Robust organ size in Arabidopsis is primarily governed by cell growth rather than cell division patterns Free

Many aspects of development are robust, meaning that they have reproducible outcomes despite internal or environmental noise. Many organs have robust size and shape, which is important for proper function (Boulan and Léopold, 2021; Hong et al., 2018). Arabidopsis thaliana (hereafter Arabidopsis) sepals, which are the leaf-like organs that enclose flower buds, have robust, i.e. uniform, size and shape (Hong et al., 2016; Zhu et al., 2020).

Often, changing cell size does not proportionally change organ size. Instead, an organ with fewer cells will have larger cells, and an organ with more cells will have smaller cells, which is called compensation. This trade-off has been observed in the leaf (Ferjani et al., 2007; Horiguchi and Tsukaya, 2011) and in Drosophila wing development (Neufeld et al., 1998). Compensation is linked to a long-standing debate of whether cells or organs are considered the basic unit of plant growth (Kaplan, 1992; Kaplan and Hagemann, 1991) and indicates that control of organ size and shape is complex.

Compensation has also been observed in the Arabidopsis sepal when there is a change in the number of the large specialized epidermal cells called ‘giant cells’ (Robinson et al., 2018; Roeder et al., 2010). These cells are created by endoreduplication, which is an alternative to mitosis in which DNA replication occurs without cell division, producing a cell with increased ploidy (Traas et al., 1998; Veylder et al., 2011). Overexpression of the cyclin-dependent kinase inhibitor LOSS OF GIANT CELLS FROM ORGANS (LGO), also called SMR1, results in an increased number of giant cells, whereas lgo-2 mutants have few to no giant cells (Kumar et al., 2015; Roeder et al., 2010; Schwarz and Roeder, 2016). These differences in cell size are compensated by changes in cell number such that mature sepal area is similar for all genotypes (Robinson et al., 2018). However, it is not well understood when this compensation occurs during sepal development, how it affects tissue growth, and whether it affects uniformity of sepal size and shape. If compensation does not occur at certain developmental stages, this may affect developmental robustness and the ability of sepals to enclose the flower bud.

Mutants with variable organ size and shape have been used to elucidate developmental mechanisms generating robust organ size and shape (Zhu et al., 2020; Kong et al., 2024a, 2024b; Trinh et al., 2023). The mitochondrial protease mutant ftsh4-5 has variable sepal size and shape, which results from elevated levels of reactive oxygen species (ROS) (Hong et al., 2016). FTSH4 (FILAMENTOUS TEMPERATURE SENSITIVE H4) is an iAAA-protease, which is a protease that also has an ATPase (AAA) domain and is located in the inner mitochondrial membrane (Urantowka et al., 2005). Both its chaperone activity, predicted to be from the ATPase domain, and protease activity have roles in eliminating aggregated and carbonylated proteins in the mitochondria (Maziak et al., 2021) and ftsh4 mutants also have abnormal mitochondrial morphology (Gibala et al., 2009). Besides the variable organ size and shape, a variety of developmental phenotypes have been reported in ftsh4 mutants (Dolzblasz et al., 2016; Gibala et al., 2009; Zhang et al., 2014). Many of the ftsh4 developmental phenotypes, including loss of robust sepal development, are linked to the increases in ROS (Gibala et al., 2009; Hong et al., 2016).

Cellular and subcellular growth during organ development is heterogeneous on a local scale even when final organ size and shape is robust. Leaves and sepals have an organ-scale basipetal growth gradient, which means that faster growth begins distally at the tip and then moves proximally towards the base (Remmler and Rolland-Lagan, 2012; Kuchen et al., 2012; Kierzkowski et al., 2019; Le Gloanec et al., 2022). The basipetal gradient is the target growth rate for the cells and the fluctuations deviate from this target. Perfectly deterministic growth matching the basipetal gradient without fluctuations would obviously lead to robust development; however, fluctuations are observed in live imaging of actual sepals and leaves (Hong et al., 2016; Uyttewaal et al., 2012). Fluctuations inevitably result from intrinsic and extrinsic sources of noise. Nearby epidermal cells can have up to fourfold difference in growth rate (Elsner et al., 2012; Tauriello et al., 2015). As cell walls prevent plant cells from moving relative to each other, heterogeneity is generated at a subcellular scale, with portions of the cell wall growing at different rates (Elsner et al., 2012). Heterogeneity may be linked to complex cell shapes (Elsner et al., 2018). It could also be due to variability in turgor pressure, which contributes to cell wall expansion but is not homogenous within a tissue (Long et al., 2020), suggesting it could lead to spatial fluctuations in growth. Another source of heterogeneity is the differentiation of cell types, such as trichomes (Hervieux et al., 2017) and stomatal lineage cells (Le Gloanec et al., 2022) which have temporal fluctuations in growth as part of differentiation. Differences in growth rate then change the mechanical stress in neighboring cells, which leads to feedback that changes the growth rates of those neighboring cells (Hervieux et al., 2017), creating spatial fluctuations.

Given that the outcome of development is uniform size and shape, it follows that local growth heterogeneity must become averaged or smoothed over time to a target growth rate (Hong et al., 2016). For example, perhaps cell A grows faster than the target growth rate and its neighbor, cell B, grows slower than the target growth rate. Later, cell A grows slower than the target growth rate and cell B grows faster than the target growth rate. The difference in growth rates between neighbors is spatial growth fluctuations and the difference in growth rates over time is temporal growth fluctuations. However, cell A and cell B will both have cumulative growth rates close to the target growth rate, even though the cells never had the same growth rate and neither cell grew exactly at the target growth rate. Similarly, the mean cumulative growth of cells A and B is closer to the target growth rate than the cumulative growth of either cell. Therefore, both the spatial fluctuations and temporal fluctuations were averaged. This is an example of spatiotemporal averaging (Hong et al., 2016), which is a general mechanism through which living organisms deal with noise (Burda et al., 2023; Hong et al., 2018; Roeder, 2018). In fact, others have shown that noise in transcription undergoes averaging over time and spatially within the tissue to result in more uniform transcript distribution and robust development (Little et al., 2013).

