Physiologia Plantarum 151: 73–82. 2014
ISSN 0031-9317
MINIREVIEW
Systems biology approaches to understand the role of auxin in root growth and development Tatsuaki Goha,b , Ute Voβ a , Etienne Farcota,c , Malcolm J. Bennetta and Anthony Bishoppa∗ a
Centre for Plant Integrative Biology, School of Biosciences, University of Nottingham, Loughborough, UK Graduate School of Science, Kobe University, Kobe, Hyogo, Japan c School of Mathematical Sciences, University of Nottingham, Nottingham, UK b
Correspondence *Corresponding author, e-mail: [email protected] Received 19 November 2013; revised 28 January 2014 doi:10.1111/ppl.12162
The past decade has seen major advances in our understanding of auxin regulated root growth and developmental processes. Key genes have been identified that regulate and/or mediate auxin homeostasis, transport, perception and response. The molecular and biochemical reactions that underpin auxin signalling are non-linear, with feed-forward and feedback loops contributing to the robustness of the system. As our knowledge of auxin biology becomes increasingly complex and their outputs less intuitive, modelling is set to become much more important. For the last several decades modelling efforts have focused on auxin transport and, latterly, on auxin response. Recently researchers have employed multi-scale modelling approaches to predict emergent properties at the tissue and organ scales. Such innovative modelling approaches are proving very promising, revealing new mechanistic insights about how auxin functions within a multicellular context to control plant growth and development. In this review we initially describe examples of models capturing auxin transport and response pathways, and then discuss increasingly complex models that integrate multiple hormone response pathways, tissues and/or scales.
Introduction As knowledge of auxin regulated root growth and development increases, it is becoming clear that many of the key regulatory components operate within complex sub/cellular/tissue-scale networks (reviewed in this special issue). As a consequence, researchers have shifted their focus from studying individual gene products, to dissecting more complex regulatory relationships between multiple components within non-linear transduction pathways (Band et al. 2012). For example, the canonical nuclear-localised TIR1-Aux/IAA-ARF auxin response machinery includes Aux/IAA-based negative feedback and/or ARF-based positive feed-forward loops to either stabilise and/or amplify pathway output,
respectively. Hence, the outputs from such pathways are often non-intuitive and new approaches are needed in order to understand these complex dynamics. As a result, researchers are turning to systems approaches and employing mathematical and/or computational models to simulate the behaviours of non-linear auxin response networks to predict their output and reveal novel emergent properties (reviewed in Middleton et al. 2012). In the past, mathematical models have been used to ‘document’ molecular processes. For example, experimental biologists may generate a hypothesis around a series of experimental results and build a model to recapitulate these observations and show that their proposed networks can recreate the observed
Abbreviations – ARF, auxin response factor; BDL, BODENLOS; DZ, differentiation zone; EZ, elongation zone; LRP, lateral root primordia; MP, monopteros; MZ, meristematic zone; ODE, ordinary differential equation; PIN, PIN-FORMED; PLT, PLETHORA; PHB, PHABULOSA; QC, quiescent centre; SHR, SHORT ROOT.
© 2014 The Authors. Physiologia Plantarum published by John Wiley & Sons Ltd on behalf of Scandinavian Plant Physiology Society. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
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behaviour. However, recent mathematical models have gone beyond describing known biological processes. Through the iterative process of combining simulation with experimentation, these models force us to question our existing assumptions about biological systems and allow us to identify gaps in our knowledge. The best models make novel predictions to fill these gaps and in doing so, guide experimental design towards testing these model predictions. In this review, we will discuss how modelling approaches are helping researchers understand the mechanistic behaviour of auxin and how this signal controls root growth and development. We initially describe examples of models capturing hormone transport and response pathways, and then discuss increasingly complex models that integrate multiple hormone response pathways and bridge spatio/temporal scales. We have selected examples where the models have challenged our understanding of how auxin regulates development, either by predicting missing components in incomplete molecular networks or through proposing new properties emerging at the organ scales. Owing to space limits, we have focused this review on recent advances on root development and apologise to readers for not being able to cover the excellent work done in the shoot apical meristem, ovules and other organs. For more information about these, we recommend several excellent reviews (Krupinski and Jonsson 2010, Band et al. 2012, Middleton et al. 2012, Murray et al. 2012, van Berkel et al. 2013).
Auxin transport Comparing and contrasting models Auxin transport has been the focus of modelling studies for several decades (Mitchison 1980a, 1980b, Mitchison et al. 1981). Auxin is actively transported by several classes of specialised carriers that include: AUX1/LAX proteins that mediate auxin influx; the PIN-FORMED (PIN) family that functions as auxin efflux carriers and exhibit polarised localisation on specific cell faces. The transport of auxin from cell-to-cell results in localised asymmetries that drive developmental processes. Long distance transport of auxin is a complex multi-scale phenomenon, incorporating the sub-cellular redistribution of PIN transporters, long-range transport of auxin across the whole plant as well as tight control of auxin perception at the organ and tissue scales. This complexity has fostered a large number of mathematical and computational models. Early auxin transport models hypothesised that the flux of auxin through cell membranes reinforces itself, resulting in sharp patterns 74
(Mitchison 1980a, 1980b, Mitchison et al. 1981). The transport of auxin was described using abstract variables representing the permeability of cell membranes and whose value was an increasing function of the directed flux of auxin (as PIN proteins were not known at the time of these studies). As an alternative to Mitchison’s flux-based model, so-called gradient-based models of auxin transport were introduced, in which the local accumulation of transporters depends on differences in auxin concentration between neighbouring cells and follows increasing gradient directions, rather than the flux across cell ¨ membranes (Jonsson et al. 2006, Smith et al. 2006). However, it is unclear whether PIN accumulation is regulated by auxin flux, its gradient, or some other mechanism. Alternative models tested include intracellular PIN distribution being jointly regulated by a hypothetical extracellular auxin receptor and intracellular auxin signalling (Wabnik et al. 2010) or where mechanical stress and its influence on microtubule orientation control the cell polarity (Hamant et al. 2008). Some studies have also adopted a composite model, incorporating both flux-based and gradient-based PIN regulation, in a tissue dependent way (Bayer et al. 2009). Several more theoretical studies considered the general patterning abilities of different models. For example, using tools from non-linear dynamical systems theory (Strogatz 2001), both gradient (Draelants et al. 2013) and flux (Farcot and Yuan 2013) based models were able to create more complex behaviours such as travelling waves and stable oscillations of auxin. Modelling root apical meristem development A large number of auxin transport models have focused on the Arabidopsis root and shoot apical meristems, and the pioneering work performed in modelling auxin flux in the shoot has had profound bearings on modelling efforts in the root. As the shoot models have been reviewed recently (for example, see Murray et al. 2012), we will focus this review on roots and the processes occurring after the embryonic root has formed. The earliest events in root development involve the establishment of an apical-basal axis during embryogenesis. This process has been modelled, uncovering a minimal mechanistic framework for generating the cell polarity within the embryo leading to the subsequent formation of the root pole (Wabnik et al. 2013). In the Arabidopsis root, two independent two-dimensional models of auxin transport have been created to explore different transport mechanisms (Grieneisen et al. 2007, Mironova et al. 2010). Both involved similar templates consisting of a structured layout of rectangular cells,
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Fig. 1. The cellular arrangements in the 2-D reflux loop and reflective flow models. (A) The cell layout described in the reflux loop model by Grieneisen et al. (2007) showing the four cell types [vascular (green), epidermal (dark blue), columella (light blue) and border cells (yellow)]. (B) The cell layout in the reflective flow model by Mironova et al (2010) uses just two cell types [vascular (green) and non-vascular (grey)]. In both images the auxin flows are shown with red arrows. Image reproduced from Mironova et al. (2010).
