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Journal of Experimental Botany, Vol. 66, No. 4 pp. 1045–1054, 2015 doi:10.1093/jxb/eru541 Advance Access publication 19 January 2015 Review Paper Molecular systems governing leaf growth: from genes to networks Nathalie González1,2 and Dirk Inzé1,2,* 1 2 Department of Plant Systems Biology, VIB, Technologiepark 927, 9052 Ghent, Belgium Department of Plant Biotechnology and Bioinformatics, Ghent University, Technologiepark 927, 9052 Ghent, Belgium * To whom correspondence should be addressed. E-mail: [email protected] Received 17 November 2014; Revised 17 November 2014; Accepted 16 December 2014 Abstract Arabidopsis leaf growth consists of a complex sequence of interconnected events involving cell division and cell expansion, and requiring multiple levels of genetic regulation. With classical genetics, numerous leaf growth regulators have been identified, but the picture is far from complete. With the recent advances made in quantitative phenotyping, the study of the quantitative, dynamic, and multifactorial features of leaf growth is now facilitated. The use of high-throughput phenotyping technologies to study large numbers of natural accessions or mutants, or to screen for the effects of large sets of chemicals will allow for further identification of the additional players that constitute the leaf growth regulatory networks. Only a tight co-ordination between these numerous molecular players can support the formation of a functional organ. The connections between the components of the network and their dynamics can be further disentangled through gene-stacking approaches and ultimately through mathematical modelling. In this review, we describe these different approaches that should help to obtain a holistic image of the molecular regulation of organ growth which is of high interest in view of the increasing needs for plant-derived products. Key words: Arabidopsis, growth control, leaf size, multidisciplinary approaches, quantitative biology, systems biology. Introduction In multicellular organisms, establishment of final organ size represents a complex mechanism that relies on the precise regulation of cell number and/or size, which are governed by two cellular processes, namely cell division and cell expansion. Various factors will influence these processes essential for the formation of a functional organ during the different phases of development. Genetic factors determine the blueprint, but environmental cues can also have very pronounced effects on the final size of a plant and its organs. This is best illustrated by Bonsai trees that, although sharing the same genetic constitution with their giant siblings grown in more optimal conditions, are spectacularly different in size. A better understanding of how plant growth and thus cell division and cell expansion are regulated at the molecular level is of great interest for the increasing needs for plant-derived products for food, feed, energy, and pharmaceuticals (Edgerton, 2009). Growth is a quantitative, dynamic, and multifactorial trait regulated by numerous genetic factors. The study of this complex machinery therefore requires the integration of multiple approaches, or system biology approaches, at different scales (plant, organ, and cell), including genetics, physiology, quantitative phenotyping, and various omics technologies in order to obtain a holistic image of the molecular regulation of organ growth. In this review, we illustrate the complexity of organ growth by focusing on the development of the Arabidopsis leaf. We describe the recent advances made in quantitative biology for Abbreviations: AN3/GIF, ANGUSTIFOLIA3/GRF-INTERACTING FACTOR; APC/C, ANAPHASE PROMOTING COMPLEX/CYCLOSOME; EBP1, ErbB3-binding protein 1; EMS, ethyl methanesulphonate; EOD, ENHANCER OF DA1; EXP10, EXPANSIN 10; gra-D, GRANDIFOLIA-D; GRF5, GROWTH-REGULATING FACTOR5; GWA, genome wide association; SAUR19, SMALL AUXIN UP-REGULATED RNA 19; T-DNA, transfer DNA; UBP15, UBIQUITIN-SPECIFIC PROTEASE15. © The Author 2015. Published by Oxford University Press on behalf of the Society for Experimental Biology. All rights reserved. For permissions, please email: [email protected] 1046 | González and Inzé the identification of the genetic basis of leaf growth regulation and discuss novel approaches that could be implemented for a better understanding of leaf growth and development (Fig. 1). Leaf growth: many events, many genes In eudicots, leaves reach their final size after a complex sequence of interconnected events (Gonzalez et al., 2012; Kalve et al., 2014). In Arabidopsis, the leaf emerges as a primordium, a group of small round cells at the periphery of the shoot apical meristem, that will undergo a series of developmental processes, resulting in the formation of a mature organ (Donnelly et al., 1999; Breuninger