For this averaging to be effective, the temporal and spatial fluctuations must be either uncorrelated or anti-correlated. Consider, for example, the growth trajectory of a single tissue patch (e.g. the lineage of a cell). If the growth is positively correlated on a timescale τ_c then there are N=T/τ_c uncorrelated growth ‘periods’ in a total growth interval T. Averaging will then suppress fluctuations in the net growth by a factor ⁠, according to the central limit theorem. Increasing the correlation time τ_c means that there are fewer uncorrelated growth periods N in the same total interval T, such that fluctuations are less suppressed. A similar argument can be made for spatial averaging, where N is the number of uncorrelated area patches in a region in which the cells are mechanically coupled. The range of this coupling depends on the mechanical properties (elastic modulus and bending rigidity) of the tissue (Liang and Mahadevan, 2009). Taken together, averaging helps achieve a robust outcome in the face of fluctuations and heterogeneity, but its efficiency depends on the properties of the fluctuations and the tissue. Correlations will affect the efficiency of this averaging. Spatial growth correlation of neighboring cells is quantified via the correlation coefficient ⁠, where the average 〈 … 〉 is taken over all neighboring cell pairs (ij) and denotes the growth deviation from the average growth ⁠. (Temporal correlations between the growth rate at two times, t₁, t₂ are defined analogously ⁠, where the average is taken over all cells.) The sign of C_S,T can either be positive or negative. In the former case we simply use the term correlation, whereas the latter case is referred to as anti-correlation. Correlated fluctuations accumulate and thus hinder their suppression through averaging. By contrast, anti-correlations will accelerate the suppression of fluctuations through averaging.

The ability of spatiotemporal averaging to result in robust size and shape is supported by modeling (Hong et al., 2016). In general, two criteria are necessary for spatiotemporal averaging to result in robust organ shape: (1) mechanical attachment of each growing element to the surrounding tissue and (2) uncorrelated or anti-correlated growth fluctuations over time and space. Simulation of a model with no fluctuations does indeed produce a robust sepal shape (Hong et al., 2016). However, heterogeneity and fluctuations in growth are observed in live imaging data of leaves and sepals (Elsner et al., 2012; Hervieux et al., 2017; Le Gloanec et al., 2022; Long et al., 2020; Tauriello et al., 2015). When growth is heterogeneous, spatiotemporal averaging is crucial to obtain a robust final shape.

During in vivo sepal development, live imaging reveals that epidermal cell growth rates fluctuate both temporally and spatially (Hong et al., 2016; Le Gloanec et al., 2022; Tauriello et al., 2015). The heterogeneous growth in the developing sepal has been observed to undergo spatiotemporal averaging to produce robust mature sepal size and shape (Hong et al., 2016). There is decreased spatial and temporal fluctuations in cell growth rates in ftsh4-5 sepal development (Hong et al., 2016).

As both growth fluctuations and cell division have roles in organ size and shape, we examine how they relate to spatiotemporal averaging and developmental robustness. We use LGO expression level to modulate the number of cell divisions and ftsh4-5 to alter developmental robustness of sepal size and shape. We find that compensation occurs during the developmental stages when the sepals enclose the flower bud. Changes in cell division do not affect localization of growth, cell growth rate, correlations in growth fluctuations or averaging of growth fluctuations. In contrast, the ftsh4-5 mutation causes increased temporal correlations in cell growth, leading to the accumulation of patches of faster and slower growth, and disorganized expansion of the tissue. Together, our results suggest that changing the correlations in cell growth fluctuations, but not the amount of cell division, affects the accumulation of growth and developmental robustness.

To test whether cell division affects robustness of sepal size and shape, we used the loss-of-function lgo-2 allele, which increases the number of cell divisions, and the gain-of-function pATML1::LGO transgenic plants (hereafter referred to as LGOoe), with a decreased number of cell divisions in the sepal epidermis. Wild-type, lgo-2 and LGOoe have sepals that appear to be uniform in size and shape (Fig. 1A-C). Double mutants were made with ftsh4-5 and have sepals of variable size and shape, similar to the ftsh4-5 single mutant (Hong et al., 2016) (Fig. 1D-F). During flower development, four sepals enclose each flower bud, and the sepals must have robust size and shape to maintain closure of the bud. Wild-type and lgo-2 buds are closed (Fig. 1G,H), whereas LGOoe buds often have small gaps between adjacent sepals (Fig. 1I) owing to decreased sepal width as previously reported (Roeder et al., 2012). In contrast, ftsh4-5, lgo-2 ftsh4-5 and LGOoe ftsh4-5 often have large gaps between sepals, particularly when buds have sepals with large differences in size or shape (Fig. 1J-L). Therefore, the phenotypes of wild type, lgo-2 and LGOoe are indicative of robust sepal development, whereas the phenotypes of ftsh4-5, lgo-2 ftsh4-5 and LGOoe ftsh4-5 are indicative of a loss of robustness.

To quantify the variability in sepal size within a flower, the standard deviation of sepal area within one flower was calculated. Wild type, lgo-2 and LGOoe have similar levels of variability in sepal size and have less variability in sepal size compared with ftsh4-5, lgo-2 ftsh4-5 and LGOoe ftsh4-5, respectively (Fig. 1M) (the difference between wild type and ftsh4-5 shows the same trend but does not reach statistical significance). To quantify variability in shape alone, the sepal contours were normalized by size. Wild type, lgo-2 and LGOoe (Fig. 1N-P; Fig. S1A-C,H-J) have similar levels of variability around the average sepal shape, and have less variability compared with ftsh4-5, lgo-2 ftsh4-5 and LGOoe ftsh4-5, respectively (Fig. 1Q-T; Fig. S1D-F,K-M) (the difference between lgo-2 and lgo-2 ftsh4-5 is statistically significant and the others have the same trend but do not reach statistical significance). Our results show that uniformity of sepal size and shape within a flower is preserved when the number of cell divisions is increased or decreased. Similarly, the ftsh4-5 variability of sepal size and shape is unaffected by changes in cell division.

To determine how sepal shape robustness is preserved despite extreme changes in cell size and number, we time-lapse imaged living sepals every 24 h for 6 days (n=3) during development. This spans the time during which the ftsh4-5 phenotype first becomes visible. MorphoGraphX (Barbier de Reuille et al., 2015; Strauss et al., 2022) was used for segmentation of cell and lineage tracking in two and a half dimensions on the curved surface of the sepal.

