Multiscale Modelling of Plant Hormone Signalling: Auxin Regulated Lateral Root Emergence Nathan Mellor February 2013 Abstract The formation of lateral roots is an important post-embryonic developmen- tal process that allows plants to adapt to their environment via exploitation of soil mineral resources. New lateral roots initiate as lateral root primordia (LRP) in the pericycle cell layer adjacent to the central vascular tissue in theprimaryroot, andmustpassthroughtheoutercelllayersofendodermis, cortex and epidermis to emerge as mature roots. A key regulator of emer- gence is the plant hormone auxin and it has been shown previously that in Arabidopsis the auxin induced expression of the auxin influx carrier LAX3 in specific cortical cells over LRP is required for emergence to occur, as this leads to the expression of cell wall remodelling enzymes such as polygalac- turonase (PG). By developing mathematical models of auxin transport and LAX3 expression the work in the thesis aims to test the existing concep- tual models for lateral root emergence, and provide testable hypotheses for the existence of additional gene regulatory components. An initial single cell model demonstrates that hysteresis and bistability may explain the ex- perimentally observed ‘all-or-nothing’ LAX3 spatial expression pattern in corticalcellscontainingagradientofauxinconcentrations. Byfittingmodel parameters against experimental data, the model is then used to show that some auxin homeostasis mechanism is present, with both endogenous and exogenous sources of homeostasis investigated. The single cell model also investigates the validity of several alternative gene regulatory networks for LAX3, and its apparent repression by a key mediator of the auxin response, ARF19. Finally, the model is extended to a multicellular context, in which the auxin distribution from a simulated LRP source cell is used as a basis for the expression of LAX3, leading to the expression of PG in specific cells between which the LRP must pass. 1 Acknowledgents The work was funded by the University of Nottingham as part of the IDTC program at the Multidisciplinary Centre for Integrative Biology (My- CIB). Thanks to my Supervisors John King, Malcolm Bennett, Matt Loose and Charlie Hodgman, and all at the Centre for Plant Integrative Biol- ogy (CPIB). In particular, thanks must go to Alistair Middleton for help and discussions, and to my experimental collaborators at Nottingham, An- toine Larrieu, Benjamin P´eret and Silvana Porco, and at Ume˚a University, Ilkka Sairinen and Karin Ljung, for providing me with data thoughout the project. Finally, thanks to Chris for all her support, and giving me the self-belief that i could actually do this! 2 Contents 1 Introduction 6 1.1 Biological Background . . . . . . . . . . . . . . . . . . . . . 6 1.1.1 Motivation and objectives . . . . . . . . . . . . . . . 6 1.1.2 Plant root architecture and cellular structure . . . . . 8 1.1.3 Auxin and plant development . . . . . . . . . . . . . 11 1.1.4 Auxin biosynthesis, metabolism and transport . . . . 14 1.1.5 Auxin signalling and gene activation . . . . . . . . . 17 1.1.6 Lateral root development in Arabidopsis . . . . . . . 20 1.2 Modelling of Plant Hormone Signalling . . . . . . . . . . . . 28 1.2.1 Auxin transport models . . . . . . . . . . . . . . . . 28 1.2.2 Auxin signalling and gene regulation models . . . . . 29 1.2.3 Frameworks for model implementation . . . . . . . . 31 1.3 Thesis Summary . . . . . . . . . . . . . . . . . . . . . . . . 31 2 Gene Regulatory Network Model: One Auxin Response Factor (ARF7) 35 2.1 Initial LAX3 Gene Network Model . . . . . . . . . . . . . . 35 2.1.1 The LAX3 gene regulatory network . . . . . . . . . . 35 2.1.2 Model Formulation and Initial Parameter Estimates . 36 2.1.3 Steady State Analysis . . . . . . . . . . . . . . . . . 42 2.1.4 Time Course Simulations . . . . . . . . . . . . . . . . 48 2.2 Parameter Fitting and Predictions From Initial LAX3 Models 51 2.2.1 Fitting Algorithm . . . . . . . . . . . . . . . . . . . . 51 2.2.2 Parameter Fitting using Full Model . . . . . . . . . . 53 2.2.3 Model Simplifications . . . . . . . . . . . . . . . . . . 55 2.2.4 Parameter Fitting Using Reduced Model . . . . . . . 61 2.3 Short and long term behaviour of Aux/IAA (DII-VENUS model) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 2.3.1 Model formulation . . . . . . . . . . . . . . . . . . . 65 2.3.2 Parameter Fitting . . . . . . . . . . . . . . . . . . . . 66 2.4 Model Predictions . . . . . . . . . . . . . . . . . . . . . . . . 69 2.4.1 IAA14 mRNA . . . . . . . . . . . . . . . . . . . . . . 70 2.4.2 LAX3 mRNA . . . . . . . . . . . . . . . . . . . . . . 71 2.5 Discussion and Conclusions . . . . . . . . . . . . . . . . . . 75 3 Auxin Inducible Auxin Conjugation 79 3.1 Introduction and Model Formulation . . . . . . . . . . . . . 79 3.1.1 Model formulation . . . . . . . . . . . . . . . . . . . 79 3 3.2 Parameter Fitting Using Conjugation Model . . . . . . . . . 83 3.3 Time Course and Parameter Sensitivity . . . . . . . . . . . . 