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author:("trafs, Jan")
1.  A Computational Framework for 3D Mechanical Modeling of Plant Morphogenesis with Cellular Resolution 
PLoS Computational Biology  2015;11(1):e1003950.
The link between genetic regulation and the definition of form and size during morphogenesis remains largely an open question in both plant and animal biology. This is partially due to the complexity of the process, involving extensive molecular networks, multiple feedbacks between different scales of organization and physical forces operating at multiple levels. Here we present a conceptual and modeling framework aimed at generating an integrated understanding of morphogenesis in plants. This framework is based on the biophysical properties of plant cells, which are under high internal turgor pressure, and are prevented from bursting because of the presence of a rigid cell wall. To control cell growth, the underlying molecular networks must interfere locally with the elastic and/or plastic extensibility of this cell wall. We present a model in the form of a three dimensional (3D) virtual tissue, where growth depends on the local modulation of wall mechanical properties and turgor pressure. The model shows how forces generated by turgor-pressure can act both cell autonomously and non-cell autonomously to drive growth in different directions. We use simulations to explore lateral organ formation at the shoot apical meristem. Although different scenarios lead to similar shape changes, they are not equivalent and lead to different, testable predictions regarding the mechanical and geometrical properties of the growing lateral organs. Using flower development as an example, we further show how a limited number of gene activities can explain the complex shape changes that accompany organ outgrowth.
Author Summary
In recent years, much research in molecular and developmental biology has been devoted to unravelling the mechanisms that govern the development of living systems. This includes the identification of key molecular networks that control shape formation and their response to hormonal regulation. However, a key challenge now is to understand how these signals, which arise at cellular scale, are physically translated into growth at organ scale, and how these shape changes feed back into molecular regulation systems. To address this question, we developed a computational framework to model the mechanics of 3D tissues during growth at cellular resolution. In our approach, gene regulation is related to tissue mechanical properties through a constitutive tensorial growth equation. Our computational system makes it possible to integrate this equation in both space and time over the growing multicellular structure in close to interactive time. We demonstrate the interest of such a framework to study morphogenesis by constructing a model of flower development, showing how regulation of regional identities can, by dynamically modulating the mechanical properties of cells, lead to realistic shape development.
PMCID: PMC4288716  PMID: 25569615
2.  A correlative microscopy approach relates microtubule behaviour, local organ geometry, and cell growth at the Arabidopsis shoot apical meristem 
Journal of Experimental Botany  2013;64(18):5753-5767.
Cortical microtubules (CMTs) are often aligned in a particular direction in individual cells or even in groups of cells and play a central role in the definition of growth anisotropy. How the CMTs themselves are aligned is not well known, but two hypotheses have been proposed. According to the first hypothesis, CMTs align perpendicular to the maximal growth direction, and, according to the second, CMTs align parallel to the maximal stress direction. Since both hypotheses were formulated on the basis of mainly qualitative assessments, the link between CMT organization, organ geometry, and cell growth is revisited using a quantitative approach. For this purpose, CMT orientation, local curvature, and growth parameters for each cell were measured in the growing shoot apical meristem (SAM) of Arabidopsis thaliana. Using this approach, it has been shown that stable CMTs tend to be perpendicular to the direction of maximal growth in cells at the SAM periphery, but parallel in the cells at the boundary domain. When examining the local curvature of the SAM surface, no strict correlation between curvature and CMT arrangement was found, which implies that SAM geometry, and presumed geometry-derived stress distribution, is not sufficient to prescribe the CMT orientation. However, a better match between stress and CMTs was found when mechanical stress derived from differential growth was also considered.
PMCID: PMC3871827  PMID: 24153420
Arabidopsis thaliana; cortical microtubules; growth; mechanical stress; organ geometry; shoot apical meristem.
3.  The Flux-Based PIN Allocation Mechanism Can Generate Either Canalyzed or Diffuse Distribution Patterns Depending on Geometry and Boundary Conditions 
PLoS ONE  2013;8(1):e54802.