To measure how genotype changed cell division, the number of daughter cells per lineage over the 6 day time series was calculated. The wild-type epidermis had giant cells that never divided, interspersed with dividing lineages of smaller cells (Fig. 2A; Fig. S2A). lgo-2 had more daughter cells per lineage, and few to no non-dividing cells (Fig. 2B; Fig. S2B). LGOoe had fewer daughter cell per lineage and many non-dividing giant cells (Fig. 2C; Fig. S2C). Thus, LGO expression modulates cell division. ftsh4-5 had slightly fewer daughter cells per lineage than wild type, and a similar number of non-dividing lineages (Fig. 2D; Fig. S2D). lgo-2 ftsh4-5 had more daughter cells per lineage than ftsh4-5, and few to no non-dividing cells (Fig. 2E; Fig. S2E). LGOoe ftsh4-5 had fewer daughter cells per lineage than ftsh4-5, and mostly non-dividing giant cells (Fig. 2F; Fig. S2F). Our results demonstrate that LGO expression level strongly modulates the number of daughter cells per lineage in the ftsh4-5 background as well as wild type (Fig. 2G,H). We conclude that LGO and FTSH4 function in separate pathways, because the phenotype caused by each mutation is not affected by the other mutation in the double mutant. Our results confirm that these genotypes can be used to test how cell division affects robustness in young developing sepals.

To determine how the amount of cell division affects cell size, cell area was measured at each time point. At the start of the time-lapse imaging, cell areas of wild type, lgo-2 and LGOoe were relatively homogenous and similar between genotypes (mean cell size in lgo-2=99.4 µm², LGOoe=157 µm² and wild type=106 µm²; Fig. 3A,D; Fig. S3A-F). Over development, all cell size distributions widened. The wild-type distribution was skewed slightly to larger sizes compared with lgo-2 (Fig. 3A,B,D; Fig. S3A-D). The LGOoe distribution was the most skewed towards larger sizes (Fig. 3C,D; Fig. S3E,F). The largest cells were differentiating into giant cells, which continued to endoreduplicate and grow in area (Roeder et al., 2010). At the final time point, the mean cell size of lgo-2 was the smallest at 221 µm², the mean cell size of LGOoe was the largest at 797 µm², and the mean cell size of wild type was 342 µm². ftsh4-5 (Fig. 3D,E; Fig. S2G,H), lgo-2 ftsh4-5 (Fig. 3D,F; Fig. S3I,J) and LGOoe ftsh4-5 (Fig. 3D-G; Fig. S3K,L) mirror the cell area distributions of wild type, lgo-2 and LGOoe, respectively. Therefore, the trade-off between cell size and cell division becomes pronounced during these developmental stages.

As ftsh4-5 has variable organ size and shape, we also quantified the variability in cell area (Fig. S3M). Wild type, lgo-2 and LGOoe had similar amounts of variability in cell area compared with ftsh4-5, lgo-2 ftsh4-4 and LGOoe ftsh4-5, respectively. This implies that variability in cell area and loss of robustness are not correlated.

Classical multidimensional scaling, which can be used to represent the main features of the probability distribution in a two-dimensional (2D) plane, was used to visualize the cell area distributions in each time point and genotype. This analysis revealed that cell areas of all genotypes clustered together at the 0 h and 24 h time points, but over the course of the time lapse, the cell size distributions diverged depending on LGO expression level but not on ftsh4-5 (Fig. S4).

We also characterized differences in the spatial localization of cell division over 24 h time intervals. Cell divisions are represented as the change in number of cells in a lineage over each 24 h time interval. In wild type, cell division was localized primarily at the distal half of the sepal at 0-24 h, and then progressed proximally towards the base over time (Fig. 4A; Fig. S2G,H). This tip-to-base progression is called a basipetal gradient. Both sepals (Hervieux et al., 2016) and leaves (Andriankaja et al., 2012; Kazama et al., 2010) have this localization of division, also called an arrest front. Interestingly, lgo-2 (Fig. 4B; Fig. S2I,J) and LGOoe (Fig. 4C; Fig. S2K,L) cell division also follows a basipetal gradient, but with increased and decreased divisions, respectively. Therefore, changing the number of cell divisions does not affect the localization of cell division.

Cell division localizations in ftsh4-5 (Fig. 4D; Fig. S2M,N), lgo-2 ftsh4-5 (Fig. 4E; Fig. S2O,P) and LGOoe ftsh4-5 (Fig. 4F; Fig. S2Q,R) are similar to those in wild type, but occasionally appear to be slightly skewed towards the left or right side of the sepal rather than evenly across the sepal. Therefore, ftsh4-5 has little to no effect on the localization of cell division.

To understand how dramatic differences in the number of cell divisions are compensated to have little effect on sepal shape, we examined cell growth. The epidermal cell layer drives morphogenesis (Savaldi-Goldstein et al., 2007), so we focused our analysis on epidermal cell growth. In wild type, the highest rates of cell growth were localized distally at the 0-24 h time interval, and then cell growth formed a band-like localization that moved proximally over time (Fig. 4G; Fig. S5A,B). This basipetal growth gradient matched previously described sepal growth (Hervieux et al., 2016; Hong et al., 2016). Organ-scale localization of cell growth in lgo-2 (Fig. 4H; Fig. S5C,D), LGOoe (Fig. 4I; Fig. S5E,F), ftsh4-5 (Fig. 4J; Fig. S5G,H), lgo-2 ftsh4-5 (Fig. 4K; Fig. S5I,J) and LGOoe ftsh4-5 (Fig. 4L; Fig. S5K,L) was remarkably similar to that of wild type. The organ-scale pattern of cell growth localization was also captured by plotting cell growth rates as a function of the proximal-distal axis of the sepal, and then fitting with a third order polynomial. This quantified the organ-scale profile of growth along the basipetal axis. (Fig. 5). As a result of the basipetal growth gradient, the growth profiles at the initial time points had a peak towards the distal end of the axis, and the subsequent time points had peaks that progressed proximally. There was some variation in the location of the basipetal gradient at each developmental stage, which is likely due to biological variability or slight differences in staging. However, the progression of the basipetal gradient was similar in all genotypes. We conclude that the organ-scale basipetal growth gradient is not eliminated by ftsh4-5 or LGO levels. Thus, the number of cell divisions has little effect on sepal shape because the overall basipetal gradient of cell growth is unchanged. Local deviations from the stereotypical organ-scale growth profile manifest as fluctuations that will be quantified below.

