (excluding giant cells at the image border) in the analysis: n = 68 (leaf, segmentations), n = 68 × 400 (leaf, randomizations), n = 74 (sepal, segmentations), n = 74 × 400 (sepal, randomizations). See also S14, S15, S16, S21, and S22 Figs. The code and data associated with this figure can be found at Open Science Framework (osf.io), https://doi.org/10.17605/OSF.IO/RFCWS.

https://doi.org/10.1371/journal.pbio.3003469.g005

Several measures (S16 Fig), such as the mean number of giant cell neighbors per giant cell, which captures the amount of contacts between giant cells, were computed in the experimental data and the corresponding randomized tissues. To statistically assess the randomness of the giant cell pattern, these measures in the real biological tissues (segmentation) were compared with the same measures in all the randomized tissues (randomizations), which formed a null distribution (Figs 5A and S16).

In the randomized tissues, cell sizes were well preserved, but cell shapes were affected in the leaf (Figs 5A, 5B, S15D, and S15E). To ensure that these shape artifacts did not introduce bias in our analyses, we tested our method on a randomly selected population of cells in both leaves and sepals (see Materials and methods) and confirmed the absence of significant bias in the null models (S17 Fig). Additionally, we reconstructed the original leaf tissues with shape artifacts similar to those in the randomized tissues (S18 Fig), and found that giant cell connectivity was largely preserved and that the results remained consistent (S18 Fig) (see Materials and methods).

For both wild-type 25-dpg leaves and mature sepals, when considering the six pooled replicates, the mean number of giant cell neighbors per giant cell was greater than in a randomized null model, and the null hypothesis could be rejected (p < 0.05) (Fig 5C). This result shows the presence of clustering among giant cells both in the leaf and the sepal. It was less probable to find isolated giant cells, and more probable to find giant cells in contact with two or more other giant cells compared with what was expected by chance (Fig 5D). Similar results were found in the leaf using an alternative randomization method we developed based on cutting and merging cells (S19 Fig). The nonrandom pattern of giant cells was also supported by the analysis of other spatial measures (S16 Fig). The similar distribution of the number of giant cell neighbors in leaves and sepals (Fig 5C and 5D) reflects a similar spatial organization, supporting the idea of common patterning mechanisms.

Different cell sizes are organized into different spatial patterns

To investigate whether the clustered pattern is exclusive to giant cells, we applied the same analysis to distinct sub-populations of pavement cells in the leaf tissues. Four populations of pavement cells were defined: giant cells (Fig 6A–6C), middle-sized cells (Fig 6D–6F), small cells (Fig 6G–6I), and a control population of randomly selected pavement cells of any size (Fig 6J–6L). In contrast to the clustered pattern of giant cells (Fig 6A–6C), middle-sized pavement cells exhibited a more random organization (Fig 6D–6F; the null hypothesis could not be rejected, with p = 0.195). Conversely, small pavement cells showed a clustered organization (Fig 6G–6I), because the mean number of neighbors between small pavement cells significantly exceeded the value observed in the randomized tissues. Notably, these small cells were clustered around the stomata, and their spatial arrangement is probably a consequence of the stomatal patterning process. A random cellular pattern was found in randomly selected pavement cells, as expected (Fig 6J–6L). Overall, these analyses highlight a relationship between pavement cell size and cell spatial organization within the tissue. Furthermore, these findings underscore the distinctive clustered arrangement of giant cells in comparison to middle-sized and randomly selected pavement cells.

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Fig 6. Different cell sizes display different spatial patterns in the wild-type leaf.

The method used to assess the randomness of the giant cell patterns (Fig 5) was applied here on different pavement cell-size populations within the mature 25-dpg leaf: (A–C) giant, (D–F) mid-size (around 5,000 µm²), (G–I) small (smallest pavement cells), and (J–L) random (randomly selected pavement cells). The number of cells in each category was determined such that the total cell area of the cell population was approximately equal to the area occupied by the giant cells. (A, D, G, J) Example of representative segmentation of a 25-dpg wild-type leaf (left) and one of its corresponding randomized tissue randomization (right), where cell locations have been computationally shuffled. Cells colored in magenta represent the cells within the studied pavement cell-size population. (B, E, H, K) Mean number of cell neighbors per cell within the same-size population. (B) The mean number of giant cell neighbors per giant cell is higher than expected by chance (p < 0.05), indicating that giant cells are clustered. Same data as in Fig 5C, top. (E) Middle-size cells are less clustered than giant cells and more randomly organized (the null hypothesis cannot be rejected, p = 0.195). (H) The mean number of small cell neighbors per small cell is significantly higher than in the randomized tissues (p < 0.05), highlighting that small cells form clusters. (K) As expected, the randomly selected pavement cells (with area > 2,000 µm²) show a value that falls right in the center of the null distribution (p = 0.445). (C, F, I, L) Distributions of the number of cell neighbors belonging to the studied cell population per cell of that population in the segmentations (in red) and the randomizations (in gray). All six replicates were pooled together. Total number of cells in cell populations counted in the analysis: n = 68 (giant cells, segmentations), n = 68 × 400 (giant cells, randomizations), n = 199 (middle-size cells, segmentations), n = 199 × 400 (middle-size cells, randomizations), n = 639 (small cells, segmentations), n = 639 × 400 (small cells, randomizations), n = 162 (random cells, segmentations), n = 162 × 400 (random cells, randomizations). The code and data associated with this figure can be found at Open Science Framework (osf.io), https://doi.org/10.17605/OSF.IO/RFCWS.

https://doi.org/10.1371/journal.pbio.3003469.g006

It was previously shown that, apart from small cells, pavement cells follow the theoretical topological laws based on space-filling (i.e., via entropic considerations), with larger cells being on average surrounded by smaller ones in young spch leaf tissues [38]. Our analyses on more mature wild-type leaves reveal that larger cells are surrounded by larger cells (and have fewer neighbors) than what is expected by purely random space‐filling given by our null model (Figs 6 and S18D).