and Lenhard, 2010; Gonzalez et al., 2012). First, these cells will actively divide throughout the whole primordium during a proliferation phase. At a given developmental time, cell division will then start to cease at the tip of the leaf and a so-called cell cycle arrest front will move from the tip to the base of the leaf (Donnelly et al., 1999; Andriankaja et al., 2012). During this transition phase, cell division arrest is accompanied by cell differentiation and the onset of cell expansion, a process that also involves the occurrence of endoreduplication, in which DNA is replicated without mitosis, resulting in cells with ploidy levels of up to 32C in Arabidopsis (Galbraith et al., 1991). When all cells are expanding during the cell expansion phase, the leaf will reach its final size. During these three phases (proliferation, transition, and expansion), cells dispersed throughout the leaf epidermis, called meristemoids, will divide asymmetrically to generate pavement cells and the stomatal lineage (Bergmann and Sack, 2007; Pillitteri and Torii, 2012). Meristemoid activity has been estimated to generate 67% of all pavement cells in cotyledons and 48% of all Fig. 1. Different approaches to obtain a complete image of the molecular regulation of organ growth. With the recent advances made in quantitative phenotyping, especially the development of automated phenotyping platforms, the study of leaf growth and its quantitative and dynamic features is now facilitated. Several parameters at the plant, organ, and cellular level can be quantified. The combination of high-throughput phenotyping technologies with the study of large plant populations, natural variants, or mutants will enable the identification of genes involved in the regulation of leaf size. Highthroughput phenotyping platforms can also be used to screen the effect on leaf growth of large sets of chemical compounds. This screen at the organ level should be combined with a precise, narrow secondary screen at the cellular level, corresponding, for example, to the analysis of the change in expression of a reported gene. The connections between the numerous molecular players of the leaf growth regulatory network and their dynamics can be further unravelled through gene combination approaches (crosses and multiple constructs) and ultimately through mathematical modelling. Genes and networks for leaf growth control | 1047 pavement cells in leaves (Geisler et al., 2000). In conclusion, at least five parameters influence the final leaf size: (i) the number of cells recruited from the meristem to the primordium; (ii) the rate of cell division; (iii) the extent of cell proliferation; (iv) cell expansion; and (v) the duration of meristemoid division (Gonzalez et al., 2012). Through traditional reverse and forward genetics, by studying mutants and transgenic lines with altered leaf size, numerous genes involved in the regulation of these events have been described (Gonzalez et al., 2009; Hepworth and Lenhard, 2014). Several genes have been shown to participate in the regulation of only one process, such as GRF5 (GROWTH-REGULATING FACTOR5) and EOD (ENHANCER OF DA1), which control the length of the cell division phase (Horiguchi et al., 2005; Li et al., 2008), or EXP10 (EXPANSIN 10) and SAUR19 (SMALL AUXIN UP-REGULATED RNA 19) (Cho and Cosgrove, 2000; Spartz et al., 2012), regulating cell expansion. Other regulators, on the other hand, influence various cellular processes, such as the AN3/GIF proteins (ANGUSTIFOLIA3/GRFINTERACTING FACTOR) which control both the rate of cell division and the length of the cell division phase, or the ErbB3-binding protein 1 (EBP1) which is involved in both the regulation of cell division and cell expansion (Horváth et al., 2006; Lee et al., 2009). These examples underline the interconnections existing between cell division and cell expansion, which is further supported by the fact that in some mutants, a decrease in cell division triggers an increased cell expansion (Mizukami and Fischer, 2000; De Veylder et al., 2001; Kim and Kende, 2004; Horiguchi et al., 2005). Although the genetic basis of this phenomenon termed compensation is still not completely uncovered (Horiguchi and Tsukaya, 2011), it has been frequently observed in many different experimental systems. In conclusion, growth is a complex process consisting of various events, in different tissues and cell types requiring multiple levels of genetic regulation. Although several molecular components of the machineries driving organ growth have been discovered, the picture is far from being complete. Advanced phenotyping: from harvesting to imaging Quantitative phenotyping methods at different levels are essential to obtain detailed information about the regulation of growth. Plant growth analyses investigate changes in size, shape, or number of different