A Growth-Based Framework for Leaf Shape Development and Diversity

1How gene activity translates into distinct organ morphologies remains poorly understood (e.g.,, ). To understand the complex interactions that link gene action to tissue form, we need quantitative data on cellular growth at high spatial and temporal resolution, which are technically challenging to acquire. Such data are also difficult to interpret because local gene activity can have complex non-local effects on tissue deformations, which arise from interactions between genetically specified growth and tissue mechanics. We also do not yet understand how evolutionary changes in gene activity alter how growth, patterning, and differentiation interact to produce diverse organ forms.

2Plant leaves are an attractive system in which to address these questions as they grow from almost indistinguishable primordia into shapes that vary tremendously among species. Leaves can be simple, with smooth undivided margins (the botanical term for leaf edge), or complex, with protrusions of different size and geometry. The leaves of A. thaliana are simple and bear small marginal protrusions called serrations, while those of its relative, C. hirsuta, are dissected into distinct leaflets that each resemble a simple leaf (Figures 1A and 1B). Genetic studies have identified KNOX (Knotted1-like homeobox) and RCO (REDUCED COMPLEXITY) homeobox genes as important molecular regulators of leaf complexity that are involved in the evolutionary diversification of leaf form. While target genes are known for some KNOX proteins, we still do not understand how KNOX and RCO affect cell- and tissue-level growth during leaf primordium development. Furthermore, we lack information on the growth of morphogenetically important domains at the margin and base of developing leaves, and cell-level fate maps for leaf primordia do not exist. It thus remains unclear how local growth regulation at the margin integrates with global patterns of growth, proliferation, and differentiation to produce divergent leaf forms. For example, current evidence indicates that growth polarity is vital for leaf geometry, yet the degree to which this polarity is a local or global feature of organ development and how it shapes leaf form remain unclear. Computational modeling offers one way to address these questions, by enabling us to investigate how multiple processes interact to create geometry in a growing tissue.

3Here, we identify differences in growth patterns that yield simple, elliptical A. thaliana leaves versus dissected C. hirsuta leaves with a broad terminal leaflet. We use live imaging and genetics alongside computational modeling and analyses of growth to deconstruct these two divergent leaf forms into their cell-level constituent elements: the amount and direction of growth and the rate of differentiation. Surprisingly, we find that key features of growth are conserved between these two leaf forms. Differences in leaf geometry originate from two distinct processes that act in C. hirsuta, but not in A. thaliana leaves. In the first process, which requires the KNOX gene SHOOTMERISTEMLESS (STM), delayed differentiation and slower but prolonged growth throughout the leaf primordium increase the size and number of protrusions initiated by a conserved auxin-based pattern-generating mechanism. This process also allows protrusions to grow for longer in a polarized fashion. In the second process, local growth inhibition, mediated by the RCO gene, accentuates growth differences created by marginal patterning. We demonstrate the predictive power of our approach by experimentally reconstructing key aspects of the dissected C. hirsuta leaf form in A. thaliana.

4We developed an imaging protocol (see STAR Methods) to understand how the balance of conserved versus diverged cellular growth patterns produce the simple leaf forms of A. thaliana and the dissected leaves of C. hirsuta (Figures 1A and 1B). We measured leaf primordium growth at cellular resolution, from its emergence until 7–8 days after initiation (DAI), when shape divergence between the two species is established. Our measurements included the leaf margin where serrations and leaflets form (Figure 1; Video S1). We computed complete lineage maps from these data to understand how cells in the early primordium contribute to the development of the mature leaf form. Using the lineage maps, we quantified cell growth parameters that affect form (see STAR Methods), including growth amount (rate of cell-area increase), directionality (anisotropy, the ratio of expansion in the max. and min. principal directions of growth), and cell proliferation. To assess the progression of tissue differentiation, we also measured cell size, stomatal density, and pavement cell geometry.

5We observed that despite their different final forms, leaves from these two species shared three commonalities in their growth patterns (Figures 1C–1H and S1A–S1S). (1) During leaf initiation (1–3 DAI), primordium growth is uniform and anisotropic. (2) After the initiation phase (∼3–4 DAI), dynamic marginal growth patterns are established in lateral regions, which are defined by changing patterns of proliferation, growth, and anisotropy that accompany protrusion outgrowth (Figures 1C–1F and S2A–S2F). (3) Later, in association with the basipetal (i.e., tip-to-base) progression of differentiation, tissue-dependent growth patterns emerge, with mainly isotropic growth occurring in the blade and anisotropic growth occurring along the margin circumference, midrib, and petiole (Figures 1E, 1H and S1L–S1S). Notably, in both plants, fronts of differentiation initiated at the leaf tip and each protrusion tip, rather than as a single front, and progressed toward the leaf base (Figures 1C–1D, 1G, 1H, S1A–S1D, and S2A–S2F). Proliferation decreased abruptly in the midrib/petiole region at ∼4 DAI (Figures S1A–S1D) with differentiation onset, while in the rest of the blade, proliferation decreased gradually, coinciding with the basipetal progression of differentiation. These results indicate that species-specific differences in leaf form emerge in the context of these three conserved growth patterns.