85 3.4 Steady State Analysis . . . . . . . . . . . . . . . . . . . . . . 87 3.4.1 Pulses In LAX3 expression . . . . . . . . . . . . . . . 93 3.5 Discussion and Conclusions . . . . . . . . . . . . . . . . . . 93 4 Gene Regulatory Network Model: Two Auxin Response Factors (ARF7 and ARF19) 99 4.1 Biological Background . . . . . . . . . . . . . . . . . . . . . 99 4.2 Simple ARF7 and ARF19 model . . . . . . . . . . . . . . . . 101 4.2.1 Model Formulation . . . . . . . . . . . . . . . . . . . 101 4.2.2 ARF7 and ARF19 share parameter values . . . . . . 107 4.2.3 The ARF7 model can approximate the ARF7 and ARF19 model . . . . . . . . . . . . . . . . . . . . . . 111 4.2.4 ARF19 can act as a transcriptional repressor . . . . . 111 4.3 Models with ARF19 activated repressors . . . . . . . . . . . 114 4.3.1 ARF19 activates a single repressor . . . . . . . . . . 114 4.3.2 Two Repressor Pathway Model . . . . . . . . . . . . 120 4.4 ARF7-ARF19-LAX3 model with auxin homeostasis . . . . . 124 4.4.1 Expression of LAX3 mRNA : arf19 mutant . . . . . 125 4.4.2 ARF19 Regulation Models . . . . . . . . . . . . . . . 126 4.4.3 Regulation of LAX3 by ARF19 . . . . . . . . . . . . 129 4.5 Discussion and Conclusions . . . . . . . . . . . . . . . . . . 134 5 Tissue Scale Models of Lateral Root Emergence 145 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 5.1.1 Introduction and Biological Background . . . . . . . 145 5.1.2 Model Formulation . . . . . . . . . . . . . . . . . . . 147 5.1.3 Implementation . . . . . . . . . . . . . . . . . . . . . 151 5.2 Auxin distribution: diffusion only . . . . . . . . . . . . . . . 152 5.2.1 Simulation of auxin treatment . . . . . . . . . . . . . 152 5.2.2 Apoplastic diffusion and Casparian strip . . . . . . . 154 5.2.3 Simulation of primordium auxin source . . . . . . . . 158 5.3 Modelling of influx and efflux carriers . . . . . . . . . . . . . 166 5.3.1 Fixed distribution of influx and efflux carriers . . . . 166 5.3.2 Threshold model for expression of LAX3 . . . . . . . 170 5.4 Discussion and conclusions . . . . . . . . . . . . . . . . . . . 174 6 Multi-scale Models of Lateral Root Emergence 177 6.1 Initial conditions for auxin transport simulations . . . . . . . 177 6.1.1 Exogenous auxin treatment . . . . . . . . . . . . . . 177 6.1.2 Simulation of LRP auxin source . . . . . . . . . . . . 179 6.2 Multiscale model of the DII-VENUS auxin sensor . . . . . . 181 6.3 Primary auxin response: expression of Aux/IAA . . . . . . 182 6.4 Secondary auxin response: expression of LAX3 . . . . . . . . 186 6.5 Tertiary auxin response: expression of PG . . . . . . . . . . 190 6.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 4 7 Concluding Remarks 200 7.1 Bistability in LAX3 mRNA expression . . . . . . . . . . . . 200 7.2 Sources of auxin homeostasis . . . . . . . . . . . . . . . . . . 201 7.3 The role of ARF19 in LAX3 expression . . . . . . . . . . . . 202 7.4 Multiscale Model and Ongoing Challenges . . . . . . . . . . 203 5 Chapter 1 Introduction 1.1 Biological Background 1.1.1 Motivation and objectives Food security is defined by the World Health Organisation as ‘when all people, at all times, have access to sufficient, safe and nutritious food for a healthy life’ (World Health Organisation 2012a). They cite four basic components to achieving this goal: availability, access, utilisation, and sta- bility (World Health Organisation 2012b). Availability refers to the overall quantity and consistency of food production, access refers to the presence of adequate financial or practical means to acquire food, utilisation refers to the proper use of food according to basic standards of nutrition and san- itation, and stability refers to the volatility of the food supply to temporal changes in conditions, such as sudden crises or seasonal shortages. There are currently many major challenges to global food security, in- cluding increasing demand due to population growth, the impact of climate change, high or volatile food prices, and growing competition with biofuel production for land use. The current predictions are for these challenges to become more and more critical throughout the 21st century, with demand for food projected to increase by 50% by 2030, and double by 2050 (BBSRC 2012). Whilemanyoftheproblemswithfoodsecuritymaybepoliticalorso- ciological in nature, the changes to water availabilty, temperature extremes, and pest and disease distribution, brought about by climate change may be addressed by science, with one of the stated aims of the BBSRC being ‘to use the same amount of land to grow more food of greater nutritional value, using less energy, water and pesticides whilst producing less waste’ (BBSRC 2012). Cereal crops, whether for use as feed for animals eaten as meat, or used directly for consumption by humans, play a critical role in global food production, with over 2000 million tonnes estimated to have been produced worldwide in 2011/2012 (Food and Agriculture Organization of the United Nations 2012). A key factor in crop yields is clearly the efficient utilisation by crop plants of soil nutrient, water and mineral