cells, organs, or a whole plant grown under a certain environmental condition. Although simple primary data such as weight, area, or volume are determined, the dynamic and multifactorial aspects of these traits make them complicated to study. Quantitative phenotyping methods are preferably non-destructive to allow measurement of relative growth rates over time. The first and classical approaches consisted of harvesting plants or organs and measuring biomass or size at a single or a few time points. Although these methods provide valuable information, they are often time-consuming and the time resolution is usually quite low, not providing enough details necessary to understand the dynamic aspect of plant growth. With the considerable progress in digital imaging in the past decade, non-destructive image analysis approaches have been developed, allowing the study of growth fluctuations of various plant organs such as roots or shoots by extracting several growth-related parameters, such as projected rosette area, rosette compactness, and stockiness (Dhondt et al., 2013; Sozzani et al., 2014). Automated image acquisition and data extraction methods (Arvidsson et al., 2011; De Vylder et al., 2012; Zhang et al., 2012) allow, for example, the analysis of the flat rosette of Arabidopsis, by calculating the projected rosette area, which is a good approximation for rosette biomass (Leister et al., 1999). Several of these automated methods are now combined in robotic platforms developed to follow the dynamic rosette growth by imaging of the plant shoot (Granier et al., 2006; Walter et al., 2007; Jansen et al., 2009; Skirycz et al., 2011; Tisné et al., 2013; Dhondt et al., 2014). This combination significantly improves the throughput of plant growth analysis under highly stable growth conditions that are essential for accurate characterization of various genotypes. Moreover, the use, besides digital imaging, of non-invasive imaging sensors, such as thermal infrared, multispectral, or hyperspectral sensors, enables physiologyrelated trait measurements such as water content, pigment activity, or light-use efficiency (Furbank and Tester, 2011; Dhondt et al., 2013). Further development of the imaging systems will allow for monitoring growth during the entire life cycle of plants. For example, one could analyse how the onset of inflorescence growth affects growth of rosette leaves, or how leaf and root growth are related. Very few studies have addressed the latter question, but evidence suggests that there is a relationship. For example, both leaf and root growth were synergistically enhanced in plants ectopically expressing CYTOKININE OXIDASE3 and BRASSINOSTEROID INSENSITIVE1, indicating cross-talk between cytokinins and brassinosteroids (Vercruyssen et al., 2011). The efficient image analysis methods developed so far, which are improving plant phenotyping by allowing noninvasive measurements of shoot growth, mainly relate to the analysis of the whole rosette (Fig. 1). However, individual leaf characteristics and cellular parameters are also essential to obtain a better understanding of specific growth phenotypes (Fig. 1). These parameters are usually determined destructively by dissecting the shoots, but advances have been made in the imaging tools to extract various parameters automatically from images obtained after sample preparation (Bensmihen et al, 2008; Andriankaja et al., 2012; Dhondt et al., 2012), therefore increasing the capacity to analyse many samples. By using time-lapse imaging of fluorescent markers by means of a confocal microscope, orientations and rates of cell growth have been quantified in the leaf to develop a model explaining the determination of leaf shape (Kuchen et al., 2012). This methodology has also been applied to study sepal and petal growth (Roeder et al., 2010; Sauret-Güeto et al., 2013). Further developments will, however, be required to enable the visualization of cellular parameters during the entire leaf development. For roots, a 1048 | González and Inzé high-throughput confocal microscopy imaging system has also been developed to phenotype cellular features, the length of the meristem zone, of the elongation zone, and of mature cortical cells (Meijón et al., 2014). Novel growth regulatory genes: combining natural variation with advanced phenotyping Most of the key players involved in the regulation of growth in Arabidopsis have been discovered by classical, often lowthroughput, forward or reverse genetic approaches. These studies have allowed a solid foundation to be built for a better understanding of leaf growth regulation. However, the picture is far from complete. To obtain an integrated view on the molecular machineries driving cell proliferation and expansion in the leaf, new approaches combining data from large quantitative phenotypic studies obtained by high-throughput