We examined the relationship between cell area growth and cell division because both have a basipetal gradient. Cell divisions and fast cell growth colocalized to the same regions of the sepal, although the fastest growing cells were not necessarily the ones that divided in wild type (Fig. 4G; Fig. S5A,B), lgo-2 (Fig. 4H; Fig. S5C,D), LGOoe (Fig. 4I; Fig. S5E,F), ftsh4-5 (Fig. 4J; Fig. S5G,H), lgo-2 ftsh4-5 (Fig. 4K; Fig. S5I,J) and LGOoe ftsh4-5 (Fig. 4L; Fig. S5K,L). Across all genotypes, in a given 24 h interval, cells that divided tended to have greater growth (Fig. S6). However, the frequency distributions of cell growth rates of all six genotypes did not differ from each other (Fig. S7), despite differences in cell division. Multidimensional scaling was used to compare the differences in the distributions of cell growth rates between genotypes and time points. This analysis revealed that all genotypes loosely cluster by time interval (developmental stage) but not by genotype (Fig. S8). Together this analysis demonstrates that cell division does not affect the magnitude of cell growth or the localization of growth in a basipetal gradient, explaining the robustness of sepal size and shape despite changes in cell division.

It is unclear how the basipetal growth gradient is preserved in LGOoe, which has giant cells spanning large vertical sections of the sepal. If giant cells had different amounts of expansion in different regions of the cells, this may facilitate the preservation of the normal localization of cell area growth. To test this hypothesis, giant cells were artificially subdivided into multiple ‘cells’. Cell area heat maps were created with the artificial ‘cells’ outlined in white. In both wild type (Fig. 6A; Fig. S9A,B) and LGOoe (Fig. 6B; Fig. S9C,D), different regions of the giant cells often had different amounts of area growth. Our data support the conclusion that LGOoe basipetal growth is achieved by different growth rates within cells. Differential growth within giant cells demonstrates that the preservation of the growth localization due to the regulation of growth on a subcellular scale is the mechanism through which morphogenesis is oblivious to cell division and through which compensation occurs.

In wild type, lgo-2 and LGOoe there is heterogeneity in 24 h cell growth rates (Fig. 4G-I), but development is reproducible sepal size and shape. To visualize how heterogenous growth accumulates over time, we looked at 3-day cumulative growth (24 h to 96 h). In wild type, the highest cumulative growth was in the center of the sepal, which experienced the most growth from the basipetal growth gradient, whereas the tip and base had lower growth. Both within and outside this region of faster growth, cells at the same position along the proximal-distal axis had similar growth rates, giving the localization a smoothened or averaged appearance (Fig. 7A) compared with 24 h growth rates (Fig. 4G; Fig. S5A,B). The 3-day cumulative growth in lgo-2 (Fig. 7B) and LGOoe (Fig. 7C) had the same localization as wild type. Smoothened cumulative growth rates indicate that heterogeneity accumulates in a way that results in spatiotemporal averaging. Heterogeneity in 24-h cell growth is not an artifact of cell-scale measurements because heterogeneity is also observed in a deformation map based on cell junction landmarks (Fig S10).

Cell growth does not accumulate into averaged growth in ftsh4-5 (Fig. 7D). Instead, growth accumulated in patches that cover parts of the sepal instead of encompassing the entire width of the sepal. Three-day growth in lgo-2 ftsh4-5 (Fig. 7E) and LGOoe ftsh4-5 (Fig. 7F) also accumulated into patches. Less extreme versions of these patches in the 24 h growth rates were seen as regional deviations from the organ-scale basipetal growth gradient in patches of cells that persisted over subsequent 24 h time intervals. The persistence of the patches can be described as increased temporal correlation of cell growth rates. As the patch affects more than one cell, this can be described as increased spatial correlation of cell growth rates. In some ftsh4-5 background replicates, sepal shape became abnormal during the course of live imaging, and in these replicates the sepal shape appeared to be asymmetric and more elongated where there were patches of higher growth (Fig. 7D-F). The localization of the patches varied between replicates. Thus, growth that accumulates in patches with variable location likely causes the variability in ftsh4-5 mature sepal size and shape.

On an organ-scale, wild-type cumulative growth is smoothened and reflects the global basipetal growth gradient, whereas ftsh4-5 cumulative growth is patchy, locally disrupting the basipetal growth gradient. To quantify this difference in cumulative growth on a cell scale, we focused on the fluctuations from the organ-scale growth gradient. Fluctuations of the cell growth rates were evident from the spread of individual cell growth rates around the fitted curves (Fig. 5). Fluctuations were quantified by subtracting this fitted large-scale gradient from the cell growth rates. This subtracted the effect of the organ-scale basipetal gradient on growth rate, isolating fluctuations around this organ-scale pattern and allowing for analysis of cell-scale and regional growth.

Fluctuations in growth around the organ-scale basipetal gradient appeared to be evenly distributed throughout the sepal in wild type (Fig. 8A), lgo-2 (Fig. 8B) and LGOoe (Fig. 8C). On the other hand, growth fluctuations in ftsh4-5 (Fig. 8D), lgo-2 ftsh4-5 (Fig. 8E) and LGOoe ftsh4-5 (Fig. 8F) grouped in patches of cells of increased or decreased growth. The heat maps of growth fluctuations are represented on planar projections of the sepals to better visualize all cells (Fig. S11). Patchiness is quantified by taking the mean fluctuation of a cell and its immediate neighbors, and then calculating the standard deviation of the means (Fig. 8G). In the wild-type background, any sample of cells is likely to accurately reflect the mean fluctuation of the entire population of cells, so the standard deviation is low. In the ftsh4-5 background, a sample of cells will have a different mean fluctuation based on location, so the standard deviation is high. In other words, patchiness is higher in the ftsh4-5 background because fluctuations in growth rates are more correlated in space. We conclude that cumulative growth is evenly distributed in the wild-type background, but patchy in the ftsh4-5 background.