Growth and morphogenesis in plants require controlled transport of the plant hormone auxin. An important participant is the auxin effluxing protein PIN, whose polarized subcellular localization allows it to effectively transport auxin large distances through tissues. The flux-based model, in which auxin flux through a wall stimulates PIN allocation to that wall, is a dominant contender among models determining where and in what quantity PIN is allocated to cell walls. In this paper we characterise the behaviour of flux-based PIN allocation models in various tissues of the shoot apical meristem. Arguing from both mathematical analysis and computer simulations, we describe the natural behaviours of this class of models under various circumstances. In particular, we demonstrate the important dichotomy between sink- and source- driven systems, and show that both diffuse and canalized PIN distributions can be generated simultaneously in the same tissue, without model hybridization or variation of PIN-related parameters. This work is performed in the context of the shoot apical and floral meristems and is applicable to the construction of a unified PIN allocation model.
PMCID: PMC3557273  PMID: 23382973
4.  Auxin at the Shoot Apical Meristem 
Plants continuously generate new tissues and organs through the activity of populations of undifferentiated stem cells, called meristems. Here, we discuss the so-called shoot apical meristem (SAM), which generates all the aerial parts of the plant. It has been known for many years that auxin plays a central role in the functioning of this meristem. Auxin is not homogeneously distributed at the SAM and it is thought that this distribution is interpreted in terms of differential gene expression and patterned growth. In this context, auxin transporters of the PIN and AUX families, creating auxin maxima and minima, are crucial regulators. However, auxin transport is not the only factor involved. Auxin biosynthesis genes also show specific, patterned activities, and local auxin synthesis appears to be essential for meristem function as well. In addition, auxin perception and signal transduction defining the competence of cells to react to auxin, add further complexity to the issue. To unravel this intricate signaling network at the SAM, systems biology approaches, involving not only molecular genetics but also live imaging and computational modeling, have become increasingly important.
Auxin dynamically regulates patterning at the shoot apical meristem. Transporters and local biosynthesis are involved in the control of its distribution at the shoot apex, where it is required for formation of new buds.
PMCID: PMC2845202  PMID: 20452945
5.  The auxin signalling network translates dynamic input into robust patterning at the shoot apex 
We provide a comprehensive expression map of the different genes (TIR1/AFBs, ARFs and Aux/IAAs) involved in the signalling pathway regulating gene transcription in response to auxin in the shoot apical meristem (SAM).We demonstrate a relatively simple structure of this pathway using a high-throughput yeast two-hybrid approach to obtain the Aux/IAA-ARF full interactome.The topology of the signalling network was used to construct a model for auxin signalling and to predict a role for the spatial regulation of auxin signalling in patterning of the SAM.We used a new sensor to monitor the input in the auxin signalling pathway and to confirm the model prediction, thus demonstrating that auxin signalling is essential to create robust patterns at the SAM.
The plant hormone auxin is a key morphogenetic signal involved in the control of cell identity throughout development. A striking example of auxin action is at the shoot apical meristem (SAM), a population of stem cells generating the aerial parts of the plant. Organ positioning and patterning depends on local accumulations of auxin in the SAM, generated by polar transport of auxin (Vernoux et al, 2010). However, it is still unclear how auxin is distributed at cell resolution in tissues and how the hormone is sensed in space and time during development. A complex ensemble of 29 Aux/IAAs and 23 ARFs is central to the regulation of gene transcription in response to auxin (for review, see Leyser, 2006; Guilfoyle and Hagen, 2007; Chapman and Estelle, 2009). Protein–protein interactions govern the properties of this transduction pathway (Del Bianco and Kepinski, 2011). Limited interaction studies suggest that, in the absence of auxin, the Aux/IAA repressors form heterodimers with the ARF transcription factors, preventing them from regulating target genes. In the presence of auxin, the Aux/IAA proteins are targeted to the proteasome by an SCF E3 ubiquitin ligase complex (Chapman and Estelle, 2009; Leyser, 2006). In this process, auxin promotes the interaction between Aux/IAA proteins and the TIR1 F-box of the SCF complex (or its AFB homologues) that acts as an auxin co-receptor (Dharmasiri et al, 2005a, 2005b; Kepinski and Leyser, 2005; Tan et al, 2007). The auxin-induced degradation of Aux/IAAs would then release ARFs to regulate transcription of their target genes. This includes activation of most of the Aux/IAA genes themselves, thus establishing a negative feedback loop (Guilfoyle and Hagen, 2007). Although this general scenario provides a framework for understanding gene regulation by auxin, the underlying protein–protein network remains to be fully characterized.