imaging methodologies with data from genome-wide approaches will enable the genetic network controlling leaf growth to be unravelled further (Fig. 1). Various genotypes available in Arabidopsis, such as the large collections of mutants (McElver et al., 2001; Alonso et al., 2003; Rosso et al., 2003) or the numerous accessions from diverse geographic origins (Koornneef et al., 2004; Shindo et al., 2007), can be used for such large-scale quantitative growth analyses. A systematic study of gene-indexed insertion mutants has been recently carried out to identify genes involved in leaf development (Wilson-Sánchez et al., 2014). A public web application named PhenoLeaf (http:// genetics.umh.es/phenoleaf) has been developed to query the results of the screen, including textual and visual phenotypic information. This study identified >200 T-DNA insertion mutants affected in rosette size, but this screen could not identify all leaf growth-related genes due to the under-representation of essential genes in this type of mutant collection and to the possible absence of a phenotype for functionally redundant genes. The generation of collections of double mutants for members of the same gene family (Bolle et al., 2013) or silencing of a complete gene family by artificial microRNAs (Jover-Gil et al., 2014) will probably allow this genetic redundancy to be overcome. Another approach to identify genes that affect leaf organ size is through the screening of ethyl methanesulphonate (EMS)- or X-ray-induced mutants. Many genes, when mutated, result in negative effects on leaf organ size, often by deregulating essential processes. Mutants that have large leaves, however, are difficult to find mainly because of the high variability in growth of individual plants. To our knowledge, only the semi-dominant GRANDIFOLIA-D (gra-D) mutants showing huge leaves with two to three times more cells than the wild type have been identified by a genetic screen. Genetic and microarray analyses showed that a large segmental duplication had occurred in all gra-D mutants, consisting of the lower part of chromosome 4 (Horiguchi et al., 2009). However, now genetic screens for mutants with larger leaves should be revisited. Advances in imaging technologies should allow researchers to follow the growth of many thousands of plants over time, and therefore individual plants could be identified with altered growth characteristics. Such screens could also be combined with the use of reporter constructs that faithfully allow for the visualization of growth-related processes such as cell division and cell expansion (see further). To complement this gene-centric approach, the use of natural variants represents a non-a priori strategy to discover polymorphisms responsible for growth variation (Koornneef et al., 2004; Alonso-Blanco et al., 2009; Trontin et al., 2011; Weigel, 2012). Also this approach requires the phenotyping of a large population of plants, which is now possible with the recently developed phenotyping platforms (Granier et al., 2006; Walter et al., 2007; Jansen et al., 2009; Skirycz et al., 2011; Tisné et al., 2013; Dhondt et al., 2014). The study of recombinant inbred line (RIL) populations derived from a cross between two or more parental Arabidopsis accessions has been commonly used to identify sequence polymorphisms linked to a phenotype (Loudet et al., 2005; Topp et al., 2013; Capron et al., 2014). For example, by using the automated imaging platform Phenoscope, various shoot growth parameters have been quantified for a RIL population that allowed the identification of quantitative trait loci (QTLs) that control plant rosette growth (Tisné et al., 2013). With the recent developments in large-scale sequencing, the relationship between genotype and phenotype can now be extended to the large natural variant population of Arabidopsis for which detailed genotyping information can be obtained. Various genome-wide association (GWA) experiments have recently been performed to study the natural variation explaining various sets of quantitative root growth traits using highthroughput imaging systems in Arabidopsis (Ristova et al., 2013; Ristova and Busch, 2014; Slovak et al., 2014), but also in rice (Clark et al., 2013; Courtois et al., 2013). These studies have analysed macroscopic parameters such as the primary root length or the total root system, but to explain variation in organ growth, microscopic parameters such as cell number or size are essential. Recently, a high-throughput confocal microscopy imaging system was used to analyse the natural variation of root development in a set of Arabidopsis accessions and allowed the identification of an F-box protein for which sequence variation could explain the variance in meristem length and mature cell length (Meijón et al., 2014). So far, only few studies reported the analysis of shoot