6To identify in an unbiased manner the differences in cellular growth distribution that yield these distinct leaf forms, we quantified and compared the growth and proliferation of clonal lineages of each species from 3–7 DAI (Figures 1I and 1J). In this context, we also computed growth alignment graphs by mapping growth and proliferation, according to the location of cells along a leaf’s Proximal-Distal axis (P-D axis, location assessed at 3 DAI, Figures 1K–1N). This approach provides a developmental biology equivalent of a sequence alignment, and we used it to determine the balance of conservation versus divergence in cell-level growth properties at a given developmental stage in diverse genotypes. Although primordium length was comparable between species at both 3 and 7 DAI (∼150 and ∼800 μm, respectively), the P-D distributions of growth and proliferation differed (Figures 1I–1N). Growth and proliferation were restricted to proximal regions in A. thaliana but were broadly distributed in the C. hirsuta blade (Figures 1I and 1J), increasing the contribution of the distal primordium to the leaf surface (Figures 1K–1N) and correlating with the emergence of a broad terminal leaflet. Increased distal growth in C. hirsuta, compared to A. thaliana, coincided with the delayed onset of tissue-dependent growth patterns (Figures 1C–1H), delayed differentiation (Figures S1E–S1J), and extended dynamic marginal growth (as indicated by the emergence of additional protrusions in the terminal leaflet, Figure S1K). Thus, the distribution of growth and proliferation in C. hirsuta leaves is shifted distally along the P-D axis relative to A. thaliana. This shift is associated with prolonged marginal patterning and a global delay in differentiation.

7We next investigated the local growth features that underlie the different leaf protrusion shapes of each species. Protrusion shape is influenced by the growth differential between rapidly growing protrusion tips and slow-growing adjacent tissues. We observed large differences in this growth differential between species (Figures S1T and S1U). Compared to serrations, the duration of anisotropic growth was extended in leaflets (2–6 DAI in leaflets versus 2–5 DAI in serrations; Figures 1E–1F, S2B, and S2E), as was the duration of reduced growth and proliferation in the sinus regions between leaflets (3–7 DAI in leaflets versus 3–5 DAI in serrations, Figure 1C, 1D, S1A, S1B, S2A, and S2D). Consequently, in C. hirsuta, both increased protrusion outgrowth and reduced growth at the protrusion base contributed to leaflet formation (compare Figure S1T and S1U). Reduced growth at the protrusion base likely reflects local growth inhibition but may also result from global differences in the growth of primordia (C. hirsuta growth is almost half that of A. thaliana over 1–3 DAI, Figures S1H and S1I). Thus, reduced growth at the protrusion base distinguishes leaflets in C. hirsuta from serrations in A. thaliana and likely involves both local and global growth regulation.

8The hypothesis that both global and local aspects of growth contribute to the increased growth inhibition between protrusions in C. hirsuta leaves raised the question of how these two different growth modes interact to shape leaf geometry. To investigate this, we examined the origin of protrusions and sinuses relative to the global (organ-wide) growth patterns of the leaf blade, petiole, and midrib. Based on patterns of growth, proliferation, and cell morphology (Figures 1C–1J and S1A–S1D), we divided 3 and 7 DAI primordia into three regions: (1) blade, (2) petiole and midrib, and (3) the slowly growing sinus cells that lie adjacent to emerging protrusions (Figures 1O–1P, see STAR Methods). We found that in A. thaliana, sinuses initiated in the leaf blade and were thus always surrounded by rapidly growing blade cells (Figure 1O). By contrast, at 3 DAI in C. hirsuta, growth-repressed zones appeared directly adjacent to the midrib (Figure 1P), preventing blade establishment between protrusions and enabling the formation of a dissected leaf. Thus, sinus establishment in the blade is associated with a simple leaf, and in the midrib, with a dissected leaf.

9These results suggest that three key differences distinguish dissected leaves from simple ones: (1) the local context in which protrusions initiate (midrib versus blade); (2) decreased growth at the base of initiating marginal protrusions; and (3) a global change in growth pattern, coinciding with delayed differentiation and marked by increased lateral and distal growth and by reduced growth in proximal and medial regions. Thus, both global and local factors influence growth to shape simple and dissected leaves.