In this paper, we combined experimental and theoretical analyses to understand how this pathway contributes to sensing auxin in space and time (Figure 1). We first analysed the expression patterns of the ARFs, Aux/IAAs and TIR1/AFBs genes in the SAM. Our results demonstrate a general tendency for most of the 25 ARFs and Aux/IAAs detected in the SAM: a differential expression with low levels at the centre of the meristem (where the stem cells are located) and high levels at the periphery of the meristem (where organ initiation takes place). We also observed a similar differential expression for TIR1/AFB co-receptors. To understand the functional significance of the distribution of ARFs and Aux/IAAs in the SAM, we next investigated the global structure of the Aux/IAA-ARF network using a high-throughput yeast two-hybrid approach and uncover a rather simple topology that relies on three basic generic features: (i) Aux/IAA proteins interact with themselves, (ii) Aux/IAA proteins interact with ARF activators and (iii) ARF repressors have no or very limited interactions with other proteins in the network.
The results of our interaction analysis suggest a model for the Aux/IAA-ARF signalling pathway in the SAM, where transcriptional activation by ARF activators would be negatively regulated by two independent systems, one involving the ARF repressors, the other the Aux/IAAs. The presence of auxin would remove the inhibitory action of Aux/IAAs, but leave the ARF repressors to compete with ARF activators for promoter-binding sites. To explore the regulatory properties of this signalling network, we developed a mathematical model to describe the transcriptional output as a function of the signalling input that is the combinatorial effect of auxin concentration and of its perception. We then used the model and a simplified view of the meristem (where the same population of Aux/IAAs and ARFs exhibit a low expression at the centre and a high expression in the peripheral zone) for investigating the role of auxin signalling in SAM function. We show that in the model, for a given ARF activator-to-repressor ratio, the gene induction capacity increases with the absolute levels of ARF proteins. We thus predict that the differential expression of the ARFs generates differences in auxin sensitivities between the centre (low sensitivity) and the periphery (high sensitivity), and that the expression of TIR1/AFB participates to this regulation (prediction 1). We also use the model to analyse the transcriptional response to rapidly changing auxin concentrations. By simulating situations equivalent either to the centre or the periphery of our simplified representation of the SAM, we predict that the signalling pathway buffers its response to the auxin input via the balance between ARF activators and repressors, in turn generated by their differential spatial distributions (prediction 2).
To test the predictions from the model experimentally, we needed to assess both the input (auxin level and/or perception) and the output (target gene induction) of the signalling cascade. For measuring the transcriptional output, the widely used DR5 reporter is perfectly adapted (Figure 5) (Ulmasov et al, 1997; Sabatini et al, 1999; Benkova et al, 2003; Heisler et al, 2005). For assaying pathway input, we designed DII-VENUS, a novel auxin signalling sensor that comprises a constitutively expressed fusion of the auxin-binding domain (termed domain II or DII) (Dreher et al, 2006; Tan et al, 2007) of an IAA to a fast-maturating variant of YFP, VENUS (Figure 5). The degradation patterns from DII-VENUS indicate a high auxin signalling input both in flower primordia and at the centre of the SAM. This is in contrast to the organ-specific expression pattern of DR5::VENUS (Figure 5). These results indicate that the signalling pathway limits gene activation in response to auxin at the meristem centre and confirm the differential sensitivity to auxin between the centre and the periphery (prediction 1). We further confirmed the buffering capacities of the signalling pathway (prediction 2) by carrying out live imaging experiments to monitor DII-VENUS and DR5::VENUS expression in real time (Figure 5). This analysis reveals the presence of important temporal variations of DII-VENUS fluorescence, while DR5::VENUS does not show such global variations. Our approach thus provides evidence that the Aux/IAA-ARF pathway has a key role in patterning in the SAM, alongside the auxin transport system. Our results illustrate how the tight spatio-temporal regulation of both the distribution of a morphogenetic signal and the activity of the downstream signalling pathway provides robustness to a dynamic developmental process.