growth for GWA studies in Arabidopsis (Atwell et al., 2010; Zhang et al., 2012) and one in rice (Yang et al., 2014). Using a highthroughput phenotyping platform to quantify various shoot growth parameters in 514 rice accessions, a GWA analysis has allowed the identification of loci variations explaining growth parameters including shoot biomass (Yang et al., 2014). Loci closely located to genes previously reported to affect growth parameters related to plant height, such as SD1, Hd1, and OsGH3-2, have been identified, as well as a number of novel associated loci (Yang et al., 2014). The above approaches, applying high-throughput phenotyping of large numbers of genetically diverse accessions, help to identify genetic variation responsible for a growth phenotype which will need to be validated using classical Genes and networks for leaf growth control | 1049 molecular approaches such as functional analysis of gene candidates. In addition, with the advent of RNA sequencing, transcriptome studies of numerous accessions are possible and, in combination with large-scale phenotyping analyses, will allow researchers to link growth parameter diversity not only to genetic sequence variation but also to gene expression changes. Novel growth regulatory genes: combining chemical screening with advanced phenotyping In the past decade, chemical genomics has been proven to be a highly effective method for understanding complex and dynamic biological processes in plants, such as plant immunity, hormone signalling, cell wall biosynthesis, or endomembrane trafficking (reviewed in Hicks and Raikhel, 2012, 2014). This approach is based on the use of cell-permeable small molecules that interfere with the function of target proteins and consequently lead to disruption of a process of interest in conjunction with high-throughput screening, reverse genetics, or sequencing to identify the target proteins and their function (Robert et al., 2009; McCourt and Desveaux, 2010). The phenotypic perturbations resulting from the application of chemicals are equivalent to specific mutations since they affect the activity of a protein or a pathway. However, compared with classical plant genetics, chemical genetics enables an increase in the range of observable phenotypes, such as those associated with redundant genes, as active molecules can target one or more members of a protein family causing a phenotype not always accessible through traditional mutational methods (De Rybel et al., 2009; Park et al., 2009; Hicks and Raikhel, 2012; Benson et al., 2014). Furthermore, the chemicals can be applied at any moment throughout development, rendering the analysis of causal events preceding observed phenotypes much easier. Systematic screening for effects of small molecules implies scoring phenotypes of many plants, therefore requiring high-throughput automated analysis methods (Fig. 1). With the progress of growth phenotyping technologies, chemical genomics could be combined with recently developed highthroughput imaging systems (Dhondt et al., 2013; Sozzani et al., 2014) that allow quantification of rosette or root growth parameters for large amounts of plants. Large sets of small molecules could therefore be screened to identify compounds positively influencing leaf growth, for example. However, because generalized developmental phenotypes such as shoot growth can be attributable to a large protein target spectrum, a screen for chemicals that affect leaf size must be coupled to a narrow and precise secondary screen focused on defined read-outs; for example, one of the cellular processes possibly affecting leaf size such as an increase in cell number, a longer period of cell proliferation, or an increase in cell size (Gonzalez et al., 2012). These effects at the cellular level can, for example, be visualized by analysing the changes in expression of specific marker genes. To identify molecules stimulating lateral root development, activators of the expression of the cell division marker CYCB1;1 have been investigated by screening a large compound library for a drastic increase in expression of the β-glucuronidase (GUS) reporter gene under the control of the CYCB1;1 promoter (De Rybel et al., 2012). This study identified naxillin, a non-auxin-like synthetic molecule that induces lateral root formation in Arabidopsis (De Rybel et al., 2012). Once a molecule causing, for example, an increased leaf size is identified, methods such as genetic screens, genomic tools, or direct interaction approaches can be applied to identify the protein targeted by the chemical. One of these direct interaction approaches used to identify the molecular targets of the small molecules is known as DARTS (Lomenick et al., 2009). This technique was originally developed in yeast and mammalian cell lysates and is based on the principle that when a small molecule compound