Spatiotemporal coordination of cell division and growth during organ morphogenesis
The development of an organ from a primordium typically involves two types of processes: increase in cell number through division , and change in tissue shape and size through growth ., However , how these processes are coordinated in space and time is unclear ., It is possible that spatiotemporal regulation operates through a single control point: either on growth with downstream effects on division , or on division with downstream effects on growth ., Alternatively , spatiotemporal regulation could act on both growth and division ( dual control ) , with cross talk between them ., Distinguishing between these possibilities is challenging because growth and division typically occur in a context in which the tissue is continually deforming ., Moreover , because of the correlations between growth and division it can be hard to distinguish cause from effect 1 ., Plant development presents a tractable system for addressing such problems because cell rearrangements make little or no contribution to morphogenesis , simplifying analysis 2 ., A growing plant organ can be considered as a deforming mesh of cell walls that yields continuously to cellular turgor pressure 3 , 4 ., In addition to this continuous process of mesh deformation , new walls are introduced through cell division , allowing mesh strength to be maintained and limiting cell size ., It is thus convenient to distinguish between the continuous expansion and deformation of the mesh , referred to here as growth , and the more discrete process of introducing new walls causing increasing cell number , cell division 5–8 ., The developing Arabidopsis leaf has been used as a system for studying cell division control within a growing and deforming tissue ., Developmental snapshots of epidermal cells taken at various stages of leaf development reveal a complex pattern of cell sizes and shapes across the leaf , comprising both stomatal and non-stomatal lineages 9 ., Cell shape analysis suggests that there is a proximal zone of primary proliferative divisions that is established and then abolished abruptly ., Expression analysis of the cell cycle reporter construct cyclin1 Arabidopsis thaliana β-glucuronidase ( cyc1At-GUS ) 10 shows that the proximal proliferative zone extends more distally in the subepidermal as compared with the epidermal layer ., Analysis of the intensity of cyc1At-GUS , which combines both epidermal and subepidermal layers , led to a one-dimensional model in which cell division is restricted to a corridor of fixed length in the proximal region of the leaf 11 ., The division corridor is specified by a diffusible factor generated at the leaf base , termed mobile growth factor , controlled by expression of Arabidopsis cytochrome P450/CYP78A5 ( KLUH ) ., Two-dimensional models have been proposed based on growth and cell division being regulated in parallel by a morphogen generated at the leaf base 12 , 13 ., These models assume either a constant cell area at division , or constant cell cycle duration ., The above models represent important advances in understanding the relationships between growth and division , but leave open many questions , such as the relations of divisions to anisotropic growth , variations along both mediolateral and proximodistal axes , variation between cell layers , variation between genotypes with different division patterns , and predictions in relation to mutants that modify organ size , cell numbers , and cell sizes 14 ., Addressing these issues can be greatly assisted through the use of live confocal imaging to directly quantify growth and division 15–22 ., Local rates and orientations of growth can be estimated by the rate that landmarks , such as cell vertices , are displaced away from each other ., Cell division can be monitored by the appearance of new walls within cells ., This approach has been used to measure growth rates and orientations for developing Arabidopsis leaves and has led to a tissue-level model for its spatiotemporal control 16 ., Live tracking has also been used to follow stomatal lineages and inform hypotheses for stomatal division control 23 ., It has also been applied during a late stage of wild-type leaf development after most divisions have ceased 24 ., However , this approach has yet to be applied across an entire leaf for extended periods to compare different cell layers and genotypes ., Here , we combine tracking and modelling of 2D growth in different layers of the growing Arabidopsis leaf to study how growth and division are integrated during organ morphogenesis ., We exploit the speechless ( spch ) mutant to allow divisions to be followed in the absence of stomatal lineages , and show how the distribution and rates of growth and cell division vary in the epidermal and subepidermal layers along the proximodistal and mediolateral axes and in time ., We further compare these findings to those of wild-type leaves grown under similar conditions ., Our results reveal spatiotemporal variation