however they differed in the amount of positional information provided. In the reflux loop model, PIN proteins were pre-positioned within four cell types based on experimental observations (Fig. 1A) (Grieneisen et al. 2007). When auxin was provided to the system, the model predicted that an auxin maximum formed at the root apex because of large fluxes from vascular tissues and drained via the epidermis (resembling a reverse fountain). The site of the auxin maximum proved to be robust to changes in model parameters and was stably maintained when auxin-mediated growth was introduced into the system (Grieneisen et al. 2007). Whilst the reflux loop was able to capture many aspects of auxin transport in the mature root, it is difficult to apply this model to the de novo formation of new auxin maxima in embryonic roots or newly emerged lateral roots as it requires PINs to be placed in specific orientations in a cell-specific manner. Experimental evidence shows that the shootward-localised PIN, PIN2, is not expressed during the early stages of root development (Benkov´a et al. 2003, Friml et al. 2003). To address the formation of an auxin maximum in newly formed roots
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the reflective flow model was developed (Mironova et al. 2010). When applied to a two-dimensional template similar to that used in the reflux loop model, the reflective flow model required only two cell types (vascular and non-vascular cells) and only required one PIN, PIN1, to be localised on rootward-facing membranes in the vascular cells (Fig. 1B). Crucially in this model, PIN1 synthesis is regulated by low levels of auxin and PIN1 degraded at high levels of auxin. Initially the low auxin levels in the vascular cells re-enforced the rootward flux of auxin, resulting in accumulation of auxin in the most rootward layer of vascular cells. This was followed by the accumulation of a high amount of auxin in the second most rootward layer of cells, whereupon auxin can diffuse into this from the most rootward layer of cells (the reflective flow). As soon as the auxin levels reach the threshold for auxin-dependent PIN1 degradation, auxin starts to inhibit PIN1 expression, leading to a decrease in auxin levels in the most rootward cell layer and a new auxin maximum in the second most rootward layer of cells. This process can shift the auxin maximum to the third or fourth cells until the rootward and reflected fluxes of auxin become balanced. Recently the reflux loop and reflective flow models were combined in a dual-mechanism model that could capture the benefits of both systems (Mironova et al. 2012). To introduce the reverse fountain PIN2 and PIN3 were included into the reflective flow model and localised in the same manner as the model in Grieneisen et al. (2007); however the levels of these proteins were controlled by auxin. This dual-mechanism model was able to simulate the realistic regeneration of the root apical meristem upon decapitation (previously seen in the reflective flow model but not the reflux loop model). When a basal rate of auxin synthesis was included, this was able to maintain an auxin maximum at the root apex when the shoot was removed (previously seen in the reflux loop model but not the reflective flow model) (Mironova et al. 2012). However, maintaining an auxin maximum at the quiescent centre (QC) position is unlikely to be the only requirement for maintaining root growth. Growth is controlled by maintaining the rate of cell division in the meristematic zone (MZ) of the root above QC, cell elongation in the elongation zone (EZ) and above this, cell differentiation in the differentiation zone (DZ). The activity of these domains are controlled by the level of the PLETHORA (PLT ) family of genes (Aida et al. 2004, Galinha et al. 2007). Although other factors contribute to the levels of PLT (Matsuzaki et al. 2010), they are believed to be controlled mainly through a gradient of auxin (Galinha et al. 2007). The central question is: does auxin produce a well enough defined 75
gradient to define these zonations within the root? Experimentally this is exceedingly challenging to address as even with the newest auxin sensors (Brunoud et al. 2012), we can only measure auxin response. A recent study investigated three possible gradient-generating mechanisms in silico that could potentially supply sufficient positional information to create a gradient of auxin across the root at a scale sufficient to determine the size and position of the MZ, EZ and DZ (Grieneisen et al. 2012). These included a source-decay mechanism (with auxin being synthesised at the root apex but auxin diffusion and degradation throughout the root), a unidirectional transport mechanism (comprising of a tissue with just vascular and pericycle cell files and the QC) and the reflux loop model. It was found that only the reflux loop model was able to form an exponentially increasing auxin gradient that spanned the entire MZ and part of the EZ; the auxin gradient was much too shallow with the source-decay mechanism, or much too steep with the uni-directional transport mechanism (Grieneisen et al. 2012).