To understand how growth accumulates evenly in wild type and patchily in ftsh4-5, we looked at underlying fluctuations in 24 h growth rates for individual cells over subsequent time intervals. Fluctuations in growth rate will lead to deviations from the target growth. However, over time, positive and negative fluctuations can cancel each other out, leading to cumulative growth that is close to the target growth rate despite fluctuations. This is considered temporal averaging. We hypothesized that the patchiness of 3-day growth in the ftsh4-5 background might result from temporally correlated growth. Indeed, wild type, lgo-2 and LGOoe had less correlation in growth rate fluctuations over time compared with ftsh4-5, lgo-2 ftsh4-5 and LGOoe ftsh4-5 (Fig. 8H,I). Temporally correlated growth fluctuations in the ftsh4-5 background were visible in the raw relative growth rates as clear delineations between cells that always grow slowly throughout the course of images and neighboring cells with increased growth (Fig. 4J-L).

We further assessed spatial variability (patchiness) in 24 h growth rates (Fig. S12A). When nearby cells have fluctuations around the target growth rate, this creates spatial variability. Spatial variability is decreased if neighboring cells have a similar growth rate. Patchiness in 24 h cell growth rates was slightly increased in ftsh4-5 and lgo-2 ftsh4-5 compared with wild type and lgo-2, respectively, although these differences were non-significant. LGOoe and LGOoe ftsh4-5 had similar levels of spatial variability, which could be due to low cell number. This indicated that ftsh4-5 had a minor effect on spatial variability at 24 h time intervals. We also examined the relationship between initial cell size and growth fluctuations and found that there was no association (Fig. S12B,C). Taken together, we conclude that temporally correlated cell growth in ftsh4-5 leads to the increased spatial patchiness of cumulative growth.

Growth direction also affects development of shape. In all genotypes, 24 h cell growth directions were more variable than 3-day growth directions, but the ftsh4-5 background had patches with increased variability (Fig. S13). We found that there was a negative correlation between proximal-distal growth and cell area growth in all genotypes, which became significant for wild type, ftsh4-5 and lgo-2 ftsh4-5 (Fig. S14). In other words, faster growing cells contribute more to medial-lateral expansion of the tissue than slower growing cells. Medial-lateral growth was evenly distributed in wild type and patchy in ftsh4-5, reflecting the growth fluctuation distributions. Thus, growth direction contributes to the variability in ftsh4-5 sepal shape.

Our results are similar to Hong et al. (2016), in which they found that ftsh4-5 has decreased temporal variability and spatial variability, although only spatial variability reached significance. Here, we also found that ftsh4-5 decreased temporal and spatial variability, but only the temporal variability reached significance. Together, the increased temporal correlation of growth fluctuations, and slight difference in spatial variability, indicates that the ftsh4-5 mutation changes growth heterogeneity.

Correlations in growth rate fluctuations and the resulting accumulation of growth have implications for final organ size and shape. We found that variability in the final sepal area and shape are associated with both temporally correlated growth rates (Fig. 9A,B) and patchy accumulation of growth (Fig. 9C,D). Therefore, temporal correlation in growth leads to patchy accumulation of growth, and both are correlated with loss of uniform size and shape. This strongly suggests that uncorrelated growth fluctuations lead to robust development of sepal size and shape through spatiotemporal averaging.

To understand how and when compensation occurs during development and its relationship to developmental robustness, we time-lapse imaged a mutant with increased number of cell divisions (lgo-2), a transgenic plant with decreased number of cell divisions (LGOoe), a mutant with variable organ size and shape (ftsh4-5) and double mutants. We confirmed that sepal development is robust to changes in cell division because the amount of division does not affect the organ-scale basipetal growth gradient. The arrest front of division that progresses basipetally is also preserved in mutants. The change in number of cell divisions without changing growth automatically generates the change in cell size observed during compensation because cell lineages grow the same amount but are partitioned differently. Thus, our imaging reveals that compensation occurs when the organ-scale growth pattern remains unaltered by changes in cell division.

It has been previously proposed that wild-type sepal development is robust because there is spatiotemporal averaging of growth heterogeneity. Here, we found further evidence of spatiotemporal averaging. Growth fluctuations and heterogeneity manifest as local deviations from the organ-scale basipetal gradient. Growth fluctuations are not temporally correlated in the wild-type tissue, causing growth to accumulate evenly (Fig. 9E). We found the same evidence of spatiotemporal averaging in lgo-2 and LGOoe, thus cell division does not affect spatiotemporal averaging. On the other hand, growth fluctuations are positively correlated in space and time in the ftsh4-5, lgo-2 ftsh4-5 and LGOoe ftsh4-5 mutants, causing patches of overgrowth and undergrowth to accumulate (Fig. 9E). These patches of overgrowth and undergrowth in ftsh4 mutants cause the accumulated growth to locally deviate from the smooth basipetal growth gradient, leading to asymmetries in sepal shape. Together, this demonstrates that uncorrelated growth fluctuations accumulate evenly over time and space, leading to uniform sepal size and shape. Correlated growth fluctuations reduce averaging, causing patchy accumulation of growth over time and space, which leads to variable mature organ size and shape.

The variable sepal size and shape of ftsh4-5 sepals indicates a defect in developmental robustness rather than development of a particular shape. In ftsh4-5, each sepal has a different spatial localization of growth patches, generating variability in the population. However, growth in all ftsh4-5 sepals is patchy, which can be identified from all three replicates (or the nine replicates, considering all genotypes including the ftsh4-5 mutation). Although replicates have different organ shapes, this still allows analysis of developmental robustness because statistical analysis is based on the cells within the replicates, resulting in a greater sample size. Therefore, patchiness and decreased growth heterogeneity are characteristic of ftsh4-5, leading to a loss of developmental robustness.

It has previously been proposed that decreased spatial or temporal variability in growth fluctuations disrupted robust development of size and shape (Hong et al., 2016). This was supported by a 2D model of a growing shape. Growth fluctuations that were random over space and time caused all parts of the shape to have similar amounts of growth, leading to uniform size and shape. Perfectly homogenous growth also would also create uniform size and shape, but this is not representative of tissue growth. When the model was modified so that the assigned growth rate never changed during growth (which means that temporal fluctuations are 100% correlated) and/or the size of the growth regions was increased (increased spatial correlation), this caused parts of the shape to grow more than others, creating variability in the final shapes when the model is run multiple times (Hong et al., 2016).