in both growth rates and cell properties , including cell sizes , shapes , and patterns of division ., By developing an integrated model of growth and division , we show how these observations can be accounted for by a model in which core components of both growth and division are under spatiotemporal control ., Varying parameters of this model illustrates how changes in organ size , cell size , and cell number are likely interdependent , providing a framework for evaluating growth and division mutants ., Tracking cell vertices on the abaxial epidermis of spch seedlings imaged at about 12-h intervals allowed cells at a given developmental stage to be classified into those that would undergo division ( competent to divide , green , Fig 1A ) , and those that did not divide for the remainder of the tracking period ( black , Fig 1A ) ., During the first time interval imaged ( Fig 1A , 0–14 h ) , division competence was restricted to the basal half of the leaf , with a distal limit of about 150 μm ( all distances are measured relative to the petiole-lamina boundary , Fig 1 ) ., To visualise the fate of cells at the distal limit , we identified the first row of nondividing cells ( orange ) and displayed them in all subsequent images ., During the following time intervals , the zone of competence extended together with growth of the tissue to a distance of about 300 μm , after which it remained at this position , while orange boundary cells continued to extend further through growth ., Fewer competent cells were observed in the midline region at later stages ., Thus , the competence zone shows variation along the proximodistal and mediolateral axes of the leaf , initially extending through growth to a distal limit of about 300 μm and disappearing earlier in the midline region ., To monitor execution of division , we imaged spch leaves at shorter intervals ( every 2 h ) ., At early stages , cells executed division when they reached an area of about 150 μm2 ( Fig 2A , 0–24 h ) ., At later stages , cells in the proximal lamina ( within 150 μm ) continued to execute division at about this cell area ( mean = 151 ± 6 . 5 μm2 , Fig 2B ) , while those in the more distal lamina or in the midline region executed divisions at larger cell areas ( mean = 203 ± 9 . 7 μm2 or 243 . 0 ± 22 . 4 μm2 , respectively , Fig 2A , 2B and 2D ) ., Cell cycle duration showed a similar pattern , being lowest within the proximal 150 μm of the lamina ( mean = 13 . 9 ± 0 . 8 h ) and higher distally ( mean = 19 . 4 ± 1 . 8 h ) or in the midline region ( 18 . 9 ± 2 . 1 h , Fig 2C and 2E ) ., Within any given region , there was variation around both the area at time of division execution and the cell cycle duration ( Fig 2F and 2G ) ., For example , the area at execution of division within the proximal 150 μm of the lamina had a mean of about 150 μm2 , with standard deviation of about 40 μm2 ( Fig 2F ) ., The same region had a cell cycle duration with a mean of about 14 h and a standard deviation of about 3 h ., Thus , both the area at which cells execute division and cycle duration show variation around a mean , and the mean varies along the proximodistal and mediolateral axes of the leaf ., These findings suggest that models in which either cell area at the time of division or cell cycle duration are fixed would be unable to account for the observed data ., To determine how cell division competence and execution are related to leaf growth , we measured areal growth rates ( relative elemental growth rates 25 ) for the different time intervals , using cell vertices as landmarks ( Fig 1B ) ., Areal growth rates varied along both the mediolateral and proximodistal axis of the leaf , similar to variations observed for competence and execution of division ., The spatiotemporal variation in areal growth rate could be decomposed into growth rates in different orientations ., Growth rates parallel to the midline showed a proximodistal gradient , decreasing towards the distal leaf tip ( Fig 1C and S1A Fig ) ., By contrast , mediolateral growth was highest in the lateral lamina and declined towards the midline , becoming very low there in later stages ( Fig 1D and S1B Fig ) ., The region of higher mediolateral growth may correspond to the marginal meristem 26 ., Regions of low mediolateral growth ( i . e . , the proximal midline ) showed elongated cell shapes ., Models for leaf growth therefore need to account not only for the spatiotemporal pattern of areal growth rates but also the pattern of anisotropy ( differential growth in different orientations ) and correlated patterns of cell shape ., Cell size should reflect both growth and division: growth increases cell size while division reduces cell size ., Cell periclinal areas were estimated from tracked vertices ( Fig 1E ) ., Segmenting a sample of cells in 3D showed that these cell areas were a good proxy for cell size , although factors such as leaf curvature introduced some errors ( for quantifications see S5 Fig , and ‘Analysis of cell size using 3D segmentation’ in Materials