Modelling root hair elongation Root hairs provide a vital function in increasing the surface area of roots to enable increased uptake of water and nutrients. Each hair is a thin tubular structure that forms from a single root hair forming epidermal cell (hair cell) in the DZ. The assignment of epidermal cell fate as hair or non-hair cells is determined based on cell positioning through a well characterised gene regulatory network (Grebe 2012). Auxin does not affect the determination hair vs non-hair cell fate, however the elongation of root hair is positively regulated by auxin (Yi et al. 2010). Cell type specific activation or inhibition of auxin signalling indicated that auxin signalling controls root hair growth in hair cells in a cell autonomous manner (Won et al. 2009, Ganguly et al. 2010). However, analysis of the auxin response reporter, DR5, revealed that there is a higher auxin response in non-hair cells than hair cells (Jones et al. 2008). Why should this be so? The reflux loop model of auxin transport (see section on auxin transport) shows a recycling of auxin from the root tip through the epidermal cells and this is mediated through the auxin influx carrier, AUX1 and efflux carrier, PIN2 (Blilou et al. 2005, Grieneisen et al. 2007). However, it was unknown if these proteins had differential levels of activity in hair and non-hair cells. A combination of experimental approaches revealed that AUX1 is expressed only in the non-hair cells, although PIN2 is expressed in both cell types (Jones et al. 2008). 76
In order to understand importance of non-hair cell-specific expression of AUX1, Jones and colleagues simulated auxin movement using three-dimensional geometry of the outer three layers of the root (epidermis, cortex and endodermis) (Jones et al. 2008). This allowed them to investigate both active transport of auxin and passive diffusion laterally between epidermal cell lineages and between adjacent layers. The model predicted that specific expression of AUX1 in non-hair cells causes the accumulation of an approximately 10fold higher concentration of auxin in non-hair cells than hair cells. As auxin can move by diffusion, the simulations predict that although it is at a lower level, this auxin level in root hair cells is within the measured range of biological activity in root hair assays. In simulations lacking AUX1, the model predicted a rapid decrease in auxin concentration with increasing distance from the root meristem, as auxin diffused into the stele or out of the root entirely, meaning that cells in the DZ are supplied with less auxin. This suggested that AUX1dependent transport of auxin in non-hair cells may provide a mechanism to supply auxin to the hair cells as they get progressively further away from the root tip and enter the DZ. The authors made the assumption that root hair growth occurs above a certain threshold of auxin. They speculated that if this is the case, the root hairs should stop growing closer to the root tip in aux1 mutants (as the auxin levels decrease more quickly) and subsequently confirmed this theory through experimental analyses. Together this combination of simulations and experimentation unveiled a distinct function for non-hair cells in sustaining high auxin levels in the DZ by AUX1-dependent auxin influx to enable the subsequent supply of auxin to initiate the growth of hair cells.
Modelling auxin response An auxin maximum created by active transport must elicit a localised auxin response in order to trigger a developmental output. The molecular and biochemical reactions that underpin auxin signalling are non-linear, with feed-forward and feedback loops contributing to the robustness of the system (Vernoux et al. 2011). Auxin functions in conjunction with its TIR1/AFB1-5 co-receptor to mediate the degradation of the Aux/IAA family of proteins that repress auxin response factors (ARFs) (Dharmasiri et al. 2005, Kepinski and Leyser 2005). ARFs regulate various downstream genes that include Aux/IAAs. Hence, the pathway comprises multiple negative feedback loops. To help understand the output from the auxin response pathway, Middleton et al. (2010) developed
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a mathematical model of the auxin response network using ordinary differential equations (ODEs). The model included auxin, TIR1, ARF and Aux/IAA proteins, together with their regulatory relationships. The authors built the model using realistic parameters based on quantitative data already available from molecular studies on protein turnover and transcription rates. Model simulations confirmed the importance of the turnover rates of Aux/IAA proteins. However, the model also revealed some interesting discrepancies between its behaviour and the experimental data. For example, experiments have reported up to 30-fold fold-changes in some mRNA species (Abel et al. 1995). To achieve such a fold-change in the model required an extremely large (and possibly unrealistic) increase in auxin levels. This points to the existence of additional regulatory mechanisms that may serve to amplify the response (as measured by Aux/IAA mRNA levels) made by cells to changes in auxin. A number of ARF-encoding genes are themselves auxin responsive (Okushima et al. 2005), which could represent a feed-forward loop that allows signal amplification. Lau et al. (2011) recently showed that the ARF family member MONOPTEROS (MP) upregulates both its own expression and the expression of the gene encoding Aux/IAA family member BODENLOS (BDL). The presence of a positive feedback loop can lead to bistability, i.e. when a system can rest in any of two stable states, rather than just one. This enables regulatory networks to exhibit switch-like behaviour to amplify response pathway output. For example, increasing auxin levels can switch the system from a low to a high MP/BDL concentration (Lau et al. 2011). Interestingly, as auxin levels decrease MP and BDL levels remain up regulated for several hours (Lau et al. 2011). This latter behaviour is termed hysteresis, reflecting the fact that the response of a bistable system depends on both current and past conditions. Bistable systems can also generate switchlike responses to changes in signal input. Hence, once the system is in a MP upregulated state, the behaviour of the network will be robust to large changes in the level of auxin. Such behaviour of the MP response network enables auxin to induce all or nothing developmental outputs that are likely to drive cell fate specification during embryogenesis and vascular patterning.
Modelling auxin regulated development Vascular patterning In the previous sections we have highlighted a potentially crucial role for the vascular tissues in establishing an auxin maximum at the root apex by generating a
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reflective flow of auxin (Mironova et al. 2010, 2012). In these studies the vascular cells had been considered identically, however in the mature root they represent highly specialised cell types; the phloem conducts photosynthetic accumulates from the shoot, the xylem transports water and nutrients from the roots and the cambial cells proliferate and give rise to new vascular tissues. In Arabidopsis these cell types are arranged in a distinctive pattern with a central xylem axis flanked by two domains of procambial cells and two phloem poles (Fig. 2A). In the original reflective flow model, PIN1 was included in a basal orientation in all vascular cells (Mironova et al. 2012); however this is an oversimplification as additional PINs are expressed in the vascular tissues (Blilou et al. 2005, Bishopp et al. 2011) and AUX1 is expressed in protophloem cells on shootwardfacing membranes (Swarup et al. 2001). To address this question new reflective flow models were created in two separate one-dimensional models representing the protoxylem and protophloem cell lineages (Novoselova et al. 2013). In the protophloem model the presence of AUX1 disrupts the reflective flow leading to additional auxin maxima forming. This effect can be eliminated by either increasing PIN activity in the phloem or by reducing the auxin input into the protophloem. The authors concluded that for the reflective flow to work in mature tissues the protophloem might transport less auxin and/or transport it more effectively than the protoxylem. One possible mechanism that could reduce the amount of auxin in the phloem relative to the xylem would be through the radial flux of auxin through the vascular tissues, and this was the subject of a recent modelling study (Muraro et al. 2014). To test the role of PINs in establishing an auxin maxima in the xylem axis Muraro et al. (2014) developed a two-dimensional model of the vascular tissues based on realistic cell geometries, incorporating PIN proteins within this with their expression/localisation fixed based on experimental observations. This fixed-PIN model predicted that an asymmetry in PIN distribution was sufficient to restrict auxin response to the xylem axis. This model was extended to determine a minimal set of components that could regulate PIN transport in this domain. As the fixed-PIN model had showed considerable redundancy between the PINs the authors focused on just PIN7, which is specifically expressed in the procambial cells and phloem cells (Bishopp et al. 2011). Initially they introduced the cytokinin signalling network alongside a gene network involving microRNA165/6 and the transcription factors SHORT ROOT (SHR) and PHABULOSA (PHB), as these had been shown ¨ to regulate vascular patterning (M¨ahonen et al. 2006, Carlsbecker et al. 2010, Miyashima et al. 2011). 77
These interactions included the following crosstalk mechanisms; cytokinin signalling output promoted PIN7 transcription (Bishopp et al. 2011), auxin signalling promoted the expression of the cytokinin signalling inhibitor AHP6 (Bishopp et al. 2011), AHP6 expression was inhibited by PHB (Carlsbecker et al. 2010), PHB mRNA is degraded by microRNA165/6 which is produced in the endodermis in a SHR-dependent manner and diffuses into the vascular cylinder (Carlsbecker et al. 2010, Miyashima et al. 2011). This combination of components and interactions alone was unable to provide a mechanism to maintain PIN7 expression in the procambial cells (Fig. 2C, D). However, when the authors introduced a new inhibitor of cytokinin signalling and introduced the catalytic degradation of microRNA165/6 on binding with PHB (Fig. 2B) they were able to refine the model so that its predictions matched the experimental observed patterns of gene expression in wild-type roots, uncovering a potential non-linear regulatory pathway capable of maintaining PIN7 activity in the procambial/phloem cells to maintain a robust auxin response in the xylem axis (Fig. 2E) (Muraro et al. 2014).