A comprehensive expression and interaction map of auxin signalling factors in the Arabidopsis shoot apical meristem is constructed and used to derive a mathematical model of auxin signalling, from which key predictions are experimentally confirmed.
The plant hormone auxin is thought to provide positional information for patterning during development. It is still unclear, however, precisely how auxin is distributed across tissues and how the hormone is sensed in space and time. The control of gene expression in response to auxin involves a complex network of over 50 potentially interacting transcriptional activators and repressors, the auxin response factors (ARFs) and Aux/IAAs. Here, we perform a large-scale analysis of the Aux/IAA-ARF pathway in the shoot apex of Arabidopsis, where dynamic auxin-based patterning controls organogenesis. A comprehensive expression map and full interactome uncovered an unexpectedly simple distribution and structure of this pathway in the shoot apex. A mathematical model of the Aux/IAA-ARF network predicted a strong buffering capacity along with spatial differences in auxin sensitivity. We then tested and confirmed these predictions using a novel auxin signalling sensor that reports input into the signalling pathway, in conjunction with the published DR5 transcriptional output reporter. Our results provide evidence that the auxin signalling network is essential to create robust patterns at the shoot apex.
PMCID: PMC3167386  PMID: 21734647
auxin; biosensor; live imaging; ODE; signalling
6.  Is cell polarity under mechanical control in plants? 
Plant Signaling & Behavior  2011;6(1):137-139.
Plant cells experience a tremendous amount of mechanical stress caused by turgor pressure. Because cells are glued to their neighbors by the middle lamella, supracellular patterns of physical forces are emerging during growth, usually leading to tension in the epidermis. Cortical microtubules have been shown to reorient in response to these mechanical stresses, and to resist them, indirectly via their impact on the anisotropic structure of the cell wall. In a recent study, we show that the polar localization of the auxin efflux carrier PIN1 can also be under the control of physical forces, thus linking cell growth rate and anisotropy by a common mechanical signal. Because of the known impact of auxin on the stiffness of the cell wall, this suggests that the mechanical properties of the extracellular matrix play a crucial signaling role in morphogenesis, notably controlling the polarity of the cell, as observed in animal systems.
PMCID: PMC3122027  PMID: 21258209
development; growth; auxin; microtubule; PIN1; stiffness; cell wall; biophysics; meristem
7.  Alignment between PIN1 Polarity and Microtubule Orientation in the Shoot Apical Meristem Reveals a Tight Coupling between Morphogenesis and Auxin Transport 
PLoS Biology  2010;8(10):e1000516.
Imaging and computational modeling of the Arabidopsis shoot meristem epidermis suggests that biomechanical signals coordinately regulate auxin efflux carrier distribution and microtubule patterning to orchestrate the extent and directionality of growth.
Morphogenesis during multicellular development is regulated by intercellular signaling molecules as well as by the mechanical properties of individual cells. In particular, normal patterns of organogenesis in plants require coordination between growth direction and growth magnitude. How this is achieved remains unclear. Here we show that in Arabidopsis thaliana, auxin patterning and cellular growth are linked through a correlated pattern of auxin efflux carrier localization and cortical microtubule orientation. Our experiments reveal that both PIN1 localization and microtubule array orientation are likely to respond to a shared upstream regulator that appears to be biomechanical in nature. Lastly, through mathematical modeling we show that such a biophysical coupling could mediate the feedback loop between auxin and its transport that underlies plant phyllotaxis.
Author Summary
The proper development of plant organs such as leaves or flowers depends both on localized growth, which can be controlled by the plant hormone auxin, and directional growth, which is dependent on each cell's microtubule cytoskeleton. In this paper we show that at the shoot apex where organs initiate the orientation of the microtubule cytoskeleton is correlated with the orientation of the auxin transporter PIN1, suggesting coordination between growth patterning at the tissue level and directional growth at the cellular level. Recent work has indicated that mechanical signals play a role in orienting the plant microtubule network, and here we show that such signals can also orient PIN1. In addition, we demonstrate through mathematical modeling that an auxin transport system that is coordinated by mechanical signals akin to those we observed in vivo is sufficient to give rise to the patterns of organ outgrowth found in the plant Arabidopsis thaliana.