binds to a protein, the interaction stabilizes the target protein’s structure such that it becomes protease resistant. The implementation of chemical genomics for the discovery of new leaf growth regulators represents a new research area that will only be possible using adapted methodologies for detailed phenotyping at the macroscopic and microscopic level. Complex traits: from genes to networks An increasing number of studies describing the characterization of single mutants with an altered leaf growth have been published (Blomme et al., 2014; Hepworth and Lenhard, 2014; Kalve et al., 2014; Wilson-Sánchez et al., 2014). This large number of potential regulators of leaf growth highlights the complexity of the molecular system controlling final leaf size (Gonzalez et al., 2012; Hepworth and Lenhard, 2014; Kalve et al., 2014). Only a tight co-ordination between the numerous molecular players can support the formation of a functional organ. Although relationships between some leaf growth regulators start to emerge, our current knowledge of the connections existing between all known regulators is still poor and needs further investigation. DA1, encoding a ubiquitin receptor, is a negative regulator of leaf and seed size by restricting the period of cell proliferation (Li et al., 2008). In a screen for modifiers of the da1-1 phenotype, several enhancers (eod) and suppressors (sod) of DA have been identified (Li et al., 2008; Xu and Li, 2011; Du et al., 2014). A mutation in ENHANCER OF DA1 (EOD1), also known as BIG BROTHER, encoding a ubiquitin ligase and previously described as a negative regulator of organ growth (Disch et al., 2006), enhances the phenotype of the da1-1 mutant in the leaf and the seed (Li et al., 2008). Another mutation leading to a synergistic effect on seed size when combined with da1-1, but acting independently of EOD1, corresponds to the da2-1 mutation, which causes the down-regulation of another E3 ubiquitin ligase (Xia et al., 2013). A mutation in MED15 (eod8-1), encoding a subunit of the MEDIATOR complex involved in transcriptional regulation, has also been shown to enhance the large floral organ size phenotype of da1-1 (Xu and Li, 2011). MED15 functions redundantly with DA1 to control organ growth by 1050 | González and Inzé restricting cell proliferation, but is also a negative regulator of cell expansion (Xu and Li, 2011), showing the interconnection between cell division and expansion during leaf growth. Additionally, SOD2, a suppressor of da1-1, has also recently been described (Du et al., 2014). UBIQUITIN-SPECIFIC PROTEASE15 (UBP15), or SOD2, encodes a ubiquitinspecific protease, which functions antagonistically with DA1 to regulate seed size, since sod2 mutation suppresses the seed phenotype of da1-1 (Du et al., 2014). It has also been shown that SOD2 acts independently of DA2 and EOD1 for the regulation of seed size. These studies highlight the connections between several genes regulating organ size and also raise the point of organ-specific interactions between growth regulators, adding an extra layer of complexity. Additional pathways related to leaf size control have been dissected, such as the ARGOS–ANT–CYCD3;1 pathway promoting cell division in the leaf (Mizukami and Fischer, 2000; Hu et al., 2003) and the miR396–GRF–AN3/GIF regulatory network which is also involved in the regulation of cell proliferation (Kim and Kende, 2004; Horiguchi et al., 2005; Liu et al., 2009; Rodriguez et al., 2010). AN3/GIF is part of an SWI/SNF chromatin-remodelling complex that activates transcription factors such as GRFs (Vercruyssen et al., 2014). The growthpromoting SWI/SNF chromatin-remodelling complex is negatively regulated by DELLA proteins (Sarnowska et al., 2013) that are well known growth repressors whose activity is negatively regulated by gibberellin. Interestingly, through a time-course transcriptome analysis, KLUH expression has been shown to be very rapidly down-regulated when DELLA was stabilized (Claeys et al., 2014). KLUH encodes a P450 cytochrome mono-oxygenase that forms a diffusible growthpromoting molecule of as yet unknown nature (Anastasiou et al., 2007; Eriksson et al., 2010). Because these examples concern interactions between few regulatory genes, or specific pathways, to obtain a better view of the possible connections existing between the key players in growth control, a systematic analysis of double and even multiple mutants will be needed, although estimating epistasis on a quantitative trait such as leaf growth is challenging. A recent study has performed a pairwise combinatorial screen between 13 transgenic Arabidopsis lines with an increased leaf size and has identified that a large proportion of the combinations analysed showed an additional increase in leaf size resulting from a positive epistasis on growth (Vanhaeren et al., 2014). In this