and methods ) ., At the first time point imaged , cell areas were about 100–200 μm2 throughout most of the leaf primordium ( Fig 1E , left ) ., Cells within the proximal 150 μm of the lamina remained small at later stages , reflecting continued divisions ., In the proximal 150–300 μm of the lamina , cells were slightly larger , reflecting larger cell areas at division execution ., Lamina cells distal to 300 μm progressively enlarged , reflecting the continued growth of these nondividing cells ( Fig 1E and Fig 3A ) ., Cells in the midline region were larger on average than those in the proximal lamina , reflecting execution of division at larger cell areas ( Fig 1E and Fig 3C ) ., Thus , noncompetent cells increase in area through growth , while those in the competence zone retain a smaller size , with the smallest cells being found in the most proximal 150 μm of the lateral lamina ., Visual comparison between areal growth rates ( Fig 2B ) with cell sizes ( Fig 2E ) suggested that regions with higher growth rates had smaller cell sizes ., Plotting areal growth rates against log cell area confirmed this impression , revealing a negative correlation between growth rate and cell size ( Fig 4B ) ., Thus , rapidly growing regions tend to undergo more divisions ., This relationship is reflected in the pattern of division competence: mean areal growth rates of competent cells in the lamina were higher than noncompetent cells , particularly at early stages ( Fig 3I ) ., However , there was no fixed threshold growth rate above which cells were competent , and for the midline region there was no clear difference between growth rates of competent and noncompetent cells ( Fig 3I ) ., Plotting areal growth rates for competent and noncompetent cells showed considerable overlap ( S6 Fig ) , with no obvious switch in growth rate when cells no longer divide ( become noncompetent ) ., Thus , high growth rate broadly correlates with division competence , but the relationship is not constant for different regions or times ., To determine how the patterns and correlations observed for the epidermis compared to those in other tissues , we analysed growth and divisions in the subepidermis ., The advantage of analysing an adjacent connected cell layer is that unless intercellular spaces become very large , the planar cellular growth rates will be very similar to those of the attached epidermis ( because of tissue connectivity and lack of cell movement ) ., Comparing the epidermal and subepidermal layers therefore provides a useful system for analysing division behaviours in a similar spatiotemporal growth context ., Moreover , by using the spch mutant , one of the major distinctions in division properties between these layers ( the presence of stomatal lineages in the epidermis ) is eliminated ., Divisions in the abaxial subepidermis were tracked by digitally removing the overlying epidermal signal ( the distalmost subepidermal cells could not be clearly resolved ) ., As with the epidermis , 3D segmentation showed that cell areas were a good proxy for cell size , although average cell thickness was greater ( S11 Fig , see also ‘Analysis of cell size using 3D segmentation’ in Materials and methods ) ., Unlike the epidermis , intercellular spaces were observed for the subepidermis ., As the tissue grew , subepidermal spaces grew and new spaces formed ( Fig 5A–5D ) ., Similar intercellular spaces were observed in subepidermal layers of wild-type leaves , showing they were not specific to spch mutants ( S8 Fig ) ., Vertices and intercellular spaces in the subepidermis broadly maintained their spatial relationships with the epidermal vertices ( Fig 5C , 5E and 5F ) ., Comparing the cellular growth rates in the plane for a patch of subepidermis with the adjacent epidermis showed that they were similar ( S9 Fig ) , although the subepidermal rates were slightly lower because of the intercellular spaces ., This correlation is expected , because unless the intercellular spaces become very large , the areal growth rates of the epidermal and subepidermal layers are necessarily similar ., The most striking difference between subepidermal and epidermal datasets was the smaller size of the distal lamina cells of the subepidermis ( compare Fig 6A with Fig 1E , and Fig 3A with Fig 3B ) ., For the epidermis , these cells attain areas of about 1 , 000 μm2 at later stages , while for the subepidermis they remain below 500 μm2 ., This finding was consistent with the subepidermal division competence zone extending more distally ( Fig 6B ) , reaching a distal limit of about 400 μm compared with 300 μm for the epidermis ., A more distal limit for the subepidermis has also been observed for cell cycle gene expression in wild type 10 ., Moreover , at early stages , divisions occurred throughout the subepidermis rather than being largely proximal , as observed in the epidermis , further contributing to the smaller size of distal subepidermal cells ( S10 Fig ) ., Despite these differences in cell size between layers , subepidermal cell areal