PMCID: PMC2957402  PMID: 20976043
8.  Flux-Based Transport Enhancement as a Plausible Unifying Mechanism for Auxin Transport in Meristem Development 
PLoS Computational Biology  2008;4(10):e1000207.
Plants continuously generate new organs through the activity of populations of stem cells called meristems. The shoot apical meristem initiates leaves, flowers, and lateral meristems in highly ordered, spiralled, or whorled patterns via a process called phyllotaxis. It is commonly accepted that the active transport of the plant hormone auxin plays a major role in this process. Current hypotheses propose that cellular hormone transporters of the PIN family would create local auxin maxima at precise positions, which in turn would lead to organ initiation. To explain how auxin transporters could create hormone fluxes to distinct regions within the plant, different concepts have been proposed. A major hypothesis, canalization, proposes that the auxin transporters act by amplifying and stabilizing existing fluxes, which could be initiated, for example, by local diffusion. This convincingly explains the organised auxin fluxes during vein formation, but for the shoot apical meristem a second hypothesis was proposed, where the hormone would be systematically transported towards the areas with the highest concentrations. This implies the coexistence of two radically different mechanisms for PIN allocation in the membrane, one based on flux sensing and the other on local concentration sensing. Because these patterning processes require the interaction of hundreds of cells, it is impossible to estimate on a purely intuitive basis if a particular scenario is plausible or not. Therefore, computational modelling provides a powerful means to test this type of complex hypothesis. Here, using a dedicated computer simulation tool, we show that a flux-based polarization hypothesis is able to explain auxin transport at the shoot meristem as well, thus providing a unifying concept for the control of auxin distribution in the plant. Further experiments are now required to distinguish between flux-based polarization and other hypotheses.
Author Summary
Plants continuously generate new organs through the activity of populations of stem cells called meristems. The shoot apical meristem (SAM) initiates leaves, flowers, and lateral organs in highly ordered, spiraled, or whorled arrangements via a process called phyllotaxis. Auxin, a plant hormone, plays an essential role in this process. It is actively transported from cell to cell by specific membrane-associated transporters. In the SAM, this coordinated transport creates organized auxin fluxes resulting in hormone accumulation at precise positions, where organ formation is triggered. One key question in this process is to understand how auxin transport is coordinated. To address this issue, we have investigated a specific hypothesis, the canalization hypothesis, whereby every cell senses and attempts to stabilize existing hormone fluxes. Because such a patterning process would require the interaction of hundreds of cells, it is impossible to estimate on a purely intuitive basis whether it would be able to generate the observed organ positions. We, therefore, developed a computational approach to test this hypothesis and showed that a flux-based mechanism is indeed able to generate phyllotactic patterns and is consistent with biological data describing meristem development.
PMCID: PMC2565506  PMID: 18974825
9.  The shoot apical meristem: the dynamics of a stable structure. 
The shoot apical meristem (SAM) is a group of proliferating, embryonic-type cells that generates the aerial parts of the plant. SAMs are highly organized and stable structures that can function for years or even centuries. This is in apparent contradiction to the behaviour of their constituent cells, which continuously proliferate and differentiate. To reconcile the dynamic nature of the cells with the stability of the overall system the existence of elaborate signalling networks has been proposed. This is supported by recent work suggesting that the exchange of signals between cells, rather than a rigidly predetermined genetic program, is required for the establishment and functioning of an organized meristem. Together these interactions form a stable network, set up during embryogenesis, that assures the coordination of cell behaviour throughout development. Besides meristem-specific signalling cascades such as the CLAVATA receptor kinase pathway, which controls meristem size, these interactions involve plant hormones. In particular, cytokinins and auxins are implicated in the maintenance of meristem identity and phyllotaxis, respectively.
PMCID: PMC1692983  PMID: 12079669

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