Lateral root initiation and emergence Lateral roots develop from pericycle cells that are positioned adjacent to the protoxylem and subsequently emerge through the outer tissue layers (P´eret et al. 2009).
The basis for regular spacing of lateral root primordia (LRP) is an oscillating auxin response in the primary root basal meristem that leads to lateral root initiation at sites of the resulting auxin maxima (De Smet et al. 2007, Moreno-Risueno et al. 2010). It has been showed experimentally that LRP can be initiated at the outer side of a root bend (Ditengou et al. 2008, Lucas et al. 2008, Richter et al. 2009). To uncover a mechanistic insight into why this might be, the reflux loop model of auxin flux in the root meristem was extended to investigate the effects of root curvature (Laskowski et al. 2008). A combination of modelling and experimental approaches determined a change in cell shape associated with root bending and modelling was used to quantify auxin concentration in these cells. The model predicted an increased auxin concentration peaking in the pericycle cells on the outer side of a bend, however the differences were quite small. By incorporating AUX1 into a model of a curved root and regulating the expression of AUX1 in an auxindependent manner, it was found that a stronger and more robust auxin maxima forms in the outside of bends to allow organ initiation (Laskowski et al. 2008). Auxin response and particularly LAX3 is also required for LR emergence, where it promotes cell wall remodelling enzymes and cell separation in the tissues overlaying the primordia (Swarup et al. 2008). During this process LAX3 expression is induced by auxin and
Fig. 2. A model of root vascular patterning. A and B show the tissue and network used in the model by Muraro et al. (2014). The outer cell layers were not included in this model. The endodermis is labelled in orange, pericycle in red, the central xylem axis in blue, procambial cells in green and the phloem poles in yellow. The network displayed was embedded within all cells of the template and this image displayed includes the additional inhibitor of cytokinin and the mutual degradation of PHB and microRNA165/6. (C) Without the additional interactions predicted in this study, simulations were unable to maintain PIN7 expression throughout the domain in which it has been experimentally observed (as shown in D). (E) Simulations incorporating these additional interactions are able to stably maintain PIN7 expression as observed in wild-type roots. Figure reproduced in part from Muraro et al. (2014). In panels D and E levels of gene expression are showed with a heat map with blue representing low levels of expression and red representing high levels.
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Fig. 3. A model of LAX3 activation during lateral root emergence. A and B show the three-dimensional segmented tissue and network used in ´ the model by Peret et al. (2013). The network includes the auxin efflux carrier PIN3 that was predicted by this model and subsequently confirmed experimentally. The dashed line shows the indirect activation of LAX3 by auxin. (C and D) When the sequential activation of PIN3 and LAX3 was ´ introduced into this model it was able to robustly restrict LAX3 expression to two cells overlaying the LRP. Figure reproduced from Peret et al. (2013).
its expression is typically confined to just two files of cortical cells overlying the primordia (Swarup et al. 2008). What regulates LAX3 expression in just these few cell files? Genetic experiments revealed that LAX3 expression was induced by auxin generated within the LRP and channelled towards the overlaying cortical cells (P´eret et al. 2013). To understand the network controlling the restriction of LAX3 expression to these cells, P´eret and colleagues built a multicellular model of cell-to-cell auxin transport within a realistic 3D cellular template (Fig. 3). Through an iterative cycle of model perturbation and experimental validation, the authors found that auxin, auxin transport and LAX3 alone were insufficient to generate the spatial expression pattern of LAX3 that they had observed experimentally. By introducing an additional efflux carrier to the model and sequentially inducing expression of this efflux carrier and LAX3 the authors were able to recreate the observed LAX3 expression pattern in a manner that was robust to both changes in tissue geometry and fluctuations in the auxin levels. Through experimental analyses they identified the proposed efflux carrier as PIN3 and validated the sequential activation of PIN3 and LAX3 experimentally.
Discussion This review has highlighted how mathematical and computational models are proving invaluable tools with which to generate new mechanistic insights into auxin regulated plant growth and development. Several key themes and goals are emerging as researchers attempt to develop more realistic models that better reflect the biology of the plant system being studied by: •
Integrating realistic cell and tissue geometries is often necessary to fully appreciate the importance of auxin response network composition and organisation. For example, P´eret et al. (2013) recently illustrated that testing how robust a
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multicellular model was to natural variations in tissue geometry revealed a hitherto overlooked role for PIN3 as a component of the lateral root emergence network. • Integrating temporal information is evidently crucial in order to ensure a robust output from signalling pathways. For example, studying the importance of dynamics in the lateral root emergence network led P´eret et al. (2013) to discover that the efflux carrier PIN3 and then the influx carrier LAX3 must be induced sequentially. Otherwise, if LAX3 were induced at the same time as PIN3, the former would be expressed (transiently) in all cell files. Only when the induction of LAX3 is slow compared to the induction of PIN3 will two cortical cell files be selected. • Integrating multiple models is challenging for several reasons, particularly when models often operate at distinct spatial and temporal scales. One example of where this has been done elegantly is through the combining the reflective flow (Mironova et al. 2010) and reflux loop (Grieneisen et al. 2007) models of auxin flux in the root apical meristem into a dual-mechanism model (Mironova et al. 2012). This dual-mechanism model was able to capture many aspects of root growth such as the self-organisation of the root meristem and response to decapitation that had hitherto only been present in one of the models. Acknowledgements – We thank the following agencies for funding: JSPS (T. G.); Biotechnology and Biological Sciences Research Council (BBSRC) for funding (U. V. and M. J. B.); Royal Society (A. B. and M. J. B.); the University of Nottingham (E. F.); Wolfson Foundation (M. J. B.); BBSRC Professorial Research Fellowship funding (M. J. B.); and European Research Council (M. J. B.) for financial support.