Here, we time-lapse imaged sepal development over long periods of time, which allowed us to understand correlations in growth fluctuations and spatiotemporal averaging in vivo. We found that growth fluctuations in wild type are not temporally or spatially correlated. As a result, the cumulative growth of each cell approaches the target growth rate over time and causes the mean cell growth of a group of cells to be closer to the target growth rate than an individual cell. This is spatiotemporal averaging in vivo, and it is supported by the 2D model version with random growth fluctuations.

The ftsh4-5 mutation causes increased temporal correlations in cell growth fluctuations, which can be seen in 24 h growth rates as groups of cells that grow relatively normally and groups of cells that grow slowly over multiple time intervals. Growth direction variability in ftsh4-5 mirrors the patchy growth localization. Over time, groups of slower growing cells cause patches of decreased cumulative growth which deviate from the smooth accumulation of growth in the basipetal gradient. It is possible that slow growing patches are related to inheritance of dysfunctional mitochondria in cell lineages because ftsh4 mutants have severe mitochondrial defects (Urantowka et al., 2005). This may lead to ROS accumulation which causes the sepal morphology phenotypes (Hong et al., 2016). In wild-type sepals, ROS are a maturation signal that accumulates in a basipetal gradient as the sepals mature (Hong et al., 2016), suggesting that cells in high ROS patches in ftsh4-5 may prematurely mature.

The juxtaposition of these groups of cells with different cumulative growth will lead to patchy tissue expansion, and ultimately abnormal tissue shape. This can be seen in some of the live imaging replicates, as the tissue extends further on the side with more cumulative growth. If the locations of these patches are random in every sepal, then each sepal will have a different shape. The correlated growth fluctuations, patchy cumulative growth, and variable organ size and shape that are characteristic of ftsh4-5 in vivo growth is like the 2D model version with correlated growth. To summarize, random growth fluctuations average in space and over time and lead to robust sepal development. The increased temporal correlations of growth in the ftsh4-5 background causes accumulation of growth to be patchy instead of averaged and leads to a loss of robust sepal development.

Spatiotemporal averaging is likely an emergent phenomenon that results from the interplay of many factors/processes. For example, increased mechanical stress on the cell wall from one cell growing faster could lead to opening of mechanosensitive calcium channels, similar to how tension in the growing root tip opens the mechanosensitive calcium channel PIEZO (Mousavi et al., 2021). Calcium signature interpretation is complex and allows the cell to distinguish between different types of mechanical perturbation (Howell et al., 2023), suggesting that calcium influx could lead to a variety of cell responses. Growth can influence microtubules, which orient parallel to tension in a tissue (Hamant et al., 2008; Sampathkumar et al., 2014; Verger et al., 2018) and parallel to tension created by fast growth from trichome differentiation (Hervieux et al., 2016). Increasing cortical tension in a rectangular cell also increases transverse microtubule alignment parallel to tension (Colin et al., 2020). Changes in microtubule arrangement would likely change cellulose arrangement (Paradez et al., 2006) and thus cell expansion (Coen and Cosgrove, 2023; Hervieux et al., 2016). As the cell wall affects growth, this would in turn change the tension in nearby cells and cell walls and trigger the same signaling cascade. This could create a feedback loop that causes growth to fluctuate in cells and between neighboring cells. In this scenario, heterogeneity would emerge from a variety of factors and responses in the tissue and would be an emergent phenomenon.

Accession Col-0 plants are used as wild type and all mutants are in Col-0 background as well. Isolation of the ftsh4-5 mutant is described in Hong et al. (2016). ATML1p::LGO (LGOoe) is from Roeder et al. (2010). The membrane marker p35S::mCitrine-RCI2A was crossed into lgo-2, LGOoe and lgo-2 ftsh4-5. 35S::mCitrine-RCI2A was transformed into LGOoe ftsh4-5 due to silencing. The epidermal-specific membrane marker ML1::mCitrine-RCI2A was used in ftsh4-5 plants due to silencing.

The lgo-2 mutation can be PCR genotyped with the primers CTTCCCTCTCACTTCTCCAA, CCGAACACCAACAGATAATT and TTGGGTGATGGTTCACGTAGTGGG. The wild-type band is 546 base pairs and the lgo-2 band is 753 base pairs. The ftsh4-5 mutation can be PCR genotyped with the primers AGAAAGGACTCACTTTAAAGAACAGCCATG and TCCTCTGTCCTCGATAAGAGCTCC followed by digesting the product with Nco1, which produces a wild-type band of 103 base pairs and a ftsh4-5 band of 124 base pairs. The LGOoe plants are easily distinguished by their phenotype of curled leaves.

Photographs of mature flowers and flower buds were taken using either a Canon A610 or an Excelis 4K camera mounted on a Zeiss Stemi stereomicroscope. Sepals of mature flowers were dissected, placed on a black background, flattened under a slide and photographed using the Canon A610 camera mounted to a dissecting microscope. Python programs, as described and available in Hong et al. (2016), were used to trace the outline of the sepal shapes and converted into contours of the shape and measurement of area. Shapes were normalized by size and then the variability of shape was compared between genotypes.

Inflorescences were dissected and mounted in apex culture media (Hamant et al., 2014). Media containing 2.3 g/l Murashige and Skoog, 1% sucrose and 0.1% MES was brought to a pH of 5.8 with KOH, and agarose was added to a concentration of 1.2%. After autoclaving, media was supplemented with vitamins (final concentration of 100 µg/ml myoinositol, 1 ng/ml nicotinic acid, 1 ng/ml pyridoxine hydrochloride, 1 ng/ml thiamine hydrochloride, 2 ng/ml glycine) and plant preservative mixture from Plant Cell Technology, which was used as 1000× stock. Plants then grew in 16 h light/8 h dark conditions on the media and were imaged using a Zeiss LSM710 confocal microscope once every 24 h for 6 days. Abaxial sepals were imaged because they face outwards, making them the most accessible for imaging. Flowers at stage 5 of development, when the sepals are about to enclose the floral meristem (Smyth et al., 1990), were chosen for the start of time-lapse imaging. Our imaging captures earlier stages of development than had been imaged previously (Hong et al., 2016). A 20× water dipping objective with an NA of 1.0 [W Plan-APOCHROMAT 20×.1.0 DIC (US) VIS-IR] was used. A 514 laser with a power of 5% was used for excitation. The voxel size was x=0.4151, y=0.4151, z=either 1.5 μm or 0.5 μm. The wavelengths detected were 519-622 nm. The zoom was 1. The pinhole was 2.17 airy units=3.4 μm.