growth rates showed similar spatiotemporal patterns to those of the overlying epidermis , as expected because of tissue connectivity ( compare Fig 6C with Fig 1B ) ., Consequently , correlations between growth rate and cell size were much lower for the subepidermis than for the epidermis ( Fig 4B and 4C ) ., This difference in the relationship between growth and cell size in different cell layers was confirmed through analysis of cell division competence ., In the subepidermis , at early stages there was no clear difference between mean growth rates for competent and noncompetent cells ( Fig 3J cyan , green ) , in contrast to what is observed in the epidermis ( Fig 3I cyan , green ) , while at later stages noncompetent cells had a slightly lower growth rate ( Fig 3J yellow , red ) ., To determine how the patterns of growth and division observed in spch related to those in wild type , we imaged a line generated by crossing a spch mutant rescued by a functional SPCH protein fusion ( pSPCH:SPCH-GFP ) to wild type expressing the PIN3 auxin transporter ( PIN3:PIN3-GFP ) , which marks cell membranes in the epidermis 23 ., The resulting line allows stomatal lineage divisions to be discriminated from non-stomatal divisions ( see below ) in a SPCH context ., At early stages , wild-type and spch leaves were not readily distinguishable based on cell size ( S12 Fig ) ., However , by the time leaf primordia attained a width of about 150 μm , the number and size of cells differed dramatically ., Cell areas in wild type were smaller in regions outside the midline region , compared with corresponding cells in spch ( Fig 7A ) ., Moreover , cell divisions in wild type were observed throughout the lamina that was amenable to tracking ( Fig 7B , 0–12 h ) , rather than being largely proximal ., Divisions were observed over the entire lamina for subsequent time intervals , including regions distal to 300 μm ( Fig 7B , 12–57 h ) ., These results indicate that SPCH can confer division competence in epidermal cells outside the proximal zone observed in spch mutants ., To further clarify how SPCH influences cell division , we used SPCH-GFP signal to classify wild-type cells into two types: ( 1 ) Stomatal lineage divisions , which include both amplifying divisions ( cells express SPCH strongly around the time of division and retain expression in one of the daughter cells ) ( S1 Video , orange/yellow in Fig 7C ) and guard mother cell divisions ( SPCH expression is bright and diffuse during the first hours of the cycle , transiently switched on around time of division , and then switched off in both daughters ) ., ( 2 ) Non-stomatal divisions , in which SPCH expression is much weaker , or only lasts <2 h , and switches off in both daughter cells ( S2 Video , light/dark green in Fig 7C ) ., If cells with inactive SPCH behave in a similar way in wild-type or spch mutant contexts , we would expect non-stomatal divisions to show similar properties to divisions in the spch mutant ., In the first time interval , non-stomatal divisions ( green ) were observed within the proximal 150 μm ( Fig 7C , 0–12 h ) , similar to the extent of the competence zone in spch ( Fig 1A , 0–14h ) ., The zone of non-stomatal divisions then extended to about 250 μm and became restricted to the midline region ., After leaf width was greater than 0 . 45 mm , we did not observe further non-stomatal divisions in the midline region , similar to the situation in spch leaves at a comparable width ( Fig 1A , 58-74h , 0 . 48 mm ) ., These results suggest that similar dynamics occur in the non-stomatal lineages of wild type and the spch mutant ., To determine how SPCH modulates division , we analysed stomatal and non-stomatal divisions in the lamina ., Considerable variation was observed for both the area at which cells divide ( 25–400 μm2 ) and cell cycle duration ( 8–50 h ) ( S13 Fig ) ., The mean area at which cells execute division was greater for non-stomatal divisions ( about 165 ± 28 μm2 1 . 96 × standard error ) than stomatal divisions ( about 80 ± 6 μm2 ) ( S13 Fig ) ., Similarly , cell cycle durations were longer for non-stomatal divisions ( about 25 ± 3 h ) compared with stomatal divisions ( about 18 ± 1 h ) ., These results suggest that in addition to conferring division competence , SPCH acts cell autonomously to promote division at smaller cell sizes and/or for shorter cell cycle durations ., Given the alteration in cell sizes and division patterns in wild type compared to spch , we wondered if these may reflect alterations in growth rates ., When grown on agar plates , spch mutant leaves grow more slowly than wild-type leaves ( S14A Fig ) ., The slower growth of spch could reflect physiological limitations caused by the lack of stomata , or an effect of cell size on growth—larger cells in spch cause a slowing of growth ., However , the tracking data and cell size analysis of spch and wild type described above were carried out on plants grown in a bio-imaging chamber in which nutrients were continually circulated around the leaves ., Growth