10Our data suggest that differences in tissue growth during the patterning of marginal protrusions help to create distinct leaf forms. The placement and growth of marginal protrusions requires polar auxin transport, which is controlled by the auxin efflux carrier PIN-FORMED1 (PIN1, Figures 2A and 2B) and is influenced by the transcription factor CUP-SHAPED COTYLEDON2 (CUC2). To investigate how components of the auxin-PIN1-CUC2 module influence leaf growth and differentiation, we first examined the role of auxin. Activity of this hormone, as reported by the DR5 auxin activity sensor, marks outgrowing protrusions in both A. thaliana and C. hirsuta leaves. Two lines of evidence indicated that auxin activity maxima influence the rate and direction of growth. First, we found that initial growth in protrusions is rapid and anisotropic (Figures 2D, 2F, S2A, S2B, S2D, and S2E). Second, these points of rapid anisotropic growth are absent in the leaves of C. hirsuta and A. thaliana plants treated with the polar auxin-transport inhibitor, 1-N-naphthylphthalamic acid (NPA) (Figures S3A–S3J), which lack auxin maxima. NPA treatment generated simple leaves in both species, and a growth pattern also observed in the leaves of pin1 and cuc2 A. thaliana mutants (Figures 2G–2I and S4A–S4G; Video S2), which also lack discrete marginal auxin maxima. By contrast, in addition to its role in patterning auxin maxima, CUC2 appears to inhibit growth. Following the establishment of auxin maxima, CUC2 is expressed primarily in the sinuses of A. thaliana leaves, where growth and proliferation are reduced (Figures 1C, 1I, 1J, S1A, and S1T), and this growth inhibition is lost in cuc2 mutants (Figures 2G and S4B). Thus, auxin and CUC2 shape the leaf margin by locally increasing growth at protrusions and decreasing growth at their flanks, respectively.

11To assess the role of PIN1 in tissue growth polarity in leaves, we monitored its distribution during leaf development in both species. During leaf initiation, PIN1 was uniformly expressed, with its expression later coinciding with regions of active marginal patterning (Figures 2A–2B and S5A–S5E). PIN1 polarities pointed toward protrusion tips, mirroring the directions of growth at emerging protrusions (Figures 2C–2F, S5B, and S5D). We did not detect PIN1 expression in the remainder of the blade, where we observed isotropic growth in time-lapse samples (Figures 1E and 1F). In C. hirsuta primordia, prolonged PIN1 expression coincided with delayed differentiation (Figures 2B and S5C) and with the late emergence of protrusions in the terminal leaflet (Figure S1K). To test whether PIN1 expression can influence growth direction following differentiation, we expressed PIN1 throughout the L1 layer in C. hirsuta, including in the distal leaf blade where it is typically not expressed (Figure S5F). This had no apparent effect on patterning or leaf shape, consistent with previous results in A. thaliana. Thus, our results indicate that PIN1 localization influences growth polarities but that its action is local rather than global and lost following differentiation.

12We next assessed how marginal patterning relates to differentiation. Differentiation fronts were initiated at marginal protrusions (Figures 1C–1D, S1A–S1D, and S2A–S2F) and their formation depended on the auxin-PIN1-CUC2 module (Figures 2G–2I, S3A–S3J, and S4B–S4G). We therefore reasoned that auxin maxima may direct the formation of these differentiation fronts. To test this, we treated A. thaliana leaves with auxin and observed accelerated growth and differentiation (Figures 2J–2K and S3K–S3S), indicating that auxin can promote both growth and differentiation and that auxin maxima help to establish multiple differentiation fronts.

13We developed a physically based computational model using the finite element method (FEM) to further investigate how the auxin-PIN1-CUC2 module controls the dynamic marginal growth patterns that underlie leaf shape and to understand how margin growth is integrated with overall leaf blade growth (Figure 3). We first modeled leaf growth when margin patterning was disrupted. Our results indicate that, in this case, leaf development converges on a common growth pattern characterizing pin1 and cuc2 A. thaliana mutants (Figures 2G–2I and S4B–S4G) and development of both species following NPA treatment (Figures S3A–S3J). Each of these perturbations generates a simple leaf with smooth margins. We thus used this common growth pattern to characterize the bulk growth of the leaf (Figures S4H and S4I and Methods S1). We assumed that growth of the leaf depends on tissue type (blade versus midrib/petiole) and growth rates decrease with the basipetal progression of differentiation. This model reproduced the convergent development and form observed when margin patterning is perturbed, including the emergence of a radiating pattern of anisotropy at the blade-petiole junction (Figure S4I and S4J).

14We then extended this model to incorporate both molecular regulation at the leaf margin (Figure 3A and Methods S1) and bulk interior growth. For margin growth regulation, we assumed that (1) PIN1 locally regulates growth polarities by organizing auxin maxima; (2) auxin locally increases growth rates, accelerates differentiation, and negatively regulates CUC2; and (3) CUC2 locally inhibits growth and permits the organization of auxin maxima by PIN1. The resulting model reproduces the growth patterns and leaf shapes observed during A. thaliana development (Figures 3B and 3C; Video S3). Thus, by combining time-lapse imaging with simulations of growth and patterning in a physically connected leaf blade, we obtained an integrated model of auxin-PIN1-CUC2-mediated growth regulation that conceptualizes how marginal and non-marginal tissue growth may interact to create a simple serrated leaf form.