MorphoGraphX was used for image processing (Barbier de Reuille et al., 2015; Strauss et al., 2022). One of two methods was used to detect the surface. Method one begins by trimming voxels of a trichome if one was present, then Stack/Filters/Gaussian Blur Stack (X sigma=1, Y sigma=1, Z sigma=1), Stack/Morphology/EdgeDetect (Threshold=3000-10,000, Multiplier=2.0, Adapt=0.3, Fill value=3000) to find the surface, then either Stack/Morphology/Closing (X Radius=1-10, Y Radius=1-10, Z Radius=1-10) or Stack/Morphology/Fill Holes (X Radius=1-10, Y Radius=1-10, Threshold=10,000, Depth=0, Fill value=30,000) to fix any holes and then manually trimming voxels of adjacent organs or empty space that were filled by the Fill Holes function. Method two made the surface using Stack/Lyon/Init Level Set (Up threshold=2-10, Down threshold=2-10), Stack/Lyon/Level Set Evolve (Default settings except View=5 and cancel after 5 to 15 rounds), Stack/Morphology/Edge Detect Angle, and Stack/Morphology/Closing (X Radius=1-10, Y Radius=1-10, Z Radius=1-10) and manually trimming voxels of adjacent organs. Then the mesh was created with the processes Mesh/Creation/Marching Cubes Surface (Cube size=5.0, Threshold=20,000), then 2-4 rounds (smaller meshes had 3-4 and larger meshes had 2-3) of Mesh/Structure/Subdivide and Mesh/Structure/Smooth Mesh (Passes=10, Walls Only=No). Then the mesh was segmented by projecting a 2 μm depth interval of the signal using Mesh/Signal/Project Signal (Min distance=2-8, Max distance=4-10) followed by Mesh/Segmentation/Watershed Segmentation (Steps=50,000). Lineage tracking was carried out by loading meshes for consecutive time points into mesh 1 and mesh 2 spots, overlapping mesh 1 (check scale box and increased size) and mesh 2 using the shapes of the cell lineages, then either manually or semi-automatically assigning parent labels. Parent labels were checked for errors by running Mesh/Cell axis/PDG/Check correspondence on the earlier time point. To make sure there were no cells on the periphery that were parent tracked but were partially cut off by the edge of the images in the later time point, Mesh/Heat Map/Heat Map Classic (change map checked, decreasing) was run, and Mesh/Heat Map/Heat Map Select (Lower=0, Upper=.999) was used to highlight cells that had ‘shrunk’. If the highlighted cells were at the edge of the segmentation, they were assumed to be a segmentation error and deleted. Then Mesh/Lineage Tracking/Save Parents was run on the later time point to save the parent labels as a csv file. Then Mesh/Lineage Tracking/Load Parents was run to load the csv file that was just created and then meshes were saved with the parent labels.

To make the 120 h cumulative cell division heat maps in Fig. 2 and Fig. S2, csv files specifying parent labels for the 0 h to 120 h time points were created from the 24 h parent label csv files using a python script to carry out multi-step lineage tracking as described in Hong et al. (2016). Then the corresponding parent labels were loaded onto the later time point using Mesh/Lineage Tracking/Load Parents. Mesh/Lineage Tracking/Heat Map Proliferation and Mesh/Heat Map/Heat Map Set Range (Min=1, Max=15) were run on the later time point to make the heat map and they were saved as csv files using Mesh/Heat Map/Heat Map Save.

To make the cell area heat maps in Fig. 3 and Fig. S3, Mesh/Heat Map/Geometry/Area and Mesh/Heat Map/Heat Map Set Range (Min=0, Max=4000) were run on each mesh, and csv files were saved with Mesh/Heat Map/Heat Map Save.

To make the 24 h proliferation heat maps in Fig. 4 and Fig. S2, Mesh/Lineage Tracking/Heat Map Proliferation and Mesh/Heat Map/Heat Map Set Range (Min=1, Max=4) were run on the later time point of each 24 h interval. Mesh/Heat Map/Heat Map Save was run to save the csv files.

To make the cell area heat maps with outlined divisions in Fig. 4 and Fig. S5, Mesh/Heat Map/Heat Map Classic (changed map checked, decreasing) was used to create the cell growth heat map, and then it was saved as a csv file using Mesh/Heat Map/Heat Map Save. Then the 24 h proliferation heat maps were loaded onto the later time point of the 24 h interval using Mesh/Heat Map/Heat Map Load. The Mesh/Heat Map/Heat Map Select (Lower threshold=2, Upper threshold=7) was used to outline the cells that had divided at least once. Then Mesh/Heat Map/Heat Map Load was used to load the cell growth heat map, and Mesh/Heat Map/Heat Map Set Range (Min=1, Max=3) was used to set the scale.

To make the vertex deformation heat map in Fig. S6, consecutive time points were loaded into MorphoGraphX with the parent labels active in the later time point. Then the processes Mesh/Deformation/Mesh 2D/Create Deformation Cell Surface and Mesh/Cell Axis/Deformation Gradient/Compute (Mode=Vertex) were used to calculate the deformation. Then Mesh/Signal/Rescale Signal (Zero as…=No, Percentile=0, Minimum=1, Maximum=2.5) was used to scale the heat map.

To artificially subdivide the giant cells in Fig. 6 and Fig. S10, a few giant cells were chosen to be deleted from the mesh based on nearby junctions that would be helpful landmarks. The cells were manually seeded as multiple cells using nearby junctions as landmarks, parent tracked as described above. Cell labels were outlined using Mesh/Selection/Select Labels (add the labels of the cells). Cell growth heat maps were created using Mesh/Heat Map/Heat Map Classic (changed map checked, decreasing, use manual range 1-3) on the later time point.