A cell-autonomous stochastic model can recapitulate giant cell clustering

To investigate how giant cell clustering emerges during leaf and sepal epidermal development, we wondered whether the existing cell-autonomous and stochastic model for giant cell specification in sepals [12] could also recapitulate the clustered feature of the giant cell pattern. In this multicellular computational model, the concentration of ATML1 stochastically fluctuates and is regulated by a self-catalytic feedback loop. ATML1 regulates the expression of a downstream cell-cycle regulator target (Fig 7A). At the end of a cell cycle, a cell either divides or endoreduplicates if the ATML1 target exceeds a specific threshold during the G2 phase. We used this model [12] to investigate the resulting spatial organization of giant cells in simulated tissues (Fig 7A and 7B; see Materials and methods).

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Fig 7. A cell-autonomous stochastic model can recapitulate giant cell clustering because of cell divisions of surrounding cells.

(A) Cartoon of the computational model for giant cell patterning. ATML1 activates a target (LGO), which, if above a certain threshold and during the G2 cell-cycle phase, prevents cell division and instead drives the entry into endoreduplication and giant cell formation. (B) Simulation snapshots of the simulated growing sepal, at three different time points. Color codes indicate the cell ploidy levels. Scale bars represent the same size in arbitrary units. (C) A rectangular section of the simulation output (e.g., see rectangle shown in (B)) is used to quantify the giant cell pattern. “Segmentation” refers to one simulation output (left) and “Randomization” to one randomization of the simulated output (right). Giant cells, labeled in magenta, were defined by a size threshold (see Materials and methods). (D) Mean number of giant cell neighbors (also referred to as giant neighbors) per giant cell (also referred to as giant) in the simulations (called segmentation in red) and in its randomizations (in gray). The mean number of giant cell neighbors per giant cell is higher than expected in a randomized null model (p < 0.05), indicating a clustered pattern of giant cells. (E) Distribution of the number of giant cell neighbors per giant cell. The results obtained in (D, E) are comparable with the results in experimental sepal replicates (Fig 5C and 5D). Five simulation outputs with five different initial conditions were performed and combined for the analysis. Total number of giant cells (excluding giant cells at the image border) counted in the analysis: n = 42 (segmentations), n = 42 × 400 (randomizations). (F, G) Statistical assessment of the randomness of the giant cell pattern (comparing the “segmentations” in red with the randomized tissues in gray) at initial time (top) and final time point (bottom) in (F) the simulations (at t = 55 and t = 135) and (G) the real tissues (at stage 4 and stage 9). At the initial time point, the null hypothesis could not be rejected but the mean giant cell neighbors per giant cell became significantly greater than in a randomized null model (p < 0.05) at the final time point. To the left of panel (F), a cartoon represents two neighboring giant cells surrounded by an increasing number of cells as the tissue develops. All five replicates (in simulations) and three replicates (in experimental data) were pooled. Total number of giant cells counted in the analysis: n = 83 (simulations, segmentations), n = 83 × 400 (simulations, randomizations), n = 49 (experimental data, segmentations), n = 14 × 400 (experimental data, randomizations). The dataset in (C) was also used for an independent analysis in Hervieux and colleagues 2016. See randomization snapshots related to this figure in S20 Fig. The code and data associated with this figure can be found at Open Science Framework (osf.io), https://doi.org/10.17605/OSF.IO/RFCWS.

https://doi.org/10.1371/journal.pbio.3003469.g007

To assess the randomness of the simulated giant cell pattern, we applied the same method as in the experimental images (Fig 5A) to images of the final simulation time point (Fig 7B and 7C). Giant cells were also defined by a size threshold, which was established such that all cells of ploidy 16C or above were considered to be giant (see Materials and methods). We observed that the mean number of giant cell neighbors per giant cell was greater than expected if giant cells were randomly distributed (p < 0.05, Fig 7D), showing that the current cell-autonomous model can also produce a clustered giant cell pattern. Furthermore, the distribution of the number of giant cell neighbors per giant cell (Fig 7E) was similar to the distribution observed in the experimental sepals (Fig 5D, bottom). This raises the question of what mechanisms are responsible for cell clustering in a cell-autonomous, multicellular model of dividing cells.

Cell division contributes to the clustering of giant cells

To understand how the giant cell clustering behavior emerges in our computational model, we analyzed how the cellular spatial pattern changes over time within the tissue. We hypothesize that the initial giant cell pattern arises randomly throughout the epidermis, due to the stochastic nature of ATML1 concentration fluctuations that trigger endoreduplication, and occasionally lead to giant cell contacts. As nongiant cells continue to divide, giant cells would appear more clustered in the fully grown tissue. To test this hypothesis in our simulations, we selected the first-arising giant cells (see Materials and methods) and quantified their spatial organization both at an early time point and at the end of the simulation (Figs 7F,S20A, and S20B). We found that these giant cells were more randomly distributed at the initial time point, as the null hypothesis could not be rejected (p = 0.185, Fig 7F), whereas they were more clustered compared to the randomized tissues at the final time point (p < 0.05, Fig 7F). Indeed, although the giant cell contacts were preserved over time (red bar in Fig 7F), we observed a shift in the null distribution of the mean number of giant neighbors per giant cell between the initial and the final time point (Fig 7F). As new cells arise from cell division, the number of potential cellular configurations (i.e., the number of possible spatial cellular arrangements) increases, which decreases the probability of observing giant cell clusters under a random model where all cells have random positions. Therefore, even if giant cell contacts are preserved, their arrangement in the context of the entire tissue becomes more clustered over time.