15In our simulation, we observed the emergence of an interspersed distribution of auxin activity maxima and CUC2, as has been observed in confocal micrograph snapshots. However, it is possible that the mechanism generating this interspersed distribution cannot be inferred from snapshots. For example, an oscillatory mechanism (as in somitogenesis; ) could sequentially establish auxin maxima and CUC2 domains. Or distal CUC2 expression could organize the neighboring auxin maximum (as in ectopic abaxial outgrowths of kanadi1;2 mutants; ). Both mechanisms could generate auxin maxima together with a strong CUC2 expression domain on the proximal or distal side of a protrusion. If CUC2 inhibits growth, then the asymmetric distribution of CUC2 should cause the protrusion to be asymmetric from emergence. By contrast, if a protrusion is flanked on both sides by CUC2, our model predicts it to be symmetric at initiation and to only later become asymmetric due to the proximodistal distribution of growth rates.

16To investigate these possibilities, we live-imaged CUC2 and DR5 expression during serration initiation in A. thaliana leaves. Consistent with our model’s predictions, we observed that the auxin maximum that patterns a serration is organized in a CUC2-expression domain, such that DR5 expression precedes the elimination of CUC2 at this site (Figure 3D). As in our model, we found that high growth at the auxin maxima, juxtaposed against slow growth in adjacent CUC2-expressing sinuses, created a growth differential that leads to the emergence of a symmetric protrusion. Thus, our current model captures how local growth regulation by marginal patterning involving auxin, PIN1 and CUC2 influences leaf shape in A. thaliana. It also links gene activities, as studied in real time, to specific aspects of growth amount and direction.

17We next set out to explore how both global and local growth inputs are integrated to generate leaflets in C. hirsuta (Figure 1). To do so, we constructed a geometric model of margin development (Figure 4A) (see Methods S1; ) to examine how growth activators, repressors, and differentiation interact to form marginal protrusions. In this model, the local growth of lateral protrusions in the context of global leaf blade extension generates periodic outgrowths, with forms dependent on the model’s parameter values (Figure 4B).

18We explored the parameters that affect growth at the protrusion base to evaluate their impact on margin form (Figure 4B and Video S4). In the model, decreased longitudinal growth produced more focused outgrowths. By contrast, increased longitudinal growth impeded the formation of focused protrusions by smoothing outgrowths. Increasing the duration of marginal patterning led to the initiation of intercalary protrusions but did not affect protrusion form. Extending the growth domain increased protrusion size without otherwise affecting their form. Protrusion size was further increased by both slowing longitudinal growth and by extending the growth domain. These effects coincide with the suggested role of the KNOX gene STM in retarding growth and differentiation in C. hirsuta leaves. However, protrusions still lack the narrow base found in leaflets. By introducing a domain at the protrusion base that resists longitudinal extension, the model generates outgrowths with a narrow base (Figure 4B and Video S4), thereby eliminating the characteristic asymmetric shape of serrations in A. thaliana. Local growth inhibition in this region is consistent with the proposed function of the RCO gene at the base of leaflets in C. hirsuta. In summary, our model predicts three parameters, which together contribute to the contrasting leaf morphologies of C. hirsuta and A. thaliana: (1) a global decrease in longitudinal growth, (2) an extended duration of growth, and (3) growth inhibition at leaflet bases. We hypothesized that these parameters can be mapped to the actions of STM and RCO, with STM acting to globally reduce growth and delay differentiation (1 and 2) and RCO acting to locally inhibit growth at the base of emerging protrusions (3).

19To test predictions from our geometric model in the context of mechanically connected tissues, we analyzed the roles of RCO and STM genes in leaf development. These genes are active in leaf primordia of C. hirsuta, but not A. thaliana. STM is expressed in the pluripotent shoot apical meristem of both species and excluded from A. thaliana leaves, while RCO is absent from the A. thaliana genome. To assess how these genes influence global differences in primordium growth, we compared fate maps of wild-type leaf cells at 3 DAI to those of plants with modified STM and RCO expression (Figures 4C–4L). C. hirsuta leaves can be distinguished from A. thaliana’s by the increased contribution of distal cells to the leaf blade (Figures 4G and 4J). This feature is not accounted for by RCO, as expressing RCO in A. thaliana leaves from its own regulatory sequence—or eliminating it in the C. hirsuta rco mutant—did not alter this pattern of distal cell contribution (Figures 4H and 4K). However, this feature is lost in the simple leaves of C. hirsuta loss-of-function stm mutants (Figure 4L) and appears in A. thaliana when STM expression is driven from a leaf margin promoter that is active from 2 DAI onward (Figures 4I and 4W–4X; BLS, Figure S6W; ). These results show that RCO and STM expression during leaf development increases leaf complexity (Figures 4C–4F) but that they differ in their effects on the contribution of cells to the primordium.