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Edited by K. Ljung
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ISSN 0031-9317
MINIREVIEW
Systems biology approaches to understand the role of auxin in root growth and development Tatsuaki Goha,b , Ute Voβ a , Etienne Farcota,c , Malcolm J. Bennetta and Anthony Bishoppa∗ a
Centre for Plant Integrative Biology, School of Biosciences, University of Nottingham, Loughborough, UK Graduate School of Science, Kobe University, Kobe, Hyogo, Japan c School of Mathematical Sciences, University of Nottingham, Nottingham, UK b
Correspondence *Corresponding author, e-mail: [email protected] Received 19 November 2013; revised 28 January 2014 doi:10.1111/ppl.12162
The past decade has seen major advances in our understanding of auxin regulated root growth and developmental processes. Key genes have been identified that regulate and/or mediate auxin homeostasis, transport, perception and response. The molecular and biochemical reactions that underpin auxin signalling are non-linear, with feed-forward and feedback loops contributing to the robustness of the system. As our knowledge of auxin biology becomes increasingly complex and their outputs less intuitive, modelling is set to become much more important. For the last several decades modelling efforts have focused on auxin transport and, latterly, on auxin response. Recently researchers have employed multi-scale modelling approaches to predict emergent properties at the tissue and organ scales. Such innovative modelling approaches are proving very promising, revealing new mechanistic insights about how auxin functions within a multicellular context to control plant growth and development. In this review we initially describe examples of models capturing auxin transport and response pathways, and then discuss increasingly complex models that integrate multiple hormone response pathways, tissues and/or scales.
Introduction As knowledge of auxin regulated root growth and development increases, it is becoming clear that many of the key regulatory components operate within complex sub/cellular/tissue-scale networks (reviewed in this special issue). As a consequence, researchers have shifted their focus from studying individual gene products, to dissecting more complex regulatory relationships between multiple components within non-linear transduction pathways (Band et al. 2012). For example, the canonical nuclear-localised TIR1-Aux/IAA-ARF auxin response machinery includes Aux/IAA-based negative feedback and/or ARF-based positive feed-forward loops to either stabilise and/or amplify pathway output,
respectively. Hence, the outputs from such pathways are often non-intuitive and new approaches are needed in order to understand these complex dynamics. As a result, researchers are turning to systems approaches and employing mathematical and/or computational models to simulate the behaviours of non-linear auxin response networks to predict their output and reveal novel emergent properties (reviewed in Middleton et al. 2012). In the past, mathematical models have been used to ‘document’ molecular processes. For example, experimental biologists may generate a hypothesis around a series of experimental results and build a model to recapitulate these observations and show that their proposed networks can recreate the observed
Abbreviations – ARF, auxin response factor; BDL, BODENLOS; DZ, differentiation zone; EZ, elongation zone; LRP, lateral root primordia; MP, monopteros; MZ, meristematic zone; ODE, ordinary differential equation; PIN, PIN-FORMED; PLT, PLETHORA; PHB, PHABULOSA; QC, quiescent centre; SHR, SHORT ROOT.
© 2014 The Authors. Physiologia Plantarum published by John Wiley & Sons Ltd on behalf of Scandinavian Plant Physiology Society. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
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behaviour. However, recent mathematical models have gone beyond describing known biological processes. Through the iterative process of combining simulation with experimentation, these models force us to question our existing assumptions about biological systems and allow us to identify gaps in our knowledge. The best models make novel predictions to fill these gaps and in doing so, guide experimental design towards testing these model predictions. In this review, we will discuss how modelling approaches are helping researchers understand the mechanistic behaviour of auxin and how this signal controls root growth and development. We initially describe examples of models capturing hormone transport and response pathways, and then discuss increasingly complex models that integrate multiple hormone response pathways and bridge spatio/temporal scales. We have selected examples where the models have challenged our understanding of how auxin regulates development, either by predicting missing components in incomplete molecular networks or through proposing new properties emerging at the organ scales. Owing to space limits, we have focused this review on recent advances on root development and apologise to readers for not being able to cover the excellent work done in the shoot apical meristem, ovules and other organs. For more information about these, we recommend several excellent reviews (Krupinski and Jonsson 2010, Band et al. 2012, Middleton et al. 2012, Murray et al. 2012, van Berkel et al. 2013).
Auxin transport Comparing and contrasting models Auxin transport has been the focus of modelling studies for several decades (Mitchison 1980a, 1980b, Mitchison et al. 1981). Auxin is actively transported by several classes of specialised carriers that include: AUX1/LAX proteins that mediate auxin influx; the PIN-FORMED (PIN) family that functions as auxin efflux carriers and exhibit polarised localisation on specific cell faces. The transport of auxin from cell-to-cell results in localised asymmetries that drive developmental processes. Long distance transport of auxin is a complex multi-scale phenomenon, incorporating the sub-cellular redistribution of PIN transporters, long-range transport of auxin across the whole plant as well as tight control of auxin perception at the organ and tissue scales. This complexity has fostered a large number of mathematical and computational models. Early auxin transport models hypothesised that the flux of auxin through cell membranes reinforces itself, resulting in sharp patterns 74
(Mitchison 1980a, 1980b, Mitchison et al. 1981). The transport of auxin was described using abstract variables representing the permeability of cell membranes and whose value was an increasing function of the directed flux of auxin (as PIN proteins were not known at the time of these studies). As an alternative to Mitchison’s flux-based model, so-called gradient-based models of auxin transport were introduced, in which the local accumulation of transporters depends on differences in auxin concentration between neighbouring cells and follows increasing gradient directions, rather than the flux across cell ¨ membranes (Jonsson et al. 2006, Smith et al. 2006). However, it is unclear whether PIN accumulation is regulated by auxin flux, its gradient, or some other mechanism. Alternative models tested include intracellular PIN distribution being jointly regulated by a hypothetical extracellular auxin receptor and intracellular auxin signalling (Wabnik et al. 2010) or where mechanical stress and its influence on microtubule orientation control the cell polarity (Hamant et al. 2008). Some studies have also adopted a composite model, incorporating both flux-based and gradient-based PIN regulation, in a tissue dependent way (Bayer et al. 2009). Several more theoretical studies considered the general patterning abilities of different models. For example, using tools from non-linear dynamical systems theory (Strogatz 2001), both gradient (Draelants et al. 2013) and flux (Farcot and Yuan 2013) based models were able to create more complex behaviours such as travelling waves and stable oscillations of auxin. Modelling root apical meristem development A large number of auxin transport models have focused on the Arabidopsis root and shoot apical meristems, and the pioneering work performed in modelling auxin flux in the shoot has had profound bearings on modelling efforts in the root. As the shoot models have been reviewed recently (for example, see Murray et al. 2012), we will focus this review on roots and the processes occurring after the embryonic root has formed. The earliest events in root development involve the establishment of an apical-basal axis during embryogenesis. This process has been modelled, uncovering a minimal mechanistic framework for generating the cell polarity within the embryo leading to the subsequent formation of the root pole (Wabnik et al. 2013). In the Arabidopsis root, two independent two-dimensional models of auxin transport have been created to explore different transport mechanisms (Grieneisen et al. 2007, Mironova et al. 2010). Both involved similar templates consisting of a structured layout of rectangular cells,
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Fig. 1. The cellular arrangements in the 2-D reflux loop and reflective flow models. (A) The cell layout described in the reflux loop model by Grieneisen et al. (2007) showing the four cell types [vascular (green), epidermal (dark blue), columella (light blue) and border cells (yellow)]. (B) The cell layout in the reflective flow model by Mironova et al (2010) uses just two cell types [vascular (green) and non-vascular (grey)]. In both images the auxin flows are shown with red arrows. Image reproduced from Mironova et al. (2010).