rates for wild type and spch leaves grown in these conditions were comparable for much of early development , and similar to those observed for wild type on plates ( compare Fig 7D with Fig 1B , S14 Fig ) ., These results suggest that the reduced growth rates of spch compared with wild type at early stages on plates likely reflect physiological impairment caused by a lack of stomata rather than differences in cell size ., As a further test of this hypothesis , we grew fama ( basic helix-loop-helix transcription factor bHLH097 ) mutants , as these lack stomata but still undergo many stomatal lineage divisions 27 ., We found that fama mutants attained a similar size to spch mutants on plates , consistent with the lack of stomata being the cause of reduced growth in these conditions ( S14 Fig ) ., Plots of cell area against growth rates of tracked leaves grown in the chamber showed that , for similar growth rates , cells were about three times smaller in wild type compared with spch ( compare Fig 4A with Fig 4B ) ., Thus , the effects of SPCH on division can be uncoupled from effects on growth rate , at least at early stages of development ., At later stages ( after leaves were about 1 mm wide ) , spch growth in the bio-imaging chamber slowed down compared with wild type , and leaves attained a smaller final size ., This later difference in growth rate might be explained by physiological impairment of spch because of the lack of stomata , and/or by feedback of cell size on growth rates ., This change in later behaviour may reflect the major developmental and transcriptional transition that occurs after cell proliferation ceases 9 ., The above results reveal that patterns of growth rate , cell division , and cell size and shape exhibit several features in spch: ( 1 ) a proximal corridor of cell division competence , with an approximately fixed distal limit relative to the petiole-lamina boundary; ( 2 ) the distal limit is greater for subepidermal ( 400 μm ) than epidermal tissue ( 300 μm ) ; ( 3 ) a further proximal restriction of division competence in the epidermis at early stages that extends with growth until the distal limit of the corridor ( 300 μm ) is reached; ( 4 ) larger and narrower cells in the proximal midline region of the epidermis; ( 5 ) a proximodistal gradient in cell size in the epidermal lamina; ( 6 ) a negative correlation between cell size and growth rate that is stronger in the epidermis than subepidermis; ( 7 ) variation in both the size at which cells divide and cell cycle duration along both the proximodistal and mediolateral axes; and ( 8 ) variation in growth rates parallel or perpendicular to the leaf midline ., In wild-type plants , these patterns are further modulated by the expression of SPCH , which leads to division execution at smaller cell sizes and extension of competence , without affecting growth rates at early stages ., Thus , growth and division rates exhibit different relations in adjacent cell layers , even in spch , in which epidermal-specific stomatal lineages are eliminated , and division patterns can differ between genotypes ( wild type and spch ) without an associated change in growth rates ., These observations argue against spatiotemporal regulators acting solely on the execution of division , which then influences growth , as this would be expected to give conserved relations between division and growth ., For the same reason , they argue against a single-point-of-control model in which spatiotemporal regulators act solely on growth , which then secondarily influences division ., Instead , they suggest dual control , with spatiotemporal regulators acting on both growth and division components ., With dual control , growth and division may still interact through cross-dependencies , but spatiotemporal regulation does not operate exclusively on one or the other ., To determine how a hypothesis based on dual control may account for all the observations , we used computational modelling ., We focussed on the epidermal and subepidermal layers of the spch mutant , as these lack the complications of stomatal lineages ., For simplicity and clarity , spatiotemporal control was channelled through a limited set of components for growth and division ( Fig 8A ) ., There were two components for growth under spatiotemporal control: specified growth rates parallel and perpendicular to a proximodistal polarity field ( Kpar and Kper , respectively ) 16 ., Together with mechanical constraints of tissue connectivity , these specified growth components lead to a pattern of resultant growth and organ shape change 28 ., There were two components for cell division under spatiotemporal control: competence to divide ( CDIV ) , and a threshold area for division execution that varies around a mean ( Ā ) ., Controlling division execution by a threshold cell size ( Ā ) introduces a cross-dependency between growth and division , as cells need to grow to attain the local threshold size before they can divide ., The cross-dependency is indicated by the cyan arrow in Fig 