20We then examined how the action of each gene translated into cellular behaviors. As RCO does not affect the contribution of distal cells to the primordium, we reasoned that it might affect leaf development locally, consistent with its proposed role as a local growth inhibitor. Loss of RCO activity in C. hirsuta and introduction of RCO activity in A. thaliana did not affect the global distribution of growth (Figure 4M, 4O, and S6A–S6D and Video S5) and differentiation (Figures 4N, 4P, S6E–S6H, S6S, and S6T; for wild type see: Figures 1C and 1G, A. thaliana; Figure 1D and 1H, C. hirsuta), or marginal patterning (PIN1 expression and the order of protrusion initiation, compare Figure S5G and S5J to S5H and S5K; Figure 1C to Figure 4O; and Figure 1D to Figure 4M). Instead, when expressed in either species, RCO inhibited local growth (Figure 4M, 4O, and S2G compared to Figures 1C and 1D; S2A) within its restricted expression domain at the base of emerging protrusions (Figures 4U and 4V). Thus, RCO is required for local growth repression at the base of protrusions but has no apparent global effects on leaf development.

21Our fate maps show that STM increases the relative contribution of distal cells to the primordium (Figures 4G–4L). We thus reasoned that it might broadly influence leaf development. Time-lapse imaging of C. hirsuta stm mutants and A. thaliana BLS::STM leaves confirmed that STM broadly affects patterns of growth, proliferation, and differentiation. Growth, proliferation, and differentiation were strongly accelerated in C. hirsuta stm mutant leaves (Figures 4Q, 4R, S6J, S6N, S6P, S6R, and S6V; Video S5), concomitant with an early decrease in PIN1 expression (Figures S5J and S5L) and a reduction in the lateral growth of emerging leaflets (Figure 4Q). Conversely, compared to A. thaliana wild-type leaf primordia (Figures 1C and S1A), BLS::STM primordia showed significantly reduced growth and proliferation (Figures 4S, S6I, and S6U and Video S5), delayed differentiation (Figures 4T and 1G), a broader domain of PIN1 expression and prolonged margin patterning (Figure S5G, S5I, and S6Q). Growth reduction in BLS::STM leaves was progressively restricted to proximal regions of the primordium (Figures 4S, S6M, and S6O) and was most apparent adjacent to emerging protrusions, where differentiation was particularly protracted (compare Figure 1G and S2C with Figures 4T and S2L). Nevertheless, increased growth at protrusion tips was comparable to WT but was maintained for longer (Figure 4S, S2J, and S2K). Thus, expressing STM in A. thaliana leaves increases the contribution of cells in distal and lateral regions to the early primordium (Figures 4G and 4I), shifting cellular growth patterns toward those of C. hirsuta (compare Figures 1C–1H, 4S–4T, S1A, S1B, S6I and S6M). Our observations suggest that STM retards early growth while delaying tissue maturation, thus prolonging the duration of growth and patterning. Notably, this STM-dependent redistribution of leaf growth might account both for the formation of lateral leaflets and the broad terminal leaflet that distinguish C. hirsuta from A. thaliana, consistent with the loss of both these features in C. hirsuta stm mutants (Figures 4G, 4I, 4J, and 4L).

22We observe that STM increases leaf complexity by delaying differentiation. However, accelerated differentiation can also increase leaf complexity, as seen in A. thaliana plants overexpressing KIP-RELATED PROTEIN2 (KRP2) under the 35S promoter (Figures 5A and 5B; ). Thus, both delayed and accelerated differentiation can increase leaf complexity. We investigated this contradiction by recording time-lapse images of p35S::KRP2 leaves (Figure 5C–5J), which confirmed the early onset of differentiation, relative to wild-type (∼3 DAI versus ∼5 DAI in wild type; compare Figures 5C–5J with Figures 1C, 1G, S1A, and S1C). p35S::KRP2 leaves initiated slow-growing symmetric serrations and sharp sinuses that were maintained over time, unlike in wild-type leaves (Figure 5C). Thus, a common feature of BLS::STM, RCOg and p35S::KRP2 leaves was decreased growth in the regions surrounding initiating protrusions. These observations indicate that a slow growth context enables the maintenance of more prominent protrusions, regardless of the differentiation status of surrounding tissue, as also suggested by our geometric model (Figure 4B).

23Our observations indicate that differences in A. thaliana and C. hirsuta leaf development include the local modification of growth during patterning and a global redistribution of growth that results from delayed differentiation (Figures 1, 2, and 3). Alone, neither of these features generated a dissected leaf (Figures 4 and 5), leading us to hypothesize that they act together to produce leaflets. In agreement with this hypothesis, the combined expression of RCO and STM in A. thaliana double transgenic plants reproduced key aspects of the C. hirsuta dissected leaf form (Figures 6A–6J), including a broad terminal leaflet. In A. thaliana plants expressing RCOg-VENUS (RCOg-V) and BLS::STM transgenes, protrusions were completely separated from each other and supported by a narrow base (Figure 6I). RCO expression localized to the petiolules of both terminal and lateral leaflets (Figures 6Q and 6R), and the vascular architecture of RCOg-V; BLS::STM leaves resembled that of C. hirsuta rather than A. thaliana leaves (Figures 6K–6P).