resources, and central to this is an efficient root network (Lynch 1995; Smith and De Smet 2012). Rootsystemsperformseveralessentialfunctionsinthesuccessofallcrop plants, including uptake of water and minerals, the provision of anchorage 6 within the soil, and the establishment of biotic interactions in the rhizo- sphere (Lopez-Bucio et al. 2003). Maximising a plant’s potential for growth in a heterogenous environment therefore requires an extensive, but efficient, exploration of the surrounding soil. Increasing the total root surface area may be achieved by growth of the primary root via cell division near the tip of the primary root, by the formation of root-hairs on the outer epider- mal cells, or by the creation of lateral roots (Lopez-Bucio et al. 2003). The first lateral roots branch from the primary root but, as those lateral roots mature, laterals of laterals may be formed, and so on, creating a vast array of potential root architectures (Lynch 1995). The better adapted a crop’s root architecture is to a particular environment, the greater the potential yield from that crop. A plant’s root architecture is not entirely pre-defined by its genotype, ratheritishighlyplasticandabletoadapttoarangeofenvironmentalcues. These include the content and distribution of minerals within the soil, such as nitrogen, phosphorus, iron and sulphur, all of which have been shown to alter root architecture, either by affecting primary root growth, the growth of root hairs, or the formation of lateral roots (Lopez-Bucio et al. 2003; Smith and De Smet 2012). In particular, low levels of phosphate are known to increase the density of lateral root formation, while nitrogen is seen to have an effect on lateral root elongation rather than the formation of new laterals (Zhang and Forde 1998; Linkohr et al. 2002). Additional factors affecting root architecture include the heterogeneity or ‘patchiness’ of the soil matrix(Hinsingeretal. 2005;Hodge2006), and bioticinteractions, such as those with either pathogens or mycorrhizae (Osmont et al. 2007). There is a broad and on-going body of research into the effect of en- vironmental cues on plant root systems, and how this affects agricultural yields. The focus of this thesis however, is on a particular aspect of one of the fundamental developmental processes that defines a plant’s root ar- chitecture, that of the emergence of new lateral roots. Like much of plant development, the growth of a new lateral root occurs post-embryonically and is an example of organogenesis. While this organogenesis can occur in response to exogenous cues from the environment, many of the endogenous mechanisms by which it takes place remain unknown. As will be discussed in more detail in Section 1.1.6, lateral roots are initiated in an inner cell layeradjacenttothecentralvasculartissueoftheprimaryroot, anddevelop via a series of cell divisions, which will ultimately form the new lateral root with a new meristem at its tip (Peret et al. 2009a). Before the lateral root can be fully formed, however, it must emerge through the outer cell layers of the root, without damaging the primary root, or exposing the plant to pathogens from the soil (Peret et al. 2009b). The number of cell layers through which the lateral root must emerge varies with different species, with three outer cell layers in the model plant species Arabidopsis thaliana (Arabidopsis), and as many as 15 to 20 cell layers in cereal crops such as rice and maize (Hochholdinger and Zimmermann 2008). A better understanding of lateral root emergence will require an under- standing of several inter-connected developmental processes. These include the intracellular signalling and gene regulatory events that lead up to the 7 expression of genes controlling emergence of new laterals, and how these signalling events are arranged spatially by cell position within the root. In particular, the plant hormone auxin is central to the current understand- ing and conceptual models of how emergence is regulated, as described in detail in Sections 1.1.3-1.1.6. In Swarup et al. (2008) it was proposed that the focusing of auxin into particular cells near to the developing lateral root leads to the expression of cell wall remodelling enzymes (CWREs) in these cells, allowing for cell separation, and facilitating emergence between them without further damage to root tissues. Mathematical modelling provides a means by which this conceptual model may be investigated further, and extended and refined in order to generate new hypotheses for testing. Since much of the existing literature and data on emergence relate to Arabidop- sis, this species is chosen as a basis for the models developed. However, as discussed above, due to the importance of lateral root emergence on cereal crops, it is desirable for the framework for the models to be easily trans- ferable to species with different cellular structures of their primary roots. The initial objectives for the work described in the thesis are therefore as follows: 1. Develop a gene network scale model of the key genes and auxin sig- nalling events involved in lateral root emergence in Arabidopsis. 