8A , feeding information back from cell size ( which depends on both growth and division ) to division ., An alternative to using Ā as a component of division-control might be to use a mean cell cycle duration threshold ., However , this would bring in an expected correlation between high growth rates and large cell sizes ( for a given cell cycle duration , a faster-growing cell will become larger before cycle completion ) , which is the opposite trend of what is observed ., Spatiotemporal regulators of growth and division components can be of two types: those that become deformed together with the tissue as it grows ( fixed to the tissue ) and those that maintain their pattern to some extent despite deformation of the tissue by growth ( requiring mobile or diffusible factors ) 28 ., In the previously published growth model , regulatory factors were assumed , for simplicity , to deform with the tissue as it grows 16 ., These factors comprised a graded proximodistal factor ( PGRAD ) , a mediolateral factor ( MID ) , a factor distinguishing lamina from petiole ( LAM ) , and a timing factor ( LATE ) ( S15A and S15B Fig ) ., However , such factors cannot readily account for domains with limits that remain at a constant distance from the petiole-lamina boundary , such as the observed corridors for division competence ., This is because the boundary of a domain that is fixed to the tissue will extend with the tissue as it grows ., We therefore introduced a mobile factor , proximal mobile factor ( PMF ) , that was not fixed to the tissue to account for these behaviours ., This motivation is similar to that employed by others 11–13 ., PMF was generated at the petiole-lamina boundary and with appropriate diffusion and decay coefficients such that PMF initially filled the primordium and then showed a graded distribution as the primordium grew larger , maintaining a high concentration in the proximal region and decreasing towards the leaf tip ( S15C and S15D Fig ) ., This profile was maintained despite further growth , allowing thresholds to be used to define domains with relatively invariant distal limits ., Further details of the growth model are given in Materials and methods , and the resultant growth rates are shown in S16 Fig ( compare with Fig 1B and 1D ) ., Cells were incorporated by superimposing polygons on the initial tissue or canvas ( S15A Fig , right ) ., The sizes and geometries of these virtual cells ( v-cells ) were based on cells observed at corresponding stages in confocal images of leaf primordia 16 ., The vertices of the v-cells were anchored to the canvas and displaced with it during growth ., Cells divided according to Errera’s rule: the shortest wall passing through the centre of the v-cell 29 , with noise in positioning of this wall incorporated to capture variability ., V-cells were competent to divide if they expressed factor CDIV , and executed division when reaching a mean cell target area , Ā ., As the observed area at time of division was not invariant ( Fig 2F ) , we assumed the threshold area for division varied according to a standard deviation of σ = 0 . 2Ā around the mean ., CDIV and Ā are the two core components of division that are under the control of spatiotemporal regulators in the model ( Fig 8A , 8C and 8D ) ., Variation between epidermal and subepidermal patterns reflects different interactions controlling cell division ( interactions colour coded red and blue , respectively , in Fig 8C and 8D ) ., We first modelled cell divisions in the subepidermis , as this layer shows a more uniform pattern of cell sizes ( Fig 3B and Fig 6A ) ., Formation of intercellular spaces was simulated by replacing a random selection of cell vertices with small empty equilateral triangles , which grew at a rate of 2 . 5% h−1 , an average estimated from the tracking data ., To account for the distribution of divisions and cell sizes , we assumed that v-cells were competent to divide ( express CDIV ) where PMF was above a threshold value ., This value resulted in the competence zone extending to a distal limit of about 400 μm ., To account for the proximodistal pattern of cell areas in the lamina ( Fig 3B and Fig 6A ) and larger cells in the midline ( Fig 3D and Fig 6A ) , we assumed that Ā was modulated by the levels of PMF , PGRAD , and MID ( Fig 8D , black and blue ) ., These interactions gave a pattern of average v-cell areas and division competence that broadly matched those observed ( compare Fig 8E and 8F with Fig 6A and 6B , and Fig 3F and 3H with 3B and 3D , S3 Video ) ., For the epidermis , the zone of division competence was initially in the proximal region of the primordium and then extended with the tissue as it grew ( Fig 1A ) ., We therefore hypothesised that in addition to division being promoted by PMF , there was a further requirement for a proximal factor that extended with the tissue as it grew ., We used PGRAD to achieve this additional level of control , assuming CDIV expression requires PGRAD to be above a threshold level ( Fig 8C , red and black ) ., V-cells