To investigate the emergence of the giant cell spatial pattern over time in real tissues, we used time-lapse data of developing sepals [39], where cells were tracked over time, and we similarly quantified the patterns of the first-arising giant cells at the first available time point (sepal at stage 4, 24-h time point) and a later one (sepal at stage 9, 120-h time point; see Materials and methods) (Figs 7G, S20C, and S20D). Similar to the simulations, we observed that giant cells were more randomly distributed in younger sepals and were more clustered in the more developed sepals when compared to the randomized tissues (Fig 7G). This analysis indicates that the stochastic and cell-autonomous model is a plausible model to explain the spatial organization of giant cells. Moreover, it shows that cell clustering can emerge in a growing tissue without the need for cell–cell communication but instead as a result of cell divisions.

Plant growth conditions

All seeds were sown on LM111 soil in pots and were stratified in the dark for 3 days at 4 °C. The pots were then transferred to Percival plant growth chambers set to 60% humidity, 22 °C temperature, and 24-h light provided by Philips 800 Series 32-Watt fluorescent bulbs (f32t8/tl841) (~100 μmol m⁻² s⁻¹). dpg were counted from the time the pots were transferred to plant growth chambers.

Cloning fluorescent nuclear markers

To create a teal fluorescent (TFP) nuclear marker ubiquitously expressed under the UBIQUITIN 10 promoter (pUBQ10::H2B-TFP; pAR393), an H2B-TFP fusion with an AAAPAAAAA linker was generated by PCR. TFP was amplified by PCR with primers oAR440 (5′-gct gcc gct cca gct gca gct gcc gct ATG GTT TCT AAG GGA GAA GAA ACT ACT ATG-3′) and oAR438 (5′-cct cga gtc aCT TAT AAA GTT CAT CCA TAC CAT CAG TAG-3′). The lower-case letters in the primer sequences represent linkers, restriction sites, and cloning sequences that were added to the gene sequences. H2B was PCR amplified with oAR369 (5′-CAC CGG ATC CAC AAT GGC GAA GGC AGA TAA G-3′) and oAR439 (5′-agc ggc agc tgc agc tgg agc ggc agc AGA ACT CGT AAA CTT CGT AAC CGC CTT AG-3′). Sequences encoding H2B-TFP were fused via overlapping PCR with oAR369 and oAR438 primers. The H2B-TFP PCR product was cloned into pENTR D TOPO to create the pAR198 entry clone. H2B-TFP was recombined into pUB-Dest with LR Clonase II according to the manufacturer’s instructions to generate pUBQ10::H2B-TFP (pAR393). pAR393 was transformed into Arabidopsis Col-0 plants expressing the pLH13 p35S::mCitrine-RCI2A yellow fluorescent plasma membrane marker [45] via Agrobacterium tumefaciens (strain GV3101)-mediated floral dipping [54] and selection with glufosinate-ammonium (“Basta” Neta Scientific OAK-044851-25g).

Generation of mutant plant lines containing fluorescent plasma membrane and nuclear markers for imaging

Mutant alleles and overexpression transgenes were crossed to plants expressing fluorescent cell-membrane and nuclear markers to obtain plants for imaging. The following mutant alleles were used: acr4-2, atml1-3, dek1-4, and lgo-2. In addition, two lines overexpressing either ATML1 (pPDF1::FLAG-ATML1) or LGO (pATML1::LGO) in a Col-0 background were used. All of these alleles/transgenes are in the Columbia-0 (Col-0) accession. acr4-2 (SAIL_240_B04) contains a T-DNA insertion in the codon of the second of seven 39-amino acid repeats of the beta propeller extracellular domain, which is upstream of the transmembrane domain and the kinase domain and is therefore presumed to be loss-of-function allele. The acr4-2 mutant was obtained from Gwyneth Ingram [14], who obtained it from Syngenta [55]. The atml1-3 allele is a T-DNA insertion in the homeodomain and is a loss-of-function mutant [11]. The atml1-3 was obtained from the Arabidopsis Biological Resource Center (ABRC; accession number SALK_033408) [11]. The dek1-4 allele contains a point mutation that changes a conserved arginine to a cysteine within calpain domain III (ABRC accession CS68904) [11]. Complete loss of function of DEK1 is lethal [50]; therefore, dek1-4 must retain some function. The dek1-4 phenotype is recessive and therefore, dek1-4 is likely hypomorphic [11]. The dek1-4 mutant was originally isolated in the Landsberg erecta accession and was subsequently back-crossed twice into Col-0 [12]. lgo-2 contains a T-DNA insertion within the coding sequence of the gene and is a loss-of-function allele [10]. lgo-2 was obtained from the ABRC (accession number SALK_033905 and is available as a homozygous mutant as accession CS69160). pPDF1::FLAG-ATML1 (ATML1-OX) was obtained from Gwyneth Ingram [56]. pATML1::LGO (LGO-OX) has been deposited for distribution at ABRC under accession CS69162 [11,45]. acr4-2, atml1-3, dek1-4, lgo-2, pPDF1::FLAG-ATML1, and pATML1::LGO were each crossed to plants expressing both a p35S::mCitrine-RCI2A fluorescent plasma membrane marker (pLH13) and a pUBQ::H2B-TFP fluorescent nuclear marker (pAR393). The F2 progeny were genotyped for acr4-2, atml1-3, dek1-4, and lgo-2 (primer sequences in S1 Table) and lines were isolated that were homozygous for these alleles and that also expressed both pUBQ::H2B-TFP and p35S::mCitrine-RCI2A. We could not obtain atml1-3 homozygous plants that also contained the p35S::mCitrine-RCI2A transgene after crossing, which was probably because the ATML1 gene was linked to the insertion site of the p35S::mCitrine-RCI2A transgene. To obtain plants expressing p35S::mCitrine-RCI2A in a homozygous atml1-3 background, the plasmid containing p35S::mCitrine-RCI2A was transformed into atml1-3 homozygous plants with pUBQ::H2B-TFP through Agrobacterium tumefaciens (strain GV3101)-mediated floral dipping [53]. A T1 line was chosen that strongly expressed the mCitrine membrane signal and this line was used for future experiments. For the overexpression transgenes pPDF1::FLAG-ATML1 and pATML1::LGO, seeds were collected from F2 plants and F3 plants were genotyped for pPDF1::FLAG-ATML1 or pATML1::LGO (S1 Table). Those F2 plants that produced only F3 plants having pPDF1::FLAG-ATML1 or pATML1::LGO were isolated as homozygous for pPDF1::FLAG-ATML1 or pATML1::LGO, respectively. Those lines with pPDF1::FLAG-ATML1 or pATML1::LGO homozygous and that expressed both pUBQ::H2B-TFP and p35S::mCitrine-RCI2A were used for imaging.