however they differed in the amount of positional information provided. In the reflux loop model, PIN proteins were pre-positioned within four cell types based on experimental observations (Fig. 1A) (Grieneisen et al. 2007). When auxin was provided to the system, the model predicted that an auxin maximum formed at the root apex because of large fluxes from vascular tissues and drained via the epidermis (resembling a reverse fountain). The site of the auxin maximum proved to be robust to changes in model parameters and was stably maintained when auxin-mediated growth was introduced into the system (Grieneisen et al. 2007). Whilst the reflux loop was able to capture many aspects of auxin transport in the mature root, it is difficult to apply this model to the de novo formation of new auxin maxima in embryonic roots or newly emerged lateral roots as it requires PINs to be placed in specific orientations in a cell-specific manner. Experimental evidence shows that the shootward-localised PIN, PIN2, is not expressed during the early stages of root development (Benkov´a et al. 2003, Friml et al. 2003). To address the formation of an auxin maximum in newly formed roots
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the reflective flow model was developed (Mironova et al. 2010). When applied to a two-dimensional template similar to that used in the reflux loop model, the reflective flow model required only two cell types (vascular and non-vascular cells) and only required one PIN, PIN1, to be localised on rootward-facing membranes in the vascular cells (Fig. 1B). Crucially in this model, PIN1 synthesis is regulated by low levels of auxin and PIN1 degraded at high levels of auxin. Initially the low auxin levels in the vascular cells re-enforced the rootward flux of auxin, resulting in accumulation of auxin in the most rootward layer of vascular cells. This was followed by the accumulation of a high amount of auxin in the second most rootward layer of cells, whereupon auxin can diffuse into this from the most rootward layer of cells (the reflective flow). As soon as the auxin levels reach the threshold for auxin-dependent PIN1 degradation, auxin starts to inhibit PIN1 expression, leading to a decrease in auxin levels in the most rootward cell layer and a new auxin maximum in the second most rootward layer of cells. This process can shift the auxin maximum to the third or fourth cells until the rootward and reflected fluxes of auxin become balanced. Recently the reflux loop and reflective flow models were combined in a dual-mechanism model that could capture the benefits of both systems (Mironova et al. 2012). To introduce the reverse fountain PIN2 and PIN3 were included into the reflective flow model and localised in the same manner as the model in Grieneisen et al. (2007); however the levels of these proteins were controlled by auxin. This dual-mechanism model was able to simulate the realistic regeneration of the root apical meristem upon decapitation (previously seen in the reflective flow model but not the reflux loop model). When a basal rate of auxin synthesis was included, this was able to maintain an auxin maximum at the root apex when the shoot was removed (previously seen in the reflux loop model but not the reflective flow model) (Mironova et al. 2012). However, maintaining an auxin maximum at the quiescent centre (QC) position is unlikely to be the only requirement for maintaining root growth. Growth is controlled by maintaining the rate of cell division in the meristematic zone (MZ) of the root above QC, cell elongation in the elongation zone (EZ) and above this, cell differentiation in the differentiation zone (DZ). The activity of these domains are controlled by the level of the PLETHORA (PLT ) family of genes (Aida et al. 2004, Galinha et al. 2007). Although other factors contribute to the levels of PLT (Matsuzaki et al. 2010), they are believed to be controlled mainly through a gradient of auxin (Galinha et al. 2007). The central question is: does auxin produce a well enough defined 75
gradient to define these zonations within the root? Experimentally this is exceedingly challenging to address as even with the newest auxin sensors (Brunoud et al. 2012), we can only measure auxin response. A recent study investigated three possible gradient-generating mechanisms in silico that could potentially supply sufficient positional information to create a gradient of auxin across the root at a scale sufficient to determine the size and position of the MZ, EZ and DZ (Grieneisen et al. 2012). These included a source-decay mechanism (with auxin being synthesised at the root apex but auxin diffusion and degradation throughout the root), a unidirectional transport mechanism (comprising of a tissue with just vascular and pericycle cell files and the QC) and the reflux loop model. It was found that only the reflux loop model was able to form an exponentially increasing auxin gradient that spanned the entire MZ and part of the EZ; the auxin gradient was much too shallow with the source-decay mechanism, or much too steep with the uni-directional transport mechanism (Grieneisen et al. 2012).
Modelling root hair elongation Root hairs provide a vital function in increasing the surface area of roots to enable increased uptake of water and nutrients. Each hair is a thin tubular structure that forms from a single root hair forming epidermal cell (hair cell) in the DZ. The assignment of epidermal cell fate as hair or non-hair cells is determined based on cell positioning through a well characterised gene regulatory network (Grebe 2012). Auxin does not affect the determination hair vs non-hair cell fate, however the elongation of root hair is positively regulated by auxin (Yi et al. 2010). Cell type specific activation or inhibition of auxin signalling indicated that auxin signalling controls root hair growth in hair cells in a cell autonomous manner (Won et al. 2009, Ganguly et al. 2010). However, analysis of the auxin response reporter, DR5, revealed that there is a higher auxin response in non-hair cells than hair cells (Jones et al. 2008). Why should this be so? The reflux loop model of auxin transport (see section on auxin transport) shows a recycling of auxin from the root tip through the epidermal cells and this is mediated through the auxin influx carrier, AUX1 and efflux carrier, PIN2 (Blilou et al. 2005, Grieneisen et al. 2007). However, it was unknown if these proteins had differential levels of activity in hair and non-hair cells. A combination of experimental approaches revealed that AUX1 is expressed only in the non-hair cells, although PIN2 is expressed in both cell types (Jones et al. 2008). 76
In order to understand importance of non-hair cell-specific expression of AUX1, Jones and colleagues simulated auxin movement using three-dimensional geometry of the outer three layers of the root (epidermis, cortex and endodermis) (Jones et al. 2008). This allowed them to investigate both active transport of auxin and passive diffusion laterally between epidermal cell lineages and between adjacent layers. The model predicted that specific expression of AUX1 in non-hair cells causes the accumulation of an approximately 10fold higher concentration of auxin in non-hair cells than hair cells. As auxin can move by diffusion, the simulations predict that although it is at a lower level, this auxin level in root hair cells is within the measured range of biological activity in root hair assays. In simulations lacking AUX1, the model predicted a rapid decrease in auxin concentration with increasing distance from the root meristem, as auxin diffused into the stele or out of the root entirely, meaning that cells in the DZ are supplied with less auxin. This suggested that AUX1dependent transport of auxin in non-hair cells may provide a mechanism to supply auxin to the hair cells as they get progressively further away from the root tip and enter the DZ. The authors made the assumption that root hair growth occurs above a certain threshold of auxin. They speculated that if this is the case, the root hairs should stop growing closer to the root tip in aux1 mutants (as the auxin levels decrease more quickly) and subsequently confirmed this theory through experimental analyses. Together this combination of simulations and experimentation unveiled a distinct function for non-hair cells in sustaining high auxin levels in the DZ by AUX1-dependent auxin influx to enable the subsequent supply of auxin to initiate the growth of hair cells.