2. Developatissuescalemodelofthespatialdistributionofauxinleading up to the expression of cell wall remodelling enzymes. 3. Combine the gene network and tissue scale models into a multi-scale model,whichmaybetransferabletothedifferentspatialcellularstruc- tures found in cereal roots. 1.1.2 Plant root architecture and cellular structure Before looking in more detail at the role of auxin in plant development (Section 1.1.3), in particular its role in lateral root initiation, development and emergence (Section 1.1.6), we first describe some basic aspects of plant physiology important to the discussion, and compare the overall root archi- tecture, morphology and cellular structure of Arabidopsis with cereals such as rice and maize. One of the important differences between plants and animal species is the presence in plants of a cell wall made of cellulose, outside of the cell membrane, between every cell. This provides a rigid cellular structure, support and protection, and also a fixed matrix known as the apoplast, within which water and other small molecules such as plant hormones may travel. For a lateral root to emerge without damaging the primary root, specific cell walls must be softened and separated, but this process must be tightly controlled to maintain the integrity of the root. In vascular plants there may be a secondary thickening of cell walls with lignin, providing even more rigidity, and a means to transport water, sugars, hormones and minerals over large distances. This vascular tissue consists of xylem, which conducts water and other solutes from the root 8 to the shoot and leaves, and phloem vessels, which conduct the products of photosynthesis from the leaves to the tissues of the shoot and the root. The plant embryo is part of the seed of a vascular plant and contains the precursortotheshoot,knownasthehypocotyl,theprecursortotheprimary root, known as the radicle, and one or more cotyledons. Cotyledons form the first leaves of the plant post-germination. If a plant has one cotyledon, such as cereals or grasses, it is known as a monocot, if it has two cotyledons, as does Arabidopsis, it is a dicot. Following germination, growth occurs at meristems, which are the small regions of the plant containing undifferentiated stem cells which are able to divide. The meristem near the tip of the shoot is known as the shoot apical meristem (SAM), while that near the tip of the primary root is the root apical meristem (RAM). Growth of the primary root is determined by cell division at the RAM. During the process of forming a lateral root, a new meristem must be formed near the tip of the emerging root. Lynch (1995) defines root morphology as the surface appearance of a root system, including epidermal features such as root hairs, and also the pattern of appearance of daughter roots from the main axis of the plant. In general, cereals such as rice (Oryza sativa) and maize (Zea mays) have a relatively complex root morphology, with several different types of root present in addition to the primary root established during embryogenesis (Hochholdinger et al. 2004; Hochholdinger and Zimmermann 2008). Both maize and rice form shoot-borne roots, with those initiating below ground known as crown roots and those initiating above ground known as brace roots. In addition, maize has another type of root, known as seminal roots, which originate from the scutellar node, between the primary root and the mesocotyl, which is the section of the seedling between the primary root and the developing shoot (Hochholdinger et al. 2004). In comparison to cereals, and many other plant species, Arabidopsis has a very simple root morphology, with the root system limited to the embry- onic primary root, and laterals originating from the primary root. It is this simplicity which makes Arabidopsis suitable for use as a model plant or- ganism for detailed study. Many genetic mutants affecting different aspects of root morphology have been identified, in both cereals and Arabidopsis. In cereals these mutants can affect the formation of either shoot-borne or lateral roots, primary root length, or formation of root hairs (for reviews, see Hochholdinger et al. (2004), Hochholdinger and Zimmermann (2008), Smith and De Smet (2012)). Mutants affecting lateral root formation in Arabidopsis are discussed further in Section 1.1.6. Though cereal roots are generally much larger in diameter than Ara- bidopsis roots, the basic radial cellular structure of the primary root is similar in both, with a central group of cells forming vascular tissue known as the stele, surrounded by concentric rings of cell types, divided into four layers, known as the pericycle, endodermis, cortex and epidermis (Figure 1.1, Peretetal.(2009b)). Inbothcases, thepericycleisasinglelayerofcells surrounding the stele, the endodermis a single layer of cells surrounding the pericycle, and the epidermis is the outer cell layer where the root hairs are located on the outer surface of the root. The endodermis contains a band 9