Sample preparation for imaging

Leaves and sepals were mounted in 0.01% (v/v) Triton X-100 for imaging. Leaves were imaged between two coverslips, and sepals were imaged on a slide with a coverslip. Curvy leaves were cut with a razor blade to ensure they could be placed flat under the coverslip. Samples were imaged immediately after preparation. Sepals were imaged at stage 14 [57].

Imaging with confocal microscopy

A ZEISS LSM 710 Axio Examiner confocal microscope with a W Plan-Apochromat 20×/1.0 DIC D-0.17 M27 75 mm water-immersion objective lens was used to image leaf 1 or 2 of the Arabidopsis rosette and mature (stage 14) sepals. A 458 nm laser was used to excite pUBQ::H2B-TFP (collection range 463–500 nm) and a 514 nm laser was used to excite p35S::mCitrine-RCI2A (collection range 525–645 nm). Images were captured with a 1× zoom. The gain and laser power varied slightly between images to accommodate slight differences in signal intensity between samples. Each image was composed of several tiles. The dimensions of each voxel were 0.415 µm (x) by 0.415 µm (y) by 1 µm (z).

For the images to compare cell size with nuclear fluorescence on the abaxial and adaxial faces of the same organ (two leaf replicates and three sepal replicates; Figs 2 and S2), the 458-nm laser power and gain used for imaging pUBQ::H2B-TFP were adjusted so that the TFP signal was below saturation and was then held constant for all images.

Leaf areas were calculated from confocal images of entire leaves taken using a 2.5× objective for each 9-dpg and 25-dpg leaf replicate.

Image processing

Tiles were stitched in the horizontal direction by ZEISS stitching software (overlap of 5% and threshold of 0.7) and in the vertical direction with MorphoGraphX [58,59] using the process “Stacks/Multistack/Merge Stacks” (parameters: method = max; interpolation = linear). Assembled images were saved as MorphoGraphX stack files. A surface mesh was created in MorphoGraphX from each image to perform segmentation and analysis on the epidermis. First, extraneous parts of the image were removed with the Voxel Edit tool. (Such extraneous parts of the image include trichomes on the adaxial images and pollen grains/nematode eggs on some leaf images.) Then, an image was subjected to Gaussian Blur using the process “Stack/Filter/Gaussian Blur Stack” (parameters: x = 2; y = 2; z = 2). Next, the tissue surface was identified with the process “Stack/Morphology/Edge Detect” (parameters: threshold varied between 2,300 and 7,000 according to individual image brightness; multiplier = 2.0; adapt factor = 0.3; fill value = 30,000). These steps extracted a surface of the leaf. The process “Stack/Morphology/Fill Holes” was applied to some images when holes were apparent in the surface (parameters: x-radius = 20; y-radius = 20; threshold = 10,000; depth = 0; fill value = 30,000). This surface was then used to generate a mesh with the process “Mesh/Creation/Marching Cube Surface” (parameters: cube size = 5 μm; threshold = 20,000). The mesh was smoothed with “Mesh/Structure/Smooth mesh” (parameters: number of passes varied between 20–45; Walls Only = no). The mesh obtained was then subdivided with the process “Mesh/Structure/Subdivide” either once or twice depending on its size. In order to obtain the cell membrane signal on the surface, the process “Meshes/Signal/Project Signal” (parameters: min/max distances ranged between 5 and 15 μm; MinSig = 0.0; MaxSig = 60,000) was used to project the p35S::mCitrine-RCI2A plasma membrane marker original signal onto the mesh at an optimal depth. The depth range yielding the clearest cell membrane signals with minimal distortion was selected. To perform cell segmentation, each individual cell in the leaf was first manually identified with a cell label marking (seed). Using these seeds, watershed segmentation was performed using the process “Meshes/Segmentation/Watershed Segmentation.” Adjacent pairs of stomatal guard cells were segmented together to form a single cell; these were classified as stomata. Errors in segmentation were identified and corrected by removing the label for those cells and reseeding. The Heat Map processes computed the cell area and other morphological cell features as well as the position of every cell. The cell area data was exported into a data table file for each image. In addition, other cellular shape features were computed and exported into a data table for the cell type classification (Materials and methods: cell type classification).