with PGRAD below this threshold were not competent to divide , even in the presence of high PMF ., Thus , at early stages , when PMF was high throughout the primordium , the PGRAD requirement restricted competence to the proximal region of the leaf ( Fig 8H ) ., At later stages , as the PGRAD domain above the threshold extended beyond 300 μm , PMF became limiting , preventing CDIV from extending beyond about 300 μm ., To account for the earlier arrest of divisions in the midline region ( Fig 1A ) , CDIV was inhibited by MID when LATE reached a threshold value ( Fig 8C , red ) ., As well as CDIV being regulated , the spatiotemporal pattern of Ā was modulated by factors MID and PMF ( Fig 8D black ) ., With these assumptions , the resulting pattern of epidermal divisions and v-cell sizes broadly matched those observed experimentally for the epidermis ( compare Fig 8G with Fig 1E , S4 Video ) ., In particular , the model accounted for the observed increases in cells sizes with distance from the petiole-lamina boundary , which arise because of the proximal restrictions in competence ( compare Fig 3E and 3G with Fig 3A and 3C ) ., The model also accounted for the elongated cell shapes observed in the midline region , which arise through the arrest of division combined with low specified growth rate perpendicular to the polarity ., Moreover , the negative correlations between growth rates and cell size , not used in developing the model , were similar to those observed experimentally ( Fig 4B and 4D ) ., These correlations arise because both growth and division are promoted in proximal regions ., We also measured the cell topology generated by the epidermal model ., It has previously been shown that the frequency of six-sided neighbours observed experimentally for the spch leaf epidermis is very low compared with that for other plant and animal tissues and also with that generated by a previous implementation
A developing plant organ exhibits complex spatiotemporal patterns of growth , cell division , cell size , cell shape , and organ shape ., Explaining these patterns presents a challenge because of their dynamics and cross-correlations , which can make it difficult to disentangle causes from effects ., To address these problems , we used live imaging to determine the spatiotemporal patterns of leaf growth and division in different genetic and tissue contexts ., In the simplifying background of the speechless ( spch ) mutant , which lacks stomatal lineages , the epidermal cell layer exhibits defined patterns of division , cell size , cell shape , and growth along the proximodistal and mediolateral axes ., The patterns and correlations are distinctive from those observed in the connected subepidermal layer and also different from the epidermal layer of wild type ., Through computational modelling we show that the results can be accounted for by a dual control model in which spatiotemporal control operates on both growth and cell division , with cross-connections between them ., The interactions between resulting growth and division patterns lead to a dynamic distributions of cell sizes and shapes within a deforming leaf ., By modulating parameters of the model , we illustrate how phenotypes with correlated changes in cell size , cell number , and organ size may be generated ., The model thus provides an integrated view of growth and division that can act as a framework for further experimental study .
Organ morphogenesis involves two coordinated processes: growth of tissue and increase in cell number through cell division ., Both processes have been analysed individually in many systems and shown to exhibit complex patterns in space and time ., However , it is unclear how these patterns of growth and cell division are coordinated in a growing leaf that is undergoing shape changes ., We have addressed this problem using live imaging to track growth and cell division in the developing leaf of the mustard plant Arabidopsis thaliana ., Using subsequent computational modelling , we propose an integrated model of leaf growth and cell division , which generates dynamic distributions of cell size and shape in different tissue layers , closely matching those observed experimentally ., A key aspect of the model is dual control of spatiotemporal patterns of growth and cell division parameters ., By modulating parameters in the model , we illustrate how phenotypes may correlate with changes in cell size , cell number , and organ size .
skin, cell physiology, plant anatomy, medicine and health sciences, integumentary system, cell division analysis, cell cycle and cell division, cell processes, brassica, cell polarity, plant science, model organisms, network analysis, experimental organism systems, epidermis, bioassays and physiological analysis, seedlings, plants, research and analysis methods, arabidopsis thaliana, computer and information sciences, cell analysis, animal studies, regulatory networks, leaves, eukaryota, plant and algal models, cell biology, anatomy, biology and life sciences, organisms