study, showing the potential of combinatorial approaches to discover further the connections of the leaf growth regulatory network, the binary combinations were generated by crossing homozygous parental lines. However, modifying the expression of multiple players of a network cannot easily be achieved through laborious and time-consuming crosses. The use of constructs harbouring multiple sequences leading to the simultaneous up- or down-regulation of a set of genes will therefore be required (Fig. 1). This will now be possible through the use of specific binary vectors that allow multiple fragments to be combined easily (Engler et al., 2014) and allow the transfer of large DNA fragments to plants (Untergasser et al., 2012), and through the further development of genome editing technologies (Mahfouz et al., 2014; Kumar and Jain, 2015) for plants simultaneously to target mutations in multiple genes as already developed for mice and humans (Wang et al., 2013; Sakuma et al., 2014). Modelling: from gene networks to leaf growth Using the above-described approaches, it will be possible to identify further molecular players that constitute the regulatory pathways controlling leaf growth and to determine possible relationships, primarily binary, existing between multiple components of these networks. One of the complexities is that these networks are not static but continuously changing throughout development, in different cell types and in response to the ever-changing environmental cues. To comprehend fully this extraordinary complexity and the highly dynamic behaviour of growth, mathematical modelling will be indispensable (Fig. 1). Indeed, both the number of components and the interactions between them are far too complex to grasp intuitively. Several types of models have been developed depending on the biological questions asked: (i) purely genetic models probing relationships between molecular players; (ii) models integrating genetic interactions at the subcellular, cellular, tissue, organ, or whole-plant level; and (iii) multiscale models that consider behaviours on two or more levels. Molecular networks are often not linear and include multiple branches, negative feed-back loops, or positive feedforward loops that make it difficult to predict the output of a certain pathway. Mathematical models have been developed to make such predictions for various pathways (for a review, see Middleton et al., 2012) and have helped to elucidate complex molecular networks such as the Aux/IAA auxin response network, comprising multiple negative feed-back loops (Middleton et al., 2010), or the circadian clock network which represents a complex oscillating system (reviewed in Dalchau, 2012; Chew et al., 2014a). These molecular networks obviously have an impact on different events at higher levels, and computational models are being developed to study the complexity of such processes at different scales, such as cell growth, tissue patterning, and organ growth and development, by integrating the complex molecular systems (Hill et al., 2013; Chew et al., 2014a). Several studies have modelled the growth patterns of various plant organs, such as the embryo (Bassel et al., 2014), the shoot apical meristem (Geier et al., 2008; Kierzkowski et al., 2012), the root (Laskowski et al., 2008), or flowers (Green et al., 2010; Roeder et al., 2010; Sauret-Güeto et al., 2013), based on detailed kinematic analyses using different types of imaging techniques, such as confocal microscopy or optical projection tomography. For the Arabidopsis leaf, a mathematic model, based on experimental data on cell numbers and sizes obtained over time, has been built describing the possible division patterns and expansion rates for individual epidermal cells, and therefore has helped to gain a better insight into the processes that define leaf growth (Kheibarshekan Asl et al., 2011). In addition, an open-source framework, known as VirtualLeaf, for Genes and networks for leaf growth control | 1051 cell-based modelling of leaf tissue growth and development has been built (Merks et al., 2011). VirtualLeaf-based models provide a means for plant researchers to analyse the function of developmental genes in the context of the biophysics of growth and patterning. Furthermore, by combining liveimaging at the organ and cellular level with computational modelling, a model in which the direction of growth is directed by local growth orientations has been developed, explaining Arabidopsis leaf morphology (Kuchen et al., 2012). Various morphological models incorporate molecular information (for reviews, see Hill et al., 2013; Chew et al., 2014a), especially the implication of auxin transport and polarity in root growth (Grieneisen et al., 2007), lateral root initiation (Laskowski et al., 2008), phyllotaxis (Jönsson et al., 2006), or vein formation (Bayer et al., 