To analyze the nuclear signal from images of leaves expressing pUBQ::H2B-TFP, vertical stitching of tiles (already horizontally stitched with Zeiss stitching software) was performed in MorphoGraphX (max method and linear interpolation). Because the TFP reporter was expressed under the UBIQUITIN 10 promoter, TFP was localized in nuclei of the mesophyll cells in addition to cells of the epidermis. Mesophyll nuclei were removed with the Voxel Edit tool. Nuclei were identified as being from the mesophyll by lining up the nuclear signal images with their corresponding membrane signal images and comparing the nuclei within the bounds of each epidermal cell membrane. When compared with an epidermal cell nucleus, mesophyll cell nuclei were often dimmer and lower down and therefore, excess nuclei were removed according to these criteria so that each epidermal cell had one nucleus. When it was ambiguous which of two nuclei in a single cell was from the mesophyll or epidermis, both nuclei were removed and excluded from the analysis. Segmentation of the nuclei was performed in MorphoGraphX so that the total signal could be calculated for each nucleus. To do so, the confocal image was first subjected to “Stack/Filters/Brighten Darken” (parameter: 1). Next, a gaussian blur was performed using “Stack/Filters/Gaussian Blur” (parameters: x = 1, y = 1, z = 1), followed by a binarization with the process “Stack/Filters/Binarize” (parameters: threshold = 2,000), which functioned to select pixels above a threshold value to identify the edges of each nucleus. A lower threshold value was chosen so that we could identify the entire nuclei even for dim nuclei. The Voxel edit tool was used to separate nuclei that inflated into one another. We then created a mesh from the binarized image using the process “Mesh/Creation. Marching Cubes 3D” (parameters: cube size = 1, min voxel = 0, smooth passes = 3, label = 0). To ensure that the mesh covered all fluorescence of each nucleus, we expanded the mesh using “Mesh/Structure/Shrink Mesh” with a negative value (parameter: distance = −1). Individual nuclei were manually seeded and then the watershed segmentation was performed with the process “Mesh/Segmentation/Watershed Segmentation” to identify each nucleus. The Heat Map function calculated the total H2B-TFP fluorescence within each nucleus, as a representation of DNA content. To study correlations between total nuclear H2B-TFP signal and cell size, individual cells from cell area meshes were matched with their constituent nuclei from nuclear signal meshes using MorphoGraphX parent tracking. For the leaf replicates, total nuclear H2B-TFP signal was calculated for as many cells as possible from both the abaxial and adaxial sides. For the sepal replicates, total nuclear H2B-TFP signal was calculated only on the abaxial side and only for the largest cells.

To create the heat maps overlaid with vasculature in S13 Fig, confocal images of leaves expressing p35S::mCitrine-RCI2A were used to create surfaces and were segmented as described above to create cell area heat maps. The mCitrine-RCI2A confocal images were found to have signal in the vasculature, so that the trajectories of veins could be traced in images from the abaxial surface of the image, one can see. The mCitrine-RCI2A confocal images were transformed around the z-axis in MorphoGraphX. For each leaf, the cell area heat map and the mCitrine-RCI2A confocal image transformed around the z-axis were aligned in MorphoGraphX and PNG screen captures were taken of each. These PNGs were then loaded into Adobe Illustrator and the veins were traced in white onto the heat maps.

Please note that wild-type 25 dpg leaf replicates 1, 3, and 4, lgo-2 25 dpg leaf replicates 1 and 2, and LGO-OX replicates 1, 2, and 3 were used for an independent analysis of cell shape (specifically lobeyness) [60].

Statistical analysis

To analyze the relationship between total nuclear H2B-TFP signal (DNA content) and cell area for the leaves in Figs 2 and S2, linear regressions were performed on R statistical software (https://www.r-project.org/). To compare the total nuclear H2B-TFP signal (DNA content) of the cells of largest area between sepals and leaves, the cell area at the 98th percentile was calculated for each of the three abaxial sepal replicates and these three cell areas were averaged for an area threshold of 4,308 µm². Cell area versus total nuclear H2B-TFP signal (DNA content) was plotted for cells above this 4,308 µm² area threshold for the abaxial sepals and the abaxial and adaxial leaves.

To compare positions of the largest cells on the abaxial and adaxial sides of each leaf at different stages of development (Fig 3), the abaxial and adaxial images were aligned in MorphoGraphX. Then, cell area heat maps were created and the x and y coordinates of the center of each cell were calculated (Fig 3C). Cell area thresholds for each leaf were determined from the 98th percentile cell area of the abaxial side, and the positions of cells above these area thresholds were plotted for the abaxial and adaxial images of each leaf.

R statistical software was used to analyze the cell-size distributions and create the violin plots and Wasserstein plots. The threshold for significance was set to alpha = 0.05. To create the Wasserstein plots, a Wasserstein test was performed between each pair of replicate distributions. A test statistic (also known as Wasserstein distance) and p-values were returned for every test. The p-values are listed in S8C and S8D Fig. Classical multidimensional scaling was performed to create a 2D coordinate for each replicate distribution based on the Wasserstein distances, and points from these coordinates were plotted. To ensure that the distances between 2D points adequately reflected the Wasserstein distances among replicate distributions, we plotted the Wasserstein distances against the Euclidean distances between points (S8E and S8F Fig). The linear relationships between Wasserstein distances and Euclidean distances showed that the 2D graph accurately represents the differences between distributions.

To create the Wasserstein plot of the combined 9- and 25-dpg cell area data, cell areas of each replicate in each genotype were normalized by the mean cell area for that replicate. In this way, each replicate has a mean of 1. This eliminated the difference in the mean values of the cell size between the 9- and 25-dpg leaves, such that all higher moments of the area distributions could be compared rather than the absolute sizes.

To statistically compare the differences in the number of giant cells across genotypes in the leaf at 9 dpg and at 25 dpg, two-sample, two-tailed t tests that assumed equal variance were performed on the number of giant cells per segmented area between wild type and the different genotypes.

To statistically assess the randomness of the cellular patterns, see section “Statistical analysis of the cellular patterns” below.