Modelling auxin response An auxin maximum created by active transport must elicit a localised auxin response in order to trigger a developmental output. The molecular and biochemical reactions that underpin auxin signalling are non-linear, with feed-forward and feedback loops contributing to the robustness of the system (Vernoux et al. 2011). Auxin functions in conjunction with its TIR1/AFB1-5 co-receptor to mediate the degradation of the Aux/IAA family of proteins that repress auxin response factors (ARFs) (Dharmasiri et al. 2005, Kepinski and Leyser 2005). ARFs regulate various downstream genes that include Aux/IAAs. Hence, the pathway comprises multiple negative feedback loops. To help understand the output from the auxin response pathway, Middleton et al. (2010) developed
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a mathematical model of the auxin response network using ordinary differential equations (ODEs). The model included auxin, TIR1, ARF and Aux/IAA proteins, together with their regulatory relationships. The authors built the model using realistic parameters based on quantitative data already available from molecular studies on protein turnover and transcription rates. Model simulations confirmed the importance of the turnover rates of Aux/IAA proteins. However, the model also revealed some interesting discrepancies between its behaviour and the experimental data. For example, experiments have reported up to 30-fold fold-changes in some mRNA species (Abel et al. 1995). To achieve such a fold-change in the model required an extremely large (and possibly unrealistic) increase in auxin levels. This points to the existence of additional regulatory mechanisms that may serve to amplify the response (as measured by Aux/IAA mRNA levels) made by cells to changes in auxin. A number of ARF-encoding genes are themselves auxin responsive (Okushima et al. 2005), which could represent a feed-forward loop that allows signal amplification. Lau et al. (2011) recently showed that the ARF family member MONOPTEROS (MP) upregulates both its own expression and the expression of the gene encoding Aux/IAA family member BODENLOS (BDL). The presence of a positive feedback loop can lead to bistability, i.e. when a system can rest in any of two stable states, rather than just one. This enables regulatory networks to exhibit switch-like behaviour to amplify response pathway output. For example, increasing auxin levels can switch the system from a low to a high MP/BDL concentration (Lau et al. 2011). Interestingly, as auxin levels decrease MP and BDL levels remain up regulated for several hours (Lau et al. 2011). This latter behaviour is termed hysteresis, reflecting the fact that the response of a bistable system depends on both current and past conditions. Bistable systems can also generate switchlike responses to changes in signal input. Hence, once the system is in a MP upregulated state, the behaviour of the network will be robust to large changes in the level of auxin. Such behaviour of the MP response network enables auxin to induce all or nothing developmental outputs that are likely to drive cell fate specification during embryogenesis and vascular patterning.
Modelling auxin regulated development Vascular patterning In the previous sections we have highlighted a potentially crucial role for the vascular tissues in establishing an auxin maximum at the root apex by generating a
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reflective flow of auxin (Mironova et al. 2010, 2012). In these studies the vascular cells had been considered identically, however in the mature root they represent highly specialised cell types; the phloem conducts photosynthetic accumulates from the shoot, the xylem transports water and nutrients from the roots and the cambial cells proliferate and give rise to new vascular tissues. In Arabidopsis these cell types are arranged in a distinctive pattern with a central xylem axis flanked by two domains of procambial cells and two phloem poles (Fig. 2A). In the original reflective flow model, PIN1 was included in a basal orientation in all vascular cells (Mironova et al. 2012); however this is an oversimplification as additional PINs are expressed in the vascular tissues (Blilou et al. 2005, Bishopp et al. 2011) and AUX1 is expressed in protophloem cells on shootwardfacing membranes (Swarup et al. 2001). To address this question new reflective flow models were created in two separate one-dimensional models representing the protoxylem and protophloem cell lineages (Novoselova et al. 2013). In the protophloem model the presence of AUX1 disrupts the reflective flow leading to additional auxin maxima forming. This effect can be eliminated by either increasing PIN activity in the phloem or by reducing the auxin input into the protophloem. The authors concluded that for the reflective flow to work in mature tissues the protophloem might transport less auxin and/or transport it more effectively than the protoxylem. One possible mechanism that could reduce the amount of auxin in the phloem relative to the xylem would be through the radial flux of auxin through the vascular tissues, and this was the subject of a recent modelling study (Muraro et al. 2014). To test the role of PINs in establishing an auxin maxima in the xylem axis Muraro et al. (2014) developed a two-dimensional model of the vascular tissues based on realistic cell geometries, incorporating PIN proteins within this with their expression/localisation fixed based on experimental observations. This fixed-PIN model predicted that an asymmetry in PIN distribution was sufficient to restrict auxin response to the xylem axis. This model was extended to determine a minimal set of components that could regulate PIN transport in this domain. As the fixed-PIN model had showed considerable redundancy between the PINs the authors focused on just PIN7, which is specifically expressed in the procambial cells and phloem cells (Bishopp et al. 2011). Initially they introduced the cytokinin signalling network alongside a gene network involving microRNA165/6 and the transcription factors SHORT ROOT (SHR) and PHABULOSA (PHB), as these had been shown ¨ to regulate vascular patterning (M¨ahonen et al. 2006, Carlsbecker et al. 2010, Miyashima et al. 2011). 77
These interactions included the following crosstalk mechanisms; cytokinin signalling output promoted PIN7 transcription (Bishopp et al. 2011), auxin signalling promoted the expression of the cytokinin signalling inhibitor AHP6 (Bishopp et al. 2011), AHP6 expression was inhibited by PHB (Carlsbecker et al. 2010), PHB mRNA is degraded by microRNA165/6 which is produced in the endodermis in a SHR-dependent manner and diffuses into the vascular cylinder (Carlsbecker et al. 2010, Miyashima et al. 2011). This combination of components and interactions alone was unable to provide a mechanism to maintain PIN7 expression in the procambial cells (Fig. 2C, D). However, when the authors introduced a new inhibitor of cytokinin signalling and introduced the catalytic degradation of microRNA165/6 on binding with PHB (Fig. 2B) they were able to refine the model so that its predictions matched the experimental observed patterns of gene expression in wild-type roots, uncovering a potential non-linear regulatory pathway capable of maintaining PIN7 activity in the procambial/phloem cells to maintain a robust auxin response in the xylem axis (Fig. 2E) (Muraro et al. 2014).