24These results suggest that growth inhibition at the base of emerging protrusions, combined with an increase in their outgrowth, can convert a serration into a leaflet. To test this idea, we quantified the overall form of emerging protrusions in our time-lapse series by using a triangle to approximate protrusion shape (Figure 6S, Methods S1). Our analysis showed that during serration development, the protrusion base quickly increased in width and gradually increased in length. By contrast, in leaflets, the protrusion base remained narrow while the protrusion elongated substantially. Notably, leaflets remained symmetric, whereas serrations adopted an asymmetric form during development (Figure 6S). Measurements of mature leaves are consistent (Figure 6T) and, thus, indicate that leaflets result from the combined effects of BLS::STM and RCOg on shape. Qualitatively, the changes in serration and leaflet shapes (Figures 6S and 6T) were consistent with the changes in growth predicted by the geometric model to increase the prominence and symmetry of protrusions (Figure 4B), specifically: the local effects of RCO inhibiting growth at the protrusion base, and the global effects of STM in slowing the rate of growth and differentiation, while prolonging growth duration. However, the simulations shown in Figure 4B evidently do not reproduce the narrow stalk observed in leaflets of A. thaliana RCOg-V; BLS::STM (Figure 6I and 6N) and C. hirsuta (Figure 6J and 6O).

25To conceptualize the combined effects of RCO and STM on leaf form, we thus returned to the geometric model of A. thaliana margins. Inspired by our biological data (Figure 6I, 6N, and 6Q), we explored the effects of manipulating the amount and domain of growth repression at protrusion bases (Figure 6U and Video S6). Increasing growth inhibition at the protrusion base transformed lobes into leaflet shapes but did not produce a stalked base. Extending the inhibition zone at the protrusion base to match RCO expression (Figures 6Q and 6R) yielded a leaflet supported by a narrow stalk. Taken together, our data clarify how the combined action of RCO and STM during leaf development is sufficient to account for key aspects of simple versus dissected leaf development despite the many multi-scale interactions that influence leaf shape. Both genes contribute to slow growth at the protrusion base, which enables the lateral growth anisotropy of protrusions to generate discrete leaflets (Figures 1C–1F and 4). However, STM also contributes to the sustained longitudinal extension that allows leaflets to separate. Thus, growth inhibition both shapes the outgrowths driven by anisotropic lateral growth (2–6 DAI) and enables the anisotropic extension of the central leaf stalk (termed rachis) to separate leaflets (7–8 DAI) (Figures 1D and 1F). The relatively mild phenotypes that distinguish A. thaliana RCOg-V; BLS::STM plants from C. hirsuta might reflect other differences in gene expression between the leaf primordia of the two species, including differential expression of several meristem transcription factors.

26We investigated how key regulators of organogenesis influence the rate and orientation of growth, cell proliferation, and the timing of cellular differentiation to generate different leaf forms. To do so, we acquired real-time, cellular-level growth data at an unprecedented resolution. This information, coupled with theoretical analysis, guided the in vivo reconstruction of a complex morphological trait from its cell-level constituent elements (Figure 7).

27At the single-gene level, we resolved how CUC2 can both stimulate and repress growth; first, it triggers auxin activity maxima within its own domain; then, it represses cell growth as a separate effect in the region flanking these maxima (Figure 3). We also show how the KNOX gene, STM, influences leaf form by slowing growth and delaying differentiation in the proximal domain where marginal patterning occurs. These effects enable the auxin-PIN1-CUC2 patterning module to increase both the number and prominence of marginal protrusions. These interactions also concur with previous findings on how KNOX genes act, including their possible repression by auxin. By explicitly considering dynamic cell-level growth, we extend our understanding of how these molecular regulators create simple versus complex leaves beyond the view that they mainly influence local tissue identities in the leaf. A future challenge is to resolve how other regulators affect cell growth, such as NGATHA and CINCINNATA genes, which appear to prevent marginal outgrowth independently of CUC2.

28At the organ level, we show how local foci of genetically controlled growth anisotropy at the leaf margin interact with a broadly isotropic, organ-wide growth pattern to produce leaf form. In this context, the generation of leaflets versus serrations involves both the global modification of growth by STM and local growth inhibition conferred by RCO. These effects accentuate the non-uniform growth created by the patterning of leaf margins, thus shaping form (Figure 7). Notably, the growth repressive effects of RCO do not propagate broadly, despite leaf cells being mechanically interconnected by their walls. It will be interesting to explore the biophysical basis of this restricted propagation of RCO-dependent growth inhibition, which may also limit the potentially pleiotropic effects of evolutionary changes to RCO expression.