Cell type classification

To automatically distinguish stomata from pavement cells, a supervised classification algorithm was used based on cell shape features (S9 Fig). Cell shape features were computed from each 2.5D mesh using the MorphoGraphX [58,59] process “Mesh/Heat Map/Analysis/Cell Analysis 2D” and were extracted with “Mesh/Attributes/Save as CSV” into a data table. Three distinct training datasets were created using a single wild-type replicate—one for the sepal, one for the leaf at 25 dpg and one for the leaf at 9 dpg. To get the different training datasets, we manually selected some pavement cells and stomata and labeled them as different cell types, ran the classification processes available within MorphoGraphX, and manually corrected the cells that were wrongly identified. These training datasets were then used to train a supervised learning algorithm (Support Vector Machine quadratic) using the Classification Learner App in MATLAB [61,62]. The following cellular shape features were selected to train the classifier in the 25-dpg leaf: area, average radius, length of the major axis, maximum radius, perimeter, circularity, lobeyness (ratio of the cell perimeter over that of its convex hull; convex shapes have lobeyness 1) [59], and rectangularity (ratio of the cell area over the area of the minimum bounding rectangle in the cell) [59]. For the sepal, the aspect ratio and the length of the minor axis were also taken into account. For the 9-dpg leaf, where the variety of cell types was more complex, three cell types were defined (pavement cell, meristemoid, and stomata) and meristemoid and stomata were combined in the postprocessing script. The shape features used to train the classifier were area, average radius, minimum radius, perimeter, circularity, lobeyness, and visibility stomata (it counts the proportion of straight lines that connects the cell outline without passing through a cell boundary) [59,63]. To automatically predict cell types in all replicates, a developed MATLAB script containing the trained classifier and a postclassifier filter, which corrects for potentially wrong predictions on the basis of known shape criteria, was applied. Manual corrections were finally performed, in which misclassified cells were re-labeled with their correct cell type.

Giant cells were defined by a cell-size threshold (S9 Fig). Because a few giant cells were expected in atml1-3 mutants, atml1-3 mutants were used as a reference to build this threshold. Fewer than 0.7% of the pavement cells were considered to be giant cells in atml1-3 tissues, which was supported through visual observation in the sepal. Consequently, the giant cell-size threshold was set as that corresponding to the average between the 99.3rd percentile cell-size value with the cell-size value immediately above it in the distribution, taking into account the data of three atml1-3 pooled replicates. For consistency, the same method was applied to the sepal, and to 9- and 25-dpg leaves, which gave three different threshold values (sepal: 5,290 µm², leaf 9-dpg: 2,570 µm², leaf 25-dpg: 14,160 µm²). The percentiles were only calculated on rectangular sections (omitting cells at the outline of the organs) of the sepal to maintain consistency across different organs. Classification output examples in different genotypes are shown in S10 and S11 Figs.

Randomization of the experimental images

To assess the randomness of the cellular patterns, it was essential to establish a random reference, or null model, against which the observed pattern could be compared. To produce the required random reference, the image-based method dmSET [36,37] was applied to generate 400 synthetic random equivalent tissues from each segmented image. Cell positions and orientations were randomly shuffled into new images (named randomizations) [37], while preserving individual approximate cell shapes and sizes (S15 Fig). Only the incomplete cells at the border of the images were fixed. This randomization method avoids potential biases arising from the heterogeneity of cell sizes and shapes in the tissues, which affects the number of neighboring cells. We ensured that cellular properties, and more specifically cell area and cell lobeyness (defined as the perimeter of the cell divided by the perimeter of its convex hull), were approximately conserved in the randomized leaf tissues (S15D and S15E Fig; the Pearson coefficient was 0.98 for cell area correlation and was 0.94 for cell lobeyness correlation). In the sepal randomized tissues, cell orientations were constrained between −π/6 and +π/6 compared with their initial orientation, to maintain the anisotropy of the tissue. Cell shape properties were also approximately conserved (S15I and S15J Fig). A custom-made MATLAB script was subsequently applied to both original and randomized images to correct errors introduced by the dmSET method and to compute cell shape properties and cellular network information that was used to quantify the cellular pattern.

Before randomizing the different sepal and leaf replicate images (Figs 5 and S14), each 2.5D mesh was first converted into a 2D pixel image using the process “Stack/Mesh Interaction/Mesh To Image” (with a pixel size of 1μm) in MorphoGraphX. Subsequently, a square crop (in the leaf) or rectangular crop (in the sepal) that maximized the tissue section was performed in the segmented images. These 2D segmented images were then randomized using the dmSET method.

To study the change in the giant cell spatial pattern over time, published time-lapse sepal data were used [39] that were randomized at two different time points (sepal at stage 4: 24 h, and at stage 8: 96 h). Cell segmentation and cell lineage tracking were already performed in [39]. Using MorphoGraphX, sepal cells were manually selected at the later time point, and the exact corresponding mother cells at the first time point were established using the lineage tracking analysis from [39]. In order to quantify the spatial pattern of the same giant cells at two different time points, giant cells at both stages were defined as the pavement cells that did not divide during this period of time. This approach allowed the comparison of the change in tissue organization consistently at two different time points. Then, the 2.5D meshes were projected into 2D images. These images were subsequently randomized using the dmSET method. Here, to facilitate the study of the same giant cells over time, the images were not cropped and the entire studied tissue was randomized, including the cells at the edges. To achieve this, the background region, located outside the tissue of interest, was considered as a single cell that remained fixed in the randomized tissues. Examples of randomizations are shown in S20C and S20D Fig. Three different sepal replicates were used for these analyses of the time-lapse data.

“Segmentation” and “Randomization” images appearing in figures such as Figs 5, 6, S14, S17, S18, and S20 were produced with a Python script using the multi-labeled images generated by dmSET.