2009; Smith and Bayer, 2009). Furthermore, multiscale modelling integrating models at different levels from the molecular networks to different events at the cellular, tissue, organ, or organism level start to emerge (Band et al., 2012a, b; Chew et al., 2014b). For example, a whole-plant model of Arabidopsis was developed by integrating existing models from different domains ranging from genetic regulation, metabolism, to organ development, and allowed simulation and prediction of leaf production and plant biomass (Chew et al., 2014b). By increasing our knowledge of the detailed cellular kinematics of leaf growth and the identification of growth regulators and their relationships, the development of such multiscale models for leaf size control will be feasible. Such models would not only explain the role and interactions of the various players, but also could be used to predict which genes, gene combinations, or even networks could maximize plant and plant organ growth. Such an in silico evolution approach has been used to predict which perturbations of the carbon fixation pathway could lead to enhanced biomass production (Zhu et al., 2010, 2013). Obviously, the ability to modify networks to improve growth and plant productivity is not only of great academic interest, but could also contribute greatly to the enhancement of crop yield. Concluding remarks: a complex combination of expertise to understand and improve leaf growth Understanding leaf growth is obviously of great academic interest, but a better comprehension of the molecular basis of this process can also allow for maximizing the plant’s potential for food and energy production. Due to the connection existing between the several components of the leaf growth regulatory network and the pleiotropic role of some regulators (Li et al., 2008; Xia et al., 2013; Du et al., 2014;Vanhaeren et al., 2014), it is likely that slightly altering the network by targeted and mild changes in expression of various players will be more successful to improve growth than drastic changes in expression of only one regulatory gene. Fine-tuned alteration of the expression of regulatory genes in a specific organ or tissue, or during a specific stage of development, might avoid negative effects often observed by a strong ectopic expression or a complete knock-out of a gene (Horiguchi et al., 2009). For example, the down-regulation of SAMBA, a regulator of the ANAPHASE PROMOTING COMPLEX/CYCLOSOME (APC/C), leads to the formation of larger leaves and roots, but also to low fertility due to a problem with male gametogenesis (Eloy et al., 2012). A more targeted down-regulation of SAMBA in the leaf is likely to avoid the negative effects on fertility. To permit such specific expression, the large set of expression data generated in the last decade (Zimmermann et al., 2004; Hruz et al., 2008) can be used to design synthetic promoters that can be further exploited to drive the expression of regulatory genes in a specific and controlled manner. To allow network engineering, all components of the network and their interactions should be identified and dissected. Increasingly, the study of complex dynamic systems, such as leaf growth, requires multidisciplinary approaches that are essential to develop technologies enabling quantitative assessment of growth, such as automated platforms for image-based phenotyping, but also to combine the knowledge generated to create a comprehensive view on the process studied through modelling for example (Fig. 1). Therefore, plant biologists, biotechnologists, geneticists, but also bio-informaticians, engineers, chemists, and mathematicians will have to combine their expertise to enable the creation of a holistic view on the regulation of leaf growth by expanding the regulatory networks with new players, but also to detail further the relationship between the previously identified components. Ultimately, through these combined approaches, it will be possible to model leaf growth at multiple scales: from molecular networks whose output feeds into growth at cellular scales, to cell-based models that will be the basis to model leaf growth at the organ and plant level. Acknowledgements The authors would like to acknowledge Annick Bleys who helped in preparing the manuscript, and the members of the System Biology of Yield group for fruitful discussion. The authors also apologize to colleagues whose work has not been included in this review. This work was supported by grants from the ‘Bijzonder Onderzoeksfonds Methusalem Project’ (BOF08/01M00408) of Ghent University and the Interuniversity Attraction Poles Programme (IUAP P7/29 ‘MARS’) initiated by the Belgian Science Policy Office. References Alonso-Blanco C, Aarts MGM, Bentsink L, Keurentjes JJB, Reymond M, Vreugdenhil D, Koornneef M. 2009. 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