29Finally, our work sheds new light on the regulatory logic that connects cell- and tissue-scale effects of molecular regulators. Specifically, we found that auxin activity maxima increase growth while accelerating differentiation, while STM proteins have the opposite effect on both cellular growth and differentiation. Consequently, unlike growth regulators that predominantly influence the amount of growth (e.g., RCO), STM and auxin maxima strongly influence both growth amount and its duration, where duration depends on the proliferative status of cells. In this way, the opposing effects of auxin and STM are both self-limiting. Auxin activity increases growth, but its potential to alter form is limited by the induction of differentiation. STM delays differentiation, prolonging proliferation and patterning, but its potential is limited by its capacity to retard growth. The logic of these dual activities is similar to an incoherent feed-forward loop, a well-known gene-regulatory architecture in which a single, upstream regulator both inhibits and promotes the activity of a downstream target. These networks can provide temporally limited activation (i.e., a pulse of activity) in response to activation by the upstream regulator. In growing tissues, the opposing regulation of growth and differentiation affects the spatial-temporal distribution of growth by acting inversely on growth duration and amount. This regulatory logic might be well-suited for controlling the shape of determinate organs, by allowing fine-grained geometric changes to occur during development without dramatic changes to organ size.

30Further information and requests for resources and reagents should be directed to and will be fulfilled by the Lead Contact, Miltos Tsiantis (tsiantis@mpipz.mpg.de).

31All transgenic plants and mutants were generated in the Col-0 background for A. thaliana and in the Ox background for C. hirsuta.

32Plants were grown on soil in a growth chamber under long day conditions (16 h of illumination, 110 μEm-2s-1) at 20 ± 2°C, with 65 ± 10% relative humidity. For time-lapse experiments, soil grown plants were transferred at 11 days after germination to 1/2 MS medium including vitamins (Duchefa Biochem, M0222.0050) supplemented with 1% sucrose, 0.1% PPM and grown in long day conditions.

33All transgenes were constructed using standard cloning techniques. All finished constructs were verified by sequencing. BLS::3xGFP: BLS promoter (7.1kb upstream of BLS) in pDRIVE vector (gift from Yuval Eshed lab). BLS was excised by PstI and BamHI and inserted upstream of 3xNLS-GFP in pBJ36. BLS::3xGFP was excised by NotI and inserted into pMLBART. pChSTM::3xNLS-VENUS:ChSTM promoter in pGEM-T-EASY as described before. The pChSTM fragment was excised by SalI and BamHI and inserted into pBJ97 upstream of 3xNLS-VENUS. pChSTM::3xNLS-VENUS was then excised by NotI and inserted into pMLBART. STM:VENUS in pMLBART was a gift from Markus Heisler lab. To construct OP::STM:VENUS, STM:VENUS was inserted in pVTOp ( and references therein). We used the BLS promoter to express STM in a minimal domain that is sufficient for leaflet formation in A. thaliana. The genomic locus of C. hirsuta STM was not sufficient for this purpose because gChSTM expression is active but not sustained in A. thaliana leaves and does not recreate the endogenous pattern observed in C. hirsuta. For the AtML1::PIN1:GFP construct in C. hirsuta, we confirmed that this construct complements when introduced in a C. hirsuta pin1 background.

34Plant transformations were performed using the floral dip method, using Agrobacterium tumefaciens strain GV3101. For each construct, a minimum of 10 independent lines were self-pollinated to obtain T2 seeds. Plants carrying two or more transgenes were produced by crossing and analyzed in the F2 or F3 generation.

35For 1-N-naphthylphthalamic acid (NPA) treatment, ½ MS medium supplemented with 1% sucrose was supplemented with 10μM NPA. The same concentration was added to the water used to submerge plants during confocal observations. For auxin treatment, 1μM indole-3-acetic acid (IAA, Fluka) was used as described for NPA.

36Seedlings were submerged in PI solution (10 mg/mL) for 5-10 min and then imaged immediately using a Leica SP8 up-right confocal microscope.

37To obtain leaf silhouettes and quantify leaf margin protrusions, the 8th leaf of 5-weeks-old plants was removed, flattened onto clear adhesive on paper and scanned. Protrusions were measured in Fiji and analyzed as described in Methods S1.

38To visualize vascular architecture, chlorophyll was eliminated using a graded ethanol series from 50% to 100% (v/v), and subsequent clearing with 50% to 100% (v/v) Roti Histol, followed by incubation with 50% glycerol overnight. Images were taken using a Nikon SMZ 1500 microscope equipped with a Nikon DS-Fi2 camera.