Several approaches were used to test the robustness of our method and ensure that there was no bias in our null model. In the randomized tissues, cell sizes were well preserved (S15D Fig), but cell shapes were affected in the leaf (S15E Fig). Because the leaf pavement cells in the randomizations exhibit different shapes (more convex shapes and noisier edges) compared to the original cells, we developed an additional alternative method for generating randomized tissues (S19 Fig), called Cut and Merge Cells. In this approach, each leaf replicate was first over-segmented using MorphoGraphX (autoseeding with r = 4 μm combined with manual seeding) to create templates composed of small fragments of pavement cells (S19A Fig). These templates were then used to automatically generate a random pattern of giant cells, preserving their original sizes and numbers (S19A Fig). Giant cells were created recursively: their positions were randomly allocated to a first pavement cell fragment, which was then merged with neighboring cell fragments until the original giant cell size was reached (S19A Fig). Similar results were obtained by using this randomization method (S19B and S19C Fig), confirming the tendency of giant cells to cluster more than would be expected by chance. However, while cell shapes produced by this method exhibited less noisy edges, they remained less lobed and more convex compared to those in the original segmentation (S19F Fig). Moreover, this method does not randomize all cells in the tissue, such as stomata.

We wondered whether the shape artifacts introduced by the dmSET method could introduce bias into our null model by affecting the contacts between cells in the randomized tissues differently than in the original segmentations. To explore this possibility, we generated “reconstructions” of the original images using the same dmSET method as for the randomizations, except that each cell’s position from the initial segmentation was preserved (with some added uniform noise having a maximum of ±5 μm in the y and x directions) (S18A–S18C, S18E, and S18F Fig). This resulted in cell shape artifacts that were nearly identical between the reconstructions and the randomizations (S18J–S18L Fig), making them more comparable. Indeed, the differences in cell lobeyness (defined as the perimeter of the cell divided by the perimeter of its convex hull) from the original tissues were similar between the reconstructions and randomizations for large cells (S18J Fig). The number of cell neighbors differed slightly from the original segmentations due to the introduced shape artifacts (S18M and S18N Fig), but we found that giant cell contacts remained mostly the same in the reconstructions. Specifically, we observed approximately 6% fewer contacts between giant cells in the reconstructions compared with the segmentations. When comparing reconstructions with randomizations (which are comparable because of their similar cell shapes), the results remained consistent (S18O Fig), with giant cells being more clustered than expected by chance (p = 0.005). In the sepal, cell shape was quite preserved (S15I and S15J Fig; the Pearson coefficient was >0.99 for cell area and perimeter). Sepal cell edges were noisier in the randomized tissues, with a higher cell perimeter (S15J Fig); this could potentially lead to more contacts in the randomized tissues, which would not affect our conclusion.

Furthermore, we evaluated our method by using a randomly selected population of pavement cells in both leaves and sepals (S17 Fig). The null hypothesis could not be rejected and this result was robust across five different random patterns in all replicates (one is shown in S17 Fig). Specifically, we obtained p-values ranging from 0.395 to 0.488 in leaves and from 0.178 to 0.335 in sepals. The number of giant cell contacts was either slightly more or less than the expected mean random value, attributable to variability in the random patterns. This indicates that the artificial random pattern did not deviate from true randomness, suggesting that our null models do not present a significant bias.

Statistical analysis of the cellular patterns

By comparing a spatial observable in the cellular network of the actual segmentation with the corresponding observable in the cellular networks of the 400 generated randomized tissues, whether the considered observable is likely to be observed by chance can be statistically tested [36]. Hence, the use of this method on observables measuring distances or contacts between the studied cells allows the assessment of whether the arrangement of the cells within the tissue is random, clustered or dispersed (Fig 5A).

To quantify the patterns, a custom-made Python script was used to extract pertinent observables (i.e., spatial quantities) from the cellular network, which used the NetworkX Python library [64]. In this manuscript, we mainly focused on the number of giant cell neighbors per giant cell to quantify the number of local contacts between giant cells. Other observables have been quantified, such as the minimum shortest path between giant cells, and the number of giant cells in a cluster (S16 Fig). When dealing with cropped images, giant cells (or any cell population studied, see Fig 6) at the border of the image were not considered in the analysis.

The number of giant cell neighbors was extracted for every giant cell, and the mean number of giant cell neighbors per giant cell across all giant cells was computed within each experimental replicate. Similarly, to the methodology described by the authors of the dmSET method [36], the mean value extracted from the segmentation image was compared with the approximated null distribution formed by the 400 mean values extracted from the randomized images. We first performed the analysis on each replicate independently (S21 and S22 Figs). As the cell-size distributions in the different replicates showed similarities across replicates (Figs 5, S21, and S22), replicates were pooled to increase the sample size and statistical power. Six image replicates were used for both the leaf and sepal wild-type (Fig 5), and three replicates were used for the wild-type sepal time-lapsed images (Fig 7). To test the null hypothesis assessing the randomness of the observed metric, a p-value p was obtained as the ratio of the number of random images (defined here as one random image resulting from pooling one random image per replicate) displaying the same or a more extreme value than the one obtained in the segmentation replicates (one-sided test). If the value fell within the null distribution with an associated high p-value (p > 0.05), the null hypothesis could not be rejected, indicating that the observed quantity could likely be expected by chance. If the value fell outside the null distribution, we assigned p < 0.0025, with 0.0025 corresponding to the inverse of the number of random images (400) used to create the null distribution.

In addition, the distribution of the number of giant cell neighbors for all giant cells from the pooled experimental replicates was studied, which provided more insights into their spatial organization. This was compared qualitatively with the distribution expected in a random tissue, extracted from the 400 randomized tissues of all replicates.

All plots derived from these analyses were performed with Python, with the use of the matplotlib [65] and seaborn packages [66].

Mathematical model for giant cell fate commitment and numerical simulations

To simulate the giant cell fate decisions, our published stochastic and cell-autonomous multicellular model in a growing tissue was used [12]. In that model, the transcription factor ATML1 stochastically fluctuates and drives the expression of its target LGO. In the simulated growing tissue, cells divide using a timer with some stochasticity. When the timer of a cell reaches a threshold Θ_C,S, cells undergo the S-phase, and therefore cells transition from being diploid (2C) to tetraploid (4C). By default, cells that reach a second and higher timer threshold Θ_C,D will undergo division. However, those cells that have reached a certain LGO concentration threshold Θ_T after undergoing the S-phase will not divide and are maintained in an endoreduplication cycle, which increases their ploidy.