Lateral root initiation and emergence Lateral roots develop from pericycle cells that are positioned adjacent to the protoxylem and subsequently emerge through the outer tissue layers (P´eret et al. 2009).
The basis for regular spacing of lateral root primordia (LRP) is an oscillating auxin response in the primary root basal meristem that leads to lateral root initiation at sites of the resulting auxin maxima (De Smet et al. 2007, Moreno-Risueno et al. 2010). It has been showed experimentally that LRP can be initiated at the outer side of a root bend (Ditengou et al. 2008, Lucas et al. 2008, Richter et al. 2009). To uncover a mechanistic insight into why this might be, the reflux loop model of auxin flux in the root meristem was extended to investigate the effects of root curvature (Laskowski et al. 2008). A combination of modelling and experimental approaches determined a change in cell shape associated with root bending and modelling was used to quantify auxin concentration in these cells. The model predicted an increased auxin concentration peaking in the pericycle cells on the outer side of a bend, however the differences were quite small. By incorporating AUX1 into a model of a curved root and regulating the expression of AUX1 in an auxindependent manner, it was found that a stronger and more robust auxin maxima forms in the outside of bends to allow organ initiation (Laskowski et al. 2008). Auxin response and particularly LAX3 is also required for LR emergence, where it promotes cell wall remodelling enzymes and cell separation in the tissues overlaying the primordia (Swarup et al. 2008). During this process LAX3 expression is induced by auxin and
Fig. 2. A model of root vascular patterning. A and B show the tissue and network used in the model by Muraro et al. (2014). The outer cell layers were not included in this model. The endodermis is labelled in orange, pericycle in red, the central xylem axis in blue, procambial cells in green and the phloem poles in yellow. The network displayed was embedded within all cells of the template and this image displayed includes the additional inhibitor of cytokinin and the mutual degradation of PHB and microRNA165/6. (C) Without the additional interactions predicted in this study, simulations were unable to maintain PIN7 expression throughout the domain in which it has been experimentally observed (as shown in D). (E) Simulations incorporating these additional interactions are able to stably maintain PIN7 expression as observed in wild-type roots. Figure reproduced in part from Muraro et al. (2014). In panels D and E levels of gene expression are showed with a heat map with blue representing low levels of expression and red representing high levels.
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Fig. 3. A model of LAX3 activation during lateral root emergence. A and B show the three-dimensional segmented tissue and network used in ´ the model by Peret et al. (2013). The network includes the auxin efflux carrier PIN3 that was predicted by this model and subsequently confirmed experimentally. The dashed line shows the indirect activation of LAX3 by auxin. (C and D) When the sequential activation of PIN3 and LAX3 was ´ introduced into this model it was able to robustly restrict LAX3 expression to two cells overlaying the LRP. Figure reproduced from Peret et al. (2013).
its expression is typically confined to just two files of cortical cells overlying the primordia (Swarup et al. 2008). What regulates LAX3 expression in just these few cell files? Genetic experiments revealed that LAX3 expression was induced by auxin generated within the LRP and channelled towards the overlaying cortical cells (P´eret et al. 2013). To understand the network controlling the restriction of LAX3 expression to these cells, P´eret and colleagues built a multicellular model of cell-to-cell auxin transport within a realistic 3D cellular template (Fig. 3). Through an iterative cycle of model perturbation and experimental validation, the authors found that auxin, auxin transport and LAX3 alone were insufficient to generate the spatial expression pattern of LAX3 that they had observed experimentally. By introducing an additional efflux carrier to the model and sequentially inducing expression of this efflux carrier and LAX3 the authors were able to recreate the observed LAX3 expression pattern in a manner that was robust to both changes in tissue geometry and fluctuations in the auxin levels. Through experimental analyses they identified the proposed efflux carrier as PIN3 and validated the sequential activation of PIN3 and LAX3 experimentally.
Discussion This review has highlighted how mathematical and computational models are proving invaluable tools with which to generate new mechanistic insights into auxin regulated plant growth and development. Several key themes and goals are emerging as researchers attempt to develop more realistic models that better reflect the biology of the plant system being studied by: •
Integrating realistic cell and tissue geometries is often necessary to fully appreciate the importance of auxin response network composition and organisation. For example, P´eret et al. (2013) recently illustrated that testing how robust a
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multicellular model was to natural variations in tissue geometry revealed a hitherto overlooked role for PIN3 as a component of the lateral root emergence network. • Integrating temporal information is evidently crucial in order to ensure a robust output from signalling pathways. For example, studying the importance of dynamics in the lateral root emergence network led P´eret et al. (2013) to discover that the efflux carrier PIN3 and then the influx carrier LAX3 must be induced sequentially. Otherwise, if LAX3 were induced at the same time as PIN3, the former would be expressed (transiently) in all cell files. Only when the induction of LAX3 is slow compared to the induction of PIN3 will two cortical cell files be selected. • Integrating multiple models is challenging for several reasons, particularly when models often operate at distinct spatial and temporal scales. One example of where this has been done elegantly is through the combining the reflective flow (Mironova et al. 2010) and reflux loop (Grieneisen et al. 2007) models of auxin flux in the root apical meristem into a dual-mechanism model (Mironova et al. 2012). This dual-mechanism model was able to capture many aspects of root growth such as the self-organisation of the root meristem and response to decapitation that had hitherto only been present in one of the models. Acknowledgements – We thank the following agencies for funding: JSPS (T. G.); Biotechnology and Biological Sciences Research Council (BBSRC) for funding (U. V. and M. J. B.); Royal Society (A. B. and M. J. B.); the University of Nottingham (E. F.); Wolfson Foundation (M. J. B.); BBSRC Professorial Research Fellowship funding (M. J. B.); and European Research Council (M. J. B.) for financial support.
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