39All confocal imaging was performed using a SP8 upright confocal microscope equipped with a long working-distance water immersion objective (AP 20x/0.8 or AP 40x/0.8; Leica). Excitation was performed using an argon laser with 488 nm for GFP and PI, 514 nm for VENUS, YFP and PI. Images were collected at 529-545 nm for VENUS and YFP, 499-526 nm for GFP, 600-660 nm for PI and 660-749 nm for chlorophyll auto-fluorescence. For reporter gene analysis, cell walls were visualized after staining with 0.1% propidium iodide. For scanning electron microscopy, samples were prepared as described in. Imaging was performed using a JSM-5510 microscope (Joel). Images were processed and analyzed using Photoshop (Adobe) and MorphGraphX software. Quantification of fluorescence signals for each cell in the L1 layer (1-6 μm from the surface) was performed as described previously. Signal intensity of CUC2::CUC2:VENUS and pDR5::VENUS was quantified for the entire cell. pPIN1::PIN1:GFP signal intensity was quantified for each cell membrane based on the 1 μm region adjacent to the cell wall. PIN1:GFP orientations were assessed for each cell using the polarization plugin in MorphoGraphX (see Methods S1).

40For growth analysis, cotyledons and older leaf primordia were removed from 11-days-old soil-grown plants to expose the apex for imaging. Only plants with undamaged roots, hypocotyls and emerging leaf primordia were used for time-lapse experiments. Dissected plants were then transferred into Ø60 mm Petri dishes filled with ½ MS medium including vitamins (Duchefa Biochem, M0222.0050) supplemented with 1.5% plant agar, 1% sucrose and 0.1% plant protective medium (Plant Cell Technology). To visualize cell outlines pUBQ10::acyl:YFP or propidium iodide was used. During each experiment, at least half of the abaxial epidermis of the leaf was imaged at 24 h intervals using a Leica SP8 confocal microscope. Adult leaves 8 ± 1 were imaged for all genotypes except for C. hirsuta stm mutants which produce variable and reduced leaf number and where primordia as equivalently staged as possible to wild-type were observed. Between imaging, samples were transferred to a growth chamber and cultured in vitro under standard long-day conditions. Confocal stacks were acquired at 512x512 resolution, with 0.5-0.8 μm distance in Z-dimension, and no averaging to minimalize imaging stress. The resulting confocal time-lapse series were then analyzed using MorphoGraphX as described in. For samples that were larger than the scanning area, acquired stacks were stitched using MorphoGraphX. After cells were segmented, parent relations between successive days were determined manually in MorphoGraphX. These were used to calculate cell area, area extension, cell proliferation and growth anisotropy for each cell. The extent of lobing in pavement cells (lobeyness) was calculated as in using a MorphoGraphX plugin and taking the ratio of each cell’s perimeter to that of its convex-hull (the smallest convex shape containing the cell). Lineage tracing analysis was performed automatically in MorphoGraphX. To compute corresponding cell lineages over multiple observations (i.e., multiple days), a custom python script was used that linked the parent relations between successive days to provide lineage relations over larger time-periods. We used lineages computed as described above to analyze protrusion shape and compute growth alignment graphs (see Methods S1), and the blade, petiole/midrib and slow growing sinus cells adjacent to emerging protrusions in A. thaliana and C. hirsuta (Figure 1 O,P). The blade, petiole/midrib and sinus cells in 3 and 7 DAI WT leaf primordia were identified by: 1) labeling the blade and petiole/midrib regions at 7 DAI based on cell shape, growth and proliferation, 2) mapping these regions to 3 DAI using lineage tracing, 3) marking the slow growing sinuses between protrusions, and 4) mapping the marked sinuses to 7 DAI.

41Heat-maps for area extension, anisotropy and proliferation between two time-points are displayed on the later time-point (e.g., Leaf area extension for 3-4 DAI is visualized on the leaf at 4 DAI), with the exception of Figure 3L. In Figure 3L, area extension is visualized on the first time-point for 3 and 4 DAI, to make relations between pDR5::GFP and CUC2::Venus signal intensity and growth more apparent. Unless otherwise indicated, the time interval visualized for area extension, anisotropy and proliferation heat-maps is 1 day. Representative time-lapse series shown in main and supplemental figures were obtained from a single time-lapse experiment, with the exception of wild-type C. hirsuta and chrco leaves, as well as A. thaliana BLS::STM, 35S::KRP2 and RCOg leaves, where the first days of observation (1-2 or 1-3 DAI) were obtained from other time-lapse series. A minimum of 3 time-lapse series were performed for each genotype. These covered a period from leaf primordium emergence until up to 7-8 days after primordium initiation (DAI).

42Movies of time-lapse sequences (Movies S1-2, S5) were created using images visualizing the average growth of each cell and its neighbors. Images were morphed using FantaMorph software (Abrosoft).

43Detailed description of all models can be found in Methods S1.

44Statistical analysis was performed using Microsoft Excel. Error bars in figures represent standard errors of the mean (SEM).

45Replication for imaging data shown in main and supplementary figures is provided below.