To model the dynamics of the concentrations for ATML1 and LGO, and the Timer variable, we use chemical Langevin equations [67], which are differential equations with a corresponding deterministic part, consisting of production, degradation and regulatory terms, followed by a stochastic part modeling thermodynamic fluctuations that contains a square root, whose radicand has the sum of the absolute values of the production, degradation, and regulatory terms. The dynamics of ATML1 concentration, LGO concentration and Timer variable in cell i, denoted by [ATML1]_i, [Target]_i and Timer_i, respectively, follow the Langevin equations given by

(1)

(2)

(3)

Eqn. (1) stands for the rate of change of ATML1 in cell i, and its terms on the right-hand side describe constitutive expression, self-activation (implemented via a Hill function) [68], linear degradation, and the corresponding stochastic term in ATML1; Eqn. (2), stands for the rate of change of the Target in cell i, and its terms on the right-hand side describe ATML1-induced expression of the Target (using also a Hill function), linear degradation, and the corresponding stochastic term in the Target; Eqn. (3) stands for the rate of change of the Timer in cell i, and its terms on the right-hand side are a constitutive production and the corresponding stochastic term. The parameters of the equations are as follows: P_X is the basal production rate for the X variable (where X is either A for ATML1, T for Target concentration or C for the Timer variable), V_X is the prefactor of the ATML1-dependent production rate for the X variable, K_X is the ATML1 concentration at which the ATML1-dependent production rate has its half-maximal value, n_X is the Hill coefficient, and G_X is the linear degradation rate for the X variable. ε_i(t) is a normalized cell area, ε_i(t) = E₀E_i(t), where E₀ is an effective cell area, and E_i(t) is the area of cell i in arbitrary units. η_Xi is a random Gaussian variable with zero mean that fulfills〈η_Xi(t)η_X′j(t′)〉 = δ(t − t′) δ_XX′δ_ij, where i and j are cell indices, X and X′ the modeled variables, δ_XX′ and δ_ij are Kronecker deltas and δ(t − t′) is the Dirac delta function.

Upon cell division, the Timer was reset. To implement the resetting, the following rule was applied at each time step:

(4)

where U_i is a uniform randomly distributed number in the interval [0, 0.5) and Θ_C,D is the cell division threshold for the Timer.

The multicellular template on which the simulations were run and initial conditions were the same as in Meyer and colleagues (2017). Initial conditions for ATML1 and Target were randomly uniformly distributed in the interval of [0,1) and [0,0.1), respectively. The Timer initial conditions were set in correlation with the cell areas in the initial template with some stochasticity, as performed in Meyer and colleagues (2017). The differences between the used initial conditions were just in the ATML1, Target, and Timer initial cellular values, determined by different random numbers.

Tissue growth and division were also implemented as in Meyer and colleagues (2017). The multicellular tissue grows anisotropically, to emulate the patterning process in the sepal. This anisotropic growth was implemented by imposing a displacement of the vertices with respect to the center of mass of the tissue, with a given radial and vertical exponential rate. After each simulation step, dilution effects due to growth in the modeled variables were taken into account. Cells divided using the shortest path rule together with the constraint of having the division plane through the center of mass of the cell. We assumed that molecules are homogeneously distributed within cells, and therefore, upon cell division, sister cells have the same concentration of ATML1 and Target variables at birth, but can have different cell sizes.

Numerical simulations were performed with Tissue software [12,13,69], and the integration was performed using an Îto interpretation of the Langevin equations with a Heun algorithm [70]. Integration was performed with a time step dt = 0.1, and simulations were stopped at time 135. Parameter values for the simulations are given in S2 Table. Parameters were chosen such that the wild-type behavior reported in Meyer and colleagues (2017) could be recapitulated. The outcome of the simulation in Fig 7B was displayed using Paraview software [71].

We recently proposed a more detailed model of the ATML1 regulatory network to study how giant cell specification and cell fate maintenance depend on VLCFA [13], which is still a stochastic and cell-autonomous model. Here, however, for the sake of simplicity, and the intention of using a minimal, stochastic, and cell-autonomous phenomenological model, the former ATML1 model was used [12].

Randomizations of the outcomes from the numerical simulations

To assess the randomness of the giant cell pattern in the numerical simulations (Fig 7), the same method was employed as that used for the experimental images. Although randomizations of the tissues were performed similarly (see the “Randomization of the experimental images” section above), a Python script was developed to display the output of the simulation as a multilabeled image, where each cell was colored with a different label. These images could therefore be randomized using the dmSET method [36,37]. To compare the simulated giant cell pattern (Fig 7B) to the giant cell pattern found in the experimental mature sepals (Fig 5B), the output image was cropped using the maximal rectangle in the tissue, and giant cells were also defined by a size threshold, ensuring that all cells with a ploidy of 16C or higher were categorized as giant cells (Fig 7C). The few 8C cells that exceeded this threshold were also considered as giant cells.

To study the change in the giant cell spatial pattern over time (Fig 7F), the same simulations were used, but only the first-arising giant cells (i.e., cells that stopped dividing after time t = 55 of the simulations for being committed to endoreduplicate) were studied. The same method was used to assess the randomness of the cellular patterns on these giant cells both at time t = 55 and time t = 135. Here, instead of cropping the image, the whole tissue was randomized (using the dmSET method), including the cells at the edges, such that exactly the same giant cells were considered at both time points. Examples of randomizations are shown in S20A and S20B Fig. The analysis was performed over five simulation replicates, with different cellular random initial conditions.

Related “Segmentation” and “Randomization” images appearing in Figs 7 and S20 were produced with a Python script using the multi-labeled images generated by dmSET.