To make the 3-day area growth and principal directions of growth in Fig. 7, csv files specifying parent labels for the 24 h to 96 h time points were also made using a python script for multi-step lineage tracking as described in Hong et al. (2016). Then the corresponding parent labels were loaded onto the later time point using Mesh/Lineage Tracking/Load Parents. Mesh/Heat Map/Heat Map Classic (changed map checked, decreasing, use manual range 1-10) was run on the later time point, and Mesh/Heat Map/Heat Map Save was used to save the heat map as a csv file. Then the principal directions of growth were saved as a csv file using Mesh/Cell Axis/PDG/Check Correspondence then Mesh/CellAxis/PDG/Compute Growth then Mesh/Cell Axis/Cell Axis Save. Then the process /Unselect was run on mesh 1 or the mesh was reloaded, and the csv file was reloaded using Mesh/Cell Axis/Cell Axis Load. Then Mesh/Cell Axis/PDG/Display Growth Directions (Show axis=StrainMax, Color=black, Line width=5, Line scale=2) was used to display the principal directions of growth, Mesh/Heat Map/Heat Map Load was used to load the cell growth heat map that was saved as a csv file and Mesh/Heat Map/Heat Map Set Range (Min=1, Max=10) was used to adjust the scale.

To make the 24 h principal directions of growth in Fig. S13, both time points were loaded into MorphographX and then made in the same way as described above, but the conditions for Display Growth Directions were Show axis=StrainMax, Color=red, Line width=4, Line scale=10. The 3-day principal direction of growth files were re-loaded with Mesh/Cell Axis/Cell Axis Load and then displayed with the settings Show axis=StrainMax, Color=red, Line width=4, Line scale=2.

To make the heat maps of proximal-distal growth in Fig. 9, a custom axis was created from a heat map of distance from cells at the tip of the sepal, then the proportion that the principal directions of growth were aligned with the custom axis was used to create heat map values. First, to create the distance heat map, cells were manually selected and then the process Mesh/Heat Map/Measures/Location/Cell Distance was run. This was often repeated with different cells selected until the heat map appeared to measure distance accurately instead of creating a gradient that was curved or crooked. Then the heat map was saved as a csv file with Mesh/Heat Map/Heat Map Save. Then the principal directions of growth were loaded with Mesh/Cell Axis/Cell Axis Load. Then the distance heat map was loaded with Mesh/Heat Map/Heat Map Load. Then Mesh/Cell Axis/Custom/Create Heatmap Directions (Project Directions…=Yes, Normalize=no) and Mesh/Cell Axis/Custom/Smooth Custom Directions (Weight by cell area=Yes, Project directions…=Yes) were used to create the axis from the distance heat map. Then Mesh/CellAxis/PDG/DisplayGrowth Directions (Heatmap=CustomX Growth Proportion, ScaleHeat=Manual, Heat min=.45, Heat max=.65, Show axis=StrainMax, Color+=black, Line width=5, Line scale=2) was used to create a heat map of the ratio of the amount that the principal directions of growth were parallel with the custom axis to the amount that they were perpendicular to the custom axis. Then the heat map csv files were saved and the values were modified by 2 x/(x+y)−1 so that 1 corresponds to perfectly proximal distal growth and −1 corresponds to perfectly medial-lateral growth. Then the modified heat map values were loaded onto the meshes using Mesh/Heat Map/Heat Map Load and Mesh/Heat Map/Heat Map Set Range (Min=−0.1, Max=0.3) was used to adjust the scale.

To quantify the amount of error in the segmented boundaries of cells, a mesh was re-segmented by a different individual and the change in cell size between the original and the re-segmented mesh was measured (Fig. S15). The standard deviation in cell size fold change was 0.04 with a mean of 1.00-fold change. Further, most of the differences in cell size is due to user-preferences for segmenting cells around trichomes, which distort the mesh, and cells at the periphery of the mesh, which were more carefully checked in the real dataset during the process of lineage tracking.

After the mapping to spherical coordinates, we align each sepal along the average principal direction of cell elongation to define the proximal-distal axis. To find fluctuations, we first fit a third order polynomial p(y) to the log-growth rates (which show area doubling per 24 h) along the proximal-distal axis for each time interval (t, t+dt). The fluctuations are calculated as the deviations of the growth rate from that reference. This procedure is done both for 24 h intervals (days 2, 3, 4, 5, 6) as well as for the net growth in the 3-day interval from 24 h to 96 h. Patchiness in cumulative growth is calculated from the standard deviation in the 3-day growth fluctuations after averaging locally over nearest neighbors. We calculated 24 h patchiness or spatial variability using the same method as patchiness but with fluctuations over 24 h intervals. Temporal variability is calculated using data from the three pairs of time intervals and three replicates are pooled for each genotype to calculate the correlation. Each growth rate pair is weighed with the size of the lineage's parent cell at day 2, ⁠, in the correlation calculation. The lineage's parent cell is used as weight in the calculation of the correlation coefficients.

Three-day growth fluctuations and cell size at the start of the 3-day interval are used to calculate the correlation between growth and cell size. Three-day growth fluctuations and 3-day measure of the amount of proximal distal growth are used to calculate the correlation between growth and cell size. The size of the lineage's parent cell is used to weight the data for the calculation of the correlation coefficients.

One-way ANOVA with genotype as a variable and Tukey tests were used to test for differences in shape variability, cumulative proliferation and number of non-dividing cells. Kendall rank correlation was used to test whether there was a relationship between area growth and proximal-distal growth in each genotype. Wasserstein tests were used to create the principal coordinate analysis plots. R scripts are available at doi:10.17605/OSF.IO/7NMK. The R version 4.2.2 was used for analysis. The R packages used were ggplot2_3.4.1, tidyr_1.3.0, stringr_1.5.0, dplyr_1.1.0, twosamples_2.0.0, RColorBrewer_1.1-3, ggsci_2.9, ggthemes_4.2.4, ggplot2_3.4.1.

We thank Lilan Hong, Shuyao Kong, Avilash Singh Yadav, Maura Zimmermann and Michelle Heeney for helpful discussions and comments on the manuscript. We thank Cornell Statistical Consulting Unit (Matt Thomas) for helping with analysis of cell area, proliferation and cell growth in R. We thank Mingyuan Zhu and Richard Smith for expert image analysis advice. We thank Olivier Hamant, Arezki Boudaoud, Corentin Mollier and Ya Min for helpful discussions. We thank Avilash Singh Yadav for technical help with an experiment.

The peer review history is available online at https://journals.biologists.com/dev/lookup/doi/10.